sign in sign up
<<
Home , Moderate realism, Nominalism

View metadata, citation and similar papers at core.ac.uk brought to you by CORE

provided by Göteborgs universitets publikationer - e-publicering och e-arkiv

Acta Philosophica Gothoburgensia 26

MODERATE AND

CHRISTER SVENNERLIND

Acta Universitatis Gothoburgensis

 Christer Svennerlind, 2008

Distribution: ACTA UNIVERSITATIS GOTHOBURGENSIS Box 222 SE-405 30 Göteborg Sweden

Typeface: Garamond Cover design: Peter Johnsen

ISBN 978-91-7346-618-9 ISSN 0283-2380 Printed by Geson, Göteborg 2008

For Anette, Viktoria and Carl

Acknowledgements During the years I have worked with this dissertation many persons have contributed to that progress was made. In particular this applies to my mother and father, Maj-Britt and Ingvar Svennerlind. I sincerely thank them for all their help. Equally important has been Anette Stillner, my common-law wife. With her and our two children, Viktoria and Carl, by my side life is a true pleasure. From the bottom of my heart I thank them for that. I want to thank Helge Malmgren for a lot of things. Among these is that he has employed me to work for him whenever he has had the possibility to do so. During a of years that has meant much to me. I also thank him for the many days I have spent with him in various places discussing . During the last year Jan Almäng and Kent Gustavsson have constantly helped me to make progress in my writing. For that I cordially thank them both. I also thank all the participants of the seminars at the department of philosophy at Göteborg University. They are too numerous to be mentioned by name. One person who I want to explicitly mention though is Thomas Wetterström. He is the one who interested me in . It was also he who led the seminars for many years. I have learnt very much from him. I thank Irene Karlgren, who kindly lent me her summerhouse to work in. Källby parish has also kindly helped me; for that, I am very grateful. A special person in connection with this dissertation is Ingvar Johansson. He is acting as the opponent appointed by the faculty. I have learnt very much from reading his works. I am also grateful for the discussions on various philosophical subjects we have had during the years. Genie Perdin has corrected my English. I thank her for that and also for putting up with the accelerated tempo during the last days before this book was sent to the printers. Last, but not least, I want to thank my supervisor Björn Haglund. During my time at the department of philosophy, he is among those with whom I have had the most rewarding philo- sophical discussions. I also thank him for having meticulously read the manuscript before it was sent to the printers.

Contents Chapter I: Introduction 1 1.1 Ontology 1 1.2 Terminology 8 1.3 Disposition and Method 10 Chapter II: D. C. Williams on the Elements of 11 2.1 Introduction 11 2.2 The Analytic Ontology of the Early Williams 12 2.2.1 Overview 12 2.2.2 Two Pairs of Notions: -Particular and Abstract-Concrete 13 2.2.3 The Combination of the Two Pairs 22 2.3 Williams’ Theory 30 2.3.1 Overview 30 2.3.2 Parts and Components 31 2.3.3 The Alphabet of Being: Tropes 40 2.3.4 Concrete Particulars 49 2.3.5 Surrogates for Universals 58 2.3.6 Painless Realism 70 2.3.7 Predicativity 75 Chapter III: Examination of A-S. Maurin’s Ontology 77 3.1 Introduction 77 3.2 The Notion of Trope 78 3.2.1 Overview 78 3.2.2 Single Category: Trope 79 3.3 The Problem of Universalisation and Its Solution 93 3.3.1 Overview 93 3.3.2 Another Problem: The 94 3.3.3 The Problem of Universalisation 97 3.3.4 Internal and External Relations 104 3.3.5 Internal Relations between Tropes 118 3.3.6 The Preferred Account of Internal Relations between Tropes 129 3.3.7 Degrees of Resemblance 139 3.4 The Problem of Thing-Construction and its Solution 142 3.4.1 Overview 142 3.4.2 The Problem of Thing-Construction 142 3.4.3 Compresence 147 3.4.4 Compresence and Bradley’s Regress 152 Chapter IV: Moment Nominalism 161 4.1 Introduction 161

4.2 Individual and Universal 162 4.2.1 Overview 162 4.2.2 A Modal Notion: Can 163 4.2.3 Semi-Individuality 167 4.2.4 Individuality 176 4.3 Relations and Complexes 178 4.3.1 Overview 178 4.3.2 178 4.3.3 Internal and External Relations 188 4.3.4 Elementary Connection 193 4.3.5 Elementary Ideal Relation 199 4.3.6 Objects of Different Orders 202 4.4 Qualities and Quality-Moments 211 4.4.1 Overview 211 4.4.2 Three Postulates for a Theory of Qualities 212 4.4.3 Quality Relations 216 Chapter V: Moderate Realism 223 5.1 Introduction 223 5.2 One Partial and Two Mistaken for Particularism 224 5.2.1 Overview 224 5.2.2 ’s First 224 5.2.3 Avicenna’s Second Argument 226 5.2.4 A Partial Argument from Segelbergian- Blackian 230 5.3 The Moderate Realism of D. W. Mertz 240 5.3.1 Overview 240 5.3.2 Principles of Moderate Realism 240 5.3.3 A Refined Version of Avicenna’s Second Argument 247 5.3.4 Unit Attributes: Preliminaries 252 5.3.5 Intensional Aspect: Simple or Complex? 260 5.3.6 Unit Attributes: Continuous Composites 264 5.3.7 273 5.3.8 Networks of Unit Attributes 278 References 283

CHAPTER I

Introduction

1.1 Ontology The title of this essay is ‘Moderate Nominalism and Moderate Realism’, which indicates that its subject is ontology. ‘Nominalism’ signals that in particular and appears to be (almost) exclusively used in the context of ontology. ‘Realism’, on the other hand, is used frequently in almost every area of philosophy. In any , whether a philosopher is a nominalist or a realist, what he or she takes an interest in is a project which was initiated by and . They have marked out the issues ontology centers on to a great extent. In his early work, Categories , Aristotle lists ten categories of : substance, quantity, quality, relation, place, date, posture, state, action and passivity. 1 Any true description of reality should be made in terms of these ten categories. They can be characterised as the most abstract notions used when describing something, for example, we tend to say that things have qualities. For instance, the Swedish flag is partly blue; if we look at a particular flag, its blue colour has specific nuance. In the terminology introduced by W. E. Johnson, 2 the colour is a lowest determinate of a number of determinables. Most of these determinables do not have any specific adjectives expressing them. Further, the highest determinable among the colours is colour itself, but it is not the (categorially) highest determinable in the line starting with the lowest colour determinates. A still higher determinable is quality itself. Since quality is not a determinate in relation to any higher determinable, we have by now reached the end of the line: a category. This procedure can be applied to Aristotle’s other nine categories as well. Note that in this example we started out talking of

1 The names of some of these ten categories vary between the English translations made of Aristotle’s Greek terms. 2 Cf. Johnson 1921, chapt. XI. 2 CHAPTER I notions used when describing things and were fairly soon referring to traits of the things themselves. This oscillation between and traits of things is difficult to avoid. However, we can use it to make a point. It is that the determinate–determinable distinction is applicable to traits of things as well as of concepts that are used to describe them. If our conceptual scheme is true to how things are, the con- cepts used have counterparts in rerum natura .1 According to some, the categories listed by Aristotle are not independent of each other. For example, the category of substance is said to be reducible to one or more of the others, in particular, quality. This has been a common view among empiricists and still has its proponents today.2 Others stick to the that the reduction is impossible in principle; arguing that categorial distinction between substance and quality should therefore be maintained.3 There is also a long tradition of trying to reduce relations to qualities. Aristotle himself is, at least to some extent, part of that tradition. His description of relations as the “least of all things a kind of entity or substance”4 has often been pleaded by adherents of this particular . During two millennia this was in the majority view among western philosophers. Nowadays, quite a few of the guardians of this tradition are found among trope theorists. Since it is difficult, I would say impossible, to consistently uphold this reductionism, the reductionist claim is only partly maintained by most of its adherents. Thus, while the so-called internal relations are con- sidered to be reducible, this is not so with regard to the so-called external relations. Central to the debate between proponents of nominalism and realism are the notions of particularity and universality. The distinc- tion between these two is applicable to all of Aristotle’s categories, as

1 Cf. Johansson 2000, p. 101. Ingvar Johansson points out that Johnson invented the pair of terms: ‘determinate’ and ‘determinable’. He did not invent the distinction. 2 Cf. David Armstrong, in Armstrong 1978 b, p. 67, as an example of that. 3 Cf. Lowe 1989, chapter 3, and Johansson 1989, chapter 3. 4 , 1088a22. INTRODUCTION 3 well as to those proposed by others. Particularity and universality can be characterised as transcategorial notions, though strictly speaking, only realists recognise the distinction and its applicability. In fact, this is not even the case as regards all versions of realism. According to one “extreme” version, most appropriately called ‘universalism’, everything which exists is universal. Still strictly speaking, all versions of nominalism deny the of universals. Thus, according to nominalists the distinction between particularity and universality is lacking one of its relata. However, even nominalists tend to recognise the need for something doing the work which universals perform in realistic . Keep in that the traditionally proposed surrogates for universals must themselves be particulars; if they are not, the nominalistic project of making universals unnecessary collapses. The implication is then that the need for particulars as well as (real) universals is recognised only by the major fraction of the realists. Donald Williams makes a distinction between two branches of metaphysics: (i) analytic ontology and (ii) speculative . His description of the first branch reads:

First philosophy, according to the traditional schedule, is analytical ontology, examining the traits necessary to whatever is, in this or any other possible world. Its cardinal problem is that of substance and attribute, or at any rate something cognate with this in that family of which contains also subsistence and inherence, subject and predicate, particular and universal, singular and general, individual and , and matter and form. It is the question how a thing can be an instance of many proper- ties while a may inhere in many instances, the question how everything is a case of a kind , a this-such, an endowed with existence, an existence differen- tiated by essence, and so forth. 1

1 Williams 1953 a, p. 3. 4 CHAPTER I

In the last of the preceding quote, we find versions of two questions which both have been described as expressing what traditionally is called ‘the problem of universals’. The first one mentioned is: How can a thing be an instance of many properties? The second is: How can a property have many instances? 1 The second question is perhaps the one which best expresses what traditionally has been considered to be the problem. A slightly different formulation of it is: How can numerically different particulars have the same property? Sometimes this problem is called ‘the One over Many’. However, that might be a slightly misleading name of the problem ; it seems more appropriate as a name of a specific solution to the problem. The solution to it is that particulars have the same property because they instantiate, or exemplify, the same universal. Thus, ‘One over Many’ suggests a platonistic solution. Therefore, the universal property is considered to be “over” the things having it. This proposal has its own problems; a major one is that it is difficult to understand the of instantiation or exemplification. It is easier to understand another realistic solution to the same problem. It can be called ‘the One in Many’. According to this proposed solution, different things have the same property due to their sharing the same universal. In other words, the same universal is a constituent of the particulars in question. In a series of works David Armstrong has discussed various ontological issues. What he means by the problem of universals is the second question from the preceding paragraph. One representa- tive description of his is that it is “[…] the problem of how numeri- cally different particulars can nevertheless be identical in nature.” 2 He takes the One in Many to be the correct solution.3

1 I have slightly reformulated what Williams says. 2 Armstrong 1978 a, p. 41. 3 Gonzalo Rodriguez-Pereyra points out that Armstrong’s way of formulating the problem gives it a form which Robert Nozick points out that many philosophical problems have. The form is: How is a certain thing, call it ‘X’, possible given (or supposing) certain other things? Nozick mentions the problem of free : How is it possible for us to have , supposing that all actions are causally determined? Here X is free will and what INTRODUCTION 5

The first version of the problem of universals mentioned above was: How can a thing be an instance of many properties? According to Gonzalo Rodriguez-Pereyra this is what should be considered the problem of universals. In line with that he uses the designation ‘Many over One’. This denomination indicates that the problem is that of explaining how a particular can have various properties. He quite rightly remarks that, since the problem is one of properties, not universals, the designation ‘the problem of universals’ is a misnomer. 1 Bearing in mind that he is a (classical) resemblance nominalist, the problem which he has to master can also be described as that of explaining how a particular can have properties at all. 2 Williams’ description of the second branch of metaphysics is found in the following quotation, which also hints at the relationships between the two branches.

Concerned with what it means to be a thing or a kind at all, it [analytic ontology] is in some wise prior to and independent of the other great branch of metaphysics, apparently excludes it is . The apparent excluder in Armstrong’s case is the numerical among particulars. The fact that he considers it to be an apparent excluder is indicated by his use of ‘nevertheless’. Cf. Nozick 1981, p. 9, and Rodriguez-Pereyra 2002, pp. 18-9. 1 Cf. Rodriguez-Pereyra 2002, p. 1. 2 His for considering Many over One to be the real problem is due to his resemblance nominalism in combination with his view that what should be meant by ‘the problem of universals’ is a problem regarding truthmakers. The following quotation might give a rough idea of how he sees things. That the Problem of Universals is the Many over One, that is, that the Many over One rather than the One over Many is the phenomenon to be explained, should not be surprising. For the One over Many has as its starting-point about a multiplicity of particulars sharing some property or other, facts expressed by sentences like ‘ a is F and b is F’. But given that the Problem of Universals is one about truthmakers, and that truthmakers of these conjunctive sentences are the truthmakers of their conjuncts and that, given the multiplicity of properties had by particulars, there are many such conjuncts for each particular, the One over Many vanishes into the Many over One. (Rodriguez- Pereyra 2002, p. 47) 6 CHAPTER I

speculative cosmology: what kinds of things are there, what stuff are they made of, how are they strung together? 1

If interpreted in a wide sense, speculative cosmology may include the highly speculative philosophical systems of the 17 th , 18 th and 19 th centuries. Speculations regarding the nature of reality, whether it is spiritual or material, would then fall within its field of research. The fact that this is part of what Williams intends by the designation ‘speculative cosmology’ may be concluded from another quotation:

We are only beginning to philosophize till we turn from the bloodless that things in any possible world must consist of tropes, to specific studies of the sorts of tropes of which the things in this world actually consist. It is a of our thesis that it does not strangle or eviscerate the great problems in the philosophical cradle but keeps them alive and ready for the legitimate judgment of and . It will be a further virtue if it assists, as I think it will, in their formulation and appraisal. Are there only physical objects and energies, or only or spirits, or are there both? How, specifically, is a physical constituted, and how a mind, and how are they related? These topics of gigantic hypothesis are the last of philosophy for which the first is made. 2

As we shall see in chapter II in connection with a discussion of Williams’ trope theory, ‘trope’ is his technical term for unit properties and relations. According to his first philosophy (analytic ontology) the primary denizens of the are tropes. They are the building stones of which everything consists. Among the tasks for last philo- sophy (speculative cosmology) is finding out of what sorts of tropes things consist.

1 Williams 1953 a, p. 3. 2 Williams 1953 b, p. 191. INTRODUCTION 7

Williams’ distinction between the two branches of metaphysics is referred to by Armstrong near the end of his seminal work, Arm- strong 1978 a. He says first:

Here are three world-hypotheses in decreasing order of generality. (1) The world contains nothing but particulars having properties and related to each other. (2) The world is nothing but a single spatio-temporal system. (3) The world is completely described in terms of (completed) . I put forward the view that each of these proposi- tions is true. Notice that although (2) is less general than (1), and (3) less general than (2), the seem to be logically independent. (Though it would be strange to accept (3) and deny (2).) Nor do I suggest that there is any particular epistemological order of priority among the hypotheses; although (3) seems the most dubious. 1

That is followed up with:

Following D. C. Williams […], we may distinguish between ‘analytic ontology’ and ‘speculative cosmology’. (1) is a thesis of analytic ontology, i.e., first philosophy […]; (2) and (3), by comparison, are simply theses of ‘spe- culative cosmology’. 2

A brief remark on world-hypothesis (1) — the world contains nothing but particulars having properties and these are related to each other. Armstrong 1997 is partly devoted to this hypothesis. One of its essential claims is that states of affairs cannot be analysed according to mereological composition. Furthermore, it asserts that states of affairs in themselves constitute non-mereological composition. The problem of instantiation is declared to be solved by virtue of there being states of affairs. Differently put, the instantiation of a universal

1 Armstrong 1978 a, p. 126. These world-hypotheses are discussed more in detail in Armstrong 1997, chapt. 1. They are listed there as: (1) factualism, (2) and (3) . 2 Armstrong 1978 a, p. 127. 8 CHAPTER I by a particular is nothing more than the state of affairs itself. 1 I mention Armstrong’s view here only in passing; it will not be discussed anywhere in the rest of this essay, 2 which is devoted to moderate forms of ontology, i.e., moderate nominalism and moderate realism respectively. Armstrong’s immanent realism does not adhere to the moderate form. It does hold the that the world is a world of states of affairs in common with Donald Mertz’s moderate realism, which is discussed in chapter V.

1.2 Terminology This essay falls within analytic ontology. Although I do not explicitly advocate any specific ontological view within its covers, I make no secret of the fact that I consider myself a moderate realist. Un- fortunately, terminological anarchy rules here, as in many other areas of philosophy; it is therefore not obvious what being a moderate realist amounts to. Although I realise that hoping to bring order into chaos would be in vain, I venture to propose a terminology to be applied to ontological positions, which will be used partly in this essay. The first distinction to be made is between realism and nominalism. The former recognises universals, the latter does not. No surrogates for real universals suffice to turn a nominalism into realism. The recognition of real universals is the essential divide. Within the frame of realism there is the extreme position according to which only universals exist; I propose that it be called ‘universalism’. The next distinction is between transcendent realism, or , and immanent realism. According to transcendent realism, universals are non-spatiotemporal, while according to immanent realism they are spatiotemporal. Next, we find the distinction between moderate and non-moderate realism. Moderate realism recognises unit attributes, called instances of universals; non-moderate realism does not. If a

1 Cf. Armstrong 1997, p. 119. 2 This is not completely true. A view of Armstrong concerning composition is in fact commented on in section. 5.3.4. INTRODUCTION 9 realism recognises substrates, ‘realism’ is prefixed with ‘substrate’. If substances are recognised, ‘substance’ is prefixed. I think that more or less completes the list for realism. 1 To form a denomination, one simply lines up these terms according to requirement. Matters are a bit more complicated with regard to nominalism, but regardless of that, a nominalism which recognises tropes is a moderate nominalism. 2 Tropes are property, relation or substance instances. If substrates are recognised, ‘nominalism’ is prefixed with ‘substrate’. If substance tropes are recognised, ‘substance’ is prefixed. A nominalism according to which qualitative content is due to mem- bership in a specific class is called ‘class nominalism’; corresponding to mereological sums, where ‘sums’ is left out. If concepts or predi- cates are considered to give entities their qualitative content, the positions are called ‘ nominalism’ and ‘predicate nominalism’, respectively. A nominalism which takes qualitative content to be due to resemblance between entities is called ‘resemblance nominalism’. Further, if resemblance is in fact a universal, the position should be looked upon as a form of realism. Consequently, ‘resemblance realism’ can be used. However, if need arises, I recommend that 3 ‘resemblance nominalism 2’ is used instead. Unfortunately, this solution is rather unpractical in speech. The term ‘particularism’ is used as an umbrella term for ontologies recognising instances of any sort. The denomination ‘trope

1 Mertz 1996 has inspired my use of ‘moderate realism’. In Armstrong 1989, p. xi, the same term designates what is more appropriately called just ‘immanent realism’. 2 In Hochberg 1988 and 2002, ‘moderate nominalism’ designates a position recognising one single universal, which is the tie of similarity, together with instances of qualities and relations. I believe that what David Armstrong, in Armstrong 1989 and 1991, is aiming at using ‘moderate nominalism’ is the same view as the one I have in mind. Strangely enough, Herbert Hochberg says that Armstrong is the one who has called his attention to the variant of nominalism which he himself calls ‘moderate nominalism’. The designation ‘moderate nominalism’ is used by Donald Mertz, in Mertz 1996, p. 26, as an alternative for ‘trope theory’. 3 Cf. Rodriguez-Pereyra 2002, p. 123. 10 CHAPTER I theory’ is also used as an umbrella term; preferably, it is used as an alternative for ‘moderate nominalism’. The heading of chapter IV is ‘moment nominalism’, this parti- cular denomination is a rather special case. It names Ivar Segelberg’s ontology. Since it recognises unit qualities, but no quality universals, and universal relations, but no unit relations, it is hard to fit into the proposed terminological scheme. Furthermore, Segelberg’s preferred term for unit qualities is ‘moment’.

1.3 Disposition and Method Regarding the disposition of this essay I refer the reader to the overviews at the beginning of the major sub-subsection. These over- views are easily found by consulting the table of contents at the beginning of the book. There is no royal road to agreement in ontology. Unquestion- able refutation or proof is hard to come by. As a result of that, the dispute between nominalistic and realistic minded philosophers is a perennial one. The fundamental assumption, which the realist makes and the nominalist rejects, is that universals are needed for an adequate description of reality. Being a realist myself, I am inclined to be sceptical of even moderately nominalistic ontologies. Examples of nominalistic ontologies are discussed in chapters II, III and IV using a strategy according to which I try to show that universals are pre- supposed, even though, officially, their existence is declared un- necessary. 1 I invoke a principle, which may be described as methodo- logical, saying that an analytical regress should be avoided. I would say this principle is primary in relation to Ockham’s razor. Although being a methodological principle, that principle is (just) an econo- mical one. As regards another sense of ‘method’, I would like to add that although my aim is critical, I sincerely hope that my criticism is describable as being gently polemical.

1 Universals are not totally rejected by Ivar Segelberg, whose moderate nominalism is discussed in chapter IV; he does recognise universal relations.

CHAPTERII

D.C.WilliamsontheElementsofBeing

2.1Introduction Since the 1950’s, the analytic ontology of Donald Cary Williams (1899–1983) has been a source of inspiration for quite a few philosophers working in that field of metaphysics. In particular, Williams 1953 a is frequently referred to with approval. In spite of that, detailed discussions of its doctrines, as well as of those of his otherarticlesinthesamefield,arehardtocomeby. Williams intended to write a monograph on analytic ontology, though he never did. 1 Instead of being presented in one complete , his doctrines are scattered in various articles. The discussioninthischapterisbasedonsixofthesearticles: Williams 1931,1951,1953 a,1953 b,1963and1986.Thetimestretchbetween someofthemisconsiderable,althoughnotquiteasbigasitseems, sincethesixthonthelistcannothavebeenwrittenlaterthan1959. 2 Incourseoftimehisviewscanbeexpectedtohavechanged. The most radical change would be a conversion from realism to nominalism,ortheotherwayround.Ibelievetherearegoodreasons formaintainingthatthereissuchachange.Itcomesaboutbetween the publications of Williams 1931 and 1953 a. In the former article, thepresupposedontologicalpositionisaformofmoderaterealism. Thatofthelatterisaformofmoderatenominalism.Owingtothe elusiveness of the way in which Williams expresses himself, this conversion might be overlooked. In one of the later articles the positionhearguesissaidtobeanimmanentrealism.Entitieswhich he calls ‘universals’ are explicitly said to be components of their instances. 3 This has the appearance of being a frank expression of 1Cf.theeditor’sfootnotetoWilliams1986. 2Cf.Williams1986,footnote1. 3Cf.Williams1986,p.10. 12CHAPTERII realism.Notwithstandingthat,someformofmoderatenominalismis the predominant tendency of that article. This also holds for the otherfive,laterarticles.Inotherwords,althoughpropertiesandrela tionsarerecognised(real)universalsarenot. Williams’ contribution to the philosophical vocabulary is the term‘trope’.ItmakesitsfirstappearanceinWilliams1953 a.Strictly speaking,heisnotthefirsttouseitwithintheframeofphilosophy. ThatseemstohavebeenGeorgeSantayana.Hissenseisnottheone Williamshasinmindforit;infact,theirtwosensesaretheopposites ofeachother.Ihastentoaddthatitwouldbemorecorrecttosay thatoneofthesensesWilliamsusesitinistheoppositeofthatof Santayana’s since, as it turns out, Williams’ use of ‘trope’ is rather varied. The tendency among his interpreters has been to bring out justoneofthese. The notion of trope has something of a forerunner in the ontology of the early Williams. The latter notion there is called ‘abstractparticular’.Thatdenominationissomethingwhichthetwo notionshaveincommon.Itmayeasilyobscurethefactthatwhatis called ‘abstract particular’ by the early Williams is a realist notion, whileinhislaterontology,itisanominalist notion.Thedifference betweenthetwoissignificant.

2.2TheAnalyticOntologyoftheEarlyWilliams

2.2.1 Overview WhiletheontologypresentedinWilliams1931isnotgivenanyname ofitsown,theonearguedforinthelaterarticlesisgiventwonames. The one which he prefers is ‘trope theory’. 1 This trope theory is discussedinsection2.3.Thepresentsection,section2.2,dealswith the moderate realism of the first. Since the account of it given in Williams 1931 is rather summary, what follows below is a recon structionofit,basedonthescantyinformationwhichcanbefound inthearticle. 1Theothernameis‘tropekindtheory’.ItisusedonlyinWilliams1986. D.C.WILLIAMSONTHEELEMENTSOFBEING13

In 2.2.1 two pairs of notions are introduced. The notions of thesetwopairscanbedescribedasmakinguptheframeinwhichthe restofWilliams’ontologyischiselledout.Section2.2.2dealswiththe combinationsofthetwopairs.

2.2.2 Two Pairs of Notions: Universal–Particular and Abstract–Concrete ThepronouncedpurposeofWilliams1931istoproposeascheme exhibiting the relations of two pairs of notions. One of these two pairsisthatoftheuniversalandtheparticular.1Theotheristhatof the abstract and the concrete.2 The notions of these two pairs are combinedinamatrix.Thesamematrixapparentlyappearsinthelater articlesaswell.AsaconsequenceofWilliams’conversiontonomina lism,thecontentofitisboundtobesomewhatchanged. WithamixtureofhumilityandselfconfidenceWilliamsasserts, bywayofintroduction:

On a topic so ancient I can hardly hope to disclose anything which shall be both tolerably simple and really novel. On the contrary, my principal interest is only to makeexplicitthenotionswhichmusthavebeentakenfor grantedinthemoreprofitablemomentsoftraditionaland contemporarydiscussion,andtoisolatethemfromcertain other inaccurate and incompatible notions, equally taken 1Regardinganearcognateof‘particular’Williamssays: The term “individual” is often employed in the same sense in whichIdefine“particular.”OtherwiseIdonotattempttodefine it, but leave its to be enlightened only by what incidentalilluminationisaffordedbymytotalscheme.(Williams 1931,p.585) Lateronhementionsaparticularsenseof‘individual’.Itwillbedescribed lateron. 2 As in the terminologies of many other philosophers, Williams’ terms ‘universal’and‘particular’playtheroleasnounsaswellasthatasadjectives. ‘Abstract’ and ‘concrete’ play a simple role as adjectives. While the early article has two noun counterparts of ‘abstract’, i.e., ‘abstractum’ and ‘’,thereisnonefor‘concrete’,thoughinlaterarticles‘concretum’ isused.Furthermore,eachmemberofthequartet‘universality’,‘particularity’, ‘abstractness’and‘concreteness’isusedintheearlyarticle. 14CHAPTERII

forgranted,with whichtheyhavebeendisastrouslycon fused.Asthetypicalandperhapsthemostsignificantcon fusionIshallregardtheratherpopularassumptionthatan “abstraction”is ipso facto auniversal,or vice versa .1

Itmaybeconcludedfromthisthatthenotionsoftheabstractandthe universalarenotsupposedtobeexclusivelyrelatedtoeachother.If theyweresorelated,itwouldgoagainsttheassumptionthatthetwo pairsarecombinable,withoutrestrictions,inamatrix.Theresulting fourcompoundnotionscanbelistedaccordingly:abstractuniversal, concrete particular, abstract particular and concrete universal.2 The determinationsofthesefourcompoundnotionsobviouslydependon those of the, at least relatively, simple ones which make up their content.Itseemswelladvisedtofirsttakealookatwhatisproposed regardingthefoursimplenotions. Thefirst onthelistis thatoftheuniversal.The following is offered:

Letusmeanby“auniversal”anentitywhosebeingisnot confinedtoordefinedbyitspresenceinanyoneevent, instance,orareainspaceandtime,orinaspecificplurality of such. An entity of this sort can be utterly and numericallyidenticalwithitselfinanynumberof spatio temporalcontextsoroccurrencesorinnone.Specifically, its being is that of an essence, or kind, or character, as such. It is the identity of a thing or quality or relation wherein consists what it is rather than that it is. This peculiarityIhaveclumsilycalled“universality.” 3

1Williams1931,p.583. 2Alsoconceivableare:universalabstractum,particularconcretum,particular abstractumanduniversalconcretum.IpresumethatWilliamswouldconsider thesetobethesameasthoseontheofficiallist.Hisuseof‘abstraction’in thelastsentencesupportsthis. 3Williams1931,p.584. D.C.WILLIAMSONTHEELEMENTSOFBEING15

Althoughitisabitelusive, 1thisapparentlyexpressestheviewofan ontological realist. The phrase ‘or in none’, in the second sentence, suggeststhatauniversalis,asitisoftenput,aone over many.Itwould appearthenthatsomeversionoftranscendentrealism,orPlatonism, is presupposed. If ‘or in none’ is disregarded or excused, the suggestion is instead that a universal is a one in many. The presupposed ontology would then be some version of immanent realism.Thelatterinterpretationfindssupportinanotherparagraph, whereastipulationismaderegardingtheterm‘generality’.

Theword“generality”[…]isoftenemployedtomeanthe sameas“universality.”Ishallratherfactitiouslydefineit, however, to mean a realized universality, i.e., the fact of the actual existential presence of any universal in a considerablenumberofinstances. 2

Itakeitthatthephrase‘actualexistentialpresencein’isusedliterally.3 On the other hand, the occurrence here of ‘realized universality’ suggeststosomeextentthatunrealiseduniversalityisalsoreckoned with; this might be an expression of transcendent realism. While beingaoneinnoneisnotconsideredtobeinline withimmanent 1Theenumeration—ofessence,kindorcharacter,assuch—mightevince atristinktionbetweenthreedifferentsortsofuniversals.Ifthatisindeedthe case, thing, quality and relation — which are listed immediately after the quotation—mightbeexamplesof(someof)thesesorts.Presumably,quality and relation would be characters. It is less obvious what would be the universalcounterpartofathing.Onepossibilityisthatitisessence.Itmight also bekind.Thereisalsoanotherslightlydifferentinterpretation whichis alsopossibletomake.Accordingtothat,thereferentsoftheterms‘quality’ and‘relation’areparticulars.Thesameofcourseholdsfor‘thing’.Ihastento add though that ‘quality’ and ‘relation’ are also used for universals. Furthermore,theterm‘character’isalsousedinawidersense.Cf.Williams 1931, p. 590, where the total universal content of Socrates is the intended referentofthephrase‘thecharacterofSocrates’. 2Williams1931,p.584. 3 The matter would have appeared differently if a phrase involving ‘par ticipation’ had been chosen. This since ‘participation’ is frequently used by transcendentrealists,whoforsuredonotintendittoimplythatuniversals arespatiotemporalentities. 16CHAPTERII realismtraditionally,beingaonein(just)oneis.Ontheotherhand, thephrase‘realizeduniversality’neednotimplytranscendentrealism. IfWilliamsweretouseit,hemighthaveunrealisedcombinationsof universals in mind, where the included universals taken singly are realised.Immanentrealismwouldthenstillbethepresupposedview. Theelusivenessofthetextmakesitdifficulttoestablishexactlywhat formofrealismisactuallybeingexpressed.Themayevenbe thatWilliamsoscillatesbetweendifferentversionsofrealism.How ever,heisarealisteitherway. Inthequotationspresentedsofarwehavecomeacrossseveral occurrencesoftheterm‘instance’.Asitturnsout,itcanhavevarious senses.Williamscallsattentionto,anddistinguishesbetween,twoof them. Irrespective of which one of these is intended in a certain context, the existential presence of a universal is essential. This is evidentfromthenextquotation.Initwealsofindinformationabout thesecondnotiononthelist—thatoftheparticular.

Aparticularisdefinedbythecontradictoryoftheabove. Itisanentitywhosebeingisconfinedtoanddefinedbyits presenceinsomeoneevent,instance,orareainspaceand time, or in a specific plurality or continuum of such. Specifically,itsbeingisthatofanoccurrent,orcontinuant, oroccupant,assuch.ThispeculiarityIshallcall“particu larity.”Itisgenerallysupposedthataparticularcanbean “instance”ofauniversalcharacter.Usagediffers,however, amongotherways,inthatitascribesthename“instance” either,first,tothecompletevolumeorconcretesubstance inwhichthecharacteroccursasacomponent,or,second, tothecharacterasitoccurs.Theseconduseseemstome moreaccurateandvaluable,andIshalladoptithere. 1

From this, together with what we have seen earlier regarding the notion of the universal, it is quite clear that a particular cannot be presentinitsentiretyinseveral,separateplacessimultaneously. The determination here is made in terms of space and time. Perhapsspaceandtimeareessentialforthenotionoftheparticular 1Williams1931,pp.5845. D.C.WILLIAMSONTHEELEMENTSOFBEING17 as well as for that of the universal. This might be just appearance though.Putdifferently,whethertheincapacityofaparticulartobe present in separate places simultaneously is due to its being a particular or if it is the other way round, is not clearfromwhatis stated.1Whatevertheexactansweris,therearetwodistinctsensesof ‘instance’.Toillustratethiswecanusearipetomatoandtheuniversal character redness.2 In the first sense of ‘instance’ the tomato, in its entirety,isaninstanceofredness.Ofcourse,thetomatois aparti cular, not a universal. What about the second sense of ‘instance’? Well,accordingtothelastquotation,suchaninstanceisacharacter as it occurs. In our tomato example, redness would be such an instance as it occurs. The term ‘component’ is reserved for such instances. Williams’ way of expressing himself may give the im pressionthatthecomponentsofthingsareuniversals.Unfortunately, 1InCampbell1990,p.56,itisreportedthatWilliamsoncetoldtheauthor thathewasinclinedtothinkofbeingaparticularasabasicfactaboutevery particular;hisbeingthattheextraspatiotemporalshouldnotberuled outbytheverynotionofparticularityitself.Althoughnotdependingonany unique location of any sort, the typical manifestation of being a particular, knowntous,isuniquespatiotemporallocalisation.InMaurin2002,pp.201, Williams’ view is reckoned to be in line with what the author is a thesis of G. F. Stout. It is that being particular accounts for certain facts regardingspatiotemporalposition.Stoutisquotedsaying: Two drops of water, for instance, may conceivably be exactly alikeexceptthattheymusthavedifferentpositionsinspace,and whatever further differences this may involve. Why must they have different positions in space? Because they are distinct particulars. There is no other reason. This difference then presupposestheirparticulardistinctnessandcannotconstituteit; butinallotherwaysthereisnothingintheirgeneralnatureto distinguishthem.(Stout1952,pp.767) Isupposethephrase‘differentpositionsinspace’hereisshortfor‘different positions in space and time’. What Stout says in connection with this quotationmakesitclearthatheisnotreferringtoparticularsingeneral.He is,infact,notclaimingthatbeingparticularexplainswhyparticularscannot sharespatiotemporallocationwitheachother.Someparticularssupposedly dosharesuchlocation.Theparticularsinquestionarewhathecalls‘abstract particulars’.Williamsevidentlyisofthesameview. 2Thisexampleismine.Williamsdoesnotpresentanyexampleofhisown. 18CHAPTERII phraseslike‘rednessasitoccurs’,‘characterasitoccurs’or‘universal asitoccurs’easilylendthemselvestomisunderstandings.However,a carefulreadingmakesitquiteclearthattheintended references of thesephrasesareparticulars.Thus,both‘instance’and‘component’ refertoauniversalasitoccurs.1 Inthelastsentenceofthelastquotationweseethatofthetwo distinguished senses of ‘instance’ the second is the one which is preferredbyWilliams.Thepresumptionistherefore that whenever heuses‘instance’,withoutanyreservation,theintendedreferentisa universalasitoccurs.2 Letusmoveontothenextpair.Fromtheintroductionofitwe see that its two notions are considered to make up a more murky matterthanthoseoftheformerpair.

[T]he terms “abstract” and “concrete” have not been so oftenandexplicitlyarguedashave“universal”and“parti cular.”Perhapsforthisveryreasontheconfusionthathas obfuscatedthedoctrineoftheuniversalandtheparticular isassunlightandcrystalincomparisonwiththeconfusion that hasenshroudedthedoctrineof theabstractandthe concrete. 3

1Cf.Williams1931,p.589,whereinstancesofabstractuniversalsaresaidto beabstractparticulars.InWilliams1953 a‘component’isusedfortheabstract particularsofWilliams’laterontology. 2 This having been said, the following question presents itself. What sense does‘instance’haveinthesecondsentenceofthelastquotation?Aparticular is said there to be an entity whose being is confined to and defined by its presenceinsomeoneevent, instance ,orareainspaceandtime,orinaspecific pluralityorcontinuumofsuch.If‘instance’hasthesecond,preferredsense here,theresultseemsabitodd.Ifaparticularispresentinaninstance,that instancehastheparticularasapart.Perhapsamoreplausibleinterpretation of this occurrence of ‘instance’ is that it has the sense of ‘moment’. An instanceisapointintime.Thisinterpretationofcoursealsoappliestothe determinationgivenearlierofthenotionoftheuniversal. 3Williams1931,p.585. D.C.WILLIAMSONTHEELEMENTSOFBEING19

Partoftheambiguityreferredtohereprobablyis the view that an abstractumipso facto isauniversal,or vice versa .1Furthermore,thereare manydifferentusesoftheterms,especiallyof‘abstract’. 2Thesealso contributetothestateofconfusion. Williams’ own determination of the notion of the abstract is indicatedlikethis:

Isuggestthatthemoreusefulandconsistentinterpretation of“abstract”istobefoundnearertheliteralone: 3thatis, todesignatethepartthatisartificiallyalienatedfromthe wholetowhichitbelongs;anelementwithdrawnfromits natural existential context. Hence the propriety of such familiar connotations of “abstract” as fragmentary, iso lated,impoverished,empty,thin,ortenuous.4

1Asaterriblewarningtotherestofus,fivedistinguishedphilosophers,who allegedlyidentifythenotionsoftheabstractandtheuniversal,arementioned: JohnLocke,JohnDewey,BertrandRussell,R.M.EatonandAlfredNorth Whitehead.Thislistisnotintendedtobeexhaustive.Onthecontrary,this particular identification is said to be found in countless influential philo sophers. This is obviously a deliberate exaggeration. Being that, it is a so calledhyperbole—oneofthetropesof. 2Examplesofsuchsensesareindicatedbytermssuchas‘fictitious’,‘vague’, ‘confused’, ‘indefinite’, ‘indeterminate’, ‘rational’ and ‘conceptual’. Cf. Williams 1931, pp. 5856. Still more senses, or at least connotations, are mentionedinthemaintext. 3Alsomentioned,andrejected,isC.D.Broad’ssuggestionthatabstractaare nonexistententities.Beingnonexistenttheyarenotliterallyintime.Inspite of that, they are real. Qualities and relations are included in the class of abstracta.Cf.Broad1925,pp.1920.Anotherdetermination,whichIbelieve canbefoundinWhitehead,isrejectedaswell: [T]obeabstractistotranscendparticularconcreteoccasionsof actualhappening.”(Williams1931,p.586) Perhaps,thesedeterminationsaredifferentversionsoftheviewthatabstracta areuniversals. 4Williams1931,pp.5867.Itisassertedimmediatelybeforethisquotation: Nomoralturpitude,certainly,isinvolvedinusing“abstract”as synonymous with either “nonexistent” or “universal.” But something valuable is lost out of and thought if such conductresultsinobscuringarealandmoreappropriatedistinc 20CHAPTERII

A crucial phrase here is ‘natural existential context’. The sense of ‘abstract’ will vary with how the of that phrase is fixed. Williamsdistinguishestwoprincipaldoctrinesregardingthismatter. Thedescriptionofatleastoneoftheminvolvestheterm‘concrete’. Asaresult,thedeterminationsofthenotionsoftheabstractandthe concrete are interwoven with each other, which is what could be expected.

Thereremain 1twoprincipaldoctrinesofthenaturalcon text.Theseare(a)thetraditionalatomisticandnaturalistic assumptionthatitiswhatweordinarilymeanbya“solid concrete thing,” a continuous and delimited volume of spaceorofspaceandtimewithallofitsexistentcontent; and(b)theidealisticandorganismicassumptionthatitis what we ordinarily mean by a “system,” a thread of structuralunitywithitsramifications,acoherentpatternor organization. 2

Usingthetermschosen byWilliams, the naturalexistential context according to the atomistic doctrine is a chunk . The counterpart contextoftheorganismicdoctrineisa web .Thus,theatomisttakes chunkstobetheconcreteentities.Heconsidersanythingwhich,ina certain sense, is less than a chunk to be abstract. According to the idealist,theconcreteentityisaweb.Heconsidersanythingwhichis

tionwhichthewordswouldotherwisemark. Williams’claimhereisenclairthathehasbothreasonandetymologyonhis side. 1Accordingtoathirdinterpretation,foundinWhitehead,thephrase‘natural existential context’ has the same meaning as the phrase ‘the world of existenceingeneral’.Thestatedreasonforrejectingitisthat […] the resultant meaning of the word “abstract” is already supplied by the words “subsistent” and “universal.” (Williams 1931,p.587) Ifthisissupposedtoimplythat‘universal’hasthesamesenseasthephrase ‘theworldofexistenceingeneral’,itcomesasasurprise.Thisseemstobein conflictwiththesenseassignedto‘universal’earlierinthearticle.Isuppose Williams’intentionisnottoabandonthelattersense. 2Williams1931,p.587. D.C.WILLIAMSONTHEELEMENTSOFBEING21 lessthanaweb—eventhoughitmightbeachunk—tobeabstract. Williams prefers the atomistic proposal. His justification for this reads:

[…]Ibegleavetoadherefortherestofthispapertowhat Icalltheatomisticusage,notbecauseIthinktheatomist’s metaphysicsisbetter,butbecauseIthinkthisusageisthe moreprevalentone,nearertheoriginalsenseoftheword, andbettercapableofilluminatingandconsistentdevelop ment. 1

Thedenialhereoftheclaimthattheatomisticdoctrineisbetterthan its rival is probably not completely sincere. This doctrine is most likely thought of as being an example of what has occurred in a profitablemomentoftheongoingdiscussion. 2Howeverthatmaybe, thestatementsunderlinethenotionthatstipulationsarewhatcanbe offered. The proposals regarding the notions of the concrete and the abstractareasfollows:

A concrete entity is one which affords or can afford the totalcontentofaspatiotemporalvolume,orofachunk. Anabstractentityisonewhichdoesnotandcannotafford thetotalcontentofa 3spatiotemporalvolume,orchunk. 4

Presumably,thetotalcontentofavolumeisnothinglessthanitstotal content. If a distinction is made between contents of categorially differentsorts,thetotalcontentofachunkisthetotalityofboth,or all,itssortsofcontents.Inthecaseofaspatiotemporalvolumethe total content does not coincide with just its universal content. The latter should therefore, not least for the sake of clarity, be called something else. An obvious choice is ‘total universal content’. Evidently,theterm‘totalcontent’ispotentiallyambiguous.Isuspect 1Williams1931,p.587. 2Cf.thefirstquotationofthischapter. 3Amoretransparentwayofexpressingthethesiswouldbetouse‘any’here, insteadof‘a’. 4Williams1931,p.588. 22CHAPTERII thatWilliamsdoesnotnoticethisambiguity.Thissuspicionismore orlesscorroboratedbywhathesayslaterregardingthenotionofthe concreteuniversal. The characterisation of an abstract part — when artificially alienatedfromitsnaturalexistentialcontext—asbeingfragmentary, isolated, impoverished, empty, thin or tenuous suggests that it is dependentonitssurrounding.Thelatterbeingthechunkitbelongs to. This might be in conflict though with a principle stated in Williams1953 b.Accordingtothisprinciplethereisnoentitywhich dependsonanywholewhichitisapartof;nordoesitdependonany otherpartofthewhole.1 Inthelastquotation,referenceismadetospaceandtime.One maywonderwhatthesignificanceofthatis.Doesthephrase‘being abstract’moreorlesshavethesamemeaningas‘notfillingupany spacetimevolume’?And,consequently,does‘beingconcrete’more orlessmeanthesameas‘fillingupsomespacetimevolume’?Since thestatementsaresupposedtobedefinitions 2ofthetwonotions,the suggestionisthatthereferencetospacetimeisessential.Inanycase, itisperfectlyclearthatnoabstractentitycanaffordthetotalcontent ofanyspatiotemporalvolume.Thisisstatedoncemoreinthenext quotation.Aconcreteentity,ontheotherhand,canaffordthetotal contentofsomespatiotemporalvolume.

2.2.3 The Combination of the Two Pairs Asreported,eachnotionofthepairabstract–concreteissupposedto be combinable with each one of the pair universal–particular. The firstresultantcompoundnotionisthatoftheabstractuniversal.The determinationofitisascouldbeexpected.

Triangularityisanabstractuniversal.Itisuniversalinthat itisanentitywhichcanbeidenticallypresentor exem 1Cf.Williams1953 b,p.189,whereitisstated: Partdoesnotdependonpart,norwholeonwhole,norparton whole, and that whole does depend on part is for the trivial reasonthatthewholeisatleastthesumofitsparts. 2Thedescriptionofthemisthatareinformaldefinitions. D.C.WILLIAMSONTHEELEMENTSOFBEING23

plifiedinanynumberofspatiotemporallydistinctoccur ences. It is abstract in that it does not exhaust the total content of any one of the spatiotemporal volumes in which it occurs. An existent chunk cannot be triangular and nothing else. The same status is possessed by such entitiesasorthenumberthree,and[…]byqualities likebluenessandbyrelationslikebetweenness. 1

Themessageofthisisfairlyclear,thoughthecombineduseofthe phrases ‘spatiotemporally distinct occurrences’ and ‘the spatio temporalvolumesinwhichit[i.e.,triangularity]occurs’mayobscure itabit.Mostofthetime,ifnotconsistently,theterm‘occurrence’is usedbyWilliamstorefertoaparticularwhichlacksspatialvolume. An instance of triangularity is such a particular. The notion that triangularitydoesnotexhaustthecontentofanychunkindicatesthat it is abstract. Thus, its being universal and its being abstract respectively are determined in the quotation by reference to two differentsortsofparticulars.Aslightlydifferentwayofcharacterising the ontological status of the same universal would be as follows: Since it can simultaneously be exemplified by several, separate chunks, it is universal. Since it does not exhaust the total universal content of any chunk, it is abstract as well. When applied to a relation,thisshouldbeinterpretedassayingthatitcansimultaneously be exemplified by several, separate ntuples of relata. However, it doesnotexhausttheuniversalcontentofanysuchntupleofrelata. Thesecondcompoundnotionisthatoftheconcreteparticular.

Thistableisaconcreteparticular.Itisparticular, by the usual,becauseitisconfinedtohereandnow,or to a spacetime tube uniquely continuous with here and now, and has not the peculiar space and timeleaping identityofauniversal.Itisconcrete,becauseitisachunk, thetotalcontentofadefinablespatialorspatiotemporal volume. A concrete particular is thus properly called an “individual” by those persons who mean by the latter

1Williams 1931,p.588.Thecontextsuggeststhat‘qualities’and‘relations’ referheretouniversals,notparticulars. 24CHAPTERII

wordasubstantialoccurrentchunk,withallitsoccurrent attributes. 1

Notethataconcreteparticularisexplicitlysaidheretobethetotal contentofaspatiotemporalvolume.Obviously,thisisnotthesame assayingthatitsuniversalcontentisthetotalcontent of the same volume. The disjunction — i.e., that it is the total content of a definablespatial or spatiotemporalvolume—suggeststhat,atleast twodifferentnotionsoftheconcretearecontemplated.2

1Williams1931,p.588.Thesenseoftheterm‘individual’mentionedhereis theonereferredtointhebeginningofsection2.2.1. 2 Similar hints can be found in later articles. Williams 1953 b, pp. 1734, providesasample: [A]surfacedoesseemtooccupyasortofborderlinestatus,but thisisnomorethanourdoctrineentails,forwehaveexpressly deniedthat“betweentheabstractandtheconcretetherecanbe nointerveningstages.”Astheshapeistothesurface,perhaps,so thesurfaceistothesolid.Thebiggerdifferenceisthatasurface is“concrete”intwodimensionsasatriangleonitisnotconcrete atall.Thissortofquasiconcreteness,wenote,belongsalsotoan instantaneous threedimensional solid in comparison with one which is appreciably extended in time. Only an old familiarity withthetermsofgeometry,Ithink,makesanyonesupposethata surfaceoraninstantaneoussolidhasinanyfundamentalwaya morerobustbeingthanafourdimensionalshapeortemperature. Aspatiallythreedimensionalsolidisdescribedhereasbeingquasiconcrete, indicatingthatthetemporaldimensionisrequiredforbeing(fully)concrete. ThisisconfirmedinWilliams1951,p.459:“[A]concreteobjectcannomore exist with zero duration than with zero breadth and length.” Perhaps, this reasonisfromsymmetry.Whatholdswithregardtospaceshoulddosowith regardtotimeaswell.Furthermore,thephrase‘sesquiconcrete—concrete andahalf, sotospeak’isusedfordescribinga.Cf.Williams 1953 b,p. 174.Althoughitisnotobviouswhattheintendedsenseofthephraseis,I wouldsaythatbeingconcreteandahalfisasuitabledescriptionforsomeof the entities which he came to classify as tropes. That it has been denied expressly that there cannot be any intervening stages between the abstract and the concrete might mean that they both can appear in degrees. That concretenessappearsindegreesisexplicitlyassertedinWilliams1931,p.590. InWilliams1953 a,p.6,thesameissaidtoholdwithregardtotheabstract. D.C.WILLIAMSONTHEELEMENTSOFBEING25

Thenotionofaconcreteparticular,asexemplifiedbyacertain table,isdescribedaboveasbeingasubstantialoccurrentchunkwith allitsoccurrentattributes.Thisbringstoforetheintricatequestion whether instances of substantial forms are reckoned with. Unfor tunately, it is not possible to extract more information about this issue from Williams 1931. I will come back to it below when discussingthemoderatenominalismofhislaterarticles.1 At this point, we have come to the third compound notion, whichisthatoftheabstractparticular.Ithasbeenreferredtoquitea fewtimesalready.

[S]urelythereareabstractparticulars,too.Wehavedefined and exemplified the abstract universal; and we have definedaninstance.Now,aninstanceofanabstractuni versalisanabstractparticular.Justthisoccurrenceofthe shapeofthistableisanabstractparticular.Asneezeisan abstract particular. The grin of the Cheshire cat was an abstractparticular.[…] Each of these things is particular because it is by definitionconfinedtoanimmediatespatiotemporalocca sionorcontinuity.Itisabstractbecauseitislessthanthe wholechunkinwhichitinheres,lessthananyvolumeof whichitisanelement.Itislessthanavolumeorchunkin a peculiar and otherwise nameless way, and not in the ordinarywayinwhichalittlechunkcanbepartofabig chunk,sothatitispeculiarlyimportanttoretaintheword “abstract” to mean just this way of being less than any wholechunk. 2

Although they are not explicitly mentioned here, instances of relationsareofcourseabstractparticularsaswell. The same would holdforinstancesofsubstantialforms.Furthermore,abstractparti cularsarewhathavebeenreferredtoasinstances—inthesecond senseof‘instance’. 1Myimpressionisthatinstancesofsubstantialformsarerecognisedinhis later articles. They are not mentioned more than in passing though. Cf. Williams1953 a,p.10,1953 b,p.189,and1986,p.6. 2Williams1931,p.589. 26CHAPTERII

In the second paragraph of the last quotation we find an importantpieceofinformationregardingthenotionoftheabstract. Anabstractthingissaidtheretobelessthananyvolumeofwhichit isanelement.Duetotheoccurrenceoftheword‘any’,thecharacteri sationisinlinewiththehypothesisthatthesensesof‘beingabstract’ and‘notfillingupanyspatiotemporalvolume’areintimatelyrelated. Hence, the suggestion is that an abstract entity is nonextensionally lessthanthewholewhichincludesit.Aconcretepart,ontheother hand, is extensionally less than the including whole. It seems to be takenforgrantedherethattheincludingwholeisachunk.1 Thephrase‘abstractparticular’becamepartofthephilosophical vocabularythankstoG.F.Stout. 2Williamsmakesseveralreferences to him. In one of these references, he mentions particular round nesses.

[T]hecategoryofabstractparticularityaccommodatesvery well,althoughitdoesnotdemonstratethefinalvalidityof, Mr.G.F.Stout’sconclusionthat“Eachbilliardballhasits ownparticularroundness,separateanddistinctfromthat ofanyotherball.” 3

Thesentencewithinquotationmarks 4doesnotspecifywhetherthe roundnessofabilliardballisaninstanceoftheuniversalroundness. AccordingtoStout,itcannotbeaninstanceinthatsense;however, thisisdueto his beinganominalist.Headvocates a kind of class nominalism,whichisalsoamoderatenominalism.Notwithstanding that,Williamsconsidershimtobeanallywhenitcomestothenotion ofabstractparticular. The fourth and last compound notion is that of the concrete universal.

1Inlaterarticlesconcretepartsofabstractwholesarereckonedwith.Such wholesfitthedescriptionofbeingconcreteandahalf. 2Cf.Stout1923,p.114. 3Williams1931,p.589. 4ItoriginatesfromKempSmith1927,p.394. D.C.WILLIAMSONTHEELEMENTSOFBEING27

Theeasiestwaytodefinea genuinelyconcreteuniversal wouldbe:thatitisthatofwhichaconcreteparticularisor canbeaninstance.Aconcreteuniversalisacompoundor complexuniversalwhichisconcreteinthatitisadequate toexhaustthecontentofatotalexistentvolumeorchunk, andyetauniversalinthatitmightberealizedandidentical inanynumberofexistentchunks. [] A concrete universal would be the superlative degreeofwhathe[G.Santayana]calls“complex”or“syn thetic”—suchanessence,tousehisexample,as “mydog’snature,”or,touseafamiliarhistoricalinstance, the exact whole nature of just this kind of table. The adequateandanalyticdescriptionofan“individualform” of this sort would perhaps require an infinite number of adjectives,infinitelyhyphenated. 1

Itappearsfromthefirstparagraphthataconcreteuniversalisthatof whichonlyaconcreteparticularisorcanbeaninstance.Thus,the concreteness of a concrete universal is due to its exhausting the universal content of a concrete particular. In the second paragraph Williamsseemspreparedtoconsiderkindsasbeingconcreteuniver sals.Or,perhapsheisreportingwhatheconsiderstobeacommon useoftheterm‘kind’.Ifhedecidesontheformer, the notions of kindandofindividualformcollapseintoeachother.Yetathirdname forthesamenotionwouldbe‘truly infima species ’asfoundinthenext quotation. Note that if the term ‘content’ is used a bit indeter minately,itmayresultintheappearancethataconcreteuniversalis identicalwithaconcreteparticular. 2Williamsascribessuchaviewto G.W.Leibniz.

Ifweidentifydegreesofsuchcomplexityorhyphenation withdegreesofconcreteness,wemayexpatiatebysaying thatthedefiningcharacterofaspeciesismoreconcrete (i.e.,nearerconcrete)thanthatofitsgenus,andsoforth. A thoroughly concrete universal is the defining character 1Williams1931,p.590. 2 This squares with what has been pointed out regarding an ambiguity of ‘totalcontent’. 28CHAPTERII

of a truly infima species . Leibniz believed that such a concrete universal must be ipso facto aparticularthingor person, because he believed in the identity of indiscer nibles. We need only admit, however, that a concrete universal, being perhaps infinitely complex, is perhaps infinitelyunlikelytobemanifestinapluralityofinstances; andthisisadifferentmatter. 1

Thenotionofatruly infima species isidentifiedherewiththatofthe total (universal) content of a concrete particular.This,accordingto the view ascribed to Leibniz, makes it identical with the concrete particularitisthecontentof.Evidently,thisisinconflictwithwhat Williams’ view should be. The way he uses the term ‘concrete’, in ‘concreteuniversal’,suggeststosomeextentthatheimplicitlyagrees withtheallegedLeibnizianview.Rememberthateachnotionofthe twopairsofdistinctionsissupposedtobecombinable,withoutany restrictions, with each one of the other pair. This supposition includesthateachoneofthefoursimplenotionsisthesameineach combination.Theterm‘concrete’in‘concreteparticular’supposedly hasthesamemeaningastheterm‘concrete’in‘concreteuniversal’. Thesameshouldholdmutatis mutandis withregardtothe‘abstract’of ‘abstractparticular’and‘abstractuniversal’.Butcanthissupposition hold? Well, in the phrase ‘concrete particular’ the term ‘concrete’ bearsuponthetotalcontentofachunk.In‘concreteuniversal’,on theotherhand,itonlyhasbearingonthetotaluniversalcontentofa chunk.Thesameholdsmutatis mutandis withregardtothe‘abstract’of ‘abstract universal’ and of ‘abstract particular’. Keep that in mind whenreadingthenextsentence.

Most dictionaries define the two [i.e., ‘universal’ and ‘abstract’]byreferencetooneanother,andoftentheonly way to explain to the recalcitrant student what a “universal”is,istotellhimitisan“abstraction.” 2

1Williams1931,p.590. 2Williams1931,p.586. D.C.WILLIAMSONTHEELEMENTSOFBEING29

Incontext,theimplication 1hereisthatthedictionarywriters,aswell astheteachersansweringrecalcitrantstudents,aremistaken.Iwould say that they cannot be completely wrong though. After all, how couldsomethinguniversaleverbeanythingotherthanabstract?No matterhowcomplextheuniversalcontentofaconcreteparticularis, itcanonlyexhaustitsuniversalcontent.Thus,inthetruesenseitcan neverbemorethanabstract. Thenotionthataconcreteparticularissomesortofcompound of abstract particulars seems to suggest itself here. In spite of its importance, this issue is not more than touched upon in Williams 1931.Someofthefewpiecesofinformationtherearecanbefound inthefollowing,somewhatcryptic,statement:

One way of phrasing the opposite characteristics of the abstract universal and concrete particular is to say that eachofthemevincesitsownkindof“unityindiversity.” Anabstractuniversalisaunityofcharacterpervading a diversityofoccurrences.Aconcreteparticularisaunityof occurrences which invests a plurality of characters. A completely abstract particular or (probably) a completely concrete universal misses each characteristic unityin diversityofitstype. 2

In the third sentence ‘occurrences’ is used, instead of ‘abstract particulars’or‘instances’.Thischoiceoftermmuddlesthemessageto someextent.Thesingularformoftheverb,‘invests’,contributesto the confusion. A better phrasing of what probably is the intended message of the third sentence is: a concrete particularisaunityof abstractparticulars,ofwhicheachinvestsacharacter. Williamsdoesnotpostulatetheexistenceofanysubstratum.It is therefore likely that the proposed ontology is a socalled bundle theory. 3 His particular version of the bundle theory should be con 1Itisperhapsmoreaccuratetosaythatitisaninsinuation. 2Williams1931,p.592. 3Athirdpossibilityisthatheiscontemplatinganetworktheory.Morewillbe said about this alternative to substratum and bundle theories in the last chapter. 30CHAPTERII sistent with moderate realism. The view ascribed to Leibniz in an earlierquotationmoreorlessidentifiesaconcreteparticularwitha bundle of universals. Evidently, Williams cannot agree with such a view on concrete particulars. Instead, he should take concrete par ticularstobeinstancesofconcreteuniversals.Analternativedenomi nation of compound universals of such complexity is of course ‘bundle of universals’ — or, more accurately, ‘complete bundle of universals’.Thishavingbeensaid,therestillremainsmuchexplaining to do concerning how abstract particulars compose aconcretepar ticularofwhichtheyallarecomponents. The last quotation also has some bearing on the sense of the term ‘instance’. The same issue comes to fore in another passage, whichhasalreadybeenquoted.

Theeasiestwaytodefinea genuinelyconcreteuniversal wouldbe:thatitisthatofwhichaconcreteparticularisor canbeaninstance. 1

Aconcreteparticularobviouslyisaninstanceofaconcreteuniversal inthefirstsenseof‘instance’.Howcoulditnot be? This concrete particular is also an instance of the same concrete universal in the second sense of the term ‘instance’. In reason, nothing less than a concreteparticularcanbeasuniversalasthis.Thus,withregardto theinstancesofconcreteuniversals,thetwosensescollapseintoeach other.

2.3Williams’TropeTheory

2.3.1 Overview Williams’mostcelebratednotion,trope,ispresentedinsection2.3.3. Preparationsforthatdiscussionaremadeinsection2.3.2.Bymeans of that notion Williams claims that he can give an account of properties and relations which steers clear of the alleged mistakes inherent in realism as well as in traditional forms of nominalism. 1Williams1931,p.590. D.C.WILLIAMSONTHEELEMENTSOFBEING31

Besidesthat,itisassignedtheroleasabuildingstoneofreality. 1In what follows, these two things will not be kept strictly apart. My, perhaps poor, excuse is that Williams himself does not keep them apart. Sections2.3.4and2.3.5dealwithWilliams’views onconcrete objects.Afterthathisviewsonwhatshouldsubstituteforuniversals are discussed. Evidently, the latter subject is a central one for any nominalisticontology.Intwoshortsections,sections2.3.6and2.3.7 respectively,socalled‘painlessrealism’andpredicativityarediscussed briefly.Painlessrealismgivesexpressiontoastrategywhichisquite common among moderate nominalists, however abortive. The last subjectisevidentlyanessentialnotionofanyontology.Iwouldsay thatitissomething ofatouchstone. In Williams’caseitturnsout thatonlyrelationsarelookeduponasbeingpredicative.

2.3.2 Parts and Components AccordingtoWilliams,metaphysicsisanchoredtoexperience.This viewisexpressedclearlyinthefollowingtwosentences.

Metaphysics is the thoroughly empirical science. Every item of experience must be for or against any hypothesis of speculative cosmology, and every experi enced object must be an exemplar and test case for the categoriesofanalyticontology. 2

1FredrikStjernbergcallsattentiontothefactthattropesareintroducedfor twodifferentreasons. [O]neistogiveanaccountofproperties,theotheristopresent tropesasthefundamentalbuildingblocksoftheworld.Tropes are allegedly the fundamental entities in the world, things that makeupeverythingelse.(Stjernberg2003,p.37) Heisinclinedtobelievethatthisisonetasktoomany.Cf.Stjernberg2002, p.44. 2Williams1953 a,p.3. 32CHAPTERII

Thepurposeofillustratingthecategories 1ofanalyticontologyiswell inlinewiththeviewexpressedhere,tousecommonplaceexamples insteadofmoredignifiedones.Sinceexamplesofthelatterkindare, in Williams’ own words, “darkened with a patina of tradition and partisanship”,acommonplaceexamplemayevenbeabetterchoice. Consequently, it is not surprising that among his examples there is onewhichstarsthreelollipops.Fromwhatisstatedattheendofthe firstparagraphofthenextquotation,werealizethatgreatthingsare expectedfromthisexample:

Letus[…]imaginethreelollipops,madebyacandyman who buys sticks from a big supplier and molds candy knobsonthem.Lollipop No. 1hasaredroundpepper minthead,No.2abrownroundchocolatehead,No.3a redsquarepepperminthead.Thecircumstanceherewhich mainlyprovokestheoriesofsubsistence 2andinherenceis similaritywithdifference:eachlollipopispartiallysimilar toeachotherandpartiallydifferentfromit.Ifwecangive agoodaccountofthiscircumstanceinthisaffairweshall havetheinstrumenttoexposetheanatomyofeverything, fromanelectronoranappletoarchangelsandtheWorld All. Mychiefproposaltothatendmaybeput,tobegin with, as nothing more tremendous than that we admit literallyandseriouslythattosaythat aispartiallysimilarto bistosaythatapartof aiswhollyorcompletelysimilarto apartof b.3

1 In Williams 1931 ‘category’ occurs twice. The indication is in both that abstractparticularityisacategory.Presumably,thesameholdswithregardto abstractuniversality,concreteparticularityandconcreteuniversality.Beinga nominalist in his later articles, he has reductive ambitions concerning universals.Abstractparticularityisdeclaredtobethesinglefundamentalcate gory.Itcanbeexpectedthatothercategoriesaresupposedtobereducibleto thefundamentalone. 2 Although it is suggested here that subsistence is an essential notion, Williamsdoesnotdiscussitanyfurther;atleastnotunderthatname. 3Williams1953 a,p.4.Williamsusesphrasessuchas‘whollysimilar’,‘com pletely similar’, ‘exactly similar’, ‘precisely similar’ and ‘perfectly similar’ as D.C.WILLIAMSONTHEELEMENTSOFBEING33

Mark well the statement of the second paragraph: “to say that a is partiallysimilarto bistosaythatapartof aiswhollyorcompletely similartoapartof b.”Thiswordinghastheappearanceofasemantic principlebutcaneasilybeparaphrasedintoanontologicalidiom.It then reads: every partial similarity between entities presupposes a complete similarity between parts of each. I strongly suspect that Williamsdoesnotregardittobeespeciallyimportanttodistinguish betweenthesetwoversionsoftheprincipleandthereforeembraces them both. Henceforth, when I use the definite description the similarity principle ,Iwillbereferringtotheontologicalversionofit.Do notfailtonoticethatthisprincipleisputforwardhereasthechief proposal regarding which instruments to use when exposing the anatomyofeverything.Fromwhatisstatedinthenextquotation,itis evidentthatitissupposedtobecompletelygeneral. Someoftheentitiesappearinginhisexamplesaregivenproper namesoftheirown.Theexamplewiththethreelollipopsisacasein point.Sincethesenameswillbementionedandusedfromnowon,I mayaswellintroducesomeofthem.Thethreelollipopsthemselves arecalled‘Heraplem’,‘Boanerp’and‘Rindesta’.1Heraplem’sstickis called‘Paraplete’.‘Merrinel’isthenameofBoanerp’sstick.Rindesta’s stickremainsnameless.Morenameswillappearasweproceed. The lollipop affair gives proof of a number of similarities. Amongtheseis thesimilaritybetweenParaplete,Merrinelandtheir nameless colleague, which is stipulated to be exact,2 as a result, Heraplem,BoanerpandRindestaarepartiallysimilartoeachother. An Williams provides for the situation is that the lollipops are partially similar with respect to stick. It seems more

synonyms.InwhatfollowsIwilldolikewise. 1WhilethefirsttwonamesoccuralreadyinWilliams1953 a,thethirddoes notdosountilWilliams1986.Duetoamisprint‘Rindesta’issaidtheretobe a(new)nameoflollipopNo.2.Itisclearthough,fromthedescriptionofit, that‘Rindesta’isintendedtobethenameofthehithertonamelesslollipop No.3ofWilliams1953 a. 2InWilliams1953 a,p.4,itissaidthat,onphysicalgrounds,itisnotlikely thatanysolidobjectsareexactlysimilartoeachother.Itisintelligiblethough tostipulatethatsomeofthemare. 34CHAPTERII appropriatetosaythattheyareexactlysimilarwithregardtostick.Be thatasitmay,letusmoveonandacquaintourselveswithsomeof the other similarities. In doing that we witness the introduction of entitiescalled‘propertycases’.Evidently,thesearecloselyrelatedto theinstancesofWilliams1931.

But what now of the rest of each lollipop and what of theirmoresubtlesimilarities,ofcolor,shape,andflavor? Myproposalisthatwetreattheminexactlythesameway. Sincewecannotfindmorepartsoftheusualgrosssort, likethestick,tobewhollysimilarfromlollipoptolollipop, let us discriminate subtler and thinner or more diffuse partstillwefindsomeofthesewhicharewhollysimilar. […]JustaswecandistinguishinthelollipopsHeraplem and Boanerp the gross parts called “sticks,” namely, ParapleteandMerrinel,sowecandistinguishineachlolli popafinerpartwhichweareusedtocallits“color”and another called its “shape” — not its kind of color or shape,mindyou,buttheseparticularcases,thisreddening, thisoccurrenceoroccasionofroundness,eachasuniquely itselfasaman,anearthquake,orayell. 1

Itakeitthatthedescriptionofthepropertycasesasbeingpartsof theirrespectivelollipopsismeantliterally.Comparedwiththegross parts, cases are but finer parts of the including lollipops. Further more, each part of a lollipop is thought of as being a particular. Regardingthenotionoftheparticular,itisassertedinanotherplace:

[P]articularentitiesarethosewhichdonotconformtothe principle of the identity of indiscernibles, 2 which is that identityofkindentailsidentityofcase;thatis,particulars 1Williams1953 a,pp.45. 2 In McTaggart 1921, p. 101, an apposite remark is made regarding this designationoftheprinciple: The name [‘The Identity of Indiscernibles’] […] is not a good one.Fortheprincipledoesnotassertthatthereareindiscernibles which are identical, but that there is nothing which is indiscer niblefromanythingelse.ItwouldbebettertospeakoftheDis similarityoftheDiverse. D.C.WILLIAMSONTHEELEMENTSOFBEING35

areentitieswhichmaybeexactlysimilarandyetnotonly distinctbutdiscrete. 1

ThephraseusedheretoexpressLeibniz’sprincipleis‘identityofkind entails identity of case’. Incidentally, it seems as if a consistent adherentoftheprinciplewouldnotrecognisecases.Afterall,what wouldbethepurposeofrecognisingsuchentitiesifexactlysimilar onesaresupposedtobeidentical?Therewouldbea point if they were never more than almost exactly similar to each other. Never mind that though. 2 Instead, reflect on another question and its answer: Since particulars have the capacity of being exactly similar, while still not being numerically identical, with each other, what entities do actually conform to the principle? Williams’ answer is: Universals. 3 Coming from a nominalist this has the appearance of beingproblematicattheveryleast. Anotherissuenottoucheduponaboveiswhethertwoproperty casescanbepartiallysimilartoeachother.Wehaveseenitdeclared that such subtle similarities should be treated in the same way as other similarities. Thus, the similarity principle is supposed to be applicable to property cases as well. Partial similarity between two casesimpliesthatatleastoneofthemhasapartofsomesort.This part is either exactly similar to the other case or each case has a properpartwhichisexactlysimilartoapartoftheother.Ihastento addthoughthatWilliamsmightholdconflictingviewsregardingthe similaritiesbetweenentitiessuchasthese.Thedeterminingprinciple ofoneoftheseviewsisthesimilarityprinciple;itismoredifficultto graspwhatthatoftheotherviewis.Iwillcomebacktothisbelow. InconnectionwiththeintroductionofpropertycasesWilliams starts to use ‘part’ in a more narrow sense. From then on it refers especially,butnotconsistently,towhathasbeendescribeduptothen 1Williams1986,p.3.Adistinctionbetweenbeingdiscreteandbeingdistinct ishintedathere.Whateveritamountsto,nofurtheruseseemstobemadeof it. 2IwillcomebacktothismatterinafootnoteinchapterIV. 3 Cf. Williams 1986, p. 8. Cf. also Williams 1963, p. 615, where we are informedthatwhatwemeanwhenwesaythatcertainentitiesareparticulars isthattheydonotobeytheprincipleoftheidentityofindiscernibles. 36CHAPTERII asgrosspartsofthings.Theterm‘component’isreservedfortheir finerparts.Thereisalsotheterm‘constituent’.Itcoversgrossaswell asfineparts.Inspiteofthisterminologicaldistinction,components areessentiallythought ofasbeingparts oftheir including wholes.1 Williams’repeateduseoftheterm‘part’,whenreferringtoproperty cases,iscircumstantialevidenceofthis. Asonemightexpect,therearepropernamesinstoreforsome ofthepropertycasesmentionedsofar;aswellasforsomesoontobe mentioned. For example, Rindesta’s colour case is christened ‘Rastoc’. 2Twoothernewnamesappearinthenextquotationalong withsomeconfirmationandreiterationofsomepreviousnotions.

[…] Heraplem and Boanerp are partially dissimilar in as muchtheirknobsorheadsarepartiallydissimilarbecause someoftheirfinerparts,forexample,HarlacandBantic, theircolors,aredissimilar. In like manner, to proceed, we note that Harlac, the color component of No. 1 (Heraplem), though numeri callydistinctfrom,iswhollysimilartothecolorcompo nentofNo.3.ButNo.1hasnotonlyacolorcomponent whichisperfectlysimilartothecolorcomponentofNo.3; it has also a flavor component perfectly similar to the flavor 3componentofNo.3. [] Crucialhere,ofcourse,istheadmissionofa“fine”or “subtle” part, a “diffuse” or “permeant” one, such as a resident color or occurrent shape, to at least as good

1AnnaSofiaMaurinpointsoutthatthisistheappropriateimagery,proposed byWilliams,forthepropertiesofthings.Accordingtoher,thispartimagery yieldsthreetraitsofthepropertycases:simplicity,particularityandabstract ness.Cf.Maurin2002,pp.9f.IamnotsurewhetherWilliamsissupposedto actuallyagreewithallofthis.Anyhow,thesenseMaurinassignstotheterm ‘abstract’isnottheoneWilliamshasinmindforit.Furthermore,Iamquite certain that she does not want to claim that any of the enumerated traits themselvesappearaspropertycases.Aswillbeseenbelow,Williamsisnot entirely out of sympathy though with concreteness, and by implication abstractness,doingthat. 2ThefirstappearanceofitisinWilliams1986. 3Theflavourcasesremainnameless. D.C.WILLIAMSONTHEELEMENTSOFBEING37

standing among the actual and individual items of the world’sfurnitureasa“gross”part,suchasastick.Thefact thatonepartisthusfinerandmorediffusethananother, and that it is more susceptible of similarity, 1 no more militates against its individual actuality than the fact that mice are smaller and more numerous than elephants makesthemanythelessreal. 2

Immediately after this, he states that the fine parts of things are described as being abstract and their gross parts are described as beingconcrete.Inthefollowingpassage,Williams1953 aintroduces thepair‘concrete’and‘abstract’.

Toborrownowanoldbutprettyappropriateterm,agross part,likethestick,is“concrete,”asthewholelollipopis, whileafineordiffusepart,likethecolorcomponent or shape component, is “abstract.” The colorcumshape is less abstract or more concrete or more nearly concrete thanthecoloralonebutitismoreabstractorlessconcrete thancolorplusshapeplusflavor,andsoonuptillweget tothetotalcomplexwhichiswhollyconcrete.3

Inanearlierquotationwesawthephrase‘theWorldAll’beingused. It strongly suggests that an entity including everything is assumed; perhapsthephrase‘theBigIt’ 4doessotoalargerdegree.Whether anycounterpartentitiesintheotherendarealsoreckonedwithisless certain. One looks in vain for clearcut information with regard to somethingbeing“whollyabstract”. Later in the same article there is a characterisation of the abstract,whichreferstotheonegiveninWilliams1931.

Atitsbroadestthe“true”meaningof“abstract”ispartial, incomplete,orfragmentary,thetraitofwhatislessthanits whole.[…]Themoreusualpracticeofphilosophers[…]

1Itakeitthat‘similarity’hereisshortfor‘exactsimilarity’. 2Williams1953 a,p.6. 3Williams1953 a,p.6. 4Cf.Williams1986,p.2. 38CHAPTERII

has been to require for “abstractness” the more special sort of incompleteness which pertains to what we called the“thin” or“fine”or“diffuse”sort ofconstituent,like the color or shape of our lollipop, in contrast with the “thick,” “gross,” or chunky sort of constituent, like the stickinit. 1

The noun ‘chunk’, found in the early article, appears here in its adjective form ‘chunky’. Furthermore, I take it that by using the phrase‘themorespecialsortofincompleteness’,thecharacterisation madeearlierofbeing,inacertainsense,lessthananincludingwhole isalludedto.Whatisstatedhereregardingtheabstractletsitselfbe interpretedinlinewiththedoctrineofWilliams1931. Inboththeearlyandthelaterarticles,thereissomethingofa suggestionthatthenotionsoftheabstractandtheconcreteforma continuum. At one extreme we find the wholly concrete entities. Presumably,beingwhollyconcreteisbeingasconcrete as anything can get. Lollipops are such wholly concrete entities.2 So are their sticks.Itislessevidentwhatcanbeexpectedattheotherendofthe continuum.Nothingisexplicitlysingledoutasbeingwhollyabstract. Thereareafewpossiblehintsthough,suchastheremarkthatcolour cumshapeislessabstractthancolouraloneandthat the former is more abstract than colourplusshapeplusflavour. The evident implicationhereisthatasinglepropertycaseismoreabstractthana complex of several property cases. Single property cases might thereforebefoundattheotherendofthecontinuum.Ifaproperty case itself has some sort of constituents, the latter would be even moreabstract.Partofthemessageofthefollowingquotationseems toimplythatatleastsomepropertycasesdohaveconstituents.

Weneednot proposethataredsensum,forexample,is perfectly abstract (whatever that might be). But even thoughithassuchdistinguishablecomponentsasashape andasizeaswellasacolor,andthoughthecolor itself 1Williams1953 a,p.15. 2 I suppose that the maximum entity, given that it exists, is bound to be whollyconcrete. D.C.WILLIAMSONTHEELEMENTSOFBEING39

involvesthe“attributes”ofhue,brightness,andsaturation, still it is abstract in comparison with a whole colored solid.1

Thesuggestionhereisthatacolourcasehascasesofhue,brightness and saturation as components. The quotation marks around ‘attri butes’ may evince uneasiness about cases of properties themselves having properties. 2 Regardless, I suppose the latter three are more abstract than the colour case itself. We may have reached rock bottomatthispoint,atleastinthesensethatthereisnothinginthe colour case which is more abstract still. Though itmaybethatthe insertion within parentheses is an expression of the strategy that betternotbetoocertain. 3 The reflections made above concerning the constituents of property cases being more abstract than the property cases them selvesmayappearperfectlysound.Itwillbeevident though, from what is reported in the next section, that it is not true that for all abstractparticularseachof theirpartsaremoreabstract than their includingwholes.Thisparadoxicallysoundingthesisisinaccordance withWilliams’doctrineduetoastipulationmadeinhisdefinitionof trope.

1Williams1953 a,pp.1718. 2Thepossibilityoftherebeingalevelofsubproperties,andperhapseven further levels below that, threatens to invalidate the model according to whichpropertycasesarethefundamentalbuildingblocksofreality. 3Tobringoutthematterinrelief,Whitehead,whoisreferredtoinWilliams 1931,concerninganothermatter,canbementioned.Heacceptsneitheranall inclusiveentity,norasmallestone.Hetakesrealitytobetoplessaswellas bottomless. Furthermore, between any two entities a and b, where a is a properpartof b,thereissupposedtobeanentity cwhichhas a asaproper part and is itself a proper part of b. Cf. Whitehead 1916 and 1919. Incidentally,Anaxagorasseemstohavebeenanearlyadvocateofthisview. Cf.Barnes1987,p.227.DavidLewisproposesthedenomination‘atomless gunk’foranentitysatisfyingthegivendescription.Cf.Lewis1990,p.20. 40CHAPTERII

2.3.3 The Alphabet of Being: Tropes Althoughheisnottheinventoroftheterm‘trope’,Williams’name willforeverbeassociatedwithitinitsontologicalsense.Moreover,it hasalonghistoryinrhetoric,where‘trope’isthecatchalltermfor expressions used figuratively, as metaphors, synecdoches, meto nymiesetc.Williamsisofcoursewellawareofthis,evenifhissource ofinspirationisnotrhetoric.Ifanythingoranyoneistobesingled out as being that, it would be George Santayana. But, the sense he givesthetermisnottheoneWilliamshasinmind.

Santayana[…]used“trope”tostandforthe essence ofan occurrence ;andIshalldiverttheword[…]tostandforthe abstractparticularwhichis,sotospeak,the occurrence ofan essence .1

Santayana’ssenseof‘trope’seemstobethatof‘universal’,wherethe sense of the latter is compatible with realism. While the notion of universalitywasrecognisedandassignedaprominentroleinWilliams 1931,itisnowconsideredalmostuseless. 2Inanycase,fromwhatis statedinthisquotationwelearnthattropesareabstractparticulars. Thisisconfirmedseveraltimes.Unfortunately,itturnsoutthatthe notion ofabstractparticularisrathercomplicated. That complexity rubs off on the notion of trope. We find proof of that in the paragraph in which it is introduced. What follows is approximately thefirsthalfofthatparagraph.

Iproposenowthatentitieslikeourfinepartsorabstract components are the primary constituents of this or any possibleworld,theveryalphabetofbeing.Theynotonly 1Williams1953 a,p.7. 2InthemaintextIhaveshortenedthequotationabit.Infullitreads: Santayana, however, used “trope” to stand for the essence of an occurrence ;andIshalldiverttheword,whichisalmostuselessin either his or its dictionary sense, to stand for the abstract particularwhichis,sotospeak,the occurrence ofan essence . The dictionary sense of ‘trope’ is of course that of rhetoric. Why it is condemnedasbeingalmostuselessisacompletemysterytome. D.C.WILLIAMSONTHEELEMENTSOFBEING41

areactualbutaretheonlyactualities,injustthissense,that whereas entities of all other categories are literally composedofthem,theyarenotingeneralcomposedof anyothersort ofentity.That suchacrucialcategoryhas no regular name is quite characteristic of first principles and is part of what makes the latter worth pursuing. A descriptionofitingoodoldphraseologyhasaparadoxical ring:ourthinpartsare“abstractparticulars.” 1

This expresses a view on what are the building blocks of reality. Moreover, a careful reading of it proves that two rather different tendencies can be discerned. One of these is suggested by the metaphor the alphabet of being . The description of the abstract componentsasbeingtheprimaryconstituentsofthisoranypossible world makes the same suggestion. Both indicate that the entities referredtoarefundamentalinsomesense.Oneaspectofthatisthe picture of them that is conjured by the metaphor being the letters, ratherthanthesyllables,ofbeing.Asthelettersofbeing,onewould expect them to be simple entities. The sundry complex entities constituted from them would be the syllables of being. The same tendency is enhanced by the message of the first twothirds of the secondsentencethatstatesthattheentitiesoftheothercategoriesare

1 Williams 1953 a, p. 7. In a footnote, placed where the quotation ends, a referenceismadetoWilliams1931: Iarguedthegenerallegitimacyofsuchacategory[i.e.,thatofthe abstract particular] in “The Nature of Universals and of ”[…]. Aspointedoutearlier,theterm‘abstractparticular’isalsousedbyStoutfora keynotionofhisontology.InWilliams1953 a,p.12n,weareinformedthat Stout’sontologyandhisownarealmostidentical.Thedifferencebetweenthe twoconcernsthenotionofclass. [I]fthereisadifferenceitisinhisobscureideaoftheclassasa uniqueformofunitynotreducibletosimilarity. Stout’s class nominalism is vaguely hinted at here. Being elements of the sameclassisthebasisforbeingsimilar.WhatWilliamsasserts,interpreted e contrario ,impliesthathisviewisquitetheopposite:entities areelementsof thesameclassbecauseoftheirsimilarity.Cf.Seargent1985foranexcellent accountofStout’sontology. 42CHAPTERII composed of entities of this category. This first tendency can be paraphrasedusingametaphor:eachentitywhichisnotaletterofthe alphabetofbeingiscomposedofentitieswhicharesuchletters. Therearealsotracesofasecondtendency.Thelastonethirdof thesecondsentenceofthequotationmakestheassertion,“theyare notingeneralcomposedofanyothersortofentity.”Incontext,the phrase‘ingeneral’indicatesthatsomeoftheprimaryconstituentsof beingarecomposedofentitiesofothersorts.Strangelyenough,these latter letters of being look more like syllables of being. Naturally enough, the metaphor suggests that any complex entity prima facie deservesthedescriptionofbeingasyllable.Thiswouldbeparticularly accurate for categorially mixed entities. Judging from the actual wording, these latter letters are thought of as having other sorts of entitiesasparts.Inreason,‘sort’isanalternativefor‘category’here. Anotionofcategoryisexplicitlymadeuseoftwiceinthelast quotation.ItisquiteclearthatWilliamsconsiderstheretobemore than just one category. This is particularly clear from the saying, “whereas entities of all other categories are literally composed of them”.Itakeitthatthethinpartsofthingsarewhataremeantby ‘them’here.Theyarealsoreferredtoasbeingabstractparticulars.A crucialquestioniswhethertheothercategoriesare supposed to be reducibletothatofabstractparticularity.Perhapsthatissomething whichis supposedtofollowfromtheclaimthat theentitiesofthe othercategoriesareliterallycomposedofabstractparticulars. Ithinkwearereadytoacquaintourselveswiththedefinitionof trope. From now on I will use ‘the definition of trope’, ‘the trope definition’andsimilarphraseswhenIamreferringtothefollowing formulation:

Atropethenisaparticularentityeitherabstractorcon sisting of one or more concreta in combination with an abstractum. 1

Thefirsthalfofthisdefinitionshowsvestigesofwhatisreferredto aboveasthefirsttendency.Thesameholdswithregardtoitssecond

1Williams1953 a,p.7. D.C.WILLIAMSONTHEELEMENTSOFBEING43 half and the second tendency. The notion that tropes are abstract particularsiscorroboratedinthefirsthalfofthedefinition;notsoin the second half. We can safely assume though that all tropes are consideredtobeabstractparticulars.Iventuretoclaimthat,ofthese two tendencies, it is primarily the first one which has caught the attention of those who have been inspired by Williams’ ontological writing. 1 Inanotherarticlethereisaslightlydifferentdetermination of thenotionoftrope.

Tropesincludeboththeprimitivequaliaandtheprimitive relationsandalsoallthesundrycompoundsthereof,upto, but of course not including, those thorough totalities whicharebydefinitionnotabstractbut‘concrete’. 2

Do not let the term ‘qualia’ muddle things here. It should not be takenasapretextfortropesexclusivelybelongingtothephenomenal sphere. Instead, it should be looked upon as an alternative for ‘qualities’.Withthatterminologicalmatteroutoftheway,itisstillnot evident what the import of ‘primitive’ is. It might be that of 1AnexampleisKeithCampbell.ThefollowingarefromCampbell2002,p. 151. A trope metaphysics gets its importance from the primacy it accords to unit properties. Its bite comes from the claim that these are basic elements, the ‘alphabet of being,’ as Donald Williamshasit. Thesamemessageisenhancedwhenhesays: [T]rope theory affirms that Reality consists in nothing but (monadicorpolyadic)[unit]properties. Notealsothefollowing,onthefaceofit,paradoxicalassertion: Nordoestropetheorydenytheexistenceofsimpleorcomplex individuals. It does not admit substances as a distinct category, butindividualbasictropesaresubstancesintheHumeansense —theyarecapableofindependentexistence. Theterm‘substance’isusedhereintwodifferentsenses.Initsfirstsenseit denotes concrete particulars. In its other sense it denotes independently existing entities. Tropes are supposed to be substances in the latter sense. ThisisalsoWilliams’opinion. 2Williams1986,p.4. 44CHAPTERII

‘irreducible’.InanotherofhislaterarticlesWilliamsdiscussesthree relations which are said to be irreducible. Another description of theseisthatofbeingfundamentaltypesordeterminables.Thethree are:location,partitionandcomparison.1Thesuggestionisthenthat these three are the primitive relations referred to in the quotation. Theprimitivequalitieswouldbesimplequalitytropes.Unfortunately, the content of the trope definition, to some extent, seems to be in conflictwiththatofthepresentdetermination.Theconflictisdueto the latter seemingly excluding concrete entities from being con stituentsoftropes.Thiscontradictswhatisstipulatedinthesecond half of the definition. If there indeed is a clash here, it would be reasonabletogiveprioritytothewordingofthedefinition. Itwillbe seenbelowthatthisnotiongetsdecisivesupportfromwhatisstated in direct connection with the trope definition. But apart from that, thelastquotationsuppliesuswiththeinformationthatrelationsalso appearastropes,2whichofcourseiswhatwastobeexpected.Itis confirmedinthenext,somewhatcryptic,quotation.

Locationandsimilarity(orwhateverelsethereis)provide alltherelations, 3asthetropesprovidetheterms,butthe totaloftherelationsisnotsomethingoverandabovethe totaloftheterms,forarelation Rbetweentropes aand b isaconstitutivetropeofthecomplex r' (a,b),whilecon verselytheterms aand bwillbeingeneralcomposedof constituentsinrelation—thoughperhapsnomorethan thespreadofasmoothor“homoeomorous”qualesuchas acolor.4

1 Cf. Williams 1963, p. 609. Why the epistemologically sounding term ‘comparison’isused,insteadof‘similarity,Idonotknow. 2Inspiteofthat,theway‘trope’isfrequentlyusedindicatessomethingofa resistancetoletting‘trope’denoteinstancesofrelations.Acaseinpointisthe nextquotationinthemaintext. 3 In this article, location and similarity are thought to exhaust the class of relations. In Williams 1963, partition is added as a third independent, primitiverelation. 4Williams1953 a,pp.89.Theformalismisabitopaque.Thecapital‘ R’and thelowercase‘ r’mayindicatethatadistinctionismadebetweenauniversal D.C.WILLIAMSONTHEELEMENTSOFBEING45

I reiterate some of what is said in the paragraph containing the definitionoftrope:“they 1arenotingeneralcomposedofanyother sortofentity.” 2Accordingtothelatestnews,tropesarecomposedof constituents in relation in general; however, an imminent contra dictionmightbelurkinghere.Afterall,tropescannotbothbeand notbecomposedofothersortsofentitiesingeneral.Awayoutis thattheconstituentsofcomplextropes,ingeneral,arequalitiesand relationsandthatthesebelongtothesamesort,orcategory;thesort being that of trope, or abstract particular. This would imply that Williamsisnotinsistingthateverytropeisabsolutelysimple.3Atrope may have other tropes as constituents, among these, one or more relationtropes.Rememberalsothat,accordingtothesecondhalfof the trope definition, concrete particulars may also be among the constituentsofatrope. Animportantissueiswhetherabstractnessandconcretenessare thoughtofasproperties.Ifthatisindeedthecase,onewouldexpect themtoexistintheformoftropes.Williamsseemsabituncertainon whathisviewonthismatteris.

A philosophy of tropes calls for completion in a dozen directions at once. Some of these I must ignore for the presentbecausethequestionswouldtakeustoofar,some because I do not know the answers. Of the first sort wouldbearefinementandcompletionofouraccountof substancesandofthesimilaritymanifold.Ofthesecond sortwouldbeanassimilationoftheverycategoriesofour theory — concurrence, similarity, abstractness, and so forth—tothetheoryitself,astropesliketherest,instead

andaparticular.Asforthe‘ '’(of‘ r'’)itmightbeamisprint.Theseniceties havelittleforthepresentissuethough. 1Evidently,‘they’referstowhataredescribedastheprimaryconstituentsof theworld. 2Williams1953 a,p.7. 3Thoughperhapsfarfetched,onethoughtisthatheiscontemplatingthere beingatomictropes,i.e.,entitieswhichareabsolutelysimple,aswellastropes which are bottomless. The latter would be atomless gunk à la Lewis. Cf. Lewis1990,p.20. 46CHAPTERII

of relegating them to the anomalous immunities of “”(astheoldScholasticssaid)and“meta language”(asthenewscholasticssay). 1

Concurrence, similarity and abstractness are explicitly said to be amongst the categories. The ‘and so forth’ indicates that there are othersaswell.Itisnotmaintainedherethattheverycategoriesofthe theory should be assimilated to the theory itself; though it is not wavedasideeither.Withregardtoconcurrenceandsimilaritywesaw the assimilation being made in the quotation before the last one. Whataboutabstractnessandconcretenessthen?Well,somesupport canbefoundforthesuspicionthateventhesearethoughtofasbeing properties.

Thatthereisan xwhichisgrayandsquareandconcrete meansthefactabouttheuniversalsGrayandSquare(and Concretion)thattheyconcur[…]. 2

Here,Williamsseemstobecaughtredhandedtreatingconcreteness asauniversal.Thatdoesnotmeanthatheisarealistallofasudden. 3 Though it does mean that he takes concreteness to be a property; being a property, it should appear in the form of tropes. He apparentlyplacesconcretenessonaparwithgraynessandsquareness. Thetwolatteraresurelyconsideredtooccurastropes.Whatholds forconcretenesssupposedlyalsodoessoforabstractness. Nowweturntotropes,whichasindicatedinthesecondhalfof the trope definition, have concrete entities as constituents. A short list,presentedimmediatelyafterthedefinition,suppliesanexampleof these.

1Williams1953 a,p.13. 2Williams1963,p.621. 3 More will be said below about what might be the intended meaning of ‘universal’. D.C.WILLIAMSONTHEELEMENTSOFBEING47

Thusacatandthecat’stailarenottropes,butacat’ssmile isatrope,andsoisthewholewhoseconstituentsarethe cat’ssmileplusherearsandthearidityofthemoon. 1

Weseeherethatthesmileofacatplusitsearsplusthearidityofthe moonmakeupatrope. 2Letusnotfailtonoteacertainimplication ofthis:theconstituentsofatropeneednotbelocatedatthesame spot.Althoughonewouldexpecttofindthesmileandearsofone andthesamecatquiteneareachother,thearidityofthemoonis,asa rule, far away from both of them. 3 How are these three entities supposed to form a trope? The actual wording used suggests that what wehave hereisamereologicalsum ofthem.In at least two earlierquotationsithasbeenimpliedthatcomplextropeshavecon stitutiverelations.Therelationinthisparticularcasewouldappearto bemereologicalsummation.Iremindreadersofthephrase usedin thetropedefinition:‘incombinationwith’.Wehavealsocomeacross yetanotherword:‘cum’.

Thecolorcumshapeislessabstractormoreconcreteor morenearlyconcretethanthecoloralonebutitismore abstract or less concrete than colorplusshapeplus flavor.4

Since‘plus’and‘cum’obviouslyareusedhereasalternativestoeach otherandthelatterisfor‘combinedwith’,Ipresumeallthree areusedassynonyms.

1 William 1953 a, p. 7. Perhaps he is still thinking on the Cheshire cat. Cf. Williams 1931, p. 589. Anyhow, this makebelieve of a smiling cat seems quiteharmless. 2 Never mind that this is, very strictly speaking, in conflict with the actual wordingofthesecondhalfofthetropedefinition.Itisstipulatedtherethata combinationofanynumberofconcretatogetherwithoneabstractummakes up a trope. The mixed trope on the list consists of two abstracta and one concretum—or,perhapstwoconcreta,sincetheearsaretwoinnumber.It issafetoassumethoughthatthisobjectionistoofinicky. 3Thereisnoindicationthatthisparticularcatiseffectuatingasuccessfultrip tothemoon. 4Williams1953 a,p.6. 48CHAPTERII

InWilliams1953 athereisareferencemadetothecalculusof individuals,asitisdevelopedinLeonard&Goodman1940.1Thereis also a reference to it in Williams 1986. This strengthens the impressionthatmereologicalprinciplesareconsideredtoberelevant. The latter reference occurs in connection with the mention of the sumofathreadonaboltandtheQueenofSheba.2Althoughthis sumisexplicitlysaidtobeaparticular,itisnotevidentwhetheritisa tropeornot.Itdependsonthestatusofthethread.Eitherwaythe implicationisthattheconstituentsofaparticularneednotbesimul taneous.Thepassagereferringtoreads:

That the category of abstract particulars thus indicated conformstothelogicofwholeandpart,orthesocalled calculus of individuals, that they have logical sums and products,andsoforth,andthatbeingbydefinitionfiner orlesserpartsthantheconcretainwhichtheyoccurthey are in an important sense the ‘elements of being’, I once arguedinprintinthe Review of Metaphysics ,3whereIcalled them‘tropes’,whichhasanicehistoricalconnectionwith theLatin‘modes’. 4

Unfortunately, not much is said explicitly here about the actual formation of tropes. We are just informed that abstract particulars havelogicalsums,products,andsoforth,butnotthattropescanbe sums.Ithinkthelatterisimpliedbythecollectedindicia.Jamesvan Cleveproposesthename‘mereologicalconjunctivism’foradoctrine accordingtowhichanyentitiescanformamereologicalsum.5Tothe extentWilliamsconcurswiththis,heisamereologicalconjunctivist. Fromwhathasbeenbroughtforwardsofar,itcertainlylooks like mereology is part of Williams’ conception of trope theory. In

1Cf.Williams1953 a,p.9n. 2Cf.Williams1986,p.3. 3Williams1953 aand1953 b. 4Williams1986,p.4.Nothingfurtherissaidregardingtheallegedhistorical connectionbetweenthetwoterms.Tomeitseemsprimarilyonomatopoetic. 5Cf.vanCleve1986,p.3. D.C.WILLIAMSONTHEELEMENTSOFBEING49 section2.3.4thisis givenadditionalsupport. It willalsobeevident thoughthathisaffairwithmereologyissomewhatambiguous. Iwouldliketoendthissectionwiththefollowingstatement.

Ihavefoundthat,likemostfundamentalideas,theideaof the trope is alternately treated by the professors as insignificantlyobviousandasunintelligiblyparadoxical.All thewhile,however,[…]ithasbeenimplicitlyadmittedby most philosophersandbycommonsense,inasmuchas they constantly speak of entities which in fact can be categorized only as tropes (events, sensations, processes, and so forth) and has been explicitly admitted by many (including G.F.Stout,Professor WilfridSellars, and the AristotledepictedbyhimandneoThomists). 1

Theenumerationmadeheredoesnotexplicitlymentioninstancesof qualities and relations, though I assume that they are among the entitiesreferredtoby‘andsoforth’.

2.3.4 Concrete Particulars Anobjectionfrequentlymadeagainstmereologyasananalyticaltool ofontology,isthatitistooblunt.Thespecificchargeisthatitleaves outrelationsandtherolestheyplayinstructured entities. Williams also puts forward an objection of that kind. To that purpose he presents an example, with a hammer and some hammer parts as props.Imagineahammernamed‘Hamlin’,which hasaheadanda handlenamed‘Hedder’and‘Hannel’respectivelyasitsparts.Imagine also another head, named ‘Hud’ and another handle, named ‘Hon’. HedderandHudareexactlysimilartoeachother,asareHanneland Hon.WhileHedderandHannelformahammertogether,Hudand Hondonot.InsteadofbeingonHon,intheappropriatewaytoform ahammer,Hudiscementedalong thesideofHon.Williams now says:

[A]lthough the mere sum of Hud and Hon is inherently exactlysimilartothemeresumofHedderandHannel,the 1Williams1986,p.4. 50CHAPTERII

queer object which Hud and Hon compose — call it ‘Himmler’ — is inherently very unlike Hamlin, and is indeed not even a hammer. This situation, I suggest, represents one possible meaning and justification for the commonformula,“Awholeismorethanthe(mere)sum ofitsparts.” 1

Fromthisitisconcludedthatathing,forexampleahammer,does notconsistsolelyofitsnonrelationalelements.Atleastsomeofthe relationsitinvolvesarealsoimportant.However,itisnotsufficient tojustaddwhatinfactarerelevantrelationsinasituation.

Though in a certain sense we may properly say that Hamlin“consistsof”Hedder,Hannel,andsuchandsuch relations,wehavenotspecifieditsconstitution,havenot given its analysis, till we append that the relation holds fromHeddertoHannel.This,Itakeit,isthesecondof the which somewhat justify “The whole is more thanthesumofitsparts(andmore,even,thanthesumof itspartswiththeirrelations).”Whatonenormallymeans by “the whole of parts a and b,” I think, is the object whichthuscombines aand band their relations,bonded,as itwere,by thefactthattherelations are theirs;andsuch wholes,andnotmeresumsatall,arewhatpassas“sums” inthecalculusofindividuals,whoselawsareinfact not trueofmeresums. 2

The actual relating of a constituting relation is essential when analysingawhole.Ifitisleftout,theresultof the analysis is just anothermeresum.Theactualrelatingsoftherelevantrelationsare not sufficient either. This appears from the following intellectual experiment.ImaginethesumofHud,Honandtherelationsholding betweenHedderandHannel.Therelationsofthissumareobviously oftherightsort.However,thesedonotactuallyholdbetweenHud

1Williams1963,p.604. 2Williams1963,p.605. D.C.WILLIAMSONTHEELEMENTSOFBEING51 and Hon. Since they do not hold, this sum does not constitute a hammer. 1 Notethatthesenseinwhichtheterm‘whole’iscommonlyused allegedly involves the relations actually holding between the other parts of the whole. Furthermore, in the last sentence of the last quotationitisdeclaredthatthelawsofmereology,asformulatedin thecalculusofindividuals,aretrueonlyofsuchwholes.Williamsis wrong about the latter though.2 Apart from that, it is important to note that he insists on including relations and their relating in the analysisofwholesaswell.Appliedtothetropementionedabove— theonehavingthesmileandearsofacatasitspartsaswellasthe aridityofthemoon—itincludestherelationsholdingbetweenthe enumeratedconstituentstoo.Thus,thestructureformedbythelatter togetherwithallorsomeoftherelationsholdingbetweenthemform thetropeinquestion.Thisshouldbethecasegiventhatthetropeis notjustameresumofitsconstituentparts. Williams also says things which might express another view. Ponder upon the following statement about the squares, rows and columnsofacertainwhole:

In the accompanying figure […] the class of six squares, theclassofthreerows,andtheclassoftwocolumnsare differentfromeachotherandfromtheonefigure;butthe sumofsquares,thesumofrows,andthesumofcolumns areidenticalwithoneanotherandwiththewhole. 3

1Cf.Williams1963,p.605. 2InWilliams1963noexplicitreferenceismadetothecalculusofindividuals ofLeonard&Goodman1940.Onthebasisofthereferencemadetoitin Williams1953 a,p.9n,andthatthereisnoothermereologicalcalculuscalled by that name, I presume it is what is referred to also in Williams 1963. According to postulate I.1 of that calculus the individuals of a set always form a sum. Although this postulate does not stipulate that this sum is unique,thelatterisindeedatheoremofthecalculus.Furthermore,asumof thepartsofagenuinewholehasnoarticulatedstructurewhichmirrorsthat ofthewhole.InWilliams’examplethewholeisahammer. 3Williams1953 a,p.9.Thethreekeywordsusedhere—i.e.,‘square’,‘row’ and‘column’—makeitpossibletodividethefigureinstillmorewaysthan 52CHAPTERII

Here,itisassertedthatthewhole,i.e.thefigure,isnotonlyidentical tothesumofthesquares,butalsowiththesumoftherowsaswell aswiththesumofthecolumns. Duetoidentitybeingtransitive,the threesumsareidenticalwitheachother.Nothingissaid,atleastnot explicitly,aboutthespatialrelationsholdingbetweenthesquaresas wellasthosebetweentherowsandthosebetweenthecolumns.This suggeststhatawholeissupposedtobeauniquesumofitspartsno matterhowthewholeisdividedintoparts. Williams’useofthemetaphor‘thealphabetofbeing’isnotan isolatedincident.Anothermetaphorlikeitis‘thesyllabaryofbeing’. Whatissaidinconnectionwiththeintroductionofthispartofthe ontologicalgrammaralsopresentsinformationhithertonotrevealed.

Turning now briefly from the alphabet of being to a glimpseofitssyllabary,weobservetwofundamentalways inwhichtropesmaybeconnectedwithoneanother:the way of location and the way of similarity. These are categoriallydifferentandindeedsystematiccounterpartsof one another — mirror images, as it were. Location is externalinthesensethatatrope per se doesnotentailor necessitate or determine its location with respect to any other trope, while similarity is internal in the sense that, given two tropes, there are entailed or necessitated or determinedwhetherandhowtheyaresimilar. 1

Theroleassignedtospatiotemporal location in theconstitutionof objectsisofparticularinteresthere.2Moreexactly,theroleassigned the ones intended by Williams. It is quite obvious though which squares, rowsandcolumnsheisreferringto. 1Williams1953 a,p.7. 2Besidesspatialandtemporallocationsthereareothers,whicharehintedat likethis: D.C.WILLIAMSONTHEELEMENTSOFBEING53 tothelimitingvalueoflocationinspaceandtimeisworthyofnote. ThisrelationWilliamsfindsinotherphilosophers.Someofthemare mentioned, as well as the names they propose for the relation in question.

[T]hecollocation,orpeculiarinterpenetration,theunique congressinthesamevolume,whichwecall“belongingto (or inhering in, or characterizing) the same thing.” With various interests and intentions, this nexus has been mentionedbyRussellas“compresence,”by Millas “co inherence,” by G. F. Stout as “concrescence,” by Pro fessor Goodman as “togetherness,” and by Whitehead, Keynes,andMillagainas“concurrence.” 1

The term Williams prefers is ‘concurrence’. A description of it in actionreads:

Speakingroughly,[…]thesetorsumoftropesconcurrent withatrope,suchasourcolorcomponentHarlac,isthe concrete particular or “thing” which it may be said to “characterize,”inourexamplethelollipopHeraplem,or, to simplify the affair, the knob of the lollipop at a moment. 2

The doctrine, stated in part here, is a bit more complicatedthanit may appear at first. Recall what was said in a footnote earlier regarding degrees of concreteness: the concreteness of a lollipop involvestime,notjustspace.3DescribingHeraplemasthesumofa

Locationiseasiestthoughtofaspositioninphysicalspacetime, butIintendthenotiontoincludealsoalltheanalogousspreads andarrangementswhichwefindindifferentconsciousfieldsand indeedinanyrealmofexistencewhichwecanconceive—the wholeinteriorstretchandstructureofaLeibnizianmonad, for example.(Williams1953 a,pp.78) 1 Williams 1953 a, p. 8. Cf. Russell 1948, pp. 2947; Stout 1930, p. 389; Goodman 1951, p. 178; Whitehead 1926, pp. 1578; Keynes 1921, p. 385; Mill1856,p.67. 2Williams1953 a,p.9. 3Cf.Williams1953 b,pp.1734. 54CHAPTERII number of tropes concurrent with each other, two of these being HarlacandHamis,issimplistic.Thisisindicatedbytheremarkmade attheendofthelastquotationandcorroboratedbywhatisstatedin thenext.

[T]he actual events which comprise the existence of the watchwheelnowbeforemeonthetablearenumerically asdistinctfromthosewhichcomprisethewheelinsidethe watchtenminutesago,orbackinsidethewatchagaintwo hoursfrom now,asanyof theseisfrom myfingers or fromJupiter.Theircommunityconsistslogicallyofonlya continuity of similar events or similar states strung between. 1

Evidently,theimplicationhereisthatthetropeswhichmakeupthe watchwheelatonemomentarenotthesameoneswhichdosoat anothermoment. Appliedto Heraplem,thismeansthatHarlacand Hamis are constituents of it all right, but only foramomentofits existence.Inthelastsentenceofthelastquotationwelearnthatthe watch wheel is a continuity of similar entities strung together. This also applies to Heraplem. I take it that a moment is the limiting periodoftime;i.e.,itisnotmorethanatemporalpoint. From what has been reported so far one might suspect that Williams is a fourdimensionalist. That this is in fact so is evident fromhisassertioninanotherarticle:

Ibelievethattheuniverseconsists,withoutresidue,ofthe spreadofeventsinspacetime,andthatifwethusaccept realistically the fourdimensional fabric of juxtaposed actualities we can dispense with all those dimfactual categorieswhichhavesobedevilledourrace:thepotential, the subsistential, and the influential, the noumenal, the numinous,andthenonnatural. 2

Iwillnotmakeanyindepthstudyoftheviewexpressedheresinceit isnotworkedoutinanydetailbyWilliams;Imentionitasapointof 1Williams1953 b,p.178. 2Williams1951,p.458. D.C.WILLIAMSONTHEELEMENTSOFBEING55 information. Note though that fourdimensionalism combined with the trope definition makes things a bit messy with regard to the temporal duration of a trope. Although some tropes — such as Harlac,Hamis,Bantic,Borcasetc.—haveanextremelyshortlife time,notmorethaninstantaneous,otherentitieswhicharetropesby Williams’standardsmaybeaslonglivedastheUniverseitself. Abitofreasoningonlogicaltypebringsabouttheconclusion that concrete particulars are sums, rather than sets or classes of concurrent tropes. 1Forthesakeofsafety,IletWilliamsspeakfor himself:

What a difference of logical “type” amounts to, parti cularlyinthephilosophyoftropes,isfarfromclear,but everybodyagreesthatasumisofthesametypewith its terms,asawholeisofthesametypewithitsparts,aman ofthesametypewithhisarmsandlegs.Theconceptofa classorset,ontheotherhand,isnotablymorecomplex andquestionable.Aclassissurelynot,inanyclearsense, what it is often called, “an abstract entity,” but there is someexcuseforconsideringitofadifferent“type”from itsmembers.Convincedthattropescomposeaconcretum inamannerlogicallynodifferentfromthatinwhichany otherexhaustivebatchofpartscomposeit,wehaveevery incentivetosaythattheconcretumisnotthesetbutthe sumofthetropes;andletussodescribeit. 2

This confirms what was claimed earlier: abstract particulars are thought ofasbeingpartsofthingsinthesamesensethatconcrete entitiesarepartsofthings.Wealsolearnherethatsinceaconcrete particularisaconcurrencesumoftropes,eachconstitutingtropeisof thesamelogicaltypeastheincludingwhole.Tropes’beingabstract entitiesdoesnotmakethemadifferenttypeofentitiesthanconcrete entities. Very little is said though about the notion of logical type itself.Amongwhatissaidisthatthewholematterisunclearwhenit comestotropes.ThisdoesnotstopWilliamsfrombeingcertainthat 1InthiscontextanexplicitreferenceismadetoLeonard&Goodman1940. 2Williams1953 a,pp.910. 56CHAPTERII concreteparticularsaresumsoftheirparts,though,orthatamongst these parts are tropes. 1 Below it will be seen that he also believes there are substance, or substantial, tropes. Unfortunately, very few examplesofsuchsubstantialtropesarementionedexplicitly.Among theoneswhicharementionedarethehumanitytropes. 1ItmightbeofinteresttohearwhatPeterSimons,afellowtropetheoristof Williams,saysregardingmereologicalcomposition. [Mereological] [c]omposition is always intracategorial. Provided weareentitledinsomewaytoconsiderallobjectsasbelonging to a single universe of discourse, the Universe, then assuming there is more than one category, there are limitations on the universality of composition. The principal motivation for this restrictionisthatotherwisetherewouldbeobjectswhichthem selvesstraddlecategories,hybridmonsterslikeathingwhichis partsubstance,partevent,partuniversal,partstateofaffairs,and soon.Againstsuchmonsters,thechimeras,gryphons,wyverns, andsoon,ofmythandheraldrypaleintoinsignificance.Ifthere are such monsters, they violate the separateness of categories. Whiletheyarenotasawholeintwoormoremutuallyexclusive categories,theyarealmostasbad,sincetheyareentitiesbutthey donotbelongineither.Attheveryleasttheywouldrequireusto setuparamifiedsystemofadditionalhermaphroditecategories. Itisfarbetterforclassificationtosimplydenytheexistenceof monsters, and provided it is metaphysically acceptable and semantically congruous to talk in one phrase of things from different categories, this entails denying universal composition. (Simons2006,p.605) Whenthisisappliedtotropetheory,initsbundleform,heclaimsthatthe resultisthefollowing. If,asIdo,oneacceptsatropebundletheoryofsubstance[…] thenitwouldappearthatanobjectcomposedwhollyofthings from one category, namely the category of TROPE , can be of another category SUBSTANCE . If that is right, then there is at leastonekindofcategorycrossingcomposition,andthe Verbot on categorycrossing composition is wrong. This is a good argument,butforadifferentconclusion.Itisagoodreasonto deny that there is a categorial distinction between tropes and substances. Tropes and substances both belong together in a single category, that of individual THING . Without going into detailshere,thereareanumberofsolidmetaphysicaladvantages to downgrading the substance/trope distinction to an intra categorialone.(Simons2006,p.605,footnote29) D.C.WILLIAMSONTHEELEMENTSOFBEING57

Wesawearlierthatawholeisconsideredtobesomethingother thanjustameresumofitsparts.Whenmakinganontologicalassay of a whole, interior relations 1areasrelevantasnonrelationalcon stituents. It would seem then that concurrence is such an interior relation.Therefore,tostartwith,Heraplemisaconcurrencesumof Harlac,Hamisandanumberofotherqualitytropesaswellasrela tionalandsubstantialtropes—insteadofa mere sumofthem.Being temporallyextended,Heraplemcanalsobedescribedasasequence of concurrence sums of tropes; this sequence in itself also being a sum. Spatiotemporal continuity should therefore be a constituting relationaswell.Perhaps,mereologicalsummationisanother,though itishardtosayforsuresinceWilliamsissilentonthismatter. Before I move on to the issue of surrogates for universals, I wouldliketoreturntosomethingwhichwassaidinpassingearlier.I amreferringtothethesisthattropesareexistentiallyindependentof eachotheraswellasoftheirincludingwholes.

The real question then is whether an entity which is “abstract”inthesensethatitisconjoinedinacertaincon cretumwithotherabstracta,astheshapeofawatchis,for example, may be duplicated elsewhere by an entity precisely similar internally but not thus conjoined with 2 anything. Our instincts say “No,” that there is a sort of cosmic standard of concreteness, a certain degree of richnessorthickness,whichperhapsisageneralmaximum thatnothingcanexceed,butwhichatanyrateisageneral maximum that an entity must attain in order, as the Scholastics say, “to be apt for existence,” or that, in Aristotle’sphrase,it“canexistapart.”Plausiblethoughit be,however,thatacolororashapecannotexistbyitself,I thinkwehavetorejectthenotionofastandardconcrete ness. For it means that from the awareness of even the thinnestabstraction,andindeedthethinnerthebetter,we coulddeducethepresenceoftherestofaconcretum,if not its specific character then at least that there is a 1Theterm‘interiorrelation’isintroducedinWilliams1963,p.610. 2‘Conjoinedwith’isusedhereasasynonymof‘concurrentwith’. 58CHAPTERII

concretumthere,asDescartesdeducedfromaconscious state the existence of a spiritual substance in which it inhered.Itseemstomeananalyticprinciplethatalldeduc tionmustbeanalytic,sothatwhileanypropercomponent is deducible from its compositum, no compositum is deduciblefromanyofitspropercomponents,andhence thatabstractamustinprinciplebeasindependentoftheir contextsasconcretaare.1

Williams invokes the principle saying that the partsofanincluding whole are deducible from the whole, while the whole cannot be deducedfromitsparts.Thisseemsallright.But,doesitruleoutthe possibility that existential dependence holds between the parts of a whole? I would say that the notion of existential dependence is intimatelyrelatedtothatofuniversality.Therefore,iftwoentitiesare existentially dependent on each other, this is due to their universal contents. The nominalist Williams does not recognise (real) uni versals;hemustthereforedenyanysuchdependencebetweenparti culars, at least between entities which do not have any parts in common.

2.3.5 Surrogates for Universals Since Williams is a nominalist, he renounces (real) universals. He requires something to do the work of universals, though. From an earlierquotationweknowthatsimilarityisconsideredtobeoneofa few fundamental ways in which tropes may be connected to each other.Itisalsoakeynotioninhisconstrualof“universality”.Itsrole inthisrespectisindicatedthus.

Speakingroughly,[…],thesetorsumoftropesprecisely similar to a given trope, say Harlac […], is the abstract universalor“essence”whichitmaybesaidtoexemplify, inourillustrationadefiniteshadeofRedness. 2

1Williams1953 b,pp.17980. 2Williams1953 a,p.9. D.C.WILLIAMSONTHEELEMENTSOFBEING59

Theproposalistotakesimilaritysetsassurrogatesforuniversals.In the particular case presented here the elements of the set are the tropes exactly similar to Harlac. This set is described as being an abstract universal. Note that this is not due to the set itself being abstract.IthasalreadybeenshownthatWilliamsdoesnotconsider setstobeabstractentities.Irepeattherelevantsentencewherethisis stated:

Aclassissurelynot,inanyclearsense,whatit is often called, “an abstract entity,” but there is some excuse for consideringitofadifferent“type”fromitsmembers. 1

Thetermactuallyusedhereis‘class’—not‘set’.Idaresaythateven ifheconsiderstheretobeadistinctionbetweensetandclass,itisnot likelythatoneofthemisthoughtofasbeingabstractandtheother not. The conclusion to draw from this then is that sets are not abstract entities. Incidentally, this suggests that they are concrete entities. If being abstract and being concrete form an exhaustive dichotomy,theymustbe.But,inwhatsenseisasetoftropeswhich areexactlysimilartoeachotheraconcreteentity? Since a set is not abstract in itself, the adjective ‘abstract’, in ‘abstractuniversal’,isusedonthebasisofsomethingelseduetoits elementsbeingabstractentities. The alternative hinted at in a previous quotation concerning treatingsumsofexactlysimilartropesasabstractuniversals,isinfact rejectedbyWilliams.Thishappensshortlyafterithasbeenpresented:

Whetherthe[…]conceptoftheuniversalcanbedefined asthesumofsimilars—allmerelygrammaticaldifficulties aside—isnotsoclear.Thereislittledoubtthatthesetor classwilldothejob.Foralltheparadoxeswhich attend the fashionable effort to equate the universal Humanity, for example, with the class of concrete men (including such absurdities as that being a featherless biped is then thesameashavingasenseofhumor)disappearwhenwe equate it rather with our new set, the class of abstract

1Williams1953 a,p.10. 60CHAPTERII

humanities—theclasswhosemembersarenotSocrates, Napoleon,andsoforth,butthehumantropeinSocrates, theoneinNapoleon,andsoforth. 1

Besidesthesocalledabstractuniversalthereistheconcreteuniversal. Therelevantdifferencebetweenthemisthestatusoftheirelements. Concreteparticularsaretheelementsofconcreteuniversals.Williams callsattentiontowhathecalls‘Socratesity’asbeinganexampleofthe latter.

Socrates is a concrete particular; the component of him whichishiswisdomisanabstractparticularor“trope”; the total Wisdom of which all such wisdoms are com ponentsormembersisanabstractuniversal;andthetotal Socratesityofwhichallcreaturesexactlylikehimareparts ormembersisa“concreteuniversal,”notintheidealistic butinastrictlyaccuratesense. 2

If ‘Socrates’ refers to the Socrates known from Plato’s dialogues, chancesarethatSocratesityisaunitset. 3Onemaywonderwhatthe usefulness of this socalled universal is supposed to be. Perhaps, Williamsjustwantstoseethematrix—introducedinWilliams1931 in a realistic version — completed. Here, the matrix is interpreted nominalistically. The abstract humanities are to be found among the abstract particulars.Wegetaglimpseoftheminthequotationbeforethelast one. Since they are exactly similar to each other, they cannot be constituted by the other tropes of (concrete) human . For example,thetropeortropesconstitutingNapoleon’shaircutcannot becomponentsofthehumanitytropeinNapoleonwhichconstitute himwhencombinedwithothertropes.Thesimplereasonforthisis 1 Williams 1953 a, p. 10. It is confirmed here that no distinction is made betweensetandclass. 2Williams1953 a,p.11.‘Component’and’part’areusedhereaccordingto thestipulationmadeearlierinthearticle. 3Amodalrealist,ofDavidLewis’sort,wouldofcoursedisagree.According tohimorher,theSocratesofourworldhasinfinitelymanyexactlysimilar counterpartsinotherpossibleworlds. D.C.WILLIAMSONTHEELEMENTSOFBEING61 thathishaircutdoesnotexactlyresemble,amongothers,thehaircut oftheQueenofSheba.Thesameholdsforanyarbitrarytraitofa concreteparticular. In earlier sections we have touched upon instances of sub stantial forms. I very much suspect that the humanity tropes, explicitlyrecognizedinWilliams1953 a,1arethoughtofasbeingsuch instances. Each concrete particular, which is a human being, must haveitsownexemplarcasesofthissurrogateuniversal.Thepluralis motivatedbytheassumptionthathumanitytropesareinstantaneous entities. Williamstakesthesethavingallthetropesofadefiniteshadeof rednessaselementsandthesetwhoseelementsareallthehumanity tropes to beabstractuniversals.Theelements ofsetssuchasthese arethoughtofasexemplifyingthesetinquestion.Correspondingly, this holds for sets having exactly similar concrete particulars as elements;ifthereareanysuchnonunitsets.Inotherwords,exempli ficationisidentifiedwithbeinganelementofasimilarityset.Williams also expands on characterisation, which may be regarded as the converseofexemplification.

The particular wisdom in Socrates [i] is in one sense a “characteristic,” i.e., it is a component, of him — this is thesenseinwhichStoutheld,quiteproperlytomywayof thinking,that“charactersareabstractparticularswhichare ofconcreteparticulars.”TheuniversalWisdom [ii]isinthesecondsensethe“characteristic”ofeachsuch wisdom — this is the sense in which Moore could hold plausibly that even an event such as a sneeze, has characteristicsandisnotone.[iii]Inthethirdorordinary sense,however,theuniversalWisdom“characterizes”the wholeSocrates.Fromthisimbroglioemergeatleast two senses of “instance,” the sense in which Socrates is a (concrete) “instance” of Wisdom and that in which his wisdom component is an (abstract) “instance” of it, and the two notions of class, the ordinary concreta class consisting of Socrates, Plato, and all other whole wise 1TheyarealsomentionedinWilliams1986,p.7. 62CHAPTERII

creatures, and the abstracta class of their wisdoms, our similarityset.1

IhaveinsertedtheRomannumeralsheretoaccentuate the use of ‘characteristic’—and‘characterise’—inthreedifferentways.2Thus:

(i)Theparticularwisdomwise 1isacharacteristicofSocrates.wise 1is predicableofSocrates.

(ii)Theuniversal wisdomisacharacteristicofwise 1. The universal wisdomisalsoacharacteristicofwise 2,…,wise n. (iii)TheuniversalwisdomisacharacteristicofSocrates. Ifthemeaningof‘theuniversalwisdom’,asitisusedhere,ismade explicitintermsofexactsimilaritysets,theresultisasfollows.That the universal wisdom is a characteristic of wise 1 means that

Sim{wise 1,…,wise n} is a characteristic of wise 1. That the universal wisdomisacharacteristicofSocratesmeansthatSim{wise 1,…,wise n} isacharacteristicofSocrates.Onthefaceofit,thisseemsludicrous.I suppose that, given the nominalistic of Williams’ trope theory, it should be reinterpreted as follows. That

Sim{wise 1,…,wise n}isacharacteristicofwise 1meansthatwise 1isan element of Sim{wise 1, wise n}. As stated earlier, this is Williams’ analysis of exemplification. The trope wise 1 exemplifies Sim{wise 1, wise n}.Sim{wise 1,…,wise n}beingacharacteristicofSocratesmeans that Socrates has a component which is an element of

Sim{wise 1,…,wise n}. Some of the content of the proposed inter pretationcanbefoundimmediatelybeforethelastquotation:

“Socratesiswise,”orgenerically“ aisφ,”meansthatthe concurrence sum (Socrates) includes a trope which is a memberofthesimilarityset(Wisdom). 3

In an earlier quotation similarity was declared to be a fundamental wayofbeingconnected. 1Thechoiceoftheword‘fundamental’here

1Williams1953 a,p.12. 2 I take the liberty of transforming the noun ‘characteristic’ into the verb ‘characterise’. 3Williams1953 a,p.11. D.C.WILLIAMSONTHEELEMENTSOFBEING63 signals that similarity has a special significance. It is not just any relation. This is supported by what he asserts in the two following quotations.Similarityisascribedafoundingcapacity.

Atthisstageweconjecturethatwearemuchlesslikelyto explainsimilarityasduetothepresenceofacommonor general constituent than to explain the notion of a commonorgeneralconstituentassomehowaresultantof similarity — a procedure to which, in fact, I was committedassoonasIlaiditdownthatsimilarity isan irreducibleandcategoricalelement. 2

Similarityastheresultofacommonconstituentinrelataisexplicitly rejectedhere.Instead,similarityisdeclaredtobe a prerequisite for their having a common constituent. This suggests that resemblance nominalismisthepresupposeddoctrine.Infact,Williamscomments onthematterofhisbeinga(resemblance)nominalist.Accordingto hisownstandardsheisarealist.

[I]f ‘Nominalism’ is the view for which the notion of universalsiscomposedofordisplacedbytheapplicability ofthesamenametoeachof similar objects,thetropekind theoryisveryneartoasortofnominalism.Perhaps the real issue here turns into one between those who think resemblance is an irreducible and objective ontological categoryandthosewhobelievethatitisnotobjectiveor fundamentalbutacreatureofourcomparisons.Thelatter viewisthedistilledattarofNominalism,theformer,isthe head and fount of Realism. I have pledged us to the objectivetheory,andIbelieveinfactthatthesubjectiveor creationisttheoryofresemblanceisitselfafantasticfiction whichcannotbeartheweightofanyconsiderablephilo sophy,butIcannotforgoremarkingthatthesuperiorityof thetropekindtheorywouldnotbeimmediatelyaffected

1Cf.Williams1953 a,p.7. 2Williams1986,p.6. 64CHAPTERII

by a shift from an objective to a subjective doctrine of resemblance. 1

Thereasoningherecircuitsresemblanceanditsstatus.Thesocalled realism he professes consists in taking resemblance to be objective andirreducible.Evidently,ifhewantstobearealrealist,notjustin name,hemustconsiderittobeauniversalaswell.Hewillofcourse declinetodothat. What does the irreducibility of resemblance amount to? Well, literallyitmeansthatofnotbeingreducibletoanythingelse.Inline withthatwouldbetoconsiderresemblancetobeanentityinitself— anincreaseofbeing.Alludingtoacertainsacerdotalwordofwisdom, itcanbesaidthenthatitiswhatitisandnotsomethingelse.The latter part of this statement, that it is not something else, is parti cularlysignificantsinceitquiteclearlyindicatesthatitisnotreducible tosomethingelse. Therearealsotracesofanotherviewthough.Similarityissaid tobenothinginadditiontoitsrelata.Itakeitthatthisimpliesthatit is not an increase of being. The following quotation is where this viewismostclearlyexpressed.Intheaccompanyingfigure,W,wesee theentitiesreferredtointhetextbytheletters‘ A’and‘ B’. 2

Somerelations,theintrinsic 3onesliketheresemblanceof Aand B,are not additionaltobutinvolvedinorgivenwith themandtheirsum,thoughthereareotherrelations,the extrinsic ones, like the distance between A and B, their dashconnection;andtheirwholerelationrope, 4whichin 1Williams1986,pp.101. 2AlsointhisexampleWilliams’delightatnames exposesitself.‘Sqay’and ‘Rectanga’arethenamesofthesquarenessandrectangularityrespectivelyof A;‘Grabe’,‘Squabe’and‘Rectamba’namethesquareness,rectangularityand graynessrespectivelyof B;‘Grace’isthenameofthegraynessof C;‘Whide’ isthenameofthewhitenessof D.Nonamesaregiventoanyinstancesof relationswhichareinvolved. 3InWilliams1963‘intrinsic’isusedinsteadof‘internal’.‘Extrinsic’islikewise usedinsteadof‘external’. 4‘Relationrope’denotesthetotalityofrelationsholdingbetweentherelatain question. D.C.WILLIAMSONTHEELEMENTSOFBEING65

the same sense are additional to A and B and their sum […]. 1 W A B

C D Themessagehereseemstobethattheinternalrelationsbetween A and Barenothinginthemselves. 2Aninternalrelationwouldthennot beanincreaseofbeing.Thisshouldapplytosimilarityaswell.Thisis incompatiblewithitsbeingfundamentalandirreducible. Avariation onthethemethatinternalrelationsare notaddi tionaltotheirrelataisfrequentlyusednowadaystodescribethemas supervening on relata. 3 There is also a culinary metaphor: internal relationsareontologicallyfreelunches.4Ajustifiedcommentonthat 1Williams1963,p.608. 2 I have noticed that AnnaSofia Maurin, whose moderate nominalism is discussed in the following chapter, also interprets the message of the last quotationasIdo.Sheusesitasamottoforsection3.8ofMaurin2002,in whichshearguesforanaccountofsimilarityasbeingpseudoadditionaltoits relata. 3 E.g. David Armstrong is fond of using the term ‘supervenience’, and its cognates,inthisconnection.Arepresentativeassertioncomingfromhimis thefollowing. Itwillbeusedasapremissinthisworkthatwhateversupervenes or,aswecanalsosay,isentailedornecessitated,inthisway,is not something ontologically additional to the subvenient, or necessitating,entityorentities.Whatsupervenesisnoadditionof being.Thus,internalrelationsarenotontologicallyadditionalto theirterms.(Armstrong1997,p.12) Sincethedictionarysenseof‘supervenient’isthatof‘comingassomething additionalorextraneous’,thisuseofthewordisabitbewildering. 4AnexampleofthisisMaurin2005,p.138,whereitisstated: Resemblancemaybeunderstoodinoneoftwoways:eitherasa pseudoaddition or as a genuine relationtrope. Understood as pseudoaddition,resemblanceisseenasa“freelunch”,i.e.itis considered as something we need not add to our ontological inventory. 66CHAPTERII seemstobethatsincenofoodisserved,thelowpriceisnotmuch comfort. I move on to another issue concerning similarity. Williams mightbecontemplatingaviewwhichisinconflictwiththesimilarity principle.

With respect to similarity […] we are comparatively familiarwiththenotionofitslimitingvalue,theprecise,or almost precise, similarity such as obtained between the colorsofourfirstandthirdlollipops,lessfamiliarwiththe idea of the lesser similarity which obtains between a red andapurple,andratheruncertain,unlesswearepsycholo gistsorphenomenologists,aboutsuchelaboratesimilarity distancesanddirectionsasaremappedonthecolorcone. 1

In connection with the introduction of the notions of partial simi larityandthatofpropertycaseitwasdeclaredthatthemoresubtle similarities,ofcolour,shapeandflavour,shouldbetreatedinexactly thesamewayasthosebetweenotherpartsofthings.Letusassume foramomentthatthesimilarityprincipleisapplicabletotheexample ofaredandapurple.2Sincethetwoarenotexactlysimilar,eachof thesehasacomponentwhichisexactlysimilartoacomponentofthe other. Since Williams does not mind tropes being complex entities, whatheiscontemplatingmightbethateachoneofthesetropeshas aninstanceofacertaindeterminableasacomponent. That would explainwhytheyarepartiallysimilar.Now,thephraseactuallyusedin thequotationis‘lessersimilarity,not‘partialsimilarity’.Perhapsthese denominationsdonotdenotethesamenotionofsimilarity.Ifthatis indeedso,howisthelessersimilaritybetweenaredandapurpleto beinterpreted?BeforeItrytoapproachananswertothatquestion, letmepresentanothertwoquotations.

Speakingroughly[…]thesetorsumoftropesprecisely similar to a given trope, say Harlac […], is the abstract

1Williams1953 a,p.8. 2Evidently,whatisreferredtohereby‘ared’and‘apurple’aretwocolour tropes. D.C.WILLIAMSONTHEELEMENTSOFBEING67

universal or “essence” it may say to exemplify, in our illustration a definite shade of Redness. (The tropes approximately similar to the given one compose a less definiteuniversal.) 1

In the last sentence, the one put in parentheses, we find another similarity term: ‘approximately similar’. In the following quotation thereisyetanother:‘lesserresemblance’.

Ifnewmodalobservationsarerequiredforuniversals,they areoftwocloselyanalogousvarieties.Oneistherelation betweenarelativelydefiniteuniversallikeCrimsonandthe “determinable” or less definite universal like Redness underwhichitfalls.Wemustsay,Ibelieve,thatCrimson “entails”Redness,notbecauseRednessisacomponentof Crimson,butbecausethe kind bywhichwedefine“Red ness”isconstitutedbyalesserresemblance,andhencea broader similarity stretch, or segment of the spectrum, thanisthekindwhichdefines“Crimson,”andtheformer stretch, in an obvious analogical sense, “includes” the latter. 2

What are we to make of this? Well, the last quotation seems to express a view on colours which is incompatible with the similarity principle.Ibasethatonthecombinationoftheassertionthatredness isadeterminableandthewavingasideoftheideathatitisacom ponentofcrimson. Whataboutthelessersimilaritybetweenaredandapurple?In thelightofthelastquotation,thesuggestionisthattheformerisan 1Williams1953 a,p.9. 2Williams1963,p.617.Iwouldliketomakethefollowingremark,whichI think is at least worthy enough to appear in a footnote. If redness has crimsonasapart(inanyrelevantsense),weseemtohavehereanexampleof apart“entailing”itsincludingwhole.Thisseemstobeinconflictwiththe principlestatedearlier: Partdoesnotdependonpart,norwholeonwhole,norparton whole, and that whole does depend on part is for the trivial reasonthatthewholeisatleastthesumofitsparts.(Williams 1953 b,p.189) 68CHAPTERII instanceofadeterminable. 1Anotherpossibilityisthatrednessisnot consideredto beadeterminablein Williams1953 a,which iswhere theredandthepurplearementioned.Itmayverywellbethat‘red ness’ is used there to refer to a lowest determinate. The essential questionstillremains:whatwouldbeaninstanceofadeterminable? Iseveryinstanceofalowestdeterminatealsoaninstanceofanumber ofdeterminables, 2withoutactuallyhavingthelatterasconstituents? This would mean that lesser similarity is not the same as partial similarity.Ifweletsimilaritybea(truly)primitiverelation,founding thequalitativecontentofitsrelata,therelataneednothaveanyinter nalstructures.Then,therelatawouldbenodesinasimilaritypattern. The picture might be more complicated. An alternative possibilityis that thereareentities,concreteparticulars,whichhave internalqualitativestructures.Thecontentofthecomponentswhich make up the structure of each entity would be due to their being nodesinsimilaritypatternsthough.Thesemightbeconsideredtobe twopossibleversionsofresemblancenominalism.Accordingtoone leading resemblance nominalist, resemblance nominalism is incom patiblewiththeexistenceoftropes. 3Apartfromthat,wehaveseen that Williams shows a tendency towards a position which might at leastbedescribedasaresemblancenominalisminawidesense.Iam referringtohisassertionthatthepresenceofacommonorgeneral constituentistobeexplainedasaresultantofsimilarity.Inconnec tion with this, he also informs us that this is something he was committedtoassoonashelaiditdownthatsimilarityisanirredu cibleandcategoricalelement.4Itwouldbeinlinewiththisviewto consider sets of tropes where the elements have their qualitative contentduetoexactsimilarityholdingbetweenthem,assurrogates for (real) abstract universals. Note that this would require a vast number of similarity relations. Given that these relations are (real) 1 According to the assertion in the quotation redness is a determinable in relationtocrimson.Purplewouldthenbeadeterminateinrelationtored ness. 2Thisnumbercanbeexpectedtobelarge;perhapsinfiniteeven. 3Cf.RodriguezPereyra2002. 4Cf.Williams1986,p.6. D.C.WILLIAMSONTHEELEMENTSOFBEING69 universals, therewouldinfactbe one suchrelation for each exact similarity set. This is ruled out by Williams’ being a nominalist though. There must instead be as many instances of each specific exact similarity as there are pairs in each exact similarity set. 1 This doctrine,appliedtolessersimilarity,stipulatesonesetofinstancesof eachunspecificsimilarityrelationperlessersimilarityset.Many,ifnot allof theelementsofexactsimilaritysetswillalso be elements of quiteafewlessersimilaritysets. Sofar,everythinginthegardenmayappeartobelovely.How ever,therearesomedifficulties,whichtheoutlinedviewwillcomeup against as soon as the similarity relations are scrutinised. Since, according to the nominalistic confession, everything which exists is particular, each and every similarity is so as well. The other parti culars,thosewhicharenotsimilarityinstances,havetheirqualitative contentsduetotheirbeingnodesinsimilaritypatterns.Reasonably, thesameshouldapplytothesimilarityinstances.Ifthatisnotso,one wonders why. After all, they too are abstract particulars — tropes. Thereisanobviousneedforanaccountoftheirqualitativecontents. Whatthedoctrinemustprescribearemoresimilarityinstances.Since thedirectionofthisregressisfromtherighttotheleft, 2theproposed mechanismwillnotsucceedindeliveringanyqualitativecontent. The difficulty hinted at is well known. This may account for whatItaketobeWilliams’oscillatingbetweendifferentviews.One ofthesebeingthatsimilarityisnoadditiontoitsrelata.Hedoesnot saymuchaboutitthough.Ithinkthatwemustleavethisissueasfar asheisconcerned.However,AnnaSofiaMaurinadvocatesaviewon similarity which is closely akin to that which we find traces of in Williams.Maurin’sontologyisdiscussedinthenextchapter.

1Iassumeherethatexactsimilarityisdyadic.Ifitsadicityisunlimited,the necessarynumberwould,atleastinthefirsttimeround,bereducedtoone instanceperexactsimilarityset. 2 An alternative description is to say that the regress is analytical, which indicatesthattheanalysisaimedforispostponed.Cf.Russell1903,pp.501. 70CHAPTERII

2.3.6 Painless Realism IwillsaysomethingaboutWilliams’socalled painless realism .Idonot knowifheevercalleditbythatnamehimself.1Howeverthatmaybe, this “realism” takes universals to be the results of a relaxation of identityconditions.2Here,itisparticularlywisetolethimspeakfor himself.

Thatuniversalsarenotmadenordiscoveredbutare,asit were,‘acknowledged’byarelaxationofidentityconditions of thought and language, will become attractive as we notice,forexample,that similarrelaxationsoccur in our treatment of ordinary proper names of concrete parti culars,especiallyinthecommonidiomwhich,innocentof the notion of temporal parts of a thing, finds the whole enduring object, a man or a stone, in each momentary stageofitshistory.Forhereandnow,wesay, is theperson called‘John’,notjustpart butallofhim,andnowagain here is the same ‘John’, all present at another instant, thoughinstrictontologythe‘John’oftodayisabatchof beingasdiscretefromthe‘John’ofyesterdayasheisfrom the moon. The relaxation of conditions which acknow ledgesuniversals,however,andwhichIshallcall‘generiz ing’(because‘generalizing’iscommonlyusednotforcon ceivinguniversalsbutforconceivingorassertinglaws),is muchmorefirmlyseatedinthefactsoflanguageandits objectthananyotherIknow. 3

There has been little indication of what is more or less explicitly expressed here with respect to the indication that a watch wheel at one moment in time is as numerically different from those that compriseitatlatertimes.Thewatchwheelissaidtobeacontinuity ofsimilarevents 4orstateswhicharestrungtogether. 1Thissketches 1KeithCampbellmightbetheinventorofit.Cf.Campbell1990,pp.435. 2AsimilarviewismaintainedbyIvarSegelberg. 3Williams1986,pp.89. 4Mostlikely,theseeventsarethoughtofasslicesofthe“tube”whichspace andtimesupposedlytogetherform. D.C.WILLIAMSONTHEELEMENTSOFBEING71 outatemporalpartsapproachtoconcreteparticulars.Itisnotmore thanasketchthough. ImoveontowhatWilliamssaysconcerning“universals”.

Thatuniversalsaredeterminedbya‘weaker’identitycon ditionthanparticularsdoesnotevenmeanthattheyhave aninferiorordilutedreality.Atabulationofuniversalsis justonewayofcounting,asitwere,thesameworldwhich iscounted,inalegitimatelydifferentandmorediscrimi natingway,inatabulationofparticulars.Istressthisand theword‘counting’becausetheywarnusoffthedelusion involved in the common use of the phrase ‘numerical identity’ and ‘numerical distinctness’ for particular identity and distinctness, respectively. The fact is rather that universals,including ,arenoless numerable than particulars—aswhentheinteriordecorator,forexample, says ‘I used just four colors in this room’. For a similar reason,itwasdeceptiveinmyfirstpagesabovetocontrast the case with the kind by contrasting the ‘this’ with the ‘such’, because we can and do, as we say with ‘This is Whiteness’,useallthedemonstratives,including‘This’,for universals no less than for particulars, so that only the context will tell us, when a person refers to ‘ that ’ sound, whetherheistalkingparticularwiseoruniversalwise. 2

Disregardingmostofthetorrentofwordshere,myinterpretationis thatwearesupposedtoobtainauniversalbyidentifyingexactlysimi larentities.Inotherwords,wearepretendingthatindiscerniblesare identical.Whatmightbecalleda‘painlessuniversal’ would then be anyoftheindiscernibleentitiesofacertainset.Evidently,thisdoes notinanywayalterthefactthattheseindiscernibleentitiesarenot identical with each other in any strict sense. Strict identity would meanthatthereisjustonesingleentity.Itwouldbea(real)universal. Painless realism is obviously not the same doctrine as that accordingtowhichauniversalisasetof(exactly)similartropes.They are related though, which explains why Williams so easily oscillates 1Cf.Williams1953 b,p.178. 2Williams1986,pp.89. 72CHAPTERII between them. Furthermore, he wants to describe his own onto logical position, the trope theory, 1 as being an immanent realism. I take it that the amalgamation of painless realism and the other doctrineiswhatineffectissupposedtofitthedescription.

Asthereisnothinginanythingwhichisnoteitheratrope orresolubleintotropes,soeverytrope,ofwhateverlevel of complexity, manifests its universal or kind. Generiza tion,moreover,doesnotevenstopshortofconcreteness, and does not therefore in the least depend upon de facto similarity or the recurrence of kinds. That is, having a general readiness to contemplate, by the right quirk of attentionordescription,eitherthecaseorthekindofany givenoccasion,wecanidentifyauniversalonceforallina singleinstance,onlyconceiving ipso facto thatitiscapable ofotherinstances. Thetropekindtheoryisalogicalrealisminasmuchas it holds that universals are real entities, and it is an immanentrealisminasmuchasitholdsthemtoexist in rebus —tobepresentin,andinfactcomponentsof,their instances.Tomakeplainthesenseinwhichitholdsthat anabstractuniversalis‘in’aconcreteparticular weneed onlymakeexplicittheanalysisofpredication,characteriza tion, or instantiation which has been barely implicit here allalong.ThatSocratesiswise,i.e.,thatheisaninstance ofWisdom,whichisan‘instantiation’or‘characterization’ in the full sense, is sufficiently expanded in the formula thattheconcreteparticularSocrates‘embraces’anabstract particular (trope) which ‘manifests’ Wisdom. This describes predication for inherent characters; onlyalittle less obvious is the adjustment which accommodates ad herentcharacters,asinthepropositionthatSocratesis pupil of Plato. Here Pupilof is the generization of a complex relation of which Socrates is referent, while ‘Plato’,granteditisatruepropername,stillstandsforan ungenerized concretum — so that, rather oddly but not

1Inthearticlewherethedoctrineofpainlessrealismispresentedthename usedis‘tropekindtheory’. D.C.WILLIAMSONTHEELEMENTSOFBEING73

objectionably,acharacterwhichasawholeisanabstract universal may include a concrete particular as a con stituent. No merely adherent universal, of course, is ‘immanent’inthesensethatitinheresinitssubject,butit stillis‘immanent’and‘ in rebus ’inthecardinalmetaphysical sensethatitis among thethingsitqualifies. 1

Williamshashisdoubtswhetherimmanentrealistswouldrecognise hisdoctrineasbeinganimmanentrealism.

Whetherpreviousimmanentrealistswouldrecognizetheir viewinthisopinionthatuniversalsareimmanentbecause theyare,tospeakcrudely,thesimilarityroles(or‘adjectival identities’) of abstract occurrences, I have some doubt. I amsure,fromexperiencewithmyself, 2thatanimmanent realist begins by thinking he means more, but can bring himselftosee,orthinkhesees,thathe couldn’t meanmore — that every attempt to state an alternative results in somethingverballybutnotsignificantlydifferentfromjust redefining‘identity’byresemblance. 3

Is he even a wholehearted advocate of this socalled immanent realism? A few pages earlier in the same article it looks as if it is actually rejected. The context of this rejection makes it somewhat paradoxical.

There remains the possibility, given the ideas of abstract andofconcreteandofsumandofset,thatHumannessbe equatedwith,orsupplantedby,the set ofhumanitytropes, andthisIthinkisdemonstrativelyadequate.[…]Never theless, having dallied with it briefly, I reject it on the presently unfashionable ground that the set of tropes is notwhatIoranyoftherestofus mean by‘theuniversal characterHumanness’,anditcouldnothavebeenmeant bypersonswhohadnoconceptionoftropesets,notby anyonewhospeaksoftheuniversalbeing‘in’itsinstances, 1Williams1986,p.10. 2Cf.thedoctrinesofWilliams1931. 3Williams1986,p.10. 74CHAPTERII

nor by one who declares […] that universals (‘essences’, ‘neutral entities’) both are the constituents of things and the data of . When I deny that any of these constructsiswhatwehave‘meant’,therefore,Iputusto looking, in the light of the apparatus of tropes, at what does happen, and must always have happened, when we perceiveorconceivetheabstractuniversalintheconcrete particular. 1

In this remarkable passage universals are first equated with, or supplanted by, sets of tropes, and this is alleged to be an adequate definition,thenthewholethingisrejectedonthegroundsthatitis psychologicallyinadequate. Wesawitbeingassertedearlierthatauniversalcanbeidentified onceforallinasingleinstance.Evidently,theuniversalthoughtof herecannotbeaclassofexactlysimilartropes.Thesimplereasonfor thisisthatsetsareextensionallydefined.So,whatistheuniversal,ifit is not a set? The alternatives seem to be either that it is a real universal or a painless universal. Among the indicia for the former alternativeisthemessageofasomewhatobscuresentence:

ThusSquabe 2entailsSquarenessandnecessarilyissquare, because what we mean by “squareness,” though not strictlyapartofSquabe,isjustwhatremains,sotospeak, whenwehaveleftoutofaccountthesocalled“numerical difference”ofthetropes. 3

Adistinctionismadeherebetweentwo“parts”ofthetropeSquabe. Oneoftheseisitsnumericaldifferencefromotherentities,orwhat accounts for it. The implication seems to be that the other part is squareness.Squarenesswouldappeartobearealuniversal, since it cannot reasonably be a set of exactly similar tropes or any of the elementsofsuchaset.So,itmustbearealuniversal.Thereisno otheralternativeleft,isthere? 1Williams1986,p.7. 2Thename‘Squabe’isintroducedinconnectionwiththefigureW.Itrefers totheinstanceofsquarenessinherentinB.Cf.figureW. 3Williams1963,p.617. D.C.WILLIAMSONTHEELEMENTSOFBEING75

2.3.7 Predicativity Lastly,abitmorewillbesaidaboutpredicativity.Uptonowithas beenimplicitlytoucheduponrepeatedly.Thefirstquestiontoaskis thefollowing:Whichentitiesarepredicative?IbelievethatWilliams’ mostexplicitanswertothatquestionisfoundhere:

Whereas relations, particular or universal, are the only entities intrinsically and irreducibly predicative, we can count relational properties as derivatively predicates of their terms, most notably those interior properties which constitutethe“inherence”traditionallytakenastypical. 1

Themostimportantpieceofinformationhereisthatonlyrelations areintrinsicallyandirreduciblypredicative.Oneimplicationevidently isthatqualitiesarenotpredicative.Thoughtheymayappeartobeso, this appearance is due to their being constituents of relational properties.Thus,whenaqualityisinherentinsomething,itissoin collaborationwitharelation.Thisisconfirmedinthenextquotation below.Incidentally,totheextentthatarelationhaspropertiesofits own,thelatterinhereinitbymeansofmediatingrelations. Thatrelationsconstituteterminalpointsasregardspredicativity isstatedinanotherplace.Thecontextisadiscussionontherebeing tiesconnectingrelationstotheirrelata.

Can we say anything more about intrinsicness and extrinsicness?Wemighthope,forinstance,todiscovera peculiarandmoreintimatesortof“tie”betweenanintrin sicrelationanditstermsthanbetweenanextrinsicrelation and (let us say) the same terms. But except as a mere circumlocution for what we have much circumlocuted already, I think this is illicit because I think, for various reasons, including the ones famously purveyed by F. H. Bradley (as well as our own relational physiology), that there is no essential tie. There doubtless are plenty of relations between relations and their terms, and it will appearthatwhenweascribeaqualitytosomethingwedo 1Williams1963,p.616. 76CHAPTERII

affirm a relation from one to the other; but when we affirmarelationoftwotermsweareattheendof that line,upagainst the oneultimatesortof predicative fact. To say that resemblance characterizes A and B, for example,isonlytosaystammeringlythat Aresembles B. Sincetherearenoties,eitherforintrinsicorforextrinsic relations,therecan’tbedifferentsortsoftiesforthem— whichisaswell,sinceitsavesustheembarrassment of having to sort out intrinsic from extrinsic ties , and so forth. 1

Williamsexplicitlystatesthatalotofrelationsholdbetweenarelation anditsrelata.Supposedly,therearestillmoreholding between the latter and the ones holding between it and its relata, and so on. In spite of that, he maintains that relations are ultimately predicative. Thisisabitpuzzling. Consideringthatrelationsappearintheformoftropes,justas qualitiesdo,Ibelieveitisappropriatetoonceagainmentionacertain principlethathasbeenreferredtoseveraltimesabove.

Part does not depend on part, nor whole on whole, nor partonwhole,andthatwholedoesdependonpartisfor thetrivialreasonthatthewholeisatleastthesumofits parts. 2

Theprincipledoesnotdistinguishbetweendifferentkindsofparts. Thus,evenapredicativeentity,i.e.,arelationtrope,issupposedto havethecapacityofexistinginsplendidisolation.

1Williams1963,pp.6089. 2Williams1953 b,p.189.

CHAPTERIII

ExaminationofAS.Maurin’sOntology

3.1Introduction AnnaSofiaMaurinpresentsaversionofmoderatenominalisminher writingunderthename‘tropetheory’.Herstatedenterpriseisofan explorativenature,whichisreflectedinthetitleofherdissertation:‘ If Tropes ’. The key notion of trope theory, discussed mainly in the secondchapterofthatbook,isofcoursethatoftropeitself.Inthe firstchapter,shepronouncesanidealinvolvingtropes.Dependingon howonechoosestointerpretit,thisidealgivesexpressiontoaclaim oranexpectation.

(ii)Atheoreticalideal: there are only tropes Insayingthattropesaretheonlyentitiesthatexistweare not saying that there are no tables or that there is no universal colour redness. All we are saying is that all entities that exist besides tropes are constructed from tropes. Another way of saying that there is nothing but tropes is to say that tropes are the only metaphysically fundamental entities. 1

Starting out from this theoretical ideal she finds herself confronted withtwomainproblems.Theyarereferredtounderthedesignations ‘the problem of universalisation’ and ‘the problem of thing construction’,respectively.MuchofMaurin2002isdevotedtothese twoproblems. Truthmaker theory and the notion of truthmaking are other essentialissuesdiscussedinMaurin.Truthmaking is thought of as accountingfortheconnectionbetweenthoughtsabouttheworldand

1Maurin2002,p.5.Besidesthistheoreticalideal,therearealso(i)Anonto logicalassumption: there are tropes ;and(iii)Amethodologicalframework: tropes are truthmakers. Cf.Maurin2002,pp.56. 78CHAPTERIII theworlditselforitsstructure.1Theproblem ofuniversalisationis interpretedfromthepointofviewoftruthmaking.Thisappearsin thequestforthetruthmakersfortruepropositionswhichseemingly presupposeuniversals. AfairamountofambiguityisinherentinMaurin’suseof the denomination ‘trope theory’. Sometimes when alleged fellow trope theoristsarereferredto,thestipulatedconditionsfor being atrope theoristarenotparticularlydemanding.Itsufficesto“believethatat least some of the basic constituents of the world are particular properties.” 2Thisissufficientlywidetoincorporatemoderaterealists amongtropetheorists.AristotleandEdmundHusserl,amongothers, areexplicitlysaidtobelongtothefamilyoftropetheorists,inspiteof the fact that both of them recognise (real) universals. The Swedish philosopherIvarSegelbergisalsoexplicitlyincluded.Eventhoughhe recognisesuniversalrelations.Conversely,‘tropetheory’isalsoused byMaurininamorestrictsense.Itexcludes(real)universalsofany kind. Substrates, or bare particulars, are also repudiated. When the denomination is used in this latter, narrower sense, the number of tropetheoristsdwindlesconsiderably.

3.2TheNotionofTrope

3.2.1 Overview Maurin’s notion of trope is presented in section 3.2. In the two remaining sections of the chapter, sections 3.3. and 3.4, the two problems of universalisation and thingconstruction are dealt with respectively.IfMaurin’ssolutionoftheformerproblemturnsoutto be abortive, her rejection of (real) universals is set rocking. In the proposedsolutionoftheproblemofthingconstructiontherelation of compresence is given a key part. It brings to the fore a few

1Cf.Maurin2002,p.39.Thestateddirectionoftheconnectionsuggeststhat whatisinfactaimedatistheconverseoftruthmaking:ontologicalcommit ment. 2Maurin2002,p.4. EXAMINATIONOFMAURIN’SONTOLOGY79 problems which are also of relevance when evaluating the trope theoreticalapproach. In section 3.2.2, Maurin’s notion of trope is presented and discussedalongwithafewproblemsthatareattachedtoit.Sinceitis thekeynotionofmoderatenominalism,itmustbemadesufficiently transparent. Otherwise, it may very well be a carpet under which variousareswept.Amongthesehiddenpremisesmightbe unmistakablyrealisticones.

3.2.2 The Single Category: Trope Accordingtothetheoreticalidealmentionedintheintroduction,the category 1 of trope is the only fundamental one there is. Any other categories that exist are formed out of that one.2 Two reasons for developingaonecategoryontologyareindicated,oneoftheseisthat manycategory ontologies have met with various difficulties. This raises the hope that trope theory, in its onecategorial form, might farebetter.Theotherreasonisthataonecategoryversionoftrope theorywouldbeveryeconomical. 3AmodifiedversionofOckham’s razorispleaded,prescribingthatitisalwaysbettertopostulateasfew fundamentalentitiesaspossible;‘few’refersheretothenumberof kinds of entities. 4 Furthermore, it is suggested that Maurin’s trope theorymay havesomeadvantages,whichotheronecategory onto logieslack.Theotherontologiesaretheclassicalformsofnomina

1Althoughtheterm‘category’isnotusedintheformulationoftheideal,itis usedindirectconnectiontoit. 2Weareinformedthatmosttropetheoristssharethetheoreticalideal.C.B. Martin,whorecognisesirreduciblesubstratesaswellastropes,ismentioned asanexception.Thismakeshim(atleast)atwocategorytropetheorist.Cf. Martin 1980. Aristotle is also mentioned. I suppose that he should be classifiedasbeing(atleast)athreecategorytropetheorist. 3Itwouldnotcomeasasurpriseifsomepostmodernthinkerhascomeup withanonecategorytheory.Inspiteofitsbeingmaximallyeconomical,the chancesarethoughthatitwouldhavesomevexingfailings. 4 Cf. Maurin 2002, pp. 56. Although the modified version of the razor is ascribed to David Lewis, it can be found already in Bertrand Russell. Cf. Lewis1986 b,p.87,andRussell1922,p.112. 80CHAPTERIII lism:class,predicateandresemblancenominalism.Inaddition,there isuniversalismwhich,thoughitonlypostulatesuniversals,belongsto theonecategorytheories.Tropetheorymightturnouttofillagap betweenclassicalnominalismanduniversalism.

Thetropeisparticularandthussuitablefordealing with concreteobjects,butitisalsoqualitativeandthussuitable for dealing with properties. All of this indicates that the prospects of a onecategory trope theory are unusually good. 1

Asitturnsout,theallegedqualitativenessoftropesisalinchpinof Maurin’sontology. What is a trope then? Well, each trope has three traits: simplicity, particularity and abstractness. A complication here is of course that these traits also cry out for a characterisation. In the previous chapter, we saw that Williams flirts with the idea that concretenessandabstractnessexistastropes.Simplicityleadsarather obscurelifeinhisversionoftropetheory;hedoesn’tsaymuchonits behalf. In contrast, Maurin considers simplicity to be essential. Neitherofthemthinksthatsimplicityinitselfappearsintheformof tropesthough.

(i) Simplicity Inthefollowingdiscussionthethreetraitswillbedealtwithinthe same order as they are enumerated above. First out is simplicity. According to Maurin, many of the objections raised against trope theoryinvolvesimplicity.Eithertheobjectionhasrestedonafailure toappreciatethesimplicityofatropeortheclaimhasbeenthatany meaningfulcharacterisationofitimpliesthatitiscomplex. 2 Oneof Maurin’sstatedreasonsfortreatingsimplicityasanessentialtraitof tropes, and I suspect that it is also the principal one, is that “an interesting, original and novel theory of tropes representing a true alternative to other metaphysical theories could not be developed

1Maurin2002,p.6. 2Cf.Maurin2002,p.11. EXAMINATIONOFMAURIN’SONTOLOGY81 unlessthetropewastakentobesimple.”1Whatdoesthesimplicityof tropesamounttothen? Tobeginwith,notethefollowingdiscouraginginformation:

Notions such as ‘simplicity’ (and, for that matter, ‘parti cularity’ and ‘qualitativeness’ etc.) are basic and as such theyposegreatdifficultyassoonaswetrytospelloutin more detail exactly what they mean. Normally, notions suchasthesetendtobeleftunexplainedormoreorless takenforgrantedintheliterature.Herethenotionswillbe givensomeanalysis,mainlyofanegativekind.Thatis,in thefollowing Iwilltrytoexcludesomeofthemeanings thatwemightwanttoattachtothenotionsinquestionin thehopethatthiswillatleastbegintosuggestthepositive meaningthatishereintended. 2

Althoughtheexpectationsmaybeloweredabitbythis,itshouldbe rememberedthatbeingbasicdoesnotexcludeanideafromhaving positive content. Furthermore, the proposed determination of sim plicityisnotexclusivelynegative. Oneofthefirstcommentsconcernstherelationbetween the senses of ‘being simple’ and ‘having no parts’. She is reluctant to consider the latter as bringing in anything new. An explanation of what it means to be simple in terms of having no parts is just a rephrasingofthequery.

Justaswecouldaskofsimplicity,wecannowaskofthe nopartssuggestion:whatdoesitmeantosayofthetrope that it is something without parts? Our answer to this question will depend, in particular, on exactly what we meanby‘part’here. 3

So,whatcouldbemeantby‘part’here?Coulditbethesynonymous with ‘property’? Maurin thinks not, though one wonders why. Her answeris:

1Maurin2002,p.12. 2Maurin2002,p.14. 3Maurin2002,p.15. 82CHAPTERIII

Onereasonforthisisthatthesenseinwhichthetrope is simple is, I believe, directly comparable to the sense in which many have claimed that entities such as the uni versalaresimple.Andfromthesimplicityoftheuniversal it does not seem to follow that the universal cannot (in some sense of the word) instantiate other, secondorder universals. Analogously, it does not seem to me that an acceptance of, say, the existence of secondorder tropes would necessarily have to threaten the simplicity of the trope. Rather, the notion of simplicity here involved is such that the trope could have properties and still be a simpleentity. 1

In a footnote 2 Maurin says that she is suspicious of secondorder tropes,butforreasonsotherthansimplicity.Inthelightofwhatshe saysin otherplaces,Ifindthisremarkpuzzling. More will be said about this in a moment. For now, the presumption must be that secondorderpropertieswouldbetropes.Theideathatatropecould havesecondordertropesaspropertiesandstillbesimpleimpliesthat therelevantsimplicityisnotabsolute.Thisisconfirmedinthenext quotation. In it we also find Maurin’s last word on what kind of simplicityshehasinmind.

So what is simplicity? Let us go back to Daly 3 and the distinctionhedrawsbetweenthesimpleandthecomplex trope. Complex tropes are, according to Daly, substrates instantiating universals (states of affairs). The difference between the complex substrateuniversal and the simple trope seems to be this: the substrateuniversal is con stitutedbytwo kinds offundamentalentities—thekind substrate, and the kind universal (and their connection). Thesenseinwhichthetropeis not complexis,fromthis perspective,bestputasfollows:itdoesnotcontain(itis not constituted of) more than one kind of entity. As we shall see, this means, among other things that the parti 1Maurin2002,p.15. 2Cf.Maurin2002,p.15n. 3ThereferenceistoDaly1997. EXAMINATIONOFMAURIN’SONTOLOGY83

cularity and the abstractness of the trope cannot have separategrounds‘in’thetrope.Thereissimplynoroom forsuchdistinctions. 1

Thus,theintendedsimplicityis categorial simplicity.Acombinationof asubstrateandauniversalwouldbecategoriallycomplex.However, assuggestedelsewhere,thismightnotbethewholetruth.Withinthe contextofanargumentagainstclassnominalism,presentedinArm strong1989wefindimplicationswithregardtotropes.

But if the properties in question are tropes, we simply cannot have a case where each Ftrope is made up of G tropes in the required sense. Tropes are simple entities, andsotherearenosuchtropes.Thismeansthattheargu ment’sfirsttwoassumptions —assumptionsthatinfact gettheargumentgoing—cannotpossiblybetruewithin ourtropetheoreticalframework.Notropeis‘madeup’of othertropes.Notropesare‘properparts’ofothertropes. 2

Themessageofthelastsentence,thatnotropesareproperpartsof othertropes,andofthesentencebeforeit,thatnotropeismadeup of other tropes, might imply that tropes do not have properties. If beingpartofatropeandbeingapropertyofitamounttothesame thing,thesimplicityofatropeexcludesitfromhavinganysecond orderproperties. Anotherplacewhereasimilarlineofreasoningis found is in Maurin2005,inanswertoaquestionaskedbyEricFunkhouser.He actuallyputsforwardtwoquestions.Totheextentthatthesecondof theseisanswereditisdone en passant .

Why can’t tropeshavequalitativeparts—e.g.,colortropes havehueparts,saturationparts,andbrightnessparts?[…] This seems plausible, though the possibility would raise problems like those for thingconstruction that she dis

1Maurin2002,p.15. 2Maurin2002,p.71. 84CHAPTERIII

cussesatgreatlength.Namely,whataccountsfortheunity ofsuchqualitativelycomplextropes? 1

Maurin’sanswerreads:

[I]ftropesarequalitativelycomplexinthesenseimagined byFunkhousertheymust,asIargueabove,2beregarded as complexes of more fundamental tropes . Of course, complexesofthiskindwemaycall tropes —buttheyare tropesonlyinasecondarysense.Ithereforeprefertocall them complexes of tropes (or compresent tropes ) although I do notthinkmuchhingesonourchoiceoftermshere. 3

The important information here is that fundamental entities, which are qualitatively simple, are reckoned with. Such entities are what Maurin has in view when using the term ‘trope’. The rest are complexes of tropes. Perhaps then, the three qualitative parts of coloursmentionedbyFunkhouserarefundamentalentities.Inother words,perhapstheyaretropes.Notethatthisisnottheofficialview foundinMaurin2002. Thereisanimminentconsequenceofthetheoreticalidealthat thereareonlytropesincombinationwiththenotionthatcategorial simplicity is the relevant kind of simplicity: there is practically no upperlimitforhowcomplexatropemaybe,inanintuitive sense, whilestillbeingsimple,intheadoptedsense.Thisstronglysuggests that categorial simplicity is not the only thing Maurin has in mind whenclaimingthattropesaresimpleentities.

(ii) Particularity Imoveontothetwootherallegedtropetraits—particularityand abstractness. These have been touched upon already; in an earlier quotationwesawthatneitherofthemcanhaveaseparategroundin atropeduetoitssimplicity.Thisisstatedoncemore: 1Funkhouser2004,fourthparagraph. 2The argumentationreferreddoesnotbringinanythingnewwhichis not foundinMaurin2002. 3Maurin2005,p.136. EXAMINATIONOFMAURIN’SONTOLOGY85

Given the simplicity of the trope, the way in which the tropeisparticular(and,asweshallsee,thewayinwhichit isabstract) cannot beduetotheexistenceofsomeseparate particularisingand/orqualitativeelement in thetrope.We cannotsayofthetropethatitisparticularasaresultof x andthatitisabstractasaresultof y.Wemustacceptthat the trope simply is particularandabstractandleaveitat that. The particularity of the trope must be regarded as primitive .1

Thus, tropes are assumed to be primitively particular. A traditional proposalasregardsparticularityisputintermsofsubstrates.Since substrates belongtoanother(fundamental)category,theyareofno usetoMaurin.Twootherproposalsaremoreinteresting.

[1]onewhichtriestoexplicatethenotionofparticularity with reference to how numerical distinction stands to qualitativenatureand[2]onewhichtriestospelloutthe particularity of the trope in terms of spatiotemporal position. 2

Accordingtothefirstaccount,someentities,theparticulars,donot obeytheprincipleoftheidentityofindiscernibles.3Maurinconcurs withthis,thoughshedoesnotthinkthatittellsusverymuchabout particularityinitself.

The observation that tropes cannot be entities that succumbtotheprincipleoftheidentityofindiscerniblesis very important. Tropes are entities that can be exactly similarandyetnumericallydistinct,butpointing this out doesnotreallytellusanythingaboutthe particularity ofthe trope—oratleast,itdoesnottellusverymuch.Rather, accountssuchasthatgiven byWilliamsareaccounts of whatwillfollow given thatthetropeisnotonlyqualitative 1Maurin2002,p.16. 2Maurin2002,p.16. 3ThisprincipleisalsoknownasLeibniz’sPrinciple.Informalisedversion: ∀x∀y[∀P(P(x) ↔ P(y)) → (x = y)]. Here the lowercase letters range over (concrete)particulars;theuppercaselettersrangeoverattributes. 86CHAPTERIII

(abstract) 1 but also particular. Particular qualities are entities that “may be exactly similar and yet not only distinctbutdiscrete” 2butinaskingaboutwhatismeantby particularity it seems that we are looking for something morethanthissimpletruth.Wewanttoknowwhatitis about the trope that makes this combination into a possibility. 3

Sincethisfirstsuggestiondoesnotdeliverthegoods,wegoontothe nextone,accordingtowhichtheparticularityoftropescomesfrom their being localised in space and time. Like many others, Maurin finds this attractive. Merely being localised need not immediately distinguish it from universality though. After all, immanent realists maintain that universals have position in space and time. Notwith standingthat,particularsanduniversalscanbedistinguishedinterms ofspatiotemporalposition.AremarkofKeithCampbellisquotedto showthat:

Universalsarepromiscuousaboutspacetime:theycanbe completelypresentatindefinitelymanyplacesatonce.But particulars, and in our case this includes above all the tropes,allhavealocalhabitation,asingle,circumscribed placeinspacetime. 4

Tothis,Maurinhastenstoaddthatconcreteparticularsmonopolise spatiotemporal positions in a way that tropes do not. A trope occupyingauniquepositioninspaceandtimeonlymonopolisesitin relation to tropes which belong to the same determinableasitself.5 For instance, an existing colour trope prevents every other colour tropefromhavingthatparticularspatiotemporalposition.Tropesof differentdeterminablessuchasform,weight,tasteetc.mayverywell 1 As is perhaps already evident, Maurin is not using ‘abstract’ in the same senseasWilliams. 2Cf.Williams1986,p.3. 3Maurin2002,p.17. 4Campbell1990,p.53. 5Thereareafewobviouscomplicationswiththischaracterisation.Itwilldo fornowthough. EXAMINATIONOFMAURIN’SONTOLOGY87 sharetheirpositionwitheachother.Aswillbeseenbelow,sharing positioninthiswayisbeingcompresentwitheachother. Itmightbeproposedthathavingauniquepositioninspaceand timegivesanentityitsparticularity.Atropemayevenbedescribedas beinganatureataplace.Ifthismeansthatthetropehasanatureand apositionasconstituents,Maurin’sobjectionisthatthiswouldbein conflictwiththesimplicityofthetrope. 1 JamesP.Morelandhascriticisedtheaccountofparticularityin termsofspatiotemporalposition.2Accordingtooneinterpretation,a qualityataplace amounts to a simple reality. Moreland objects to this.Oneofhisobjectionsconcernstropeswhichareelementsofthe same (exact) similarity set. It asks how the elements of such a set shouldbedistinguished.Twoexactlysimilarredtropescanbeused toillustratethis.MaurinquotesMorelandsaying:

[If]locationistheprincipleofindividuation[…][then]it doesn’tseemthatthetworedtropescanbeindividuated bytheirrednature,forthisiswhattheyhaveincommon. Andiftheirnaturediffersfromtheirlocationonly by a distinction of reason, then they would be one and not two. 3

Maurinobjectstothisonthegroundthatitconfusesparticularity,or individuality,withindividuation.PartofherrenderingofMoreland’s argumentreadsasfollows.

Ifthe particularity ofthetropeisgivenbyitsoccupyinga certain spatiotemporal position, then, Moreland argues, therewillbetroublewhenweattemptto individuate distinct

1Cf.Maurin2002, p.18.Anobviouscommentonthisobjectionisthatit presupposesthatlocationisnot qualitative in nature.Ifitis,thecategorial simplicityofthetropewouldnotbetamperedwith,wouldit? 2MaurinonlyreferstoMoreland1985.Hehasrepeatedand,tosomeextent, varied his objections in several works written after Moreland 1985. One is Moreland2001. 3Moreland1985,p.41.Itisevidentfromtherenderingofthisquotationthat Maurin has edited what Moreland says. Unfortunately, this distorts his messagetosomeextent. 88CHAPTERIII

tropesfromthesamesimilarityset.Therewillbetrouble because,inbelongingtothesamesimilarityset,thetropes willbe the same 1andsoincapableofbeingindividuatedon thebasisoftheirqualitativenature.Butastheirrespective qualitative nature is only separated from their respective positionbya‘distinctionofreason’theycannotreallyhave differentpositionseither.Iftheirqualitativenatureisthe same,soistheirposition. 2

InthisaccountitmayseemasifMorelandistalkingaboutanissueof an epistemological nature, rather than an ontological one. If we disregardthat,hispointistheoneindicatedinthelastsentenceofthe quotation:iftheirqualitativenatureisidentical,soistheirposition. 3 Interpretedinthisway,Maurinstillrejectsit.Sheevendoessoafter having stated that Moreland’s problem is the more general one of groundingthenumericaldifferencebetweenentitiessharingalltheir pureproperties. 4

[T]hismetaphysicalproblemofindividuation[i.e.,thatof groundingthenumericaldifferencebetweenentitieswhich sharealltheirpureproperties]seemsonlytoariseifwedo notacceptthebasictenetsoftropetheory.Thatis,itonly arises if we refuse to accept that two different basic facts maybetrueofoneandthesamesimpleentity.Arefusal toacceptthisissurelybothpermissibleand,tosome,quite natural. But it is not an objection to some particular development of trope theory; it is an argument directed against the very possibility of the entire tropetheoretical enterprise. As such it is of no interest in the discussions 1ItpuzzlesmethatMaurinisusing‘thesame’sofrequentlyinconnection with Moreland since she tends to use it as synonymous with ‘exactly like’. Morelandisarealistandintendsstrictidentity. 2Maurin2002,p.19. 3Ifwestartwiththetworedtropeshavingdifferentlocationsandthatthey thereforearenotidenticalwitheachother,wereachtheconclusionthatthey have separate natures. This arrangement of the premises is ignored by Moreland. 4AreferenceismadetoMoreland1985,pp.645,whichshowsthattobethe case. EXAMINATIONOFMAURIN’SONTOLOGY89

being conducted here (where the possible existence of tropesisassumed ). 1

WeseeherethatMaurinwantstodisregardanobjectionwhichcalls into question the stipulated premises of (her) trope theory. The particularpremisehereisthattropesaresimpleentities.Thiskindof argumentationmayofcoursebecalledinquestion. MaurinintimatesthatanotherofMoreland’sobjectionsismore serious.Sinceithasmoreorlessthesamepattern as the previous one,itisnotcompletelycleartomewhatherreasonforthatmight be.Forsafety’ssake,Iletherspeakforherself.

Ifthetropeissimpleitsqualitativenatureanditsposition will be one. But as tropes do not generally monopolise their places, this means that several tropes may have numerically the same position. But how can one and the same position be one with many distinct qualitative natures?Itsimplycannot,saysMoreland.And“[t]oavoid this consequence,” he continues, “it is easy to think that location or place is an entity in the trope, a coordinate quality perhaps, which individuates the two tropes.” But, again,thiswouldcontradictthesuppositionthattropesare simpleentities. 2

Whilethetropesstarringintheformerargumentsharednature,the ones in this one share position. We see in the last sentence that Moreland’sproposedrevision,whichtakeslocationtobeanentityin itself,isrejected.Onceagain,thesimplicityoftropesisinvoked. Maurin’ssummarisedresponsetothetwoproposalsisstatedin thefollowingquotation.

Itseems[…]thatwecannotexplainwhatitmeanstosay ofthetropethatitisparticularbycharacterisingthetrope asasingularunityofqualityandplace.Forevenifitistrue

1Maurin2002,p.19. 2Maurin2002,p.20.TheinsertionsaresaidtocomefromMoreland1985,p. 41. 90CHAPTERIII

thatweindividuate 1distinctbutexactlysimilartropesvia their distinct spatiotemporal positions, and even if it is truethatoneandthesametropecannotexistbutinone unique region in space and time, we may still ask why distincttropesoccupysuchdistinctspatiotemporalposi tions,or why onesingletropecannotexistbutatoneplace at one time. What is it about the trope that ensures that theseclaimsaretrue?Theanswerseemstobethatthese claimsaretrueoftropes because tropesare particulars .This turnsexplanationonitshead.Ittreatsparticularityaswhat explains certain spatiotemporal truths, rather than the reverse. 2

The message here is the same as it was from the start: particularity mustbeacceptedassomethingprimitive.Inconnectionwiththisitis addedthatbeingprimitiveisthesameasnotbeingbasedinanything atall. 3

(iii) Abstractness The third trope trait is abstractness. The notion that tropes are abstractparticularsisacommondescription.ThesenseMaurinhasin mind for ‘abstract’ may be quite peculiar to herself though. In a prefatoryremarkshecontrastsbeingabstractwithbeingbare.

Apartfrom beingsimpleand particular,the tropeisalso abstract .Itisindeeditsbeingabstractthatdistinguishesthe tropefromanotherclassicalkindofontologicalentity:the bareparticular.Justlikethetrope,thebareparticularis(as its name suggests) particular and simple. But unlike the trope,thebareparticularis(asitsnamealsosuggests)bare, whereasthetropeis,inacertainsense,‘clothed’:thetrope isqualitative;thebareparticularisnot. 4

1Here‘individuate’isanepistemologicalterm. 2Maurin2002,p.20. 3Cf.Maurin2002,p.20. 4Maurin2002,p.21. EXAMINATIONOFMAURIN’SONTOLOGY91

Theessentialmessagehereisthatbeingabstractisinasensebeing clothed.Thiswayofexpressingthethesissuggeststhatabstractnessis something a trope is “wearing”. Therefore she hastens to add that thisisanweshouldresist.Theabstractnessofatropeisnot somethingwhichhasaseparategroundinit;atropecannothavea separate ground. The reason invoked for this is its simplicity. Not verysurprisingly,tropesaredeclaredtobeprimitivelyabstract. Whyuse‘abstract’inthissense?Thestatedreasonforusingitat allisthatitissoentrenchedinitsusageintheliterature.However,in spiteofitsbeingwellestablished,thereisnotmuchofaconsensus on what its sense is. Take, for example, the sense stipulated by Williams: an abstract entity is one which, in a special sense, is less than the whole including it.1 This special sense is indicated by examples, in which the abstract entities are tropes. Maurin is not satisfiedwiththis:

The trouble with this specification is that it now seems that we have gained nothing by adding that the trope is abstract.Allwecansayaboutwhatitmeansforatropeto beabstractisthatitistobe‘likethecolourofthelolli pop’.Butitwastocharacterisesuchthingsasthecolour ofthelollipopthatthetermwasoriginallyintroduced.It was the ‘thinness’ of the trope (in contrast with the ‘grossness’oftheconcretestickpartofthelollipop)that our use of the term ‘abstract’ was originally meant to explicate.GiventhewayWilliamschoosestospelloutthe notion, the characterisation of the trope as abstract is moreorlessemptyanduninformative. 2

Williams’s characterisation of abstractness is pronounced to be empty. Campbell’s characterisation is rejected as well, more or less accusedofthesamesin.Itreads:

Thecolour ofthispea,thetemperatureofthat wire,the solidityofthisbell,are abstract inthissenseonly:thatthey (ordinarily) occur in conjunction with many other 1Cf.Williams1953 a,p.15. 2Maurin2002,p.22. 92CHAPTERIII

instancesofqualities(alltheotherfeaturesofthepea,the pieceofwireorthebell),andthat,therefore,theycanbe brought before the mind only by a process of selection, of systematicsettingaside,oftheseotherqualitiesofwhich weareaware.Suchanactofselectiveignoringisanactof abstraction.Itsresultisthatwehavebeforethemindan item which (as a matter of fact, in general) occurs in companywithmanyothers. Butthepea’scolour,thewire’stemperature,thebell’s solidity, are not in any sense products of the discriminating mind. They exist out there, waiting to be recognized for theindependent,individualitems,thattheyhavebeenall along. 1

Beingtheobjectofaprocessofselectiveattentioncalled‘abstraction’ is not much of a characterisation. Anything can be such an object. Maurindoesnotthinkitmakesanythingabstract. Something which adds to the conceptual confusion is that, in theterminologyofsomephilosophers,tropesaresaidtobeconcrete entities.PeterSimonsandGuidoKüngarementionedasexponents ofthis.

Simons, for instance, notes two mutually incompatible ways (more or less the same as those distinguished by Williams)ofregardingthedistinctionbetweenabstractand concrete:onthefirstaccountofthedistinctionanentityis abstractifithasneitherspatialnortemporallocation.On the second, an entity is abstract if it is incapable of in dependent existence. 2 According to Simons, since the trope is an entity with location, it is concrete in the first senseofthedistinction,butsinceitisalso(accordingto histheory) necessarilydependentforitsexistenceon the existence of other tropes, it is simultaneously abstract in the second sense. To avoid calling the trope a concrete abstract entity, Simons chooses to characterise it as a

1Campbell1990,pp.23. 2Thisispartlywrong.ItispartofWilliams’sownofficialdoctrinethattropes areexistentiallyindependententities. EXAMINATIONOFMAURIN’SONTOLOGY93

“dependent concrete particular.” 1Forsimilarreasons, G. Küng characterises his tropelike entities as concrete . ‘Abstract’, for him, means non-spatio-temporal , and since tropesbothhave“somedefiniteplaceinspaceandtime” and since they are “not eternal, and they may change throughtime”, 2hecallsthem concrete properties .3

Thus,theterminologyincirculationissomewhatchaotic,tosaythe least.AccordingtoMaurin,muchofthediscussioncouldhavebeen avoidediftheterm‘abstract’hadnotbeenused.Inspiteofthat,she contributestothechaosbyusingitherself. In what might be described as common usage, ‘abstract’ and ‘concrete’ have opposite senses. What about Maurin’s use of these terms?Iguessthatatleastherofficialsenseof‘concrete’isthesame asthatof‘monopolisingaspatiotemporalvolume’.Ifthatisindeed thecase,shedoesnotusethemasoppositesofeachother.4

3.3TheProblemofUniversalisationandItsSolution

3.3.1 Overview The problem of universalisation is a main subject in this rather lengthy section. The outcome of the discussion on it is in section 3.3.6,dealingwithMaurin’spreferredaccountofthenotionofinter nal relation. Another problem, the problem of universals, marches pastbeforethat.Whiletheformerproblemisinherenttomoderate nominalism,thelatterismoregeneral. The notions of external and internal relations play principal parts in Maurin’s ontology. Her version of trope theory differs somewhat from the mainstream of moderate nominalism in that it recognisesirreducibletropesofexternalrelations.Someofthedetails

1Cf.Simons1994,p.557. 2Cf.Küng1964,p.33.SinceMaurinstipulatesthattropescannot change, Küng’sconcretepropertiesarenomorethantropelikeentities. 3Maurin2002,p.23. 4WejustsawthatneitherdoesSimons. 94CHAPTERIII ofthedistinctionbetweenthetwokindsofrelationsarediscussedin sections3.3.4and3.3.5. In thelattersection,thenotion of internal relation is applied to tropes. After Maurin’s preferred account of internalrelationsisdiscussed,thereisashortsection,section3.3.7, dealing with the problematic claim that resemblances of various degreesholdbetweensimpletropes.

3.3.2 Another Problem: The Problem of Universals Maurinisanxioustodistinguishbetweenaproblemwhichshecalls ‘the problem of universals’ and another problem, ‘the problem of universalisation’,whichisherprimaryinterest.1Beforediscussingit,it mightberewardingtodwellupontheformerproblemforamoment.

Theclassicalproblemofuniversalsisduetoaphenome non found in both language and experience, at times referredtoasthatofthe‘OneoverMany’.Thephenome nonoftheOneoverManyisthis:experienceandthought unfoldtous,notonlyparticularthingsorparticularcases of qualities, but also samenesses or even identities that seemtoexist, sotospeak,overandabovethesedistinct andparticularentities.Theworld,thatis,notonlyappears particularised (as many) but also, in some sense of the word,generalisedorclassified(asone).Languagemirrors this phenomenon in providing us with a distinction between a kind of word — the singular term — whose functionitseemstobetopointto,orreferto,particular individuals;andanotherkindofword—thepredicate— whose function it seems to be to point to, or refer to, thosecommunalthingsthatparticularindividualsshare.It isthis‘unityinmanifold’whichgivesrisetotheclassical problem of universals. The problem is this: how can distinct particulars all have what appears to be the same nature? 2

1Thequestion“Howcantherebeanythinguniversalwhentropesareallthat exist?”givesahintatwhatismeant. 2Maurin2002,p.60. EXAMINATIONOFMAURIN’SONTOLOGY95

Inthesecondsentenceadistinctionisobviouslymadebetweensame ness and identity. This distinction is given a more detailed account laterinthebook.1Itstatesthatthephrase‘havethesamenature’can haveeitheroftwosenses.Oneoftheseisthatof‘sharinganidentical feature’.2Maurinremarksthat thisis whatarealistwouldsay. She adds that it cannot be accommodated within a tropetheoretical framework. The other possible meaning is that of ‘have exactly resembling natures’. The latter sense can be accommodated within her tropetheoretical framework. Now, given the context of the occurrenceofthephrase‘ the same nature’inthelastquotation, 3one would expect its intended sense to be that of ‘exactly resembling nature’.Ifthatisindeedso,theanswerwhichshehastoofferwithin theframeworkofherowntropetheoryisaratheremptyone:distinct particulars all have what appear to be exactly resembling natures becausetheyhaveexactlyresemblingnatures.Thisseemstoturnthe allegedproblemofuniversalsintosomethingofamockery.Itwould bemoreaccuratetoformulatethequestionandanswerlikethis:How candistinctparticularsallhavewhatappeartobeanidenticalnature? Itisbecausetheyhaveexactlyresemblingnatures. Thepreviousquotationcontinues:

There is of course a fundamental sense in which the classical problem of universals and the problem of universalisation deal with the same issue. They are both problemsthatemergefromaneedtoexplain,orground, thephenomenonofuniversality.Yettheproblemsremain distinct,andtheirdistinctnessisduemainlytotwofactors: (1) the problem’s origin, or that which gives rise to the queries, is different in each case. (2) That for which a solutiontotheseproblemsmayreasonablybeexpectedto beabletoaccountislikewisedifferent.

1Cf.Maurin2002,pp.778. 2Cf.Maurin2002,p.77.Presumably,themotiveforusing‘feature’hereis purelystylistic. 3 Part of this context is that a distinction is made between sameness and identity. 96CHAPTERIII

Thatthetwoproblemsdifferinoriginisdemonstrated bythefactthattheproblem ofuniversalisationdoesnot immediately arise when the phenomenon of apparent identityindifference,inlanguageandexperience,hasbeen detected. Yet, it is this very phenomenon which constitutestheproblemofuniversals. 1Infactitispossible thattheexistenceofsamenessindifference—ofapparent universality — in no case requires universality to be constructedfromtropes,atleastaslongastropetheoryis developed within truthmaker theoretical framework. As willbearguedlaterforinstance,simplepredicationssuch as‘ aisF’donotgiverisetotheproblemofuniversalisa tion, whereas it may be (and has been) argued that in including both singular and general terms, these predica tionsarepartofwhatgivesrisetotheclassicalproblemof universals. 2

Thatapparentidentityindifferenceinnocaserequiresuniversalityto beconstructedfromtropesisarathersurprisingthesis.Itiseasyto get the impression that the opposite is what actually is claimed in anotherplace.

InthefollowingtwochaptersofthisbookIwillattempt to , first the required universality, and then the required concreteness from tropes. I begin here with the first of these constructive tasks: that of constructing universalityfromtropes.Ilabelthisproblemthe‘problem ofuniversalisation’[…]. 3

Anyhow,wehavebeen toldattheendofthequotation beforethe lastonethatsimplepredicationsarenotinneedofuniversals.Nordo theypresupposeasolutionoftheproblemofuniversalisation.Thisis

1 These two sentences seem to corroborate that (apparent) identity, not sameness, of nature is what Maurin considers to be connected with the problemofuniversals. 2Maurin2002,p.60. 3Maurin2002,p.59. EXAMINATIONOFMAURIN’SONTOLOGY97 inspiteofthefactthatsimplepredicationsinvolvegeneralterms— i.e.,predicates.

3.3.3 The Problem of Universalisation Anappropriateintroductionoftheproblemofuniversalisationseems tobethattheworldistheultimategroundforthetruthofproposi tions. The world, or something about its structure, is what makes propositionstrue.AccordingtoMaurin,therearesometrueproposi tionswhichapparentlyhaveuniversalsastruthmakers.Beinganomi nalist, she sees a need for something to replace theuniversals.The problemhasitsplaceinthiscontext.Aformulationofitis:howcan therebeanythinguniversalwhenallthatexistsisparticular? 1Thetask inconnectionwiththisformulatedquestionappliestoallversionsof nominalism. However, as far as trope theory is concerned, the questionshouldbereformulated:Howcantherebeanythinguniver salwhentropesareallthatexist? Inthequotationwhichfollowsweseesomeofthemainideas behindMaurin’snotionoftruthmakingpassingby.

According to truthmaker theory any true proposition is made true. That is, for a proposition to be true the existence,intheworld,ofthisorthatentityisrequired.It is a basic assumption in this work that tropes exist. It follows from the adoption of truthmaker theory that tropesshouldbeabletofulfilthistruthmakingfunction. 2 Thusthetheoryoftruthmakingwillprovideuswithboth astartingpointandacheckpointforourtheory.Iftruths aremadetrueintheintendedsense,thenwemight,from known truths, conclude something about that which makesthemtrue.Wemightconclude,inparticular,some thingabouthowourtropes,iftheyaretosucceedintheir truthmaking function, must be structured. Truthmaker theorythusworks‘topdown’.Itprovidesus withaccess to the world and it prescribes which configurations of

1Cf.Maurin2002,p.59. 2Anadditionalpremiseofcourseisthestipulatedtheoreticalideal. 98CHAPTERIII

tropes our theory must be able to provide for. Investi gatingwhetheraonecategorytheoryoftropescansupply the configurations prescribed by truthmaker theory will, therefore,helpustodetermineifaonecategorytheoryof tropesisatallfeasible. 1

This being said, it is added that truthmaker theory is assumed in substance, not defended. It is part of the theoretical framework withinwhichherversionoftropetheoryisdeveloped. 2Asindicated earlier,ontologicalcommitment,ratherthantruthmaking,seemsto bewhatsheactuallyhasinview.Afterall,theenterpriseisdescribed asstartingwithknowntruthsinordertofigureoutwhattheworldis like.Aselfimposedconstraintisthat onlytropes exist. The catch phrase, used in the last quotation, is that truthmaker theory works topdown. Anumberofpropositiontypesareenumerated.3Atleastsome of these apparently presuppose universals. Two of these types are discussedinparticular.Thefirstoftheseiscalledsimplepredication. Itsformis:

aisF.

The second type is the comparative predication. It appears in two versions,whoserespectiveformsare:

aand barethesameF and

aisthesameFas b. 1Maurin2002,p.38. 2 Her sources for truthmaker theory are mentioned: Mulligan, Simons & Smith1984,Simons1992and1998,Restall1996andRead2000. 3Inallthereareseventypes.Besidesthetwopresentedinthemaintextthe remaining five are: (i) Identity-propositions , e.g., ‘Mary = Mary’; (ii) Kind- predications ,e.g.,‘Maryisawoman’;(iii) Singular existentials ,e.g.,‘Maryexists’; (iv) Propositions ostensibly about universals ,e.g.,‘brownisacolour’;(v) Second-order predications ,e.g.,‘rednessisacolour’and‘rednessresemblespinkmorethan green’.Cf.Maurin2002,pp.54ff. EXAMINATIONOFMAURIN’SONTOLOGY99

Thelowercaselettersmayinallthreeformulasrefereithertocon creteparticularsortotropes. The comparative predicative propositions are the ones from whichMaurintakesheredeparturewhenattemptingasolutiontothe problem of universalisation. They are therefore strategically impor tant. What is the relationship between simple and comparative pre dicative propositions? These are her beginning remarks on the subject:

While simple predications do not in general necessarily require the existence of something amounting to the realist’s universal for their truth, the same does not hold foraspecialvariantofthesimplepredicativeproposition: whatIshallcallthe‘comparative’predicativeproposition. Thesearepropositionsofthekind‘ aand barethesame F’. One might think that propositions of this form are reallyhiddencomplexpropositionsoftheform‘ aisFand b is F’. If this were so, the truth of such propositions would be a consequence of whatever makes true their constituentpropositions‘ aisF’and‘ bisF’.Butaslongas weagreethatsimplepredicationsneednothingmorethan theexistenceofsomeparticulartropefortheirtruth,Ido notthinkthatwecansaythatpropositionssuchas‘ aisthe sameFas b’havetheirtruthdeterminedmerelybywhat evermakes‘ aisF’and‘ bisF’true—atleast,notwithout some qualifications. The reason why is that, in contrast withthecaseofsimplepredications,comparativepredica tions seem to require not only the existence of, say, a particular redtrope a1 and a particular redtrope a2, but also some account of how come we can truly say that thesetropesare the same .Comparativepredications,there fore, suggest that the trope theorist with sympathy for truthmakersneedstoconstructsomethingamountingto therealist’suniversalinorderforhisorhertropestobe abletofulfiltheirtruthmakingfunction.1

1Maurin2002,pp.578. 100CHAPTERIII

Inthefirstsentenceweareinformedthatcomparativepropositionis aspecialvariantofthesimpleproposition.Inthelightofwhatissaid intherestofthequotation,thismightbeinterpretedasmeaningthat theformerpropositionisacombinationoftwoofthelatterkindplus somethingadditional;theadditionalsomethingbeingtheclausethat thesubjectsofthetwoincludedpropositionsare the same .Isuppose this can be generalised for an arbitrary number of included simple propositionsandtheirsubjects. Withthepurposeofmakingitcrediblethatuniversalsmaybe unnecessary for truthmaking in the case of simple predications, truthmaking is contrasted with meaning. This happens in the next quotation,whichstartsoutusingaredappletoillustratetheexample. Prettysoon,thesubjectbecomesaredtropeinstead.

From the perspective of meaning, it does seem that the claim that the apple is red not only tells us something abouttheinnerconstitutionoftheapple,butalsorelates the apple to various other things, things with the same colour: in this perspective, the proposition seems to involve universality, then. Yet from the perspective of truthmaking, it is less evident that the existence of anythinguniversalisreallyrequiredfortruth.Fortruthitis arguablysufficientthatthis particular rednessexists.Thatis, evenifthisparticularrednessisinfactrelatedbysimilarity tonumerousotherparticularinstancesofredness,itisnot necessarilythisrelationshipthatconstitutesthisinstance’s being red .Ifyouareatropetheoristitissurelynot.Tothe tropetheorist,theparticularredness(thetrope)isredasa consequenceofits being the way it is ,andsoareallotherred tropes. To a trope theorist, therefore, the fact that each particular redness (each trope) is such that it resembles everyotherparticularrednessisaconsequenceofthefact that each particular redness is what it is and nothing else. Therefore,thetropetheoristcanarguethatthetruthofa simple predicative proposition need not require the existenceofmorethantheparticularredness(inthiscase instantiated in the apple). So although simple predicative EXAMINATIONOFMAURIN’SONTOLOGY101

sentences initially seem to require universals as truth makers,abelieverintropescaninfactdenythis.1

A central credo of Maurin is expressed here: a trope is what it is independentlyofeverythingelse.Neitherauniversal,similarity,class, predicate nor sum, or what have you, bestow it with a qualitative nature.Itisselfsufficientinthatrespect. ThataconcreteparticularaisFisduetoitsinstantiatinganF trope.Instantiatingatropeamountstohavingitaspart.Thingsare supposedlydifferentwhenaisatropeitself.Inthatcase,aitselfisthe Ftrope.Whatever amaybe,whetheritisaconcreteparticularora trope,thepropositionaisFisclassifiedasasimplepredication.An Ftropeissupposedtotakecareoftruthmakingineithercase. A containment model for predication 2 is suggested in the previousparagraph.Appliedtotheproposition‘ aisF’,when aisan Ftrope,isperhapsthat aiscontainedinitselfinthesensethatitisa part,althoughnotaproperpart,ofitself.Ifthatisindeedthecase, thengiventhat aisatropewhichisF,thoughnotitselfanFtrope, themodelimpliesthatanFtropeisaproperpartofit.Asindicated earlier,theideathatatropecanhaveanothertropeasapartofitis rejected. So, what denomination should be used then of an entity which consists of more than one trope but which is still not a concreteparticular?InanotherworkMaurincallsentitiesofthatkind ‘complexesoftropes’or‘compresenttropes’. 3 Keith Campbell distinguishes between two questions: the A questionandtheBquestion,respectively.Maurinisimpressedbythis distinction. It is intimately related to the distinction she makes between single and comparative predications. Let us acquaint our selveswithsomeofwhatCampbellsayswithregardtohisdistinction.

1Maurin2002,p.57. 2Cf.Maurin2002,p.62,whereitisconfirmedthathertropetheoryinvolves acontainmentmodelforpredication. 3Cf.Maurin2005,p.136,whichiswhereitisexplicitlyassertedthathue, saturationandbrightnesspartsofcolourtropesmustberegardedasmore fundamental tropes. The phrase ‘more fundamental tropes’ is of course a misnomer. 102CHAPTERIII

[W]ecanposetwoverydifferentquestionsabout,say,red things.Wecantake one singleredobjectandaskofit:what isitaboutthisthinginvirtueofwhichitisred?Weshall callthatthe A question . Secondly,wecanaskofany two redthings:whatisit aboutthesetwothingsinvirtueofwhichtheyare both red?Letthatbethe B question . Discussions of the problem of universals invariably takeitforgrantedthatthetwoquestionsaretobegiven parallel answers. Indeed, realists about universals have their answers ready. The A question’s answer is: it is in virtue of the presence in theobject of the universal red ness,thatthethingisred.AndtheBquestion’sansweris parallel:itisinvirtueofthepresenceineachofthemof theuniversalredness,thattheyarebothred. TheconflationoftheAandBquestionsisresponsible formakingtherealistpositionseemmuchmoreinevitable thanitreallyis. 1

InCampbell’sformulations therearenotracesofa role for truth making to play. In Maurin’s reformulations, in which Campbell’s originalnamesarekept,truthmakinghasarole.Herversionsread:

TheAquestion:Whatmakesittruethat‘ aisF’? TheBquestion:Whatmakesittruethat‘ aand bare thesameF’? 2

ItistheBquestionwhichanaccountofuniversalisationattemptsto answer.Thebasicuniversalisationrequiringquestionisdeclaredtobe theBquestionwith aand bastropes. 3So,whatisheranswertothat question, when a and b are tropes? Since Maurin’s answer pre supposesanaccountofuniversalisationintermsof (exact)resemb lance,anexaminationthelatteriscalledfor. Resemblance is said to be objective as well as primitive. Its beingobjectivemeansthatitiscomparisonindependent;i.e.,itholds 1Campbell1990,p.29. 2Cf.Maurin2002,p.61. 3Cf.Maurin2002,p.63. EXAMINATIONOFMAURIN’SONTOLOGY103 between relata independently of any observer. What is there to be said about its being primitive? Well, ponder upon the following statements.

Just as some believe that resemblance is obviously not objective,othersbelievethatresemblanceisobviously not primitive.Itmayevenbesuggestedthatanysuchrefusal to accept the primitiveness would raise a very serious objectiontotheentireresemblanceapproachtouniversa lisation,andindeedtotropetheoryasawhole,sincethe assertionthatresemblance is primitivecanbeconstruedas begging the question against the universal realist (who believesthatresemblanceisanalysableintermsofpartial identity).Butfirstofall,themainthemeofthis book is notan overallcomparisonof tropetheorywithuniversal realism — a search for the best theory. Instead, we are attemptingtodeveloptropetheorywithinaveryparticular theoreticalframework.Assuchitisaninvestigation that needstobemade,asfaraspossible,independentlyofany comparisonwithrivalviewssuchasuniversalrealism.And even if such comparison were the main theme of this book, we would need to remember that the trope theorist’s claim that resemblance is one of the basic differences between trope theory and universal realism. Comparisonisthereforeimpossibleunlessbothprimitive (fortropetheory)andnonprimitive(forrealism)resemb lanceisallowedfor.Nointrinsicvalueattachesprimitive ornonprimitivenotionsofresemblance.Whatmattersis whether, and how, resemblance helps to achieve our theoreticalaims. Let us assume from now on, therefore, that unless otherwiseindicated,theresemblancewearedealingwithis objective and primitive .1

Itmaybesafelyconcludedthattheprimitivenessofresemblanceat leastamountstonotbeinganalysableintermsofuniversals,accord ingtothequoteabove.Thisisnotmuchofacharacterisationthough.

1Maurin2002,pp.7980. 104CHAPTERIII

As for the rest, the message here is that the primitiveness of resemblanceissomethingwhichisassumed.Itisassumedinorderto achievethetheoreticalaimsoftropetheory. Resemblance is said to exist in degrees. This holds true also when the relata are tropes. Each trope resembles countless other tropes to countless degrees. 1 However, only exact resemblance is thoughtofasbeingrelevanttothesolutionoftheproblemofuni versalisation.Thatismadeclearinthefollowing:

Herearethebarebonesofwhatwill,Ihope,becomeafull accountofuniversalisationintermsofexactresemblance: atomic propositions that require universalised truth makers are made true by classes of tropes. Not just any class of tropes will be able to provide us with the truth makersweneed[…].Onlythoseclassesoftropesformed bythe equivalence or exact resemblance oftheincludedtropes willdo. 2

Nothinglessthanexactresemblancewilldoasatoolforforminga surrogate universal. More is said in section 3.3.7 about degrees of similarity.

3.3.4 Internal and External Relations Thepredominantdescriptionofresemblanceisthatitisaninternal relation. Various determinations of internality have been presented. Maurindiscussesfouroftheseandmakesnoclaimthatthisinventory is exhaustive. 3 Her discussion makes preparations for a modal characterisation of exact resemblance. That characterisation will be followedherebyanontologicalcharacterisation. The first determination of internality is ascribed to David Armstrong. The following indicates what he considers to be the distinctionbetweeninternalandexternalrelations:

1Cf.Maurin2002,p.80. 2Maurin2002,p.79. 3Maurin’sfoursensesof‘internalrelation’arefoundamongthetenthatare distinguishedinEwing1934,chapterIV. EXAMINATIONOFMAURIN’SONTOLOGY105

Iproposethefollowingdefinitions: (1) Twoormoreparticularsare internally relatedifandonly if there exist properties of the particulars which logicallynecessitate 1thattherelationholds. 2 (2) Two or more particulars are externally related if and onlyiftherearenopropertiesoftheparticularswhich logically necessitate that the relation, or any other relationwhichispartoftherelation,holds. 3

1EarlierinthesameworkArmstrongasserts: If logically equivalent predicates which are not logically empty applyinvirtueoftheverysameuniversals,andlogicallyequiva lentpropositionswhicharenotthemselveslogicallynecessaryare trueinvirtueoftheverysamestateofaffairs,thensome de dicto accountoflogicalnecessitymustbecorrect.Thelogicalnecessity of propositions must, in some way, derive from the words or concepts in which the propositions are expressed. (Armstrong 1978 b,p.42) This indicates that logical necessity is thought of as being of a conceptual nature. 2Thisdeterminationis,orapproximates,the“logicalpart”ofthesixthsense onEwing’slist:aninternalrelationisgrounded,eitherlogicallyorcausally,in thenatureoftherelatedterms.Similarityissaidtobeinternalinthissense. Cf.Ewing1934,p.126. 3 Armstrong 1978 b, p. 85. A reduction principle for internal relations is introducedonthenextpage: Iftwoormoreparticularsareinternallyrelated,thentherelation is nothing more than the possession by the particulars of the propertieswhichnecessitatetherelation. Armstrongcommentsonit: In§1itwasarguedthatalthoughrelationalpropertiesarereal, theyarereducible(tononrelationalpropertiesandrelations).It is now being argued that internal relations are reducible to properties of the related terms. […] External relations, on the other hand, involve irreducible relations holding between the externally related particulars. (Monads could have internal, but notexternal,relations.)(Armstrong1978 b,p.86) TherearesimilarpassagesinotherworksofArmstrong.Thefollowingisan example. An internal relation is one where the existence of the terms entails the existence of the relation. Given our definition of 106CHAPTERIII

Statement(1)isquotedbyMaurin.Herinterpretationofitisthatan internalrelationisfoundedinthenatureofthatwhichitrelates.1We can safely assume that Armstrong, in the quoted passage, does not consider tropes as being the relata of either internal or external relations. However, Maurin thinks that his determination can be appliedtotropesifneedbe,slightlymodified.

It is the particulars’ being the way they are that logically necessitates their standing in an internal relation. Trans latedintotropelanguage,Armstrong’stakeonthedistinc tionimpliesthattropes,sincetheyaresimpleentities,will be such that any internal relation holding between two tropesmustdoso,notasaconsequenceofcertainproper ties the related tropes exemplify, but rather because the related tropes are what they are. And, since there is nothingmoretoaparticulartropethanitsparticularand simple nature, this also means that the mere existence of twointernallyrelatedtropesisenoughtoensurethattheir internalrelationsnecessarilyhold. 2

Here,itisindicatedonceagainthattropesdonothaveanyproper ties.Thenatureofeachtropeissimpleasisthetrope“aswell”.Note

supervenience, it follows that the relation supervenes on the existenceoftheterms.Usingthepicturesqueextensionalmodel provided by possible worlds, in every world in which all the terms exist, the relation holds between them. If, as I further contend, what supervenes is not something ontologically more than what it supervenes upon, then, once given their terms, internal relations are not an addition to the world’s furniture. Externalrelationsarethosethatarenotinternal,andarethere foretheontologicallyimportantrelations.Itshouldnotbeover looked, however, that given this purely negative definition of ‘external’, some external relations, on analysis, resolve into a mixtureofinternalandpurelyexternalcomponents.(Armstrong 1997,p.87) Theviewexpressedhere,ignoringthatArmstrongconsiderspropertiesand relationstobeuniversals,comesneartowhatisMaurin’sownview. 1Maurin2002,p.88. 2Maurin2002,pp.889. EXAMINATIONOFMAURIN’SONTOLOGY107 alsothatseveralinternalrelations,supposedlynotidenticalwitheach other,mayholdbetweentwotropes. Armstrong’sdistinctionbetweeninternalandexternalrelations issummarisedbyMaurininthefollowing“figure”.1Init,theword ‘foundation’ is used, which Armstrong himself does not use in the workquoted.Idonotthinkthatthismisrepresentshisviewthough, sinceheusesthesameterminlaterworks. 2 Internalrelations Externalrelations Relationshavefoundationsin Relationsdonothave thetermstheyrelate.(For foundationsinthetermsthey tropes: aisinternallyrelatedto b relate.(Fortropes: ais iffgiventhe existence of aand b externallyrelatedto biffgiven —their‘beingwhattheyare’— theexistenceof aand bitis theirbeingrelatedis‘entailed’.) contingent whetherornotthe relationholds.) ThereisapotentialambiguityinArmstrong’sdetermination.Oneof itsspecificationshassomeaffinitywiththesenseascribedtoGeorge EdwardMoorebelow;evenmoresowiththesenseinwhichKeith Campbell uses ‘internal relation’. It can be expressed this way: ‘an internal relation between relata is founded in the identities of the relata’.3Anotherspecificationisexpressedbythephrase,‘aninternal relationbetweenrelataisfoundedintheirnatures,butnotnecessarily intheiridentities’. Maurin ascribes the second determination of internality to GeorgeEdwardMoore.

Accordingto Moore,ifRis aninternalrelation holding between aand b,itwillbethecasethat,had aand bnot 1Cf.Maurin2002,p.89. 2Cf.forexampleArmstrong1989,p.44.ThecorrespondingwordinEwing is‘grounded’. 3ThefollowingisperhapsmoretruetoArmstrong’sownformulationinthe quotedpassage:‘aninternalrelationbetweenrelataisfoundedinproperties whichareessentialtotheidentitiesoftherelata’. 108CHAPTERIII

beenrelatedbyR,thennecessarily aand bwouldnothave beentheselfsame aand b.ToMoore,then,thedistinction between internal and external relations should be under stood in terms of what is and what is not essential to the identity of the related terms .1

Thisdeterminationisalsosummarisedinafigure: 2 InternalrelationsExternalrelations Relationsareessentialtothe Relationsarenotessentialto identityoftherelatedterms. theidentityoftherelated terms. It is mentioned that Moore puts the matter in terms of relational properties,notrelations,andthatthismaybesignificant.Mooredoes indeed do so. 3 I would say that it is significant, not least of all for reasons of intelligibility. After all, what does it mean to say that a relationisessentialtotheidentityofitssubjectandtheidentityofits relatum? It seems to be a misleading way of saying that a certain relationalpropertyisessentialtotheidentityofthesubjectandthat this holds mutatis mutandis for the relatum. Put differently, that the relational property Rb is essential to the identity of a is taken as a pretextforR’sbeingessentialtotheidentityof a.Thesameapplies, mutatis mutandis ,to bandtherelationalproperty aR. Ofcourse,the formula‘ aR ’isunorthodox.Whatismore,ifRisasymmetric,oreven nonsymmetric, it is inaccurate as well. It should instead be R*a , where‘R*’namestheconverseof R.Though,ifthelatterrenderingis used,thepointofmyremarkismoreeasilymissed.

1Maurin2002,p.89.ThisisEwing’ssecondsense.Cf.Ewing1934,p.121. 2Cf.Maurin2002,p.89. 3ItisstatedinMoore1922,p.282: [T]hefundamentalproposition,whichismeantbytheassertion thatallrelationsareinternal,is,Ithink,apropositionwithregard torelationalproperties,andnotwithregardtorelationsproperly socalled. EXAMINATIONOFMAURIN’SONTOLOGY109

Maurin ventures to assert that Moore and Armstrong’s deter minationsdonotdifferfromeachotherinanysignificantway.

Thereissomeevidencetosuggestthat,forMoore,‘being foundedin’doesmeanthesameas‘beingessentialtothe identity of’. He does not always characterise the internal relationasonethatis essential to the identity of its terms ,but alsotalksofitasarelation,R,suchthat“given aand b,R isentailed”andsuchthat“ aand bcouldnothaveexisted in any possible world without standing in R to each other.” 1Mooreseemstoconsiderthesepropositionsequi valent ways of expressing the same point and when this point is put in terms of logical necessitation and entail ment,evenhisverbaldifferenceswithArmstrongseemto disappear. 2

IremindthereaderthatMooreisexplicitlydiscussinginternalrela tionalproperties.Hisviewoninternalrelationsmustbederivedfrom that.FormyownpartIdoubtthattheconclusionsinthelastquota tioncanbedrawn. Moore’s considered view on internal relational properties is statedinthefollowingquotation.Theletter‘P’representsarelational property.

WecansaythatAPisitselfanecessarytruth,ifandonlyif theuniversalproposition“( x=A)entails xP”(whichwe haveseenfollowsfromAP)isanecessarytruth:thatisto say,ifandonlyif(x=A)entails xP.Withthisdefinition, whatthedogmaofinternalrelationsassertsisthatinevery caseinwhichagiventhingactuallyhasagivenrelational property, the fact that it has that property is a necessary truth;whereaswhatIamassertingisthat,iftheproperty inquestionisan“internal”property,thenthefactinques tionwillbeanecessarytruth,whereasiftheproperty in

1MyimpressionisthatthisismeanttobeaquotationfromMoore1922,pp. 2912.Itcannotbethough,sinceMooredoesnotusethe“formalism”‘ aand b’there—oranywhereelseinMoore1922. 2Maurin2002,p.90. 110CHAPTERIII

questionis“external,”thenthefactinquestionwillbea mere“matteroffact.” 1

Thus,aninternalrelationalpropertyofathingisonewhichthething has by necessity. According to what Moore calls ‘the dogma of internalrelations’,whichherejects,everyrelationalpropertyathing has it has of necessity. He supplies examples of internal and non internalrelationalpropertiesrespectively.

It seems quite clear that, though the whole [which is a colouredpatchhalfofwhichisredandhalfyellow]could nothaveexistedwithouthavingtheredpatchforapart, the red patch might perfectly well have existed without beingpartofthatparticularwhole.Inotherwords,though every relational property of the form “having this for a spatial part” is “internal” in our sense, it seems equally clearthateverypropertyoftheform“isaspatialpartof thiswhole”is not internal,butpurelyexternal.Yetthislast, accordingtome,isoneofthethingswhichthedogmaof internalrelationsdenies. 2

I strongly suspect that Maurin is influenced by what Campbell considersMoore’sdoctrinetobe.Unfortunately,hedoesnotspecify whichpagesofMoore1922supporthisinterpretation.However,the followingispresentedastheresultofhisexaminationofthetext.

The examination reveals that as Moore uses the term ‘internalrelation’notonlydoestheexistenceofaninternal relation aRb imply that its terms possess suitable foundations in virtue of which the relation holds, but further,itimpliesthatthosefoundationsarecriticaltothe identity of the terms to which they belong. Were the relationtochange,should aRbceasetoobtain,theterms wouldceasetoexist,i.e.ceasetobethetermstheyare. 3

1Moore1922,pp.3023. 2Moore1922,p.288. 3Campbell1990,p.111. EXAMINATIONOFMAURIN’SONTOLOGY111

Aphrasesuchas‘weretherelationtochangethetermswouldcease toexist’suggeststhatthetermsaredependentontherelation.Thisis ofcoursesomethingdifferentfromtherelationbeingfoundedinthe terms,irrespectiveofwhetherthepropertiesconstitutingthefounda tionareessentialtotheidentitiesofthetermsornot. Mooresuppliesanotherexampleofaninternalrelational pro perty. Campbell refers to it, but he misrepresents it. The relational propertyMooreactuallyusesasanexampleis:beingintermediatein shadebetweenthequalitiesyellowandred.InCampbell’srendering ofitonlytherelationremains.

Being intermediate in colour ,forexample,asarelationamong colour patches, is internal in this sense. If a patch of colourbeginsbybeingintermediateincolourbetweentwo others,andthenceasestobeso,thisrequiresthatatleast oneofthepatchesmusthavelostitsidentity,thatis,must haveceasedtobethecolourpatchitwas. 1

DoesCampbellassertthataspecificcolourpatchlosesitsidentityif itlosesaparticularrelationalpropertyithastoanotherpatchandthat thisisduetothefactthatthelatterchangesincolour?Probablynot. Thepatchwhichlosesitsidentityisthelatterone,nottheformer. InMoore’soriginalexample,thequalityorangeisintermediate betweenthetwoqualitiesyellowandred.Sinceaqualitywhichlacks therelationalpropertyinquestionwouldnecessarilybeanotheroneit would not be orange; therefore, the relational property is internal. Mooresays:

[I]f any quality other than orange must be qualitatively different from orange, then it follows that “intermediate betweenyellowandred”isinternalto“orange.”Thatisto say, the absence of the relational property “intermediate betweenyellowandred,” entails theproperty“differencein qualityfromorange.” 2

1Campbell1990,p.111. 2Moore1922,p.287. Entailment istheconverseof following .Cf.Moore1922, p.291.Twoillustratingexamplesofthelatteraregiven: 112CHAPTERIII

Thisrelationshipcanperhapsbedescribedaccordingly:sincenoneof thethreequalitiescanchange,ordisappear;therelationalpropertyof beingintermediatebetweenyellowandredisinternaltoorange. MaurinbasesherthirddeterminationofinternalityinCampbell. Internal relations are founded in the natures of their relata. Addi tionally, the foundations must also be essential to the identities of relata.Arelationfoundedinthenaturesofitsrelata,butnotinwhat is essential to their identities, is said to be external and founded. If neitheroftheseconditionsismet,therelationisexternal—andof courseunfounded.Thus,theexternalandfoundedrelationscovera sortofmiddlegroundbetweeninternalandexternalandunfounded relations.Theexampleofarelationwhichisexternalandfoundedis onethatexistsbetweentwoshoes.

ShoeCisnotequallydirtyinallpossibleworldsinwhichit exists,norisshoeD.Nonetheless,C’sbeingacleaner shoe than D depends only on how dirty C and D are. Furthermore, this is a necessary truth: if X 1 and X 2 are equallydirty,andY 1andY 2areequallydirty,thenifX 1is 1 cleanerthanY 1thenX 2iscleanerthanY 2.

Thus,sincebeingdirtyisnotessentialtoashoe,itneednotbedirty. Thecolourofacertainpatchisessentialtoit.Withoutit,thepatch losesitsidentity;orceasestobe.2Contemplateupontherebeingan TosayofapairofpropertiesPandQ,thatanytermwhichhad hadPwouldnecessarilyhavehadQ,isequivalenttosayingthat, ineverycase,fromthepropositionwithregardtoanygiventerm thatithasP,it follows thatthattermhasQ: follows beingunder stoodinthesenseinwhichfromthepropositionwithregardto anyterm,thatitisarightangle,it follows thatitisanangle,andin whichfromthepropositionwithregardtoanytermthatitisred it follows thatitiscoloured.(Moore1922,pp.2845) 1Campbell1990,p.112. 2ThisremindsofsomethingMooresays: [T]hosewhosaythatallrelationsareinternaldosometimestend tospeakasifwhattheymeantcouldbeputintheform:Inthe case of every relational property which athinghas,itisalways truethatthethingwhichhas it wouldhavebeendifferentifit had not had that property; they sometimes say even: If P be a EXAMINATIONOFMAURIN’SONTOLOGY113 essentiallydirtyentity,asmudge,whichiscleanerthananotherentity, which is extremely dirty though this is accidental. Is the relation of being cleaner than ,thatexistsbetweenthesetwoentitiesinternalorisit external and founded? Is it perhaps internal while its converse is externalandfounded?Andwhataboutasmudge,coulditbeacci dentallydirty?Isupposenot. Campbell’stristinctionsummarised: 1,2 Internalrelations Externalrelations Founded Founded Unfounded Relationshave Relationshave Arelation’sholding foundationsinthe foundationsinthe ornothasnocon termsthatare terms,buttheseare sequenceforthe essentialtothe notessentialtothe existence,ormona identityofthose identityofthose diccharacteristicsof terms. terms. theterms. Maurindoesnotrecogniseanyexternal,foundedrelations between tropes. Their simplicity is supposed to exclude that. What about Campbell?Well,itisevidentthathedoesnotrejectcomplextropes.

relational propertyandAaterm whichhas it,thenitisalways true that A would not have been A if it had not had P. This is, I think, obviously a clumsy way of expressing anything which could possibly be true, since, taken strictly, it implies the self contradictorypropositionthatifAhadnothadP,itwouldnot havebeentruethatAdidnothaveP.(Moore1922,p.283) 1Cf.Maurin2002,p.91.AsimilarsummaryappearsinCampbell1990,p. 112, where three examples are presented. Internal relation: is a darker colour than ; external and founded relation: is a cleaner shoe than : external and un foundedrelation: is to the left of . 2 This summary does not show, and neither does the account given in the maintext,thatCampbellconsidersallinternalrelations—infact,allrelations — to, as he says, supervene on their relata. He calls this doctrine ‘foundationism’.Asthename,tosomeextent,suggests,internalrelationsare supposedtobereducibletoitsfoundationsinrelata.Cf.Campbell1990,p. 101.Maurintosomeextentconcurswiththis.Moreissaidaboutthisbelow. 114CHAPTERIII

Atthecoreofthetropeontologyisthisthought:thebasic items,the‘alphabetofbeing’,inWilliams’phrase,arecases ofkinds.Theyareentitiesthatareparticulars,butnotbare particulars. Each of them, if truly basic, has a simple nature.(Therearecomplexderivativetropes.Butthebasic onesaresingleincharacter.) 1

AreasonablehypothesisisthatCampbellalsoacceptsnonconcrete complexes of tropes as tropes since they are not concrete entities. Whetherhealsoconsiderstheretobeexternalandfoundedrelations betweenthemdependsonwhathethinksoftheircapacitytocontain accidentalelements.Unfortunately,thereisnotenoughinformation providedtosettlethismatter. Thefourth,andlast,determinationofinternalityishintedatin thefollowingway.

[T]wo entities are, on this view, internally related if they could not have existed independently of one another (or of the relation ). To our surprise, regarding the distinction in this way — that is, regarding it in terms of the existential dependenceoftherelatedentities—renderstheinternal relationsofatleastArmstrongandCampbell external .2

Inthisversionofinternality,internallyrelatedentitiesareexistentially dependentoneachother. Ifoneceasestoexist,sodoestheother. Thus,internallyrelatedentitiesonlyexistinpairsorgroups.

1Campbell1990,p.20. 2Maurin2002,p.91.MaurinreferstoIngvarJohanssonashersourceforthis determination of internality. He is inspired by Ewing’s tenth sense. Cf. Johansson 1989, p. 113, and Ewing 1934, p. 136. The following is his determinationinJohansson1989,p.117.

Ais internally related toBifandonlyifitislogicallyimpossiblefor AtoexistifBdoesnotexist,andviceversa. TheterminologyusedinthemaintextdiffersfromJohansson’s.Hemakesa tristinction between internal, grounded and external relations. Thus, the groundedrelationsarenotclassifiedasbeingexternal.Cf.Johansson1986,p. 219,and1989,pp.11720. EXAMINATIONOFMAURIN’SONTOLOGY115

Inthisdeterminationthereisalsoatristinctionmadebetween relations.ThesearesummarisedbyMaurin:1,2 Internalrelations Externalrelations TermsareexistentiallyTermsareexistentiallyindependent Dependent Relationis Relationisnot foundedinthe foundedinthe termsitrelates. termsitrelates. ThisconcludesthepreparationsmadebyMaurinforhermodal characterisationofexactresemblance.Whencarryingoutthecharac terisation,shestartswiththefourthdeterminationofinternality.

Wecanbeginwhereweleftoffandask,first,whetherER [=exact resemblance] is internal in the strong sense of 1Cf.Maurin2002,p.91. 2InJohansson1989themiddleformiscalled‘groundedrelation’. Rxy isa grounded relation ifandonlyifitislogicallyimpossiblefor theretoexista z anda wwithexactlythesamequalitiesas xand y,respectively,butbetweenwhichtherelation Rdoesnothold. (Johansson1989,p.120) Johansson’snotionofinternalrelationcanbefoundalsoinArmstrong,who asserts,inArmstrong1978 b,p.3: [A]lthough particularity and universality are inseparable aspects ofallexistence,theyareneitherreducibletoeachothernorare theyrelated.Thoughdistinct,theirunioniscloserthanrelation. Scotustalkedofamere“formaldistinction”betweenthethisness and the nature of particulars. The situation is admittedly pro foundlypuzzling,but,itissuggested,theScotistviewisthemost satisfactoryonewhichcanbefound.Acomparisonwhichmay beusefulisthewayinwhichshapeandsizeareunitedinaparti cular. Johanssonmakesthefollowingappositecomment:“[I]fArmstronghadnot alreadyuseduptheterm‘internal relation ’hewouldnothavebeenforcedto saythat‘theirunioniscloserthanrelation’,butcouldhavewritten:‘Though distinct, their union is so close that there is an internal relation between them.’”(Johansson1989,p.126) 116CHAPTERIII

being such that two exactly resembling tropes are also existentially dependent ononeanother.Thatis,isitthecase that distinct tropes standing in the relation in question necessarily exist?Doestheveryresemblanceoftwotropes in this way restrict the contingent existence of each individualtrope?Togiveanexample:iftropesred1,red 2 and red 3 are exactly similar, does this imply that the existenceofeachoneoftheresemblingtropes necessitates , notonlytheexistenceofthe relation ofexactresemblance holdingbetweenthem,butalsotheexistenceofeachone oftheother tropes withwhichitisinfactrelated? 1

Allthesequestionsareansweredwitha‘no’.Thereseemstobeno reasonwhyoneredtropeshouldnecessitateanotherredtrope.The sameholdswithregardtoallothertropesrelatedbyexactresemb lance. However this relation is regarded, the relata of each exact resemblancepairshouldbeexistentiallyindependentofeachother. What about the three other determinations of exact resemb lance?Sincetropesarenotentitieswhicharenormallythoughtof,but ordinarythingsare, Maurinstartswith ordinarythings.Afterintuit tionshavebeentestedonthem,shewillmoveontotropes.

Thefirstthingwecanaskourselvesiswhetherthesevery objects[i.e.,theexactlyresemblingconcreteparticulars a and b] could have existed without exactly resembling one another.Wecanask,thatis:istheexactresemblanceof a and bessentialtotheidentityif aand b?Ithinkthatthe answer to this question is quite obviously ‘no’. Imagine thatthetwoobjectschange,i.e.,imaginethattheyarestill aand b,thattheyretaintheirrespectiveselfidentity,but thattheyarenowdifferent.Theyhaveeachperhapslostor gainedsomeoftheirproperties.Itisquitepossible,given this change in circumstance, that they no longer exactly resemble one another. It is possible for a and b to exist withoutbeingrelatedbyexactresemblance. aand bare not necessarily related by exact resemblance, and so exact resemblanceisnotessentialtotheidentityof aand b.But 1Maurin2002,p.92. EXAMINATIONOFMAURIN’SONTOLOGY117

let us go back a moment in time when the object in fact exactlyresembledoneanother.Althoughwehavealready decidedthattheobjectsarenotnecessarilyrelatedbyexact resemblance,thereisasenseinwhich at that very moment in time theyhadtoexactlyresembleoneanother.So: granted the way the objects are at a given moment of time ,iftheyexactly resemble one another, then they — the objects in that particular state —couldnothavebeenthesame(i.e.could nothavebeen in that same particular state )andyetnotexactly resemble one another. But does this mean that exact resemblancebothisandisnotarelationthatisessentialto theidentityof aand b?Ithinknot.Exactresemblanceis, inthiscase, founded in aand b(at t),butitisnotessentialto the identity of a and b, since a and b may change, may ceasetoresemble,andyetcontinuetoexist.InCampbell’s terms,itseemsthatexactresemblanceisexternal/founded withrespecttotheconcreteparticulars aand b.1

Hereweseeareviewoftheremainingdeterminations.Theideathat the concrete particulars a and b exactly resemble each other is not essential to either of them. The reason is that either of them can changeandstillbeitself,eventhoughtheexactresemblancebetween themnolongerholds.Anotherwayofsayingthisis in terms of a relational property that has exact resemblance as its relational part: theidentityof aisnotdependentonitsbeingexactlysimilarto b.The sameofcourseholds, mutatis mutandis ,for b. The exact resemblance between concrete particulars is not consideredinternalinCampbell’ssenseeither.Thereasonforthatis thatitsfoundationisnotexclusivelytheidentitydeterminingpartsof the natures of its relata. It seems to be taken for granted here that thereisnoconcreteparticularwhosequalitativecontentisexhausted bywhatisessentialtoitsidentity. This brings us to the conclusion that an exact resemblance which is held between concrete particulars is, in Campbell’s sense, external and founded. Although Maurin does not mention it, I wonderabouttheexactresemblanceholdingbetweentwoveryshort 1Maurin2002,pp.923. 118CHAPTERIII lived,infactinstantaneousentities,butcomplexentities.Woulditbe internal in Campbell’s sense? I suppose the answer depends on whethertheshortlifespanisaccidentaloressential.

3.3.5 Internal Relations between Tropes Afterhavingtrimmedherintuitionsonconcreteparticulars,Maurin goesontotheresemblancesthatholdbetweentropes.

Tropes[…]arenothingbuttheirnatureandtheirnature —which,incidentally,they‘are’anddonotmerely‘have’ — is simple. For a trope, […] it would, given this characterisationofwhatitistobeatrope,be impossible to havebeendifferent.Forifatrope a1weretochange,the trope emerging from this change would not be a1. As tropesarenothingbuttheirparticularnaturetheycannot change. They can only begin and cease to exist (and perhapsmovethroughspaceandtime,butthatisatopic foranotherdiscussion).Consequently,iftropes a1 and a2 exactlyresembleoneanother, it is impossible for them (these very tropes) not to be related by exact resemblance. For tropes,therefore,exactresemblanceappearstobea founded relationthatis essential to the identity of its related terms .Infact, forthespecialcaseoftropes,sayingofarelationthatitis foundedinthetropesitrelatesandsayingofitthatitis essential to the identity of the tropes it relates will necessarilyamounttothesamething. 1

Judgingfromtheactualwordingofthelastsentenceitseemstobe essential to the identities of tropes that they resemble certain other tropes. This would mean that if one of them ceases to exist, that affectstheidentityoftheothertropes.However,Idonotthinkthat this is the considered view. Instead, the notion is that since tropes cannot be different from what they are, the resemblances holding betweenthemareduetotheiressences.ThisisinternalityinCamp bell’ssense.

1Maurin2002,p.93. EXAMINATIONOFMAURIN’SONTOLOGY119

The purpose of making a modal characterisation of exact resemblanceistogaininsightsforsuccessfullymaking an adequate ontological characterisation of it. Three attempts at such an onto logicalcharacterisationarediscussed.Althoughnodecisiveargument infavourofanyoneinparticularisoffered,Maurinprefersthethird alternative. 1Accordingtothethirdalternative,exactresemblanceisa pseudoaddition to the basic trope theoretical scheme. The term ‘pseudoaddition’ indicates that exact resemblance is nonexistent. Thisofcoursegivescauseforacomment.

Although the invocation of ‘unreal’ additions to solve philosophicalproblemsmayseemnothingshortofmagic, Iwilltrytoshowthatthislastresortisnotasdesperateas itmayinitiallyseem.Itisthealreadyestablishedinternality of exact resemblance that makes the move to ‘pseudo additions’ not only acceptable but attractive to the trope theorist. 2

InwhatfollowsIwilldiscussthefirstandthethirdaccountsbutskip thesecondone. 3 According to the first account, exact resemblance is an un derivedrelation.Theintroductionofitreads:

Anunderivedrelationisanentity‘initsownright’,i.e.the kind of entity that needs to be given a place of its own within the basic metaphysical scheme. The metaphysical scheme so far considered contains tropes and nothing else. 4

Sincetheprojectistoinvestigatewhetheraonecategoryontologyof tropesissufficientlyrichtoaccountforwhatneedstobeaccounted for,exactresemblanceshouldalsobeatrope,giventhatitisanentity initsownright.Twopotentiallyseriousobjectionsagainstitsbeinga tropearediscerned.Bothtaketheformofregresses. 1Cf.Maurin2002,p.94. 2Maurin2002,p.94. 3Ittakesexactresemblancetobeanonrelationaltie. 4Maurin2002,p.94. 120CHAPTERIII

The first regress is the socalled ‘Bradley’s regress’. 1 It targets theconnectionbetweenexactsimilarityanditsrelata.

The idea is now that the exact resemblance which thus unifies tropes that are ‘the same’ is, in turn, to be onto logically characterised as yet another trope. For exactly similar tropes a1 and a2,theirexactsimilarityis,inother words,accountedforbythepostulationofanothertrope, r1,holdingbetween a1and a2.Butiftheunionoftropes a1 and a2requires r1,whataccountsfortheunionoftropes a1, a2 and r1? If the answer to the question is of what unified a1and a2was r1,whyshouldnottheanswertothe questionofwhatunifies a1, a2and r1beyetanothertrope r2? Yet conceding this, it seems that we embark on an endlessregress[…],andthisseemstostandinthewayof 2 ourever really connectingtheoriginal a1and a2.

Thisregressmightbeathreattoanyrelationwhichisanentityinits own right. In Maurin’s proposal of how to solve the problem of thingconstruction,therelationofcompresenceisthekeynotion.As itwillturnout,sheconsidersittobeanentityinitsownrightand, forthatreason,wantstodealwiththisargumentinconnectionwith theproblemofthingconstruction.Iwillagreewithherinthatand simplygoon. Atthispoint,wewilltakealookontheotherregressargument. The source of it is Bertrand Russell. He intended it to show that

1Despiteitsentrenchedname,Bradleyisnottheinventorordiscovererof thisregress.AversionofitcanbefoundinAristotle,whousesittoshowthe necessity of form as an organising constituent of a whole. Cf. Metaphysics , 1041b11ff.TheregressisalsopleadedbytheearlymediaevalMuslimschool Mutakallimun,accordingtowhichitshowsthenotionof(polyadic)relation tobeincoherent.Inexplicitoppositiontothis,Avicennamaintainsthatthe infinite line of relations is purely conceptual. Things are of course compli catedbyhisreductionistviewonpolyadicunitrelations.Cf.Avicenna1495, tractiii,chap.10.Cf.alsoWeinberg1965,pp.78,8993,andMertz1996,pp. 1324. 2Maurin2002,pp.956. EXAMINATIONOFMAURIN’SONTOLOGY121 particulars are not enough for constructing properties. Versions of theargumentarefoundinseveralofhisworks. 1

[W]eexplainthelikenessoftwotermsasconsistinginthe likenesswhichtheirlikenessbearstothelikeness oftwo otherterms,andsucharegressisplainlyvicious.2

Accordingtotheviewagainstwhichtheargumentisdirected,entities have their properties due to their being similar to each other. For example,alltheentitieswhichareblueresembleeachotherandthat iswhytheyareblue,nottheotherwayround.Sincenouniversalsare recognised, the resemblances themselves are particulars. But, what about the resemblances which exist between pairs of blue things? Well,theirpotencyisduetotheirresemblingeachother.Thus,there mustbeyetanothersetofparticularresemblancesthatholdbetween resemblances. The original question reappears though, calling for a third set of particular resemblances. The pattern is then that to explain the unity of the resemblances holding on the nth level, resemblancesholdingonthe n+1 th levelmustbepostulated. TheregressRussell hasinviewcan bedescribedas analytical . Analytical regresses are vicious. There is also a virtuous kind of regress.Regressesofthelatterkindare implicative .Thesecharacterisa tionsareinspiredbyRussell,whoinoneofhisworkswrites:

Aninfiniteregressmaybeoftwokinds.Intheobjection ablekind,twoormorepropositionsjointoconstitutethe meaning ofsomeproposition;oftheseconstituents,thereis oneatleastwhosemeaningissimilarlycompounded;and soon ad infinitum .Thisformofregresscommonlyresults from circular definitions. Such definitions may be ex pandedinamanneranaloguestothatinwhichcontinued fractions are developed from quadratic equations. But at everystagethetermtobedefinedwillreappear,and no definition will result. Take for example the following: “Twopeoplearesaidtohavethe same ideawhentheyhave 1 Cf. for example Russell 1912, p. 55. The argument is also found in Mill 1843,p.117n. 2Russell1911,p.9. 122CHAPTERIII

ideas which are similar; and ideas are similar when they containanidenticalpart.”Ifanideamayhaveapartwhich isnotanidea,suchadefinitionisnotlogicallyobjection able;butifpartofanideaisanidea,then,inthesecond placewhereidentityofideasoccurs,thedefinitionmustbe substituted; and so on. Thus wherever the meaning of a propositionisinquestion,aninfiniteregressisobjection able, since we never reach a proposition which has a definite meaning. But many infinite regresses are not of this form. If A be a proposition whose meaning is perfectlydefinite,and Aimplies B, Bimplies C,andsoon, wehaveaninfiniteregressofaquiteunobjectionablekind. Thisdependsuponthefactthatimplicationisasynthetic relation, and that, although, if A be an aggregate of propositions, A implies any proposition which is part of A,itbynomeansfollowsthatanypropositionwhich A impliesispartof A.Thusthereisnologicalnecessity,as there was in the previous case, to complete the infinite regressbefore Aacquiresameaning. 1

Here, the regresses mentioned concern meaning. In the case of the resemblance regress meaning is not the issue though. According to Maurinitconcerns existence instead.Therefore,shecharacterisesthe differencebetweenviciousandvirtuousregressesintermsofexisten tialdependence.

Aregressis(modified)Russellvirtuousifthe‘later’terms in the regresshierarchy depend for their existence on the existenceofits‘earlier’terms. Aregressis(modified)Russellviciousifthe‘earlier’terms of the regresshierarchy cannot exist unless the ‘later’ termsoftheregresshierarchyexist.Thatis,itisviciousif the ‘earlier’ terms depend for their existence on the ‘later’ terms. 2

1Russell1903,pp.3489. 2Maurin2002,p.101. EXAMINATIONOFMAURIN’SONTOLOGY123

WhileamodifiedRussellvirtuousregressisimplicative, a modified Russellviciousregressisanalytic.Ifwereturntothequotationfrom Russell1911,itlooksasiftheearlierresemblancesneedthelaterones inordertofulfiltheirtask.Thelaterones,inturn,needtheevenlater onesinordertofulfiltheirtask,etc.Itwouldappearthereforethat earlier resemblances are existentially dependent on the later ones. Though,thisisnotMaurin’sviewofthematteroftropes.

Is the resemblance regress vicious in this modified Russellian sense? To answer this question we need to invokethealreadyestablishedinternalityofexactresemb lance.Onthepresentaccount,simplygiventheexistence oftropesa1and a2,theirexactresemblance, r1,mustfollow necessarily.Exactresemblanceisaninternalrelation,and this means that it is strongly existentially dependent on the existenceofthatwhichitrelates.Giventheexistence of theexactresemblancetrope r1,moreover, its exactresemb lance to other exact resemblancetropes must likewise followbynecessity;andsoon.Fromtheinternalityofthe exact resemblance relation it seems to follow, to use Russellianterms,thattheearliertermsoftheregress imply the later terms — they do not presuppose them. On a modifiedversionoftheRusselliandistinctionputinterms of‘directionofexistentialdependence’,therefore,thereis reasontothinkthatthe metaphysical regressofresemblance is not vicious.Thisisgoodnewsforanyonewhowishesto characteriseexactresemblanceontologicallyasunderived relation. 1 a1 a2 a3 Inthefigureabove,everylinerepresentsaresemblancetropewhich is holding between what is at its ends. The line between a1 and a2

1Maurin2002,pp.1012. 124CHAPTERIII

represents r1;thelinebetween a1and a3representsyetanotherexact resemblance trope, r2; the line between r1 and r2 represents a third 1 resemblancetrope r3;etc. Thereisaninfinitenumberoftrianglesin sidethefirstone. Iftheregressisimplicative,theremustbesomethingatthestart which implies what comes later. Remember that Maurin’s charac terisationoftropesisthattheyaresimple,abstractparticulars.Here ‘abstract’hasthesenseof‘qualitative’.Thisgivesahintofwhyshe considers the regress to be implicative, instead of analytical. The abstractness of tropes is no doubt taken as a pretext for that. The pointofdepartureforRussell’sregressargument,ifappliedtotropes, isthatresemblancetropesarewhatfurnishtheirrelatawithqualita tive content. That premise is denied by Maurin. It is incompatible withtheassumptionsof(her)tropetheory. Weknowfromanearlierquotationthatresemblanceisassumed to be objective as well as primitive. In the present context, where Russell’sregressargumentisclaimedto beabortive if used against trope theory, what does this primitiveness amount to? Since the resemblance which holds between two relata allegedly is strongly existentially dependent on the two latter ones, does not that imply thattheformerisnonprimitiveinarelevantsense?Andwhatabout itsownqualitativecontent,isitnotdependentontherelata?Afterall, aresemblancetropeholdingbetweenapairofbluetropesisitnot qualitatively different from a resemblance trope between a pair of redtropes?Or,evenmoreso,fromaresemblancetropewhichholds betweenapairofsquaretropes? 2Thedifferenceswillbereproduced astheimplicativeregresspropagates,willtheynot?

1AfarasIknow,thisfigureoriginatesfromKüng1967,p.69. 2Cf.Campbell1990,p.72,wherethisseemstobedenied: [T]heonlydifference(apartfromirrelevanceslikeplaceandtime) between an exactly resembling pair of reds and an exactly resembling pair of greens lies in the fact that the first pair are reds and the second greens. The resemblings do not have any addeddistinguishingcharacter. EXAMINATIONOFMAURIN’SONTOLOGY125

Perhaps the resemblance regress is analytical after all? The nearestanadmissionofthatMaurincomesisinhersummaryofthe resultsofthediscussionaboutthefirstproposal.Shesays:

[A]s long as the exact resemblance between tropes is founded on the existence of yet another (resemblance) trope,we will havetoacceptsomekindofendlessregress, inthisRussellwassurelyright.Yetastheregressinques tion will be of what I call a ‘metaphysical’ kind, the viciousnessoftheregressremainsanopenquestion.Ifthe regressisimpossible,thenobviouslyyes,theresemblance regresswillbevicious.Butif,instead,itisthe‘directionof existentialdependence’ofthenecessarilyinducedresemb lances which turns out to be what decides whether the regressisviciousornot,thenperhaps,no,wedonothave toregardtheregressasvicious. 1

Whatthefirstsentencedescribesisaregresspatternoftheanalytical kind since an exact resemblance trope is said to be founded on another exact resemblance trope. In an implicative regress this description does not apply to the first exact resemblance trope. Whetherornottheregressismetaphysical 2doesnotchangethat. In the last sentence of the above quotation the regress is no longerconsideredtobeanalytical.Beforethathappens,areferenceis madetoimpossibilityasacriterionofviciousness.Itishintedatin thesecondparagraphofthefollowingquotationfromKüng1967.

[T]he concrete relations [i.e., relation tropes], which are “thesame”inasmuchastheyareallequalityrelations,must alsoberelatedtooneanother—probablybyanequality relationofhigherorder;andwecancontinueaskingabout the status of this equality of higher order; and so on in infinitum .[…] Thenominalists,especially,whoregardwithsuspicion the “teaming” infinity of abstract entities, will be very

1Maurin2002,p.103. 2Itakeitthatitsbeingmetaphysicalinkindmeansthatitconcernsexistence, notmeaning.Cf.Maurin2002,pp.1001. 126CHAPTERIII

reluctant to end up in this way with another infinity of concreteentities.However,itseemsnotatallimpossible that our concrete world should include an infinity of concreteentitiesofdifferentlevels,aninfinitywhichour limitedintellectwillneverbeabletoexhaustexplicitly. 1

WhenKüngtalksaboutequality,wecaninterpretitasbeingonapar with exact resemblance. The phrase ‘and we can continue asking aboutthestatusofthisequalityofhigherorder’indicatesthatKüngis referringtoananalyticalregress. 2Theregressinquestion wouldbe impossibleifourconcreteworldcouldnotincludeaninfinitenumber of concrete entities. Among the concrete entities are the tropes. 3 Evidently,theconcreteworldcanincludeaninfinitenumberofsuch entities.Küngconsidersaninfinitenumberofthemtobeenoughto fulfil the needs. What he misses, though, is that the point of the

1Küng1967,p.168. 2InsupportofthisKüng1967,pp.689,canbequoted: InRussell’sviewidenticallythesameentitymustcorrespondto thisword[i.e.,‘similar’,whichisshortfor‘exactlysimilar’]inall instances,i.e.,theentitymustbeaplatonisticuniversal.Hisargu mentisthatotherwiseaninfiniteregresswouldresult.Suppose […]thatitistrueofindividuals a, b,and c,thataand baresimilar to one another, that b and c are similar to one another. If the word‘similar’doesnotstandforidenticallythesameentityinall threeinstances,butforthreenumericallydifferententities,then theremustbeanotherreasonwhythesameword‘similar’isused inallthreeinstances.Itmustbebecausethesethreenumerically different relational entities designated by the word ‘similar’ are somehow similar to one another. Indescribing how these rela tionalentitiesaresimilartooneanotherweagainusetheword ‘similar’severaltimes.(Orperhapsinplaceof‘similar’wemight use‘similar 2’,sincewearetalkingnowofasimilarityofahigher order.) And again in all these new instances either the word ‘similar’ (i.e., ‘similar 2’) stands for identically the same entity, namelyforaplatonisticuniversal,orelseitstandsfornumerically differententities,i.e.,forentitieswhichinturnhavetobesimilar (similar 3)tooneanother;andsoon ad infinitum . Thereisnodoubtthattheregressdescribedhereisanalyticalinnature. 3Küng’stropelikeentitiesareconcrete,whichmeansthattheyexistinspace andtime. EXAMINATIONOFMAURIN’SONTOLOGY127

(analytical)regressargumentisthattherewillnotbeenoughofthem forallthat. Aspointedoutaboveinthelastsentenceofthequotationfrom thesummary,Maurintakestheregresstobeimplicative.Differently put, the direction of existential dependence is supposed to occur from right to left, which means that the entities totheleftarethe existentialgroundfortheentitiestotheright. The first proposal, which is that exact resemblance occurs as tropes,isrejectedbyMaurinthough.Whyisthat?Campbellseemsto provideherwiththereason.Toseewhatthisreasonis,afragmentof hisargumentationisaccountedfor. The things Campbell asserts regarding regress arguments has bearingonlyontheimplicativekind.

Russell’sargument 1wasthat,toreverttoKüng’sdiagram, 2 a, b and c are certainly particulars, but there must be the same resemblance between aand basthereisbetween aand c, since a, band careall, ex hypothesi ,ofjustthesameshadeof red. But then if we have the same resemblance between these two pairs of items, this is a multiplyinstantiated entity,inshort,auniversal. Theonlyreplythiscallsforisstrongmindedness.We mustrejecttheclaimthat,inthesensethatmatters,there isthesameresemblancebetween aand band between a and c. These are two different, but very similar, even exactly similar, resemblances. And the resemblances be tweentheresemblancesarelikewisematchingparticulars, notuniversals.InKüng’sregress,theitemsareparticulars all the way down .Ifweinsistonthis,thenRussell’sobjection canfindnopurchase. 3

Campbell’sstrongmindednesscauseshimtomissthewholepointof the regress argument. All he sees in the regress isitsallegedimpli cativeness and he is completely untroubled by it. This becomes

1HereferstotheversionofRussell1912. 2Küng’sdiagramisthetrianglepresentedearlier. 3Campbell1990,p.38. 128CHAPTERIII apparent when hediscusses whathecalls‘Küng’s objection’.Three reasonsareputforwardtoshowthattheregressisnotvicious.The first one is that “it proceeds in a direction of greater and greater formalityandlessandlesssubstance.” 1 Thesecondreasonisthatrealistsdonotescapeiteither.Letthe first level of resemblances of Küng’s figure be instances of resemblancewithrespecttoredness.Thesethreeinstantiatethesame universal;thereforetheymustresembleeachother. The conclusion drawn from this is: “[I]f the regress is a serious problem for resemblance theory [i.e., Campbell’s own doctrine], the parallel regress of instantiated universals is an equally serious problem for realism.” 2 Thethirdreasonisthat“itis norealtroubleforeither[trope theoryorrealism].” 3Thisissosinceeverythingafterthefirsttrio— a, band cinthelastquotation—followsautomatically.Thisphenol menoniswhathecalls‘supervenience’.Thefollowingisasomewhat contradictorydescriptionofit:

Ontheresemblancetheory,ifresemblanceistrulyprimi tiveandungrounded,theterms d, eand f[whichareexact resemblancetropes] 4willbethestartingpointfromwhich all subsequent supervenient terms flow. If, as this work favours, resemblance is an internal relation grounded in particularnaturesintheterms,thentheredtropes a, band cwillgeneratethewholeedificeofsuperveningresemb lancetriples. Either way, there is a manifestly finite base for this efflorescenceofdependencies.AndItakeitasacardinal principleinontologythat supervenient ‘additions ’ to ontology are pseudo-additions .Nonewbeingisinvolved.IntheCreation metaphor, to bring supervenients into being calls for no

1Campbell1990,p.35. 2Campbell1990,p.36. 3Campbell1990,p.37. 4Onepageearlier—i.e.,inCampbell1990,p.36—thethreeletters‘ d’,‘ e’ and ‘ f’ are used as names of the first three exact resemblance tropes in a diagramàlaKüng. EXAMINATIONOFMAURIN’SONTOLOGY129

separateandadditionalactonGod’spart.LetHimcreate thethreereditems a, band c.That by itself willsufficeto generateKüng’sregress. 1

What supervenes on already recognised entities constitutes no real ontologicalexpansion.Itisanontologicalfreelunch. 2Fromthisitis concluded: “[…] Küng’s regress has no power to damage a theory that proposes to deal with Question B by appeal to resemblance amongtropes.” 3 AlthoughCampbellhimselfseemssatisfiedwiththisrejectionof whathetakestobetheregressargument,Maurinisnot.Thisisher judgementonit:

Is the regress that follows from regarding exact resemb lance as yet another trope vicious or virtuous given Campbell’stakeonthedistinction?Itisobviouslyvicious. Itcrowdstheworldwithaninfinitenumberofnecessarily incurred and idle, yet ‘substantial’, tropes. It is therefore, on the present view, unacceptable. Given Campbell’s distinction,then,thestrategythatconsistsinacceptingthe regressbutdenyingthatitisviciouswillnotwork,andso we should give up our attempt at characterising exact resemblanceontologicallyasyetanothertrope. 4

Thus,thepresumptionisthattheworldwillbeoverpopulatedwith entities if exact resemblance is supposed to exist as an underived relation — i.e., as tropes. This is a misleading way of describing Campbell’sviewthough.Ineffect,hehasthesameviewasMaurin. Thiswillbemadeevidentbelow.

3.3.6 The Preferred Account of Internal Relations between Tropes TheontologicalcharacterisationofexactresemblancewhichMaurin findsmostattractiveissuggestedlikethis: 1Campbell1990,p.37. 2Notethatnonewdishwillbeserved. 3Campbell1990,p.37. 4Maurin2002,pp.1023. 130CHAPTERIII

Thealternativeaccordingtowhichexactresemblancecan be ontologically characterised as a pseudoaddition rests ontheadoptionofcertainprinciplesconcerningwhenand wheretheexistenceofanentity must beassumedandwhen and where it must not. The proposal has the following generalform: (i) Atomic propositions of the form ‘ a and b are the sameF’(where aand baretropes)aremadetrueby equivalenceclassesoftropes. (ii) Two tropesbelongtothesameequivalenceclass if theyexactlyresembleoneanother. (iii) Two tropes exactly resemble one another because theyarethewaytheyare(i.e. aand bexactlyresemble oneanotherbecause aistheway ais,and bistheway bis). (iv) aistheway aisbecause aexists(i.e. ais‘nothingbut’ itsparticularnature),andthesamegoesfor b. (v) Therefore,propositionsoftheform‘ aand barethe same F’ merely require the existence of a and b to providefortheirtruth. 1

This looks very much like Campbell’s doctrine; he even uses the phrase‘pseudoadditions’whencharacterisingsupervenienttropes,of which resemblance tropes are examples. He makes the elucidatory remarkthatnonewbeingisinvolved.Itsoundsperhapsabitpara doxicaltocharacterisethesepseudoadditionsasparticulars. AccordingtoMaurinitisunnecessarytoaddexactresemblance tropes to the metaphysical scheme of trope theory. Judging from whatshesaysinoneplace,thismeansthatsuchtropesareunreal.2In thenextquotationtheyareexplicitlysaidnottoexist.Ontologically they can be characterised as being nothing at all. Two sources of justificationsforthisarefound.Oneoftheseisthe internal character ofexactresemblance.Sheexpressesthisviewinthefollowing,some whatparadoxical,way.

1Maurin2002,p.109. 2Cf.Maurin2002,p.94. EXAMINATIONOFMAURIN’SONTOLOGY131

If the exact resemblance between distinct tropes can obtain without the addition of some relation of exact resemblance,itbecomesimportantthatthemereexistence oftherelatedtropes necessitate theirexactresemblance.But thisisjustwhatwehavetakenittomeantosayofexact resemblancethatitisinternal. 1

Maurin does not want to use the term ‘supervenience’. Her stated reasonisthatitisusedinmanyothersenses.Therefore,shethinksit issafertousetermssuchas‘internal’,‘pseudoadditional’ or ‘non additional’. The other source of justification used is Ockham’s razor in combinationwiththegoalofmakingmetaphysicaltheoriesaselegant and simple as one possibly can. These constitute guidelines for any metaphysicaltheory.

Even if the fact that exact resemblance is necessarily incurred given the mere existence of the related entities doesnotforceyoutotreatitasapseudoadditionrather thanasarealandsubstantial addition, thiscircumstance together withtheabovelistedguidelinesdoesmoreorless prescribesotreatingit. 2

I take it that elegance and Ockham’s razor together demand that anything which is considered not necessary should be shaved off. Furthermore,theallegedpseudoadditional“nature”ofexactresemb lancefitsperfectlywhensolvingthesocalledBradley’sregress.

Thatregressensuesbecauserelationsconsideredasentities intheirownrightarejustasdistinctfromthatwhichthey relateastheentitiestheyaremeanttorelateare distinct from each other. Pseudoadditions can hardly be said to be,inthesameway,distinguishablefromthatwhichthey relate.Infactthebasicideaisthat,existentiallyspeaking, theyare nothing but thatwhichtheyrelate.Andiftheyare nothingbutthatwhichtheyrelate—atleast,iftheyare

1Maurin2002,p.110. 2Maurin2002,p.110. 132CHAPTERIII

only a pseudo addition to that which they relate — there seems to be no reason to require that they be, in turn, relatedtothatwhichtheyrelate. 1

Themessageexpressedhereis:thatwhichisnothinginitselfneeds notreallyberelatedtothatwhichitjustseeminglyrelates. Whatabouttheotherregress,theonereferredtoRussell?Itis supposedtobesolvedineitheroftwoways.(i)Iftheexistenceofthe infinitenumberofexactresemblancetropesistakenasproblematic, the pseudoadditional nature of these solves it, since there is no infinitenumberofsuchtropes.Infact,thereisnotevenasingleone. (ii)Iftheontologicalstatusofthatwhichisnecessarilyinducedisnot consideredtobeimportant,whatisimportantisinsteadthenecessita ting;itisassertedregardingthelatter:

[P]erhapsevenonthisalternativetherewillbearegress(a regressof‘pseudoadditional’exactresemblances).Butthe problem with the resemblance regress, one might argue, will nevertheless be solved, since we can now claim that this regress is not vicious. For, surely, a regress of non existent,pseudoadditionalrelationsisextremelyinnocent and,therefore,obviouslyvirtuous. 2

ChrisDalyobjectstotheclaimthatsomethingwhichisinternalwith regard to something else is only pseudoadditional. Why could the exactresemblancewhichisnecessitatedbytworelatanotbeanontic addition to them? Maurin admits that they may very well be so. Though,inreferencetotheguidelinesmentionedearliershebelieves that supervenient 3 additions need not be postulated. Everything which needs to be accounted for can allegedly be accounted for withoutincludingtheseentitiesinthebasicmetaphysicalscheme.Her lastwordonthisissueseemstobe:

Yet, ultimately, whether or not one accepts that this is enough to justify a refusal to treat exact resemblance as 1Maurin2002,p.111. 2Maurin2002,p.111. 3Sheusesthetermherselfinthiscontext. EXAMINATIONOFMAURIN’SONTOLOGY133

real boils down to faith. In truth, no knockdown argu mentfor(oragainst)thisrefusalexists. 1

Idaresaythatthereareatleastindiciaagainstconsideringresemb lance to be pseudoadditional. This is shown by a remark on the alleged importance of strictly distinguishing between the A and B questions. Maurin is emphatic about the A and Bquestions not havingparallelanswers.Accordingtowhatshereferstoasclassical theoriesofproperties,theyhaveparallelanswers.Tropetheory,orat leastMaurin’sversion ofit,isnotincluded.Irepeatwhathasbeen saidregardingthedistinctionbetweenthetwoquestions.

Since tropes are inherently particular that which explains why,orsaysinvirtueofwhat,oneredobjectisredcannot bestrictlythesameasthatwhichexplainswhy,orsaysin virtue of what, another object is also red. Given trope theory,eachparticularredobjectisredinvirtueofits very own particular redtrope. It is this circumstance which moreorlessforcesthetropetheoristtodistinguishclearly between thequestion ofwhatmakesittruethat ‘ a is F’ andthequestionofwhatmakesittruethat‘ aand barethe same F’. To answer the latter (i.e. the Bquestion) the existenceofdistincttropes—onebelongingto aandone belongingto b —issurelyrequired,butitisnotenough. AnadequateanswertotheBquestionalsorequiressome accountofthespecialrelationinwhichthesetwotropes stand—somethingthatisnotrequiredifthequestionis oftheAtype.InthiswaythedistinctionbetweentheA andBquestionishighlyrelevantbytheverystructureof tropetheory. 2

Now,whataretheanswerstotheAandBquestions respectively, accordingtoMaurin’stropetheory?Althoughtheobjectsreferredto in this quotation are not tropes, the two questions are particularly relevant with regard to tropes. In fact, the questions asked with regard to tropes are thought of as being the fundamental ones. 1Maurin2002,p.113. 2Maurin2002,p.63. 134CHAPTERIII

Rememberalsothat‘thesame’,accordingtoMaurin,canhaveeither oftwosenses.Oneoftheseisaccountedforintermsofnumerical identity, the other in terms of exact resemblance. Thus, the B questioncanberenderedintwoways:

B1.Whatmakesittruethat‘ aand barenumericallyidenticalFs’? B2.Whatmakesittruethat‘ aand bareexactlyresemblingFs’?

TheAquestionremains:

A.Whatmakesittruethat‘ aisF’?

Theanswertothelastquestion,questionA,is: a.Morestrictly:the existenceof a.Theanswertothefirstquestion,questionB1,would seemtobe:nothing,since aand barenotnumericallyidentical.The strictanswertothesecondquestion,questionB2,wouldseemtobe: theexistenceof aand b.Accordingtothepreferredaccountof“the special relation in which these two tropes stand” the relation is pseudoadditional to its relata. This makes it numerically identical withthepairofaand b.Initselfitisnotanincreaseofbeing. 1 Ingenuineresemblancetheorytheexactresemblancerelations arenotjustincreases of being,theyarewhat provide entities with their qualitative contents. Thus, one exact resemblance relation is needed per quality. The same of course holds mutatis mutandis for relations.AlthoughMaurindeclaresexactresemblancetobeneeded asapartofanadequatetropetheory,shedoesnotgiveittheroleit shouldhaveinagenuineresemblancetheory. 2

1Thatresemblanceinitselfdoesnotmakeanycontributiontotruthmaking iscommentedoninMaurin2005,p.23: Tomaketrue‘ aand barebothred’theexistenceof aand bis required.Fromtheirexistence,theirresemblancefollowsnecess arily—andsowillnotmakeaseparatecontributiontotruth. Thisseemstoconfirmthattheclassofalltropesexactlyresembling aand bis irrelevantforansweringtheBquestion.Ifanyclassatallisrelevantitisthat having aand basitsonlyelements.Theexpression‘increaseofbeing’isused inArmstrong1997,p.141.Idonotthinkheistheinventorofitthough. 2 Gonzalo RodriguezPereyra advocates an analytic ontology which he classifiesasaresemblancenominalism.Infact,hisnameforitis‘resemblance EXAMINATIONOFMAURIN’SONTOLOGY135

Ifacertainrelationispseudoadditionaltoitsrelata, it would seem to be identical with another relation which is also pseudo nominalism’.Sincetheonlyparticularsherecognisesareconcreteparticulars, thetheoryisnotamoderatenominalism.Resemblancesbetweenparticulars are said to be what give them their qualitative contents. So far, everything seemstobeinlinewithwhatcanbeexpected.Itturnsoutthoughthatexact resemblance relations in themselves are supposed to be dispensable. The followingiswhatheassertsatthecrucialmoment. Whatthenmakesittruethat aand bresembleeachother?The Resemblance Nominalist’s answer is: just a and b together. In general any two resembling entities x and y (whether they are particularsorordered ntuples)resembleeachotherinvirtueof being xand y.If aand bresembleeachotherthentheirresemb lanceisafactbecauseoftheirbeingtheentitiestheyare,andso a and barethesoleTruthmakersof‘ aand bresembleeachother’. Thereisthennoneedtopostulateextraentitiestoaccountfor facts of resemblance: the resembling entities suffice to account forthem.Andsonoregressofresemblancesarises,sincethere are only resembling particulars and no resemblances at all. (RodriguezPereyra2002,p.115) Dispensingwiththeresemblancerelationsiswhatmakesitpossibleforhim to seemingly avoid Russell’s analytical regress. This move is obviously not availableforhimthough.Itisnotpossibletofoundresemblancesbetween relataontherelatathemselves,ifthelatteraresupposedtohavetheircontent by virtue of that which they found. If it could be done, it would be an ontologicalversionoftheIndianropetrick.Althoughconcreteparticularsare therelataofresemblancerelations,theyareinthemselvesnothingmorethan nodes in resemblance nets. It is its resemblance net which gives each particular its qualitative content. This is confirmed in a footnote in connectionwiththeformerquotation. Notethatthis[i.e.,thatresemblingentitiessufficetoaccountfor factsofresemblance]doesnotmakeResemblanceNominalism collapse into Ostrich Nominalism. According to the latter a is sufficienttomakeittruethat aisscarletwhileaccordingtothe formerotherparticularsarenecessary.Also,accordingtoOstrich Nominalism aand baresufficienttomakeittruethat aisbigger than b,whileaccordingtoResemblanceNominalismotherpairs ofparticularsarenecessary. Here we see that RodriguezPereyra does not allow just one entity to be scarlet;northatthereisjustonepairinwhichthesubjectisbiggerthanthe relatum.Inbothcasestheremustbeotherstoresembleandbyvirtueofthat obtainqualitativecontent. 136CHAPTERIII additionaltothem.Thislineofreasoninghasaffinitywithanobject tionmadebyHerbertHochberg.Heisreportedtohavesaidinone ofhislectures:

[I]f,asseemsprobable,both‘ aand baredistinct’and‘ a and barethesame’ 1(where aand baretropes)areatomic propositions,thenthesepropositionsmust(onthecurrent ‘pseudoaddition view’) have the same truthmakers — namely, aand b.Butthisisimpossible,becausethepropo sitionsinquestionnotonlymeandifferentthingsbutare also logically independent ofoneanother. 2

Maurin’sresponsetothisobjectionistoinvokethreeputativeobser vations.Thefirstoneis:

(1) Giving the truthmaker(s) for a proposition is not as wehaveseenthesameasgivingitsmeaning.There foreitisentirelypossiblethattwopropositionsmight havedifferentmeaningsandyetbemadetruebythe sametruthmaker(s). 3

Hochberg claims though that since the two propositions are atomic , they are also logically independent of each other. This makes it impossible for them to have the same truthmaker(s). In Maurin 2005,theprinciplestipulatingthatlogicallyindependentbasicpropo sitionshavedistincttruthmakersiscalled‘Hochberg’sprinciple’. 4To beabletorejectit,astronger“observation”mustbeinvoked:

1 The two sentences are not supposed to constitute a contradiction. The messageofthefirstisthat aand barenumericallydistinct.Thatofthesecond isthattheyexactlyresembleeachother. 2 The lecture was given at the Philosophical Society in Lund, Sweden, 20.10.1999.ThequotationisfromMaurin2002,pp.1134. 3Maurin2002,p.114. 4Cf.Maurin2005,p.141.Theprincipleisimpliedinthefollowingstatement, madeinHochberg2004,p.39. Letabasicpropositionbeonethatiseitheratomicorthenega tion of an atomic proposition. Then consider tropes t and t* where“tisdifferentfromt*”and“tisexactlysimilartot*”are bothtrue.Assumeyoutakeeither“diversity”or“identity”aspri EXAMINATIONOFMAURIN’SONTOLOGY137

(2) Logicallyindependent,atomicpropositionsmayhave thesametruthmaker(s). 1

As support for this, an authoritative statement of three prominent philosophersissupplied:

We conceive it as in principle possible that one and the sametruthmakermaymaketruesentenceswithdifferent meanings: this happens anyway if we take nonatomic sentences into account, and no arguments occur to us which suggests that this cannot happen for atomic sentences as well. 2

I suspect that the nonatomic sentences referred to here are dis junctive sentences.3 Disjunctions are a bit too special though to be suitedforgeneralisationsinthiscontext. Maurinalsopleadsathird“observation”:

(3) ‘aand barethesame’and‘ aand baredistinct’arenot, andcontrarytothehypothesis, logically independent .4

Hercommentarytothisis:

In other words, they are not both atomic. The relation between the propositions might be something like the following: a could not exactly resemble b unless a and b

mitive.Thenbothpropositionsarebasicpropositions.Butthey arelogicallyindependent.Hencetheycannothavethesametruth makers.Yet,foratropetheoryofthetypeMaurinespouses,they doandmusthavethesametruthmakers.Thusthetheoryfails. 1Maurin2002,p.114. 2Mulligan,Simons&Smith1984,p.300.TheitalicsareMaurin’s. 3Onepageearlierinthesamearticleitisasserted: Thegloryoflogicalwasthatitshowedthatnotevery kindofsentenceneedsitowncharacteristickindoftruthmaker. Providedwecanaccountforthetruthandfalsehoodofatomic sentences, we can dispense with special truthmakers for, e.g., negative,conjunctive,disjunctive,andidentitysentences.(Mulli gan,Simons&Smith1984,p.299) 4Maurin2002,p.114. 138CHAPTERIII

weredistinct.(Thisalsomeansdenyingthattherelationof exactresemblanceisreflexive.) 1

Thesuggestionhereisthat‘ aand barethesame’(i.e.‘ aand bexactly resembleeachother’)implies‘ aand baredistinct’.Thus,atleastthe formerisjustapparentlyatomic. FraserMacBridehaspresentedwhatperhapsisthebestsupport for the thesis that (strict) logical independence is not adequate as a general criterion of independence. He is invoking an exhortation madebyRusselltoallhisfellowontologists.

Russellfamouslyexhortedustomaintaina‘robustsense of reality’ when engaged in ontological enquiry. This attitudeisevidencedherewhenRussellinsiststhatitisthe same“externalfact”thatmakes“ Aisbefore B”and“ Bis afterA”true[…][This]suggeststhatRussell—farfrom being guided by Hochberg’s principle that logically independentstatementsrequiredistincttruthmakers—in fact rejects this conception. For the statement that “ B is after A”nomorelogicallyfollowsfrom“ Aisbefore B” (withouttheaidofanadditionalmeaningpostulate)than “S( b,a)”logicallyfollowsfrom“S( a,b)”. 2

Hochberg’s principle does not distinguish between formal and material(in)dependence.Thisisillustratedbythesentences‘ Bisafter A’and‘ Aisbefore B’. Formally thesetwoarelogicallyindependentof eachother; materially theyarenotthough.Neitherofthemcanbetrue whiletheotheratthesametimeisfalse.Thisis an indication that

1Maurin2002,p.115. 2MacBride2004,p.189.Itmightbethatbynotkeepingapartthenotionsof sentence, proposition and statement respectively, MacBride scores some unmeritedpointsatHochberg’sexpense.Itisobviousthatsentencesmight beinneedofadditionalmeaningpostulates.But,doesthatholdequallyfor statements and propositions? Are they not interpreted per definitionem ? That thestatement(orproposition)“ Bisafter A”followsfromthestatement(or proposition)“ A isbefore B”doesnotseemtodependonany additional inter pretation rule. Such a rule is needed though, mutatis mutandis , for the sen tences‘S( b,a)’and‘S( a,b)’. EXAMINATIONOFMAURIN’SONTOLOGY139

Hochbergneedstoarguefortheassumptionthatsentenceswhichare formallyindependentfromeachotherrequiredistincttruthmakers. There seems to be something to be learnt from what has appeared above. Whether or not one believes that a distinction shouldbemadebetweenbeingformallyandmaterially(in)dependent ofsomethingelse,oneshouldnotconsiderarelation as being no thingbutapseudoadditiontoitsrelata.Since‘pseudoadditionalto’ isanotherwordfor‘numericallyidenticalwith’,aconsequenceofthe doctrine is that the exact resemblance between a and b is identical withthenumericaldistinctnessof aand bsinceidentityistransitive. However,exactresemblanceisnotthesameas numerical distinct ness,evenif‘thesame’isbeingusedinthesenseof‘exactlysimilar’. Thus, the two relations should be recognised as increases of being. This argument can be generalised. If each internal relation holding betweentwotropesispseudoadditionaltotherelata,itmeansthatit is identical to them; since identity is transitive all internal relations whicharepseudoadditionaltothesamepairsofrelataareidentical witheachother.Theonlyresortavailableseemstobetoclaimthat thereisonlyoneinternalrelationper ntupleofrelata.Appliedtothe exampleused,exactresemblance or numericaldistinctnesswouldthen besomethingotherthananonticrelationholdingbetweenitsrelata. Sincetropesareallthereis,onewonderswhatitcouldbe,ifnota trope.

3.3.7 Degrees of Resemblance There is yet another difficulty with considering resemblance to be pseudoadditional.Resemblanceissaidtoexistindegrees.Asregards concreteobjectsthisisexplainedwithreferenceto the tropes they haveascontents.Iftheconcreteobjects o1and o2resembleeachother todegree d,thisisduetotheirhavingcertainnatures,sayN1and N2. These natures are constituted by a number of tropes. However, it seems inaccurate to assert that their having these naturesisidentical withtheirresemblingtodegree d.Ifitwereso,theirresemblingto degree dwouldimplyhavingthenatures N1and N2.Evidently, o1and 140CHAPTERIII

o2mayverywellresembleeachothertodegree dduetoothernatures, 1 say N3and N4. Furthermore,“[e]achtrope[…]resemblescountless others to countless degrees.” 2 Given Maurin’s official determination of sim plicity,thisisnotinitselfincompatiblewiththesimilarityprinciple.3 Givenwhatheractualdeterminationofsimplicityis, it is incompa tiblewiththesameprinciple.Ifthesimilarityprinciplewouldapplyto tropesandtheyareabsolutelysimple,sotospeak,itwouldbeim possibleforthemtoresembleoneanotherotherthanexactlyornot atall.HowdoesMaurinaccountfortheallegedfactthateachtrope resembles countless others to countless degrees, without either of themhavinganytropesasparts?Theexhaustiveanswerseemstobe: shedoesnotaccountforitatall. Inhersummaryoftheresultsnewinformationconcerningthe primitivenessofresemblanceispresented.

We might say that, as long as truthmakers are what interestus,therelationofexactresemblanceis‘reducible’ tothatwhichitrelates.Butitisalsoprimitiveinthesense thatnoeliminativedefinitionofresemblanceisavailable. 4 Treatingexactresemblanceasprimitiveinthislattersense meanshavingtoacceptahostofformalcharacteristicsas indefinable. 5

Theformalcharacteristicsreferredtoherearesuchasthesymmetry andtransitivenessofexactresemblance.Iwonder,arethesecharac teristics secondorder tropes? If they are, it would appear that that theyaresecondordertropes.Sincetherearenointernalrelations,in

1 A precondition for this is that the concrete objects o1 and o2 can change propertiesovertime.Iftheyarelikeotherconcreteobjects,theycan.Thisis partofMaurin’sfifththingconstitutivefeature.Cf.section3.3.3. 2Maurin2002,p.80. 3Cf.chapterII,section2.3.2. 4Cf.Campbell1990,p.38,whereitisalsoassertedthatthereisnoelimina tivedefinitionofresemblance,thoughnohintisgivenofwhatismeantby that. 5Maurin2002,p.115. EXAMINATIONOFMAURIN’SONTOLOGY141 the sense of entities in their own right, these characteristics must belong to ntuples of relata. Presumably, they are not pseudoaddi tionaltothelatter. Maurinpointsoutanotheraspectoftropetheorywithregardto exactresemblance:

Interestingly enough, the pseudoadditional approach to exactresemblancecanberegardedasavariantoftheclass primitivist and Stoutinspired account with which our investigation began 1 […]. Stout was right, it seems, in claiming that universalisations were made true by ‘brute’ classes, but he failed to account for the fact that these classes were ‘brute necessities’ rather than ‘brute contin gencies’. By taking a detour over exact resemblance the relevant classes grounding universalisation can now be distinguishedfromtherest.Notjustanyclassescanserve as a truthmaker for universalisations: the job requires classesformedbyinevitablenecessitygiventhemere(and contingent)existenceoftheirmembertropes. 2

WhileinMaurin’sontologyresemblingisprimarytobeinganelement ofasimilarityset,itistheotherwayroundinStout’s.Intheformer ontology, resemblance, in turn, is secondary to the natures of its relata.IsupposethatisthecasealsoinStout.Adifferencebetween them though is that, according to Maurin, these natures necessitate certainsets,whicharedescribedasbrutenecessities.Sincebelonging toasetiswhatgivestropestheirnature,inStout’sview,setscannot benecessitatedbythenaturesoftheirelements.Isupposethisiswhy Maurindescribesthemasbeingbrutecontingencies. It is part of the assumptions made by Maurin that there are tropes which are simple, abstract and particular. If either of these traits is taken away, she claims that trope theory will not be an alternativetootherontologies.Though,Iwouldsaythattoassume awaytheproblemswhichareblockedbypostulatingabstractness asa primitive is to misconstrue the subject of ontology. Given that

1ThispartofthediscussioninMaurin2002hasnotbeendealtwithhere. 2Maurin2002,p.116. 142CHAPTERIII postulation,Russell’sanalyticalregresswithregardtoexactresemb lanceiswavedaside.Notethattheimplicativeregressisalsowaved aside.Thisisdonebymeansofdeclaringinternalrelations,including exactresemblance,pseudoadditional.Whilethatmighttakecareof theregress,itmakesexactresemblanceimpotenttoperformanyreal work. It is instead the abstractness of tropes which supposedly performsallthework.

3.4TheProblemofThingConstructionanditsSolution

3.4.1 Overview In spite of the heading of section 3.4, the problem of thingcon structionanditssolutionarenotreallydealtwith.Whatisdealtwith is the external relation of compresence. Maurin takes it to be the fundamentalrelationtostartwith,whenattemptingasolutionofthe problemofthingconstruction. There is a problem or argument, named after F. H. Bradley, which is supposed to constitute a major obstacle for anyone who recognises external relations. Since the relation of compresence is a keynotionofherontologicaledifice,Maurinisanxious torebutit. Howthatisdoneisdiscussedinsection4.4.4.

3.4.2 The Problem of Thing-Construction One problem of thingconstruction is of constructing concrete particulars from tropes. This is obvious enough. Another is the followingone:

Thereasonthings needtobe constructedfromtropesis thattheexistenceofthingsseemstoberequiredforitto bepossibletoaccountforthetruthofcertainatomicpro positions.Therearecases,thatis,forwhichtropescannot (atleastnot prima facie )fulfiltheirtruthmakingroleunless EXAMINATIONOFMAURIN’SONTOLOGY143

they are in some sense of the word ‘structured’ so as to constitute‘whole’concretethings. 1

Ifordinarythingsarenottobepostulatedasafundamentalcategory, itmustbeconstructedfromtropes;tropebeingthesinglefundamen talcategoryoftropetheory. Theproblemsstatedaredifficultonesbecauseitisnotaseasy to spell out exactly what a thing is as it may initially seem to be. Maurinenumeratesfivefeaturesofwhatitisto be a thing. These featuresatmostareintendedtobenecessaryforbeingathing,but arenotthoughtofasbeingjointlysufficient.Althoughthelistdoes notsupplyuswithasufficientconditionofthinghood,itisintended tobeayardstickagainst whichproposals ofwhatathingiscanbe measured. Thefirstfeatureisthatthingsareparticular:“[j]ustlikeatrope, athingisa‘onceforalloccurrence’.” 2Ipresumethisdoesnotmean thatathingisinstantaneoussince,asweshallsee,thatwouldcontra dictthefifthfeature. The second feature is that things have properties. This dis tinguishesthemfromtropes.Thesimplicityofthelatterisinvoked. Thethirdfeatureofthingsisthattheymonopolisetheirplaces. Weareinformedthatanotherwayofformulatingthisistosaythat thingsareconcrete. 3 Thefourthfeatureofthingsisthattheyareindependent;thisis short for being existentially independent. In a certain sense things dependontropes,whichconstitutethem.Thisiscommentedon.

[I]f things are constructions from tropes then it is clear thatthething cannot beexistentiallyindependentina general sense.Itcannot,sinceitcannot( ex hypothesi )existifthe tropesconstitutingitdonotexist.Insteaditseemstome that issues of dependence and independence will arise elsewherefortropetheory.Firstly,andmostimportantly, thereistheissueofthe internal unity ofthething.[…][I]f 1Maurin2002,p.117. 2Maurin2002,p.120. 3Cf.Maurin2002,p.121n. 144CHAPTERIII

thingsareindeedconstructedfrom(asinthiscase)tropes, thenthesetropesmust,insomesenseoftheword,depend ononeanother—thatis,iftheyarereallyalltropesthat belongtothesamething,thensomethingmustholdthem together. An important issue in spelling out a theory of things for a theory of tropes is therefore the characteri sationofthisdependence(orspecialunity).Asecondissue of dependence (which may possibly be regarded as a corollary to the first) concerns the external independence of distinctthings.Itseemsthatoncewehavewhatmightbe called a ‘maximal’ congregation of tropes (i.e. once we haveathing)thenthiscongregationacquirestheadditional characteristicofindependence;independence,thatis,from othermaximalcongregationsoftropes(otherthings). 1

I would say that ‘depend(ence)’ is used elusively here. On the one hand, the tropes constituting a thing are said to depend on each other. This reciprocal dependence just means that they are united. Thisdoesnotmakethemexistentiallydependentoneachother.On the other hand, the independence of distinct things is genuine existentialindependencefromotherthings. The fifth feature of things is that they can change their properties over time. Things also have the ability to move through space.Thisisalsocommentedon.

Things,inotherwords,exhibitacertainamountof stability over time. Stability in this sense does not rule out the possibility of there being momentary things (i.e. things that existonlyataninstantandthat,consequently,willnever besubjecttochangeormovement).Allthatisintendedis that,ifathingdoesexistoveranextendedperiodoftime the possibility for movement and change should be providedfor. 2

Thus, in spite of their ability to change properties and position in space,thingsarestable.

1Maurin2002,pp.1212. 2Maurin2002,p.122. EXAMINATIONOFMAURIN’SONTOLOGY145

What is called ‘the sixth feature’ of things is in itself a list of features. Unlike the previous five, the ones on this list are clearly modelledonthenotionwehaveofaphysicalthing.Maurindoesnot wanttorestrictthediscussionsolelytophysicalthings.Therefore,the features gathered under this heading are not included as general featuresofallsortsofthings.Threefeaturesarelisted,butIsuppose afewmorecouldhavebeenmentioned. 1

(i)thingsaretemporallybounded(meaningthattheycome intoexistenceatatime,existforacertainstretchoftime andfinallypassoutofexistenceatatime);(ii)thingsare contingent (meaning that they exist, but their non existenceispossible);and(iii)thingspossessadeterminate positioninspaceateachmomentoftime(and,unlessthey arephysicalsimples,theyhavephysicalpartsthat,likewise, occupydeterminateregions ofspaceateachmoment of time). 2

Thesethreeadditionalfeatureswillbefulfilledbymostthings. Maurin’stheoryofthingsisatropebundletheory.Thisisthe majority view among trope theorists. A minority view postulates substratesaswell.Itisofcoursedoubtfulwhetherthelatterisatrope theoryatall,giventhestipulatedconditions.Asubstrate,inreason,is of another fundamental category. It is not abstract, i.e., qualitative. Sheisliberalthough:

Now, a ‘theoretical ideal’ is, as we know, something towardswhichwestrive,somethingthatwewould prefer to betrue.Itisnotsomethingthatnecessarily is true.There fore, just because the tropesubstrate view has, in this sense,beenruledoutinadvancethisdoes not meanthatit has been finally rejected. To reject the substrate view, arguments directed directly against it would have to be provided. 3

1ThethreeareborrowedfromLoux1998,pp.934. 2Maurin2002,p.122. 3Maurin2002,p.123. 146CHAPTERIII

Shemakesafewcommentsonthesubstrateview.Thesecomments areintendedtomakeitlikelythatitisnotthepreferableview.Iwill notgointothesespecificcommentshere.Anyhow,thebundleview istheonewhichshouldbechosen. Instead,Imoveontoherversionofthetropebundleview.Itis statedbywayofintroduction:

A bundle consists of nothing but its constituent tropes. Yet,abundleoftropesisnotthesameasaclassoftropes, nor is it the same as an aggregate of tropes. Classes are bothtooundiscriminating(theyprovideuswithtoomany things)andtootightputtogether(thethingstheygiveus cannot change, cease to or begin to exist). Instead, a bundleisa connected conglomerationoftropes.This,then, isthedifferencebetweenaclassoftropesandabundleof tropes: thebundleisatightcollectionof connected tropes. Tight enough to exclude arbitrary and gerrymandered collectionsoftropesfromthedomainofthings,butalso tightintherightsensesoastoprovideforthepossibility ofchange.Themaindifficultyinworkingoutadetailed bundle theory, naturally, is giving a plausible account of thisessentialconnection. 1

Astheterm‘bundle’isusedhereitisnotagenerictermforvarious types of collections; it names a specific type. It should also be observedthattheessentialconnection,referredtoattheendofthe quotation,isperhapsnottheonlyoneworthstudying.Thereisahint regardingthat.

When dealing with the bundle approach to thing construction it may seem that all things, on this view, consistoftropeswhichareallconnected in the same way to one another. But, clearly, things are normally more complex than that. Rather, our paradigm cases of things consistperhapsofanumberofsuchbundlesthatare,in turn, connected with each other etc. I will disregard all such complications in what follows. Not because I am

1Maurin2002,p.127. EXAMINATIONOFMAURIN’SONTOLOGY147

convinced that they are easily dealt with once the more fundamentalconnectionshavebeenprovided,butbecause the more fundamental connections must, in any case, be handledfirst. 1

Whatisstatedhereis en clair thatthingsarenotjustbundlesoftropes in which the constituting tropes are united by the same sort of bundlingconnection.Atropebundlemayverywell turn out to be buta(very)smallbuildingblockofathing.Asisseeninthequota tion,allcomplicationsduetothisaredisregarded.Itisfarfrombeing an insignificant detail though. It should be kept in mind that from now on when the phrase ‘bundlingfeature’ is used, it is potentially ambiguous.Inoneofits sensesitstandsforthecompresencerela tion, which is supposed to hold between the tropes of a bundle in thatsenseof‘bundle’thatishintedatinthelastquotation.Infact, thisisdeclaredtobethemostfundamentalconnection. The other sense is bound to be more complicated. It involves theconnection betweenthebundlesconstitutingathing.Asanameoftheproblem which is actually dealt with by Maurin, the denomination ‘the problemofthingconstruction’ismisleading.

3.4.3 Compresence Theterm‘compresence’ has beenusedseveraltimes above. A few hintshavealsobeenmadeastowhattherelationreferredtomight be.Itwillnowbediscussedmorethoroughly. Concerning the choice of the term ‘compresence’ Maurin informsusthatitisarbitrary.Therearequiteafewtermswhichhave beenusedforrelationsthatareatleastsimilartotheoneshehasin view. 2Anyoneofthesetermscouldhavebeenused. 3 It needs to be settled whether compresence is an internal or externalrelation.Tothatpurpose,thefourdistinguisheddetermina

1Maurin2002,p.127n. 2Someoftheseareenumeratedinsection2.3.4. 3Cf.Maurin2002,pp.1289. 148CHAPTERIII tionsofinternalityareapplied.Thefirstoneexaminedisthefourth, thesocalled‘stronginternality’.

Understanding the distinction as strong not only means treating it as if the internality of a relation makes it necessarily obtain given the existence of that which it relates,butalsoasifitissuchastonecessitatetheexist enceofthatwhichstandsintherelation.Entitiesthatare internally related to each other in this sense are, con sequently, existentially dependent on one another. For 1 example:iftropesred 1,round 1andsoft 1arecompresent, and if their compresence is in this sense strongly internal, thentheexistenceofeachoneofthecompresenttropes necessitates ,2notonlytheexistenceoftherelationofcom presence which serves to connect them, but also the existence of each one of the other tropes standing in the relationinquestion. 3

AccordingtoMaurin,compresencecannotbestronglyinternalsince thereisnoreasontobelievethataparticularrednesstropeisexisten tiallydependentontheexistenceofaparticularextensiontrope. It would make better sense to say that the existential dependence is between some colourtrope and some extensiontrope. However, Maurinpointsoutthattherelataofthecompresencerelationarenot kindsoftropes.Noristhecompresencetropewhichconnectsquality tropes.

Itholdsbetweenparticulartropessuchas this rednessor 4 this extensionandsurely this rednessmightverywellcease toexist(perhapstobeexchangedforaparticularblueness 1 Here we have three quality tropes which are said to be compresent with each other. Does that mean that they are related by a triadic compresence trope?Or,aretherethreedyadiccompresencetropes,eachrelatingapairof thethreequalitytropes? 2Theterm‘necessitates’heresuggeststhattheexistenceofoneoftherelata forcestheothertoexist.Thisis amisleadingwayofsayingthatexistential dependenceisholding. 3Maurin2002,p.129. 4Isuspectthatthis‘or’shouldberead‘and’. EXAMINATIONOFMAURIN’SONTOLOGY149

trope)withoutthisinanywayaffectingtheexistence of this extensiontrope. Surely we want our notion of com presencetobesuchthatroomismadeforthepossibility thatanyoneofthetropesinacompresentbundlemight cease to exist without this affecting the existence of the other tropes in the bundle (although it might of course affecttheobtainingoftherelationofcompresence). 1

Themainmessagehereisaratherstrongone:itshouldbepossible foranyofthetropesinacompresentbundletoceasetoexistwithout thataffectingtheexistenceofanyothers.Notealsothattheremark putinbrackets,inthelastsentence,seemstoleaveitopenwhether thesamecompresencetropewouldceasetoexistornotwhenoneof its relata do that. I take it that a new qualitytrope is supposed to replace the one lost. All this suggests that Maurin is open to the recycling of tropes. Compresencetropes cannot be recycled; this is evidentfromwhatissaidbelow.Furthermore,itwillbeseenthatthe notionofstronginternalityreappears. We move on to what is considered to be Moore’s notion of internality.

Ifcompresenceisessentialtotheidentityofthatwhichit relates,thenineverycasewhereitseemsthatpreexisting tropes (perhaps former constituents of other things) are puttogethertocreateanewthing,whatinfacthappensis thatasthesetropesenterintonewcompresencerelations, they are first destroyed and then replaced by new (althoughexactlysimilar)tropesnowessentiallyrelatedin this new thing. Since this seems simply wrong, even on Moore’s understanding of the distinction, compresence shouldbetreatedasanexternalrelation. 2

Also here the implication is that tropes can enter into new com presence relations. That notion that they cannot is part of the Moorean internality; therefore compresence is not internal in that sense. I would say that the intuition that (quality) tropes can be 1Maurin2002,pp.12930. 2Maurin2002,pp.1301. 150CHAPTERIII recycledindicatesthattheylackadicity.Inotherwords,theyarenot predicativerather,theyarethoughtofas(small)substances. 1More over, as substances which lack predicativity, they can be used over andoveragain. SinceMaurinlumpsArmstrong’snotionofinternalitytogether with Moore’s, whatcomesnextisCampbell’s notionofan external and founded relation. Maurin reminds us that it has already been pointed out that Campbell’s considered view is that there are no external and unfounded relations. Campbell calls his doctrine, according to which all relations are either internal or external and founded,‘foundationism’.Iffoundationismistrue,norelationsneed to be posited as entities in their own right. Although it might be temptingtoembracethisdoctrine,itshouldberesisted.

Unfortunately, Campbell’s foundationist programme seemstobreakdownjustatthepointwhereitisarguably needed the most. It breaks down, that is, for the truly fundamental relation of compresence. This is why: an externalfoundedrelation cannot beafundamentalrelation holding between individual tropes and so compresence cannotbeexternalfounded. 2

Ithinkthisneedstobecommentedon.Rememberthatthenotionof anexternalandfoundedrelationisdefinedasholdingbetweenrelata duetotheirnatures.Howeveritisoneofthesefragments of their natures 3 that is relevant: the fragment which does not define their identities.Aconsequenceofthatisthatthesameentitiescanchange andretaintheiridentitiesbutceasetoberelatedbytheexternallyand founded relation. Thus, an external and founded relation can only 1 In Armstrong 1989, p. 115, the apposite comment is made that bundle theorists,whoarealsotropetheorists,“trytobuilduptropesintosomething alittlebitmoresubstantial.”Theytreattropesas“juniorsubstances”.This phraseoriginatesfromAyer,whousesitforsensedata. 2Maurin2002,pp.1312. 3Theterm‘nature’isusedinwidesense.Thenatureofanentitymightbe anyqualitativecontentofit.IntheexampleusedbyCampbellitisthedirton shoeswhichconstitutesthenaturesonwhichtherelation being cleaner than is founded. EXAMINATIONOFMAURIN’SONTOLOGY151 hold between entities which have the capacity to change and yet continuetoexist.Tropesdonothavethatcapacity.InMaurin’sown words:

[I]ndividualtropescanneverstandinarelationwhich is bothfoundedinthem and whichissuchthatitneednot relatetheentitiesinquestion. Suchacombinationwould requirethattropescouldchange,buttropessimplycannot changeandwecannotsayaboutatropethatthewayitis ‘isnotessentialtoitsidentity’.Tropesaresimpleentities. Thewaytheyare(theirnatures)isalsoalltheyare. It is what theyare. 1

The conclusion is then that compresence is an external (and un founded)relation.Onthesubjectofcompresenceanditsrelata,we cannowstate:

(i) its terms are existentially independent of one another, (ii)itisnotessentialtotheidentityofitsterms,and,(iii)it isnotfoundedinthenatureofitsterms. 2

Aconsequenceofthisissupposedtobethattwotropescanstartout beingcompresentwitheachotherandceasetobecompresentaftera while.Judgingfromwhatissaidinanearlierquotation,eachonecan goonexistinginotherconstellationsaftertheseparation.Compres enceisalsoanontologicaladditiontoitsrelata,anincreaseofbeing. Thus, as regards the ontological characterisation of compres ence,itisconcludedthatitisyetanothertrope.Itdiffersfromthe tropestowhichitrelatesbybeingarelation.Doesnotthatmakeit belong to another (fundamental) category? Maurin’s answer is a bit evasive.

This is a serious objection since I have gone to great lengths in this book to avoid positing any category of entitiesotherthanthecategoryoftropes.Thatthere is a differenceherethatmightbeconsideredasadifferencein

1Maurin2002,p.132. 2Maurin2002,p.133. 152CHAPTERIII

categoryis,Ibelieve,impossibletocontradict.Howmuch the addition of a separate category of relations would tarnish the theoretical appeal of trope theory I do not know.AllIcansayis,oncemore,thattheadditionofa separatecategoryofrelationsisalessseriousadditionthan wouldbe,forinstance,theadditionofaseparatecategory of universals. Adding universals to a theory of tropes would,forone,probablymeanakindofdoublecounting. And,whynotthenrestcomfortablywithonlyuniversalsin the first place? Why complicate the theory by adding tropes?Addingrelationsdoesnot,inthesamesense,strike atthecoreoftropetheoryanditdoesnottamperwithits particularist(or,ifyouwill,nominalist)ideal. 1

The statement here, that a theory including both tropes and uni versalswouldmeanakindofdoublecounting,evidently reveals an inabilitytoseetherelevanceofmoderaterealism.Besidesthat,wesee thattheadditionofrelationswhichareparticularsisnotconsidered to tamper with the ideals of nominalism. That seems to settle the matter. Furthermore, relation tropes are also simple, abstract par ticulars. 2 The characterisation of compresence is continued in the next section.

3.4.4 Compresence and Bradley’s Regress Being a true relation compresence might fall victim of Bradley’s regress. That would be a problem threatening the tropetheoretical edifice. This includes its key notion: trope. 3Iftheregressisareal problemfortropetheory,itmustberesolved. Maurin’s own rendering of part of what underlies Bradley’s argumentagainstrelationsisasfollows:

1Maurin2002,p.166. 2Cf.Maurin2002,p.164,wherethisissaidtoholdforcompresence. 3ThenotionoftropewouldbesetrockingiftheholisticconclusionBradley drawsfromhisargumentisfoundtobevalid. EXAMINATIONOFMAURIN’SONTOLOGY153

Premise: If the world ‘truly’ includes a variety of distinct entities (whether they be things, universals or tropes) then these entities mustbeinsomeway‘truly’related. Premise: Everyattemptatspellingouttherelations requiredfortheseparateexistenceofthese distinctentitieswillendupincontradiction. Conclusion: Therefore, the world cannot include a variety of distinct entities. Instead, the worldis‘truly’asingleentity,undividedand whole,andalldistinctionbelongstoappear ancesonly. 1

Maurinagreeswiththefirstpremise.Isuspectthatthisisthemajority viewamongphilosophers.Itisthereforethesecondpremisewhichis the really interesting one. The regress argument is put forward to supportthatpremise. AccordingtoBradley,arelationiseitherfoundedinitsrelataor itisnot.Whatisthecasefortruerelations?Unfortunately,whatever the answer is, true relations are impossible. As a consequence, no thingintheworldcanbeseparatefromanythingelse.Theworldis really an undivided whole. What looks like distinctions between thingsarejustthat—appearances.Howdidthishappen? Bradleyasks:whenwesaythatsomethingisinarelationwith something else, what does the ‘is’ mean? It cannot be the ‘is’ of identity.Abetterwordtousewouldthereforebe‘has’.Whatisthe meaningof‘has’then?Bradleythinksthatthereareonlytwopossible meanings it can have. The first is that of ‘is predicated by’. Thus, whenappliedtotwoqualitiesortropes,whicharesaidtoberelated to each other by compresence, the relation is one of predication. ‘Predication’candenoteeitheroftwothings,according to Bradley. First,whatispredicatedofsomethingisadescriptionofit,oratleast apartofadescription.Ifonepredicatesaqualityofathing,oneis sayingwhatitistobethatthing,oratleastpartofwhatitistobe thatthing.Allegedly,thisisanotherwayofsayingthatthequalityin 1Maurin2002,p.135.Cf.Bradley1908,p.25. 154CHAPTERIII questionisfoundedinthething.Appliedtoarelation,itshouldalso befoundedinthethingsrelated.Maurinremarksthatbeingfounded inrelataisnorealpossibilityinthecaseofcompresence.

For,ifitwere,itwouldmeanthat partofwhat we are sayingwhenwesaythattrope aiscompresentwithtrope b isthatpartofwhatitisto be trope aisto‘beinrelation with b’ (or, at least, it is ‘to be compresent’). 1 But this seems to blatantly contradict the that tropesaresimpleentities. 2

Itisnotobviousthatthesimplicityofatroperulesoutthepossibility thatithasarelationalproperty.PerhapsMaurin’sreasonfordenying thetropearelationalpropertyaspartofitsidentityisthatitwould mean that the trope must consist of at least two components: the relational property and a qualitative content; that would be one contenttoomany. 3 Sincetheformersenseof‘predication’cannotbetherightone, weturntowhatissaidtobeitssecondsense.Therelatanowhave compresenceinthesenseofbeingpredicatedbyit,althoughwithout being compresent.Aboutthisproposalitcanbesaid:

The trouble with this alternative should be apparent. Turning the ‘is’ of ‘is compresent [with]’ into the ‘is’ of predicationwasoriginallythoughttobeaconvenientway ofprovidingthemissinglinkbetweentherelationandthe entities it relates. Predication could provide such a link because it in part describes the actual contribution of the relatedentities.Thisishowpredicationworks.Now,this veryfeature(thatis,thefeaturewhichmadepredicationa goodcandidateforconnectingrelatawithrelation)turned outtomaketheentitiesrelatedcomplexinanillegitimate

1Thisissosincecompresence,assomethingpredicatedofthepair,is‘part’ ofthem,accordingtoBradley’scontainmentmodelofpredication.The‘part’ whichisin aisexpressedby‘beingcompresentwithb’. 2Maurin2002,p.137. 3Iwouldsaythoughthatthisdependonthecuriousviewthatarelational propertyiscontainedintheentitywhichhasit. EXAMINATIONOFMAURIN’SONTOLOGY155

way.Wecannotdealwiththisproblembysayingthatthe ‘is’of‘iscompresentwith’isthatofpredicationbutthatit doesnotfunctionaspredicationdoes.Thisissimplynon sense.Therefore,Bradleyconcludes,‘true’relationscannot befoundedintheentitiestheyrelate. 1

Sincetruerelationscannotbefoundedintheirrelata,anothersense of‘has’in‘hascompresence’mustbesearchedfor,asensewhichis not that of ‘predication’. Bradley’s proposal is to make the relation “moreorlessindependent.” 2Ifitisindependentofitsrelata,itisnot anattributeofthem.Maurinremarksthatthisisanunderstandingof atruerelationwhichseemstofollownaturallyfromwhatshehassaid aboutcompresenceasanexternalrelation.Anexternalrelationdoes notaffecttheexistenceoridentityofitsrelata,sothispromisestobe the right interpretation. According to Bradley, all this has as its consequencethoughthatatruerelationleadstoaviciousregress.In hisownfamouswords:

TherelationChasbeenadmitteddifferentfrom Aand B, andnolongerispredicatedofthem.Something,however, seemstobesaidofthisrelation C,andsaid,again,of A and B.Andthissomethingisnottobetheascriptionof one to the other. If so, it would appear to be another relation, D,inwhich C,intheoneside,and,ontheother side, Aand Bstand.Butsuchamakeshiftleadsatonceto theinfiniteprocess.Thenewrelation Dcanbepredicated innowayof C,orof Aand B;andhencewemusthave recourse to a fresh relation, E, which comes between D andwhateverwehadbefore.Butthismustleadtoanother F;andsoon,indefinitely. 3

Evidently,themoralofthisisthatanindependentrelationisincap ableofrelatinganything. Maurin’s response to the regress argument is that the external relationcompresencecertainlydorelate;thetask at this point is to 1Maurin2002,p.137. 2Bradley1908,p.21. 3Bradley2008,p.21. 156CHAPTERIII explainhowthismightbe.Itshouldbekeptinmindthatwhatshe has to say about how to solve it is a tentative effort to begin the formulationofasolution,notacompletesolution. Letusstartwithwhatistheconclusion.

For it to be true that a is compresent with b there must exist, apart from a and b, a compresence-trope . A compres encetrope is, contrary to an ‘ordinary’ trope, a relation trope. The difference between an ordinary trope and a relationtropeisthis:arelationtropeissuchthat,although its existence is contingent (that is, it might or might not exist)itmust, given that it exists ,relateexactlytheentitiesit does in fact relate. In other words, any relationtrope is specifically dependent on the tropes it relates. This is true while,ontheotherhand,therelatedtropesare not likewise dependentontheexistenceoftherelationtropeinques tion.Thatis,thespecificdependencewhichcharacterises therelationtropeisoneway.Wemightalsoputtheposi tionasfollows:therelationofcompresenceis external to thetropesitrelates,but,simultaneously,therelatedtropes are internal totherelationofcompresence. 1

Weareinformedherethattherelataofacompresencetropearenot dependentonitfortheirexistence.Remembertherelata,whichare specificqualitytropes,arenotexistentiallydependentoneachother either. Specific existential dependence does hold from a compres encetropetoitsrelatathough.Thus,thereissomethingspecialwith compresencetropes. Presumably, the same also holds for all the otherexternalrelations.Ifitdoesnot,onewonderswhy. Pondernowuponthemessageofthefollowingstatement.

Therelationalviewnowincorporatesthisintuitivediffer ence[i.e.,thatitisoftheveryessenceofrelationsthatthey neednotberelatedtothethingstheyrelate] 2andprovides

1Maurin2002,p.164. 2Cf.Grossmann1992,p.55,whichMaurinreferstohere.Itakeitthatthe message is not intended to imply that relations are related to their relata if theydoinfactrelatethem.Instead,theintendedimplicationisthatrelations EXAMINATIONOFMAURIN’SONTOLOGY157

us with an ontological account of it. It tells us that, although there is no necessary connection from relata to relation, there is one from relation to relata. Putting a relationtrope alongside the entities it relates will not, on the present account, generate endless regress. In being a relationtrope it is of its essence that it does connect the entitiesitrelates.Thisisabrutefactaboutrelationsandno furtheradditionofrelationsisneededtoprovideforit. 1

Thewaythingsaredescribedhere,aswellasinthepreviousquota tion,itseemsasifarelationdoesholdbetweenrelationandrelata afterallsincethereissupposedtobeanecessaryconnectionfromthe formertothelatter.Necessaryornot,aconnectionisarelation,isit not? According to Maurin then, mutual existential dependence does notholdbetweenany 2tropes,thoughthereareunilateralexistential dependencesholdingbetweenspecificcompresencetropesandtheir relata.Acompresencetropeisspecificallyexistentiallydependenton itsrelata.Aparticularcompresencetropemustrelateaspecificpair. 3 Everyotherpairisruledout.SinceMaurinseemstocontemplatethe possibilityofrecyclingqualitytropes,theremightbemorethanone compresencetropeperpairofrelata. Why is a compresence trope considered to be unilaterally dependentonthequalitytropesitrelates?Maurin’s reason for that seemstobethat,beingarelation,itmustrelate.Ifitdoesnot,itfails tofulfilthefunctionofarelationandwouldthereforenotbeareal relation (trope). Presumably, this holds for each and every external relationthereis.Thequalitytropesdonotneedtoberelatedbya specificcompresencetrope.Doesthatmeanthateachofthemcould

areneverrelatedtotheirrelata,notevenwhentheyinfactrelatethem.This mightseemtobeasubtledistinction;itisnot.Itiswhatmakesthedifference betweentherebeingaBradleyanregressornot. 1Maurin2002,p.165. 2Maybethisistooverstatethethesis,thoughIdonotthinkthatMaurinsays anythingthatcontradictsit. 3Itakeforgrantedherethatcompresenceisdyadic. 158CHAPTERIII befreefloating,i.e.notcompresentwithanything? 1 I do not think thatMauringivesanyclearindicationaboutwhatheranswertothat questionmightbe.Itisclearthoughthatsheinfactconsidersquality tropes to lack predicativity. If she had recognised that it is of their veryessencetoqualify,thenshewouldhavebeenforcedtorecognise thattheyarepredicativeaswell. To corroborate my claim that quality tropes are deprived of their predicative nature, I will remind readers of what was said in connectionwithaquestionaskedbyErikFunkhouserinhisreview ofMaurin2002.

Why can’t tropeshavequalitativeparts—e.g.,colortropes havehueparts,saturationparts,andbrightnessparts?[…] This seems plausible, though the possibility would raise problems like those for thingconstruction that she discusses at great length. Namely, what accounts for the unityofsuchqualitativelycomplextropes? 2

Maurin’sansweris:

[I]ftropesarequalitativelycomplexinthesenseimagined byFunkhousertheymust[…]beregardedascomplexes of more fundamental tropes .Ofcourse,complexesofthiskind wemaycall tropes —buttheyaretropesonlyinasecond arysense.Ithereforeprefertocallthem complexes of tropes (or compresent tropes )althoughIdonotthinkmuchhinges onourchoiceoftermshere. 3

Trytoignorethedetailsofthespecificexampleused.Instead,con centrateonwhatisrelevanthereregardingtheissueofpredication.It seemsnaturaltointerpretthisasgivingexpressiontoacontainment modelofpredication.Thatanentityhasacertainpropertyisanalysed asitshavingitascontent.Thisatleastholdsforentitieswhichare

1AccordingtoWilliamstheycoulddothat,thoughbymerecosmic theydonot. 2Funkhouser2004,fourthparagraph. 3Maurin2005,p.136. EXAMINATIONOFMAURIN’SONTOLOGY159 not simple.1 Note that even on the rather fundamental level of a colourtrope 2theanalysisiscarriedourintermsofcompresence.Asa result,thequalitativecontentoftheanalysedentitylackspredicative. In the light of all this, the description of quality tropes as being monadic appearsmisleading.Sincetheylackadicity,theyarenotontic predicates. Thetendencytoconsiderqualitytropesas(small) substances, ratherthanonticpredicates,ismanifestedbymanymoderatenomina lists.Toexplainwhythisissoisinitselfaninterestingtask.

1 In Maurin’s terminology ‘simple’ actually means the same as ‘absolutely simple’. 2Unfortunately,languagedesertsushere.Sincethisentity,referredtobythe term‘trope’,is ex hypothesi notsimple,itisnotropeaccordingtothedoctrine. CHAPTERIV

MomentNominalism

4.1Introduction IntheanalyticontologyofIvarSegelberg(1914–1987)relationsand qualities belong to different categories. In it, universal relations are recognised straight out, but not universal qualities. When using the term‘quality’,Segelbergusuallyhassomethinglikeatropeinmind.In exceptionalcasesitcanalsobeaclassof(quality) instances, where theelementsareexactlysimilartoeachother. The term ‘trope’ is not used by Segelberg. His three books, 1 which make up almost the whole body of his writing, had been written when D. C. Williams published the article in which ‘trope’ first occurs. Though I doubt that Segelberg ever read anything by Williams, he was versed in the writing of G. F. Stout, which apparentlyinspiredhim.However,thewritingofEdmundHusserlis thatwhichinspiredhimmost;heborrowedtheterm‘moment’From Husserl,2whichishispreferreddesignationforqualityinstances. Qualitymomentsanduniversalrelationsconstitute,inacertain sense,theelements of which theuniverseisultimatelyconstituted. 3 Thus, the ontology in question can be described as a mixture of nominalisticandrealisticelements.Segelbergwould object to being describedasanominalist,eveninpart,sincehehasaspecificposition 1ThesearetranslatedintoEnglishbyHerbertHochbergandSusanneRing strömHochberg,andcollectedinSegelberg1999.Referenceswillbemadeby firstindicatingthepageinSegelberg1999andthenthecorrespondingpagein theSwedishoriginal;i.e.,eitherSegelberg1945,1947or1953. 2ItispresentedinSegelberg1999/1947,chapterIV,thoughnotusedasa technicaltermuntilSegelberg1953.InitsGermanformitisusedinthethird investigationofHusserl1970.Adistinctionismadetherebetween Momente and Stücke , which are dependent parts and independent parts of things respectively.Segelbergdoesnotagreewiththatprincipleofdivisionthough. 3Cf.Segelberg1999/1947,p.228/137. 162CHAPTERIV in mind for the denomination ‘nominalism’. It takesqualitiestobe constitutedbyresemblancesbetweenconcreteobjects.1 WhenclassifyingSegelberg’sontologyas(partly)nominalistic,it isdonewithitsqualitativesideinview.Ithinkthatthisincombina tion with the fact that universal resemblances, at leastofficially,are notassignedanyconstitutiverolewithregardtothequalitativecon tentsofmoments,providesufficientlygoodreasonsforclassifyingit asamoderatenominalism.

4.2IndividualandUniversal

4.2.1Overview Thetwonotions,individualanduniversal,aredeterminedrespectively intermsofamodalnotion.Thisnotionisdealtwithinsection4.2.2. Insection4.2.3anallegedintermediaryformofentityisdiscussedin connection with a presentation of an intellectual experiment. In section 4.2.4 the final determination of the notion of individual appears.Thedeterminationofuniversalwillbepresented as we go along.

1 A position which is called ‘resemblance nominalism 2’ by Gonzalo RodriguezPereyra claims that there is for each quality a specific, universal resemblancerelation.Itobtainsbetweenallthe(concrete)particularswhich havethequalityinquestion.AccordingtoRodriguezPereyra’sstandards,this isanominalismsinceittakestheresemblancerelationstobeprimitive;ithas tomeetthetraditionaldifficultieswhich(ordinary)resemblancenominalism is beset with as well. Cf. RodriguezPereyra 2002, p. 123. Segelberg dis tinguishesbetweentwoversionsofwhathecalls‘nominalism’.Oneofthese satisfiesthedescriptionofbeingaresemblancenominalism 2.Itisadvocated byC.D.BroadinBroad1933,pp.111ff.Theotherversionisabitelusiveas regards the status of resemblance. It takes typical examples, or paradigms, andtheresemblancesofthingstothesetobeconstitutiveofpossessionof qualities.Thespecificversionofif,discussedbySegelberg,isthatofHans Cornelius.Cf.Cornelius1900,pp.103ff.Segelbergrejectsboththeseforms ofnominalism.Cf.Segelberg1999/1947,ChapterIII. MOMENTNOMINALISM163

4.2.2AModalNotion:Can AccordingtoSegelberg,therearenorelationmoments.Relationsare (real) universals. All moments belongs to the qualitative side of ontology. An idea can be formed of what he means by the terms ‘universal’and‘individual’ 1fromthefollowingstatement:

No one would deny the following three statements. 1) Theremaynotbetwoexactlysimilarobjects 2intheuni verse, but it is not impossible that there be two objects, twosensedataforexample,thatareexactlyalike.2)If ais auniversal,therecannotbeanotherobjectexactlylike a.3) Ifthereisanobjectotherthan athatisexactlylike a,then aisanindividual.But, acanbeanindividualeventhough thereisnoobject,otherthan a,thatisexactlylike a.For a to be an individual, it is only necessary that there can be otherobjectsthatareexactlylike a.3

We learn here that universals cannot resemble each other exactly. Thus,Leibniz’sprinciple—theidentityofindiscernibles—seemsto beinvokedwithregardtouniversals.Moments, 4ontheotherhand, can be exactly similar to each other, like other individuals. If the principlewereapplicabletothem,itwouldseemthattheycouldbe almost exactlysimilartoeachotheratbest.5

1Inthepreviouschapterstheterm‘particular’hasbeenusedconsistently.In thepresentchapterIadaptmyselftoSegelberg’sterminology.HisSwedish terms are ‘individuell’ (adjective) and ‘individ’ (noun). The translators have chosen‘individual’(adjectiveaswellasnoun)insteadof‘particular’. 2InSegelberg’sterminology‘object’(inSwedish:‘föremål’)isthemostgene ralterm.ItcorrespondstotheGerman‘Gegenstand’,asthelatterisusedby Alexius Meinong within the frame of his Gegenstandstheorie . Cf. Segelberg 1999/1953,p.239/5.IfithadnotbeenforthefactthatSegelbergprefers ‘föremål’ to ‘entitet’, the English word ‘entity’ may have been used just as well. 3Segelberg1999/1947,pp.145/189. 4Sinceallmomentsaresupposedtobequalitymoments,theprefix‘quality’ willoftenbeleftout. 5 Kenneth Clatterbaugh convincingly argues that G. W. Leibniz is an ad 164CHAPTERIV

Modalnotionsareobviouslyusedinthesedeterminationsofthe notionsofindividualanduniversal.Thatgivescauseforacomment:

What do we mean when we say that an object a is an individual? One may reply: we mean that there can be several objects, including a, that are exactly similar to a. Thatanobject bisauniversalwouldthenmeanthatthere cannot be another object that is exactly similar to b. It is possiblethatthisiswhatonesometimesmeansby‘indivi dual’and‘universal’.Buttheconcept“can”,whichoccurs inbothanalyses,issoindefinite,thattheterms‘individual’ and‘universal’,sounderstood,becomefairlyworthlessin atechnicalcontext. 1

herentofinstanceattributes—ormomentsifwelike.Cf.Clatterbaugh1973. Sincetheprinciplebearinghisnamestipulatesthatexactlysimilarentitiesare identicalwitheachother,thismightcomeasasurprise.IfIhavecorrectly understoodhim,DonaldMertzsuggeststhatLeibnizrestrictstheapplicability of the principle, as regards individuals, to concrete individuals. Cf. Mertz 1996,pp.1489.HeadducesthefollowingasevidenceforLeibniz’srecognis ingpropertyinstances. Therefore,sincesubstanceandaccidentdependuponeachother, othermarksarenecessaryfordistinguishingasubstancefroman accident.Amongthemmaybethisone:Thatasubstanceneeds someaccidentbutoftendoesnotneedadeterminateonebutis content,whenthisaccidentisremoved,withthesubstitutionof another.Anaccident,however,needsnotonlysomesubstancein general but that very one in which it inheres, so that it cannot changeit.(Leibniz1969,pp.3901) Thisletsitselftotheinterpretationthatthesubstanceinwhichtheattributeis inheringisessentialtoitsidentity.Thefollowingisevenmoreexplicit. [T]wo different subjects […] cannot have precisely the same individual affection, it being impossible that the same individual accident should be in two subjects or pass from one subject to another.[Myitalics](Leibniz1969,p.704) ItshouldbenotedthatLeibnizconsidershisprincipletobemetaphysically, but not logically, true. Logically it could be that, say, two pieces of matter wereperfectly alike.Thiswould notbeconsistentwiththeorder ofthings though.Cf.Leibniz1969,p.699. 1Segelberg1999/1947,pp.156/356. MOMENTNOMINALISM165

What more information is added then to the impressionistic deter minationsmadehere?Iwouldsaythatitislittlemorethanvariations onthesametheme. One thing is added, though: the notion that an object cannot have a certain property implies that it has another property which, accordingtoalaw,preventsitfromhavingtheformer. 1

Actually, it seems that each modal statement refers to a certainlaw oracertaingroupoflaws—differingindiffer ent cases. If one wishes to give an analysis of a modal statement,onemustcitethelaworgroupoflawsreferred tobythemodalstatementinquestion. Applying this point to the above modal sentences about individuals and universals, we arrive at the follow ing.Wetake‘ xhas p’so: xhas pimpliesthereareatleasttwoobjects,including x,whichareexactlysimilarto x. If xisauniversal, xcannothave p,whichistosaythat x musthavesomeproperty gwhichissuchthateveryobject whichhas g2lacks p.If xisanindividual, xcanhave p;that is to say, x does not have the property g. But, which property gisreferredtohere? 3

Itwillturn outthattheproperty,whichiscalled‘g’here,is that of being (spatiotemporally) nonlocalised. 4 A prerequisite for there being exactly similar entities is that they are spread out in space and/ortime.Thisisarguedforbymeansoffourexamples.5 (1)Onecanimaginetwoexactlysimilarvisualsensedatalocated indifferentpartsofthevisualfield.Onecannotimaginethemlocated inexactlythesameplace,atthesametime,though.

1ItisalsoexplicitlystatedinSegelberg1999/1947,p.157/36. 2IntheSwedishoriginalthereisamisprint:ithas‘y’insteadof‘ g’. 3Segelberg1999/1947,p.158/37. 4Cf.Segelberg1999/1947,p.164/45. 5Thewaytheseexamplesarepresentedisapparentlyfraughtwithmodality. 166CHAPTERIV

(2) Two exactly similar sensations of can be imagined as beinglocatedinseparatepartsofone’sbody.However,onecannot imagine them being located in exactly the same place at the same time. (3) The notion that there are two exactly similar impulses of volition or two exactly similar of emotion in the same consciousnessatthesametimeseemsabsurd.Onecanimaginethem occurringatdifferenttimes,orindifferentpersons,though. (4)Onecannotimaginetwoexactlysimilarfacts.Thereasonfor thatisthatfactsarenotlocalisedintimeorspace.Onecanimagine two exactly similar events; but these cannot existat the same place andtime.1 Withthesefourexamplesaspremises—or,perhapstheyare morelikeindicia—theconclusionisdrawn:

Inorderforamultitudeofexactlysimilarobjectstooccur, it thus seems to be necessary that the objects are “dispersed”inspaceandtime,orinshort,inanextended complex,whichistosaythattheobjectsareinacertain senselocalized.Thatanobjectislocalizedthenmeansthat theobjecteitherispartofanextendedcomplexorthatthe objectisacomponentofacomplexwhichispartof an extendedcomplex.Ifweadoptthetheorythatanobjectis acomplexofitsqualities,thenwemustholdthat every qualitativegradationofalocalizedobjectisitselflocalized andthatitoccursinoneorseveralinstances. 2

The answer to the question about what characterises individual objectsisthenthatindividualobjectsarespatiotemporallylocalised. According to the same line of reasoning, universals are not as localised. There is a further condition which individual objects must satisfy. We willcome backtoitin section4.2.4 below after some preparatoryinformationinthenextsection.

1TheseexamplesarefoundinSegelberg1999/1947,p.159/38. 2Segelberg1999/1946,pp.159/389. MOMENTNOMINALISM167

4.2.3SemiIndividuality It is tempting to maintain that each individual entity is relationally different from every other individual entity.1 The following intel lectualexperiment 2ispresentedinordertoproblemisethatclaim 3.

[O]ne can imagine a spatial whole so structured that it contains a number of objects which are not relationally different.Theobjectswillthenbe‘localized’,inthesense inwhich wejustusedtheword,buttheydonot occupy differentpositionsintheusualsense[…]. 4

Thethemeoftheintellectualexperimentcanbevariedinterminably. Segelberg’sfirstvariationofitrunsasfollows.

1)Weimagineaninfinitespace(spatialwhole) S,towhich we cannot apply the concepts updown and leftright . In S therearetwoequallylargespheres, aand b; aisredand b isblue.Between aand bthereobtainsarelation R,which we shall call the distance between a and b. R is obviously symmetrical[…].Itisalsoobviousthat ahasarelational propertywhich blacks,namely,“having Rto b”,and bhas arelationalpropertywhich alacks,namely,“having Rto a”. From this […] we can conclude the following: if a space (spatial whole) contains two objects that are not

1 Segelberg ascribes to Konrad MarcWogau the view that an individual object is relationally different from every other individual. Cf. Segelberg 1999/1947,p.160/39.Cf.MarcWogau1945,pp.164ff. 2 More or less the same experiment is found in an article by Max Black, publishedafewyearslater.Cf.Black1952. 3 As I hope will be evident, Segelberg’s reasoning in connection with the intellectualexperimentisabitelusive.Thismakesitdifficulttosayforcertain whathisexactpurposewithitis. 4Segelberg1999/1947,pp.160/3940.Twosensesseemtobefiguringhere. Oneoftheseconcernstherelationsofanobjecttospaceandtime.Theother concernsitsrelationstootherobjects. 168CHAPTERIV

congruent 1witheachother,onenecessarilyhasarelational propertywhichtheotherlacks. 2

Due to their difference in colour the two spheres are incongruent witheachother.Asaconsequenceofthat,theyarealsorelationally differentfromeachother.ThetworelationalpropertieswhichSegel bergmentionsareexpressedby‘having Rto b’and‘having Rto a’ respectively.Withaneyetowhatwillappearsoon,Iwouldliketosay that there is probably no doubt that the number of spheres in this universeistwo. Thereisasecondvariationofthesametheme.

2) We now imagine instead that a and b are two exactly similar spheres. Even in this case, a distance R obtains between the spheres. Consequently, the sphere a has the relationalproperty“having Rto b”,and bhastherelational property“having Rto a”.Butthiscaseisdifferentfrom thepreviouscaseinafundamentalway.Since aand bare congruentinthislattercase,thereisnodifferencebetween “having R to a” and “having R to b” — rather, we deal withoneandthesamerelationalproperty.Wewillcallthis relationalproperty‘ r’. 3

It is maintained that since a and b are congruent with each other, “having Rto a”isthesamerelationalpropertyas“having Rto b”.As aconsequencethisrelationalpropertycannotdifferentiatebetweena and b, since they both have it. The notion that there is only one relationalpropertyherecanbecalledinquestion.Afterall,aand bare

1 The sense of this term of geometry is extended to apply to all kinds of entities, not just geometrical figures. Cf. Segelberg1999/1945, p. 38/29. It canbeassumedherethatithasthesenseof‘exactlysimilar’.Inthenextquo tationwefindthembeingusedalternately.Insection4.3.2afewuncertainties regardingtherelationsbetweenthesensesofthesetwoterms, as wellas a fewothers,arediscussed. 2Segelberg1999/1947,p.160/40. 3Segelberg1999/1947,p.160/40. MOMENTNOMINALISM169 not the same individual sphere. Their being (qualitatively) exactly similartoeachotherdoesnotchangethat. 1 Someone mightcomeupwiththebright ideathatarelational differencebetweenthetwospherescouldbeproducedbymeansof callingoneofthem‘a’andtheother‘ b’.Eachspherewouldthenhave asemanticalpropertywhichtheotherlacks.Thisproposalisrejected though.

Ifweat t1calloneofthespheres‘ a’,thereisnopossibility ofdecidingwhetheritisthe“same”sphereorthe other spherewhichwewillcall‘ a’atthenextmoment.And,if wespeakaboutthesphere aintwosentences,thereisno possibilityofdecidingwhethertheterm‘ a’inbothsenten ces refers to the same sphere. The impossibility of deci dingisnotduetoanylimitationoftheinquiringsubject’s capability,butisduetothetaskbeingmeaningless.With regardtothisspace,itmakesnosensetospeakof “the 1 This is a consequence of Segelberg’s moderate nominalism, according to which moments are individuals through and through. Herbert Hochberg commentsonthis. It is […] obvious that Segelberg’s view, appealing to individual properties,whileprovingapparentgroundsforindividuation,in thatthequalityinstanceswillbenumericallydifferentinthetwo spheres, cannot distinguish them […], in the sense he requires. For he can only refer to such different quality instances by referring to the spheres — “the spherical shape of sphere x. ” Thus he can not do what his argument against MarcWogau requiresthelattertodo.Neitherphilosophercanformadescrip tion of either the qualities or the spheres. This is the case whetheroneresolvestheproblemofindividuation[…]bymeans ofnumericallydiversequalityinstances,orbysubstrata,[…]or byanappealtorelationaldifferences.(Hochberg1999,p.28) HochbergseemstoassertthatSegelbergcannotindividuateamomentother thanbyreferringtothesphereitbelongsto.Isuspectthathetakesthattobe circularthough,sincethesphereisdefinedintermsofitsmoments.Segel bergdoesnotappealtonumericallydifferentqualityinstancesinconnection withtheintellectualexperiment.Hochbergpointsthatoutimmediatelyafter whathasjustbeenquoted.IwouldsaythatSegelbergdoesinfacttreatthe relationalpropertieshereas(real)universals.Furthermore,Istronglysuspect thatontologicalandepistemologicalproblemsarebeingamalgamated. 170CHAPTERIV

one” sphere, “the other” sphere, “the same” sphere, “which of” the spheres, or to use proper names for the spheres.Inordertobeabletoapplysuchexpressions[…] itisnecessarythatthedifferentobjectshavedifferent non semantical properties.[…]Inotherwords,theremustbea nonsemanticalexclusivedescriptionwhichfits a1butnot anyoftheotherobjects,anexclusivedescriptionof a2,and soon. 1

WeseeherethatSegelberginsistsontherebeinganexclusive,non semanticaldescriptionforeachobject.Withoutthat,itisnotpossible todistinguishbetweentheentitiesinhabitingthisuniverse.Thetaskis evendeclaredtobemeaningless.Itsmeaninglessnessisexplicitlysaid nottobeduetoanylimitationoftheinquirer’scapability.Inother words, what we are being presented is supposed not to be an epistemologicalproblem.Thesuggestionisthenthattheproblemis purelyontological.Ihavemydoubtsthough. Incidentally, if the spheres have different names, one would assume that someone must have named them. An inquirer is men tioned. The existence of that person automatically destroys the symmetryoftheimagineduniverse.Thatcomplicationisdisregarded though. Perhapsthemostinterestingvariationisthethird—particularly itssecondhalf.

3)Evenif Scontainsmorethantwomutuallycongruent spheres,itcanbethecasethatthespheresdonotdiffer relationally: that will be the case, for example, in the followingsituations.(i)thecentersofthespheresformthe corners in an equilateral polygon; (ii) the spheres are infinitelymanyandthedistancebetweenanytwoadjacent spheresiseverywherethesame. 2

Again, it is explicitly asserted that all the spheres inhabiting the universehavealltheirrelationalpropertiesincommon.Thisisdueto

1Segelberg1999/1947,p.161/41 2Segelberg1999/1947,p.162/42. MOMENTNOMINALISM171 their being congruent as well as symmetrically arranged. What was claimedwithregardtothesecondvariationthenappliestothethird aswell. Aconspicuousdifferenceisofcourse thatinthethird— version(ii)—itissupposedtobemeaninglesstodistinguishbetween thespheresinspiteofthefactthattheyareinfiniteinnumber. Theessentialdifferencebetweenthefirstandfourthvariations isthatthespheresofthelatteraremutuallycongruent,whilethoseof the former are incongruent. In addition, in the latter variation the spheresareasymmetricallyarranged.

4)If Scontainsanumberofmutuallycongruentspheres, andwedonothaveacaseeitheroftype(i)or(ii)in(3), thenrelationaldifferencesobtainbetweenthespheres.By sayingthat,oneisnotnecessarilysayingthat every spherein the group is relationally distinguished from every other sphereinthegroup. 1

Whenthespheresmakeupaconfigurationinwhichtheirrelational propertiesdiffer,itispossibletoapplyindividuatingexpressions to them:‘theonesphere’,theothersphere’,etc.Ifwewant,wecangive thempropernamesoftheirownaswell. Iamabitpuzzledbythemessageinthelastsentenceofthelast quotation,whichseemstobethatsomeofthespheres,whichinhabit the asymmetrical universe, might be relationally indifferent. That claim may seem more plausible if applied to moments, instead of spheres.Iftherearenoreasonsofprincipleagainsttherebeingmore than one congruent moment in one and the same place simul taneously, these moments might be relationally indifferent as well. 2 But,wearetalkingspheresnow.Notwoormoreofthemcanoccupy thesameplacesimultaneously.

1Segelberg1999/1947,p.162/42. 2 Francisco Suárez explicitly contemplates this as a possibility. Cf. the fifth ofhis DisputationesMetaphysicae ,translatedinGracia1982.Cf.also Mertz1996,pp.1289. 172CHAPTERIV

The heading of this section is ‘SemiIndividuality’. The notion referredtobythatdenominationisaccountedforbyusingwhathas appearedinthepresentationoftheintellectualexperiment.

In (1)–(4) we have studied four sets of objects, M1 , M2 , M3 , M4 , where each M has one of the following “extreme”properties: a) every element in M is congruent with every other elementin M; b) every element in M is incongruent with every other elementin M; c) every element in M is relationally indifferent with respect to every other element in M; that is, every relationalpropertywhichbelongstooneelementin M belongstoeveryelementin M; d ) everyelementin Misrelationallydifferentfromevery other element in M; that is, there is a set N of relationalpropertiessuchthateveryelementin Nisa propertyofoneandonlyoneelementin Mandevery elementin Mhasoneandonlyoneelementin Nasa property. 1

Nowthatwehavethesefoursetsathand,wecanformamatrix.2Of thefourcombinationsoneisdeclaredcontradictory:( bc ).Thethree remainingcombinationsarethen:(ac ),( ad )and( bd ). 3

1Segelberg1999/1947,pp.1623/43.Therearetwounfortunatemisprintsin theoriginal.Whatcomesafterthesemicolonin( c)hasbeenmixedupwith thatwhichcomesafterthesemicolonin( d).Inthetranslationthismishapis corrected. 2Thetwodistinctionsfromwhichthematrixisformedareofcoursethose of congruence and incongruence, on the one hand, and of relational indifferenceandrelationaldifference,ontheother. 3SeeSegelberg’spuzzlingassertioninconnectionwiththefourthvariation. Notethatifitisnotnecessarilythecasethateverysphereofthatuniverseis relationally distinguished from every other, the universe in question would neitherbean( ac )set,an( ad )setora( bd )set.Itwouldbean( a)set,sincethe spheresarecongruentwitheachother.Itcouldnotbea( c)setora( d)set though,sincesomeoftheelementsarerelationallyindifferentwithrespectto MOMENTNOMINALISM173

Inthelightofwhathasappeared,Segelbergnowasserts:

Ifwedonotundertakeanythoughtexperiments,butonly consider the circumstances in our universe, where every setofobjectshastheproperty( d),and,consequently,each element in an arbitrary group of objects is relationally differentfromeveryotherelementofthegroup,weeasily overlookthefactthatitisnotlogicallynecessaryforaset to have the property ( d).Thiscircumstanceresultsinan ambiguityintheconceptof“numericaldifference”.Ifan object xisqualitativelydifferentfromanobject y, xmust be“numericallydifferent”from y.1Butevenif xand yare qualitatively identical, i.e. congruent, 2 x can still be “numerically different” from y. Suppose that x is con gruentwith x';doesthestatement‘ xisnumericallydiffer entfrom x'’thenonlymeanthatwhatwecall‘ x’andwhat wecall‘ x'’“are”morethanone x?Or,dowealsomean that the set with only x and x'asmembersisa ( d)set? Thisquestioncannotberesolved,sincethepossibilityof an ( ac )set was not considered when we introduced the conceptof“numericaldifference”. 3

According to Segelberg, we live in a universe where no two indi vidualssharealltheirrelationalproperties.Ouruniverseisa(d)set. Thishasanimplicationwhichwillbementionedinsection4.2.4.

eachotherwhileothersarerelationallydifferentfromeachother. 1ThisgivesexpressiontoLeibniz’sLaw—theindiscernibilityofidenticals —initscontrapositiveform:thenonidentityofdiscernibles. 2 Note that congruenceandqualitative identity are explicitlysaidtobethe samerelation.Cf.section4.3.2,whereitisdiscussedhowtherelationsnamed by ‘congruence’, ‘exact similarity’, ‘absolute similarity’, ‘qualitative identity’ and‘havingallinternalpropertiesincommon’arerelatedtoeachother. 3Segelberg1999/1947,pp.163/445.Thephrase‘whenweintroducedthe conceptof“numericaldifference”’doesnotrefertoanyintroductionmade bySegelberghimself.Whathemeansisthatthenotionof“numericaldiffer ence”isundecidedwithregardto( ac )sets. 174CHAPTERIV

Whatabout(ac )sets?Rememberthattheelementsofsuchsets aresupposedtobeexactlysimilaraswellasrelationallyindifferent. RegardingtheelementsofsuchsetsSegelberg’sfinalwordis:

Perhaps,itisbesttosaythattheelementsofan( ac )setare neitherindividualsnoruniversals,butwhatwemightcall ‘semiindividuals ’. 1

The claim that there is a principal difference between symmetrical and asymmetrical universes, as they have been determined in the intellectualexperiment,canbecalledinquestioninvariousways.The followingisoneobjection. Imagine a universe inhabited by almost indiscernible entities, spheresforinstance.Assumethatthenumberofalmostindiscernible spheresistwoandthattheyaretheonlyentitiesintheuniverse.This approximatesboththefirstandthesecondvariation accounted for above.Asamatterofprincipleitcoincidesexclusivelywiththefirst variationthough.Segelberg wouldsaythattherearetwospheresin thisuniverse.Heisboundtoagreethattheyaretwoevenwhenthe qualitativedifferencebetweenthemis. 2 If they instead werecongruentwitheachother,wouldhemaintainthattheyareonly one in number? If that is indeed what he would do, his use of ‘meaningless’wouldmakesomesense.Ifhewouldclaiminsteadthat the number of spheres is still two but that they are now semi individuals,itisdifficulttograspwhat‘meaningless’issupposedto mean.Inavariationhavinganinfinitenumberofalmostcongruent spheres,arrangedsothatthe universeisappropriatelygeometrically symmetrical, the step from an infinite number to just one sphere standsoutascompletelyabsurd.Thisissoeitherifweassumethat complete symmetry would result from the smallest change of the spheres with regard to their intrinsic qualitative contents,3 or if we

1Segelberg1999/1947,p.164/45. 2 Remember that the intellectual experiment is not supposed to concern . 3Thiskindofargument,fromthepossibilityofalmostindiscerniblestoin discernibles,originatesfromRobertAdams.Cf.Adams1979,pp.179. MOMENTNOMINALISM175 assume that they are all congruent from the start and arranged in geometrical symmetry except for one sphere and that complete symmetrycomesintoexistencewhenitsrelativepositionischanged slightly. The next comment concerns space. Roughly, there are two viewsonspace:absolutismandrelationism.Accordingtotheformer, spaceissomethinginitself.Letussaythatitisasetofpoints.Ifa sphereisinacertainplace,itissobyoccupyingaparticularpointor points. According to moderate nominalism the points making up space might, or should, be thought of as moments, instances of pointhood.Thus,inauniversethatisinaccordancewiththesecond variation,thepointsoccupiedbysphere aandsphere barenotthe same. The same holds mutatis mutandis for universes in accordance withthethirdvariation. 1Nomatterhowsimilartheyaretotherest, no spheres share the same spatial relational properties; the spatial relationalpropertiesbeingtheoneswhichareholdingbetweeneach sphereandspaceitself. 2 Assume instead relationism about space. Space is then con stituted by (spatial) relations that hold between entities, in our case spheres. Since space is not an entity in itself, norelationscanhold betweenasphereandspace.Thespheresarethenprerequisitesofthe relations.Not the otherwayround.Thus,also withrelationismthe numberofspheresiswhatitappearstobe,irrespectiveofwhether theuniverseissymmetricalornot. MyimpressionisthatSegelbergdoesnotdistinguish between universals and individuals when formulating the intellectual experi

1 Needless to say, the points occupied by incongruent spheres are not the sameeither. 2AccordingtoHochberg,Segelbergexplicitlyconsidersabsolutespatialloca tionsinhisdiscussion.Cf.Hochberg1999,p.27.The followingstatement mightbewhatissupposedtojustifyHochberg’sclaim. Iftheobjects a, b, caredispersedinspace—thatis,if a, b, care localized in space (in the sense just specified above) — the different objects have different positional properties. a has one which band cdonothave; bhasonewhich aand cdonothave, andsoon.(Segelberg1999/1947,p.160/39) 176CHAPTERIV ment. According to the doctrines of the moment nominalism he champions, the spheres are not bundles of universals; though they can be described as bundles of moments. The bundles are then individualthroughandthrough.Thus,giventhat a≠b,therelational property Rb isnotthesameoneasRa .Evenwhen aand barecon gruent with each other, that does not change. Seemingly, Segelberg maywrigglefreefromthischargebyreferringtoclasses of exactly similar moments as surrogates for (real) universals. My objection would, still seemingly, be blocked by saying something in line with thefollowing.Asitisusedabove‘havingRto a’isashortfor‘having Rtosomeelementofthecongruenceclassinwhich aisanelement’; thesameholds mutatismutandis withregardto‘havingRto b’.Inthat sense “having R to a” and “having R to b” are the same relational property.Thereisnoindicationofthatinconnectionwiththeintel lectualexperimentthough.Thetwo,“having Rto a”and“having R to b”,arewhatmightbecalled‘impure relationalproperties’.1

4.2.4Individuality Wesawitbeingmaintainedabovethatanentitycan be congruent withanotherentityonlyiftheybotharespatiotemporallylocalised. Thatispartalsoofthemessageofthefollowingtwosentences.

When one says that there are several objects congruent with x, one means that x does not have any property f which is incompatible with there being several objects congruentwith x.Theresultofourreasoningisthatthe

1 Impure relational properties involve determinate individuals. In the par ticularcaseathandthedeterminateindividualsarethetwospheresaand b. Therelation Risauniversal;itisthesamein“having Rto a”and“having R to b”.Purerelationalpropertiesareuniversalthroughandthrough.Accord ing to my understanding of the prevalent terminology in the literature, the distinction is supposed to hold between pure and impure properties . The examplesgivenarealwaysrelationalpropertiesthough.E.g.“beingmarried toHenryVIII”and“beingastudentofSocrates”.Cf.Loux1978,pp.1323. MOMENTNOMINALISM177

property f being considered here is the property of being nonlocalized .1

A prerequisite for being an individual entity then is being spatio temporallylocalised.Segelbergdoesnotthinkthatsufficientthough, as the intellectual experiment accounted for in section 4.2.3 is supposedtoshow.Thepossibilityoftherebeing( c)setscomplicates thematter.

[A]difficultyariseswhenweaskwhethertheelementsof an ( ac )set are individuals or not. This difficulty clearly stemsfromthefactthatthepossibilityof( c)setswasnot considered in the earlier discussion of the concepts of individual and universal . Perhaps, it is best to say that the elementsofan( ac )setareneitherindividualsnoruniver sals,butwhatwemightcall‘ semiindividuals ’. 2

Asecondconditionforbeinganindividualisthenthatitmustnotbe anelementofany( ac)set.AlthoughSegelbergdoesnotexplicitlysay anything about it, this means that relational properties which have internalrelationsastheirrelationcomponentalsomustbeincluded. Otherwise, there will be a lot of moments which are relationally indifferent from each other since they are thought of as being instantaneous and, with certain restrictions, also as sharing their spatiotemporalpositionwitheachother.Thoseactuallysharingtheir position with each other are not congruent though. Therefore, no two moments have all their relational properties in common. In particular, those sharing their positions with each other will differ withregardtorelationalpropertiesinvolvinginternalrelations. 3This isaconsequenceoftheirbeingincongruentwitheachother.Iremind

1Segelberg1999/1947,p.164/45. 2Segelberg1999/1947,p.164/45. 3Notethat ifthe(dyadic)internalrelations betweenmomentsare pseudo additionaltotheirrelata,amomentcanshareaninternalrelationalproperty withatmostoneothermoment.Thissince q1Rq2issupposedtoequal q1+q2, whichobviouslyisnotthesameas qm+qn,whereeitherm≠1orn≠1.Cf. thediscussioninchapterIII. 178CHAPTERIV readers of Segelberg’s claim that the individuals which inhabit our universetogetherforma( d)set.

4.3RelationsandComplexes

4.3.1Overview Section4.3dealswiththerelationalsideofSegelberg’sontology.The principal distinction is the one between external and internal rela tions.Itismadeintermsofsimilarity,whichisaninternal relation itself.Beforethenotionsofexternalandinternalrelationsaredealt with in section 4.3.3, a few obscurities regarding similarity are discussed in section 4.3.2. In the same section two kinds of com plexesarepresented:collectionandcomplexunity.Segelbergattaches greatimportancetothedistinctionbetweenthesetwo. Whatmightbedescribedasthefundamentalontologicalglueof reality,theelementaryconnection,isdealtwithinsection4.3.4.Inthe following section, 4.3.5, the analogue on the ideal side is also dis cussed. In the final section, Segelberg’s doctrine about entities of differentordersispresented.

4.3.2Similarity InSegelberg1945,wefindhisfirstproposeddeterminationsofinter nalandexternalrelations.Asimilarityrelationcalled‘congruence’is essential for these determinations. As it is described in Segelberg 1945, it is evident that congruence is closely related to — if not identicalwith—exactsimilarity.Anindicationofthatisthat‘exactly similar’ and ‘congruent’ are used interchangeably. There are indicia though suggesting that there might be a difference between con gruence and exact similarity. Among the first which is said about congruenceisthefollowing.

Theconcept congruence anditscontradictory incongruence are elementaryconcepts,whichcannotbedefinedbyanalysis. Theirmeaningcanonlybemadeclearbyexamples.That x and yare congruent impliesthattheyare exactlysimilar ;there MOMENTNOMINALISM179

byimplyingthattheyhaveallinternalpropertiesincom mon.Ontheotherhand,congruencedoesnotimplythat allexternalpropertiesareshared. 1

Four relation terms can be extracted from this quotation:2 ‘con gruence’, ‘exact similarity’ and ‘having all internal properties in common’.Doeseachoneofthesenameitsownrelationorarethey perhaps three different names of the same relation? Yet a third possibilityisthattwoofthemnamethesamerelation,whilethethird namesitsown.Furtherrelevantinformationonthismatterisfound inwhatisstatedconcerningthedifferencebetweencongruenceand themirrorrelation.

Wemustdistinguishcongruencefromtherelationwhich obtains between an asymmetrical object and its mirror image.Wecallthisrelationthe mirrorrelation .Arighthand stands,atleastapproximately,inthemirrorrelation to a left hand. As one can distinguish them, without taking external properties (location) into consideration, they are incongruent.Twoobjectswhichstandinthemirrorrela tion toeachother,wecall mirrorcorrelates . Itisimportant thatapairofmirrorcorrelatescanagreeinalltheirinter nalproperties.Suchisthecaseinfigure3.Thestatement ‘xiscongruentto y’isthusnotequivalenttothestatement ‘xand yhavealltheirinternalpropertiesincommon’. 3

Theillustration,referredtoasfigure3,is:4

1Segelberg1999/1945,p.38/29.TheterminologyofSegelberg1945ispartly differentfromthatofthetwolaterbooks.Intheformer,‘internalproperty’ and‘externalproperty’areused;notsoinSegelberg1947and1953.Inthe twolatterworks,thatpairisreplacedby‘quality’and‘relationalproperty’. 2Idisregard‘incongruence’forthemoment. 3Segelberg1999/1945,p.39/30. 4Thesquares x, yand zcanbetakentobered,blueandgreenrespectively. Furthermore,notasingleoneofthesquaresisrecycled.Thetotalnumberof squaresappearingin B, band B'isnine,notthree.Cf.Segelberg1999/1945, p.127/113. 180CHAPTERIV

BbB' y x x y z y z z x Of these three figures B and baresaidtobemirrorcorrelates;the sameholdsfor band B'.Band B'arecongruencecorrelates. WhathasjustbeenreportediscomplicatedbywhatSegelberg saysinafootnote.Itismentionedtherethatingeometryobjectsare congruentiftheymatcheachotherinsizeaswellasinshape;headds thatgeometryalsodistinguishesbetweendirectcongruenceandsym metry.

Directcongruenceobtainsbetweentwofiguresiftheycan bemadetocoveroneanotherbymovementintheplane. The symmetry relation obtains between a pair of con gruentfiguresifamovementinthreedimensionalspaceis necessary for one figure to cover the other. The term ‘symmetry’has thesamemeaning hereasourexpression ‘mirrorrelation’. 1

Allofthisisrelevantwheninterpretingthedistinctionbetweencon gruence,inSegelberg’sextendedsenseofit,andthemirrorrelation. Notethat,accordingtothelastquotation,themirrorrelationobtains betweenapairofobjectsifmovingtheminthreedimensionalspace isnecessaryforonetocovertheother.Inthequotationbeforethe lastone,arightandalefthandaresaidtobemirrorcorrelates.In fact, they are not since they cannot be moved in threedimensional space in a way which makes one cover the other. Using a meta phorical description, a right hand is entered in threedimensional spacedifferentlyfromalefthand.Handsaresocalledenantiomorphs eveninthreedimensionalspace.Iftherewereafourthspatialdimen sion,thatmightmakeitpossibleforthemtocovereachother.On theotherhand,thetwotwodimensionalfigures Band b'aremirror

1Segelberg1999/1945,p.123n/110n. MOMENTNOMINALISM181 correlates. Although they are enantiomorphs in twodimensional space,theyarehomomorphsinthreedimensionalspace. 1 What are we to make of the determination of the mirror relation?Themostnaturalthingtodowouldbetoleaveoutwhatis saidregardingthetwohands.Afterall,theydonotsatisfytheexplicit definitionofwhatitmeanstobemirrorcorrelates.Ifwedecideto keepthetwohandsasexamplesofmirrorcorrelates,thedefinition providedinthefootnotemustbechanged.Arevisedversionmight bethattwoobjectsaremirrorcorrelatesiftheycanbemadetocover each other in n+1dimensional space, where ndimensional space is thespacethepairofobjectsispresentlyinandinwhichtheycannot bemovedsothattheycovereachother.Thiswouldimplyarelational viewofspacethough.Thissince,accordingtoabsolutism,realspace doesnothavemorethanthreedimensions.Iproposethatwechoose theformersolution. Thus, according to the geometrical definition, two figures are mirrorcorrelatesiftheycovereachotherinthreedimensionalspace butnotintwodimensionalspace.Iwouldsaythatthemirrorrelation is,atleast,primarilyageometricalrelationinSegelberg’sterminology aswell.Congruence,ontheotherhand,isageneralnotionwhichis supposedtobeapplicabletoallkindsofentities. Letusreturntothequotationinwhichcongruenceandthemir rorrelationareintroduced.Sincetheexamplewiththeleftandright handsisinadequate,itmustbechanged.Isuggestthatweinsteaduse the figures B and b. Segelberg asserts then that they can be dis tinguished without taking their locations into consideration. From that, it is concluded that they are incongruent. However, when the mirror relation obtains between two objects, the relata agree in all theirinternalproperties.Thisisabitpuzzling.Onewouldexpectthat there is something in virtue of which congruence holds between congruencecorrelatesbutnotbetweenmirrorcorrelates.Whatmight 1 Cf. Nerlich 1994, Chapter 2. In that chapter — which has the heading ‘Hands, knees and absolute space’ — the notions of enantiomorphism, homomorphism, etc. are discussed. As the heading suggests, there being handsandkneesis,orcanbeturnedinto,anargumentfortheexistenceof absolutespace. 182CHAPTERIV thatbe?Inprefacetoananswertothatquestion,Iaddafigurewhich isnotfoundinSegelberg1945.1 C x y z Segelberg would say that C is neither congruent with any of the formerthreefigures,norisitamirrorcorrelateofanyofthem.Do thefourfiguresatleasthavealltheirinternalpropertiesincommon? Band bdo,accordingtowhatisstated.Since Band B'arecongruence correlates, B'alsohasallitsinternalpropertiesincommonwithitand b.IsthesametrueofC?Iwillcomebacktothatquestionafteryet anothernotionhasbeendescribed:isomerism,which,inturnrequires theintroductionofthenotionsofcollectionandcomplexunity. Collection and complex unity are essential notions in Segel berg’sontology.Theyaresaidtobeurphenomena;neitherofthem can be derived from the other. 2Thatdoesnotimplythattheyare completelyindefinablethough.Bothofthemaredefinedintermsof therelationofbeingdisparate.

Twoobjects xand yaresaidtobedisparateifandonlyif thefollowingstatementshold:(1) xand yarenotidentical; (2) xdoesnotcontain y;(3) ydoesnotcontain x;(4)there isnocontentof xwhichisalsoacontentof y.3

Thiscanberenderedinthefollowingway,whichismoreinlinewith therenderingofthedefinitionswhichfollow.

1Noneofthethreesquaresof Carethesameasanyofthenineabove.Its squares x, yand zarered,blueandgreenrespectivelythough. 2Cf.Segelberg1999/1945,p.55/46. 3Segelberg1999/1945,pp.42/33.Thedefinitionpresupposesthatweknow themeaningsoftheterms‘contain’and‘content’. MOMENTNOMINALISM183

I. A pair of objects x and y are disparate if and only if the followingconditionsobtain: (1) xand yarenotidentical. (2) xdoesnotcontain y. (3) ydoesnotcontain x. (4) Thereisnocontentof xwhichisalsoacontentof y.

Furnishedwiththisdefinition,thenotionsof complex , collection , unity , complexunity and totalcollection aredefined. 1

II.Anobjectxisa complex ifandonlyifthereisapairofobjects yand zsuchthat: (1) x containsy. (2) xcontains z. (3) yand zaredisparate.

III. An object x is a collection, if and only if the following conditionsobtain: (1) xisacomplex. (2) Thereareatleasttwoobjects yand z,disparatefromeach other,andsuchthat,ifthereisanobject H,whichcontains x,then“ Hcontains x”=“ Hcontains y& Hcontains z”.

IV.Anobject xisa unity, ifandonlyifthereare not twoobjects, yand z,suchthat,ifthereisanobject Hwhichcontains x,then “Hcontains x”=“ Hcontains y& Hcontains z”.

V.Anobject xisa complexunity ifandonlyifthefollowinghold: (1) x isacomplex. (2) xisaunity.

VI. A collection y+z is a total collection of x,ifandonlyifthe followingconditionsobtain: (1) x containsy. (2) x containsz. (3) yisdisparatefromz.

1 The five definitions which follow are presented in this way in Segelberg 1999/1947,pp.20910/1101. 184CHAPTERIV

(4) Thereisnoobject usuchthat xcontains uand uisdispar atefromboth yand z.

Segelberg often uses the term ‘tcollection’ instead of ‘total collec tion’. Thedefinitionofthenotionofisomerismnowreads:

Ifacomplex khasatcollection[totalcollection] x+y+z, andanothercomplex k'hasatcollection x'+y'+z',where xiscongruentto x', yiscongruentto y'and ziscongruent to z', kand k'aresaidtobe isomeric (adjective)or isomers (substantive). 1

Twolawsofisomerismforcollectionsarediscerned:

(1)Iftwocollections kand k'arecongruent,theyareisomeric aswell. (2)Iftwocollections kand k'areisomeric,theyarealsocon gruent. 2

Neither of these laws holds for complex unities. An illustrative exampleisthepairofthetwodimensionalfiguresBand babove.

Thereisnocontentinthefirstfigurethatdoesnothavea congruent correspondent in the second. But, in spite of this,thefiguresareincongruentwitheachother;nomatter how the figures are rotated, one can not get them to match.3

From this it is concluded that incongruent entities can be isomers. Now,isCisomericwiththeotherfigures?Ifatotalcollectionof Cis x+y+z,itwouldseemthatitisisomericwitheachoneofthem.Butis x+y+zatotalcollectionof C?Isthecorrespondingcollectionofany of the other figures a tcollection of their contents? All of these

1Segelberg1999/1945,p.50/41.InSegelberg1945thecollectionoftwoen tities xand yisdesignated‘ x, y’.Inthetwolaterbooksthisisrevisedto‘ x+y’. Intheirrenderingofthefirstbookthetranslatorsusetherevisedversion. 2Cf.Segelberg1999/1945,p.50/41. 3Segelberg1999/1945,p.51/42. MOMENTNOMINALISM185 questions should get the same answer: no. To see why this is so, examine them more closely. Each of the figures obviously has a propertywhichislostif x+y+zissupposedtobeitstotalcollection. Whatislostistheshape ofeachfigure,i.e., theshapeofasquare. The collection x+y+z+s, where ‘ s’ stands for the shape in question might better suit our requirements. The same holds mutatis mutandis withregardto C.Itsshapeisobviouslynotcongruentwith sthough.1 Onemightthinkthat B’s“turntotheright”shouldseparateit from b,whichmakesa“turntotheleft”.Thesedifferencesarerela tional, existing as a result of how B and b are related to the two dimensionalspace.Thetwowouldbecongruentinthethreedimen sionalspace.Thisshowsthatthetopologyoftheuniverseisrelevant. 2 IfitwereSegelberg’sviewthattherelationtospacedidnotmakeany difference with regard to whether two objects like B and b are congruent,hewouldhave to saythat Band barecongruentinthe twodimensionalspaceaswell.3 Thatcongruenceisnot thesamerelationasthat ofhaving all internalpropertiesincommonhasexplicitlybeenstatedabove.Being congruentimplieshavingallinternalpropertiesincommonthough. 1Cf.Segelberg1999/1945,p.49/40,whereitismentionedthatthreesquares x, yand zmayformafigurewhichdoesnothavetheshapeofarectangle. Thisalsoappliestothepresentexample. 2EnteredintoauniversewiththetopologyoftheMöbiusstriportheKlein bottle,theywouldbecongruenttheretoo.Cf.Nerlich1994,pp.514. 3ThatviewisexpressedinWittgenstein1961,sentence6.36111: Kant’s problem about the right hand and the left hand, which cannotbemadetocoincide,existsevenintwodimensions.In deed,itexistsinonedimensionalspace[…].Therighthandand the left hand are in fact completely congruent. It is quite ir relevantthattheycannotbemadetocoincide. Arighthandglovecouldbeputonthelefthand,ifitcouldbe turnedroundinfourdimensionalspace. A comment on this, made by Ingvar Johansson, is that Wittgenstein pre supposesarelationalconceptionofspace.Sincehetakesspacestobemerely constructions,itbecomesarbitraryhowmanydimensionsaspacehas.There wouldnotbeanylefthandorrighthandpropertiesifthenumberofdimen sionswerearbitrary.Johanssonisanadvocateofabsolutespace,or,container space,ashecallsit.Cf.Johansson,1989,p.157. 186CHAPTERIV

Thatmaybeconcludedfromanotherquotation.Therearepassages, which,atleasttosomeextent,pointinanotherdirection.Thefirstis inSegelberg1945.Notethatthingsarecomplicatedbythefactthat anaccountisgiventhereofaviewwhichisnothisown.Anyhow,the relevantstatementisthatcongruenceisthesameasqualitativeiden tity.1Andhowis‘qualitative’tobeinterpretedifnotasbeingsynony mouswith‘withregardtointernalproperties’?Thus,congruenceand havingallinternalpropertiesincommonmightbethesamerelation afterall.RecallSegelberg’sassertioninhissecondbook:

Ifanobject xisqualitativelydifferentfromanobject y, x mustbe“numericallydifferent”from y.Butevenif xand y are qualitatively identical, i.e. congruent, x can still be “numericallydifferent”from y.2

Herewefindqualitativeidentitybeingexplicitlyidentifiedwithcon gruence.Andwhatismore,thisisnotareportontheviewofsome oneelse. In addition to the terms already mentioned, there is a fourth one:‘absolutesimilarity’.Itisusedinonesingleplace.

One can distinguish two senses of the word ‘similarity’: absolutesimilarity 3andrelativesimilarity.“Absolutesimi larity” is the same as congruence; “relative similarity” obtains between objects which are “like” in one respect and“different”inanother.Thatrelativesimilarityobtains between a pair of objects, x and y, implies: x is incon gruentto yand xhasacontent zand yhasacontent z'and z is congruent to z'. We will assume in the future that every “similarity” between incongruent objects has this character. 4

1Cf.Segelberg1999/1945,p.41/32. 2Segelberg1999/1947,pp.163/44. 3 The translators have inserted ‘(exact)’between ‘absolute’ and ‘similarity’. Sincethereisnosuchinsertionintheoriginal,Ihaveremovedit. 4Segelberg1999/1945,p.43/34. MOMENTNOMINALISM187

‘Exact similarity’ is not mentioned here as a name of a variant of similarity.Nodirectinformationisthereforesuppliedconcerningit. Another piece of information is given though: similarity between objectsalwaysinvolvescongruence. 1An“extreme”formofrelative similarityholdsbetweenmirrorcorrelates.Thissince they are what Segelbergcalls‘absoluteisomers’;meaningthatforeachtotalcollec tionofeithercorrelatetheotherhasacongruenttotalcollection. Wheredowestandnowregardingcongruenceandexactsimi larity?Itcouldbethatthereisnodifference.Theway‘exactsimi larity’ is used in the two later books is a strong indication of that. There is also the possibility though that, at least in the first book, congruenceisnotthesameasexactsimilarity.Perhapsitfallssome wherebetweencongruenceandhavingallinternalpropertiesincom mon.Thetranslationreinforcestheindicationoftherebeingatris tinction in this case. I repeat the relevant sentence to show what I meanbythat.

That xand yare congruent impliesthattheyare exactlysimi lar ;therebyimplyingthattheyhaveallinternalproperties incommon. 2

This way of rendering the relationship between the (possibly) three relationssuggeststhatexactsimilarityisamiddleman,duetothetwo wordschosenbythetranslators:‘implies’and‘implying’.Theformer mightbemisleading.AbettertranslationoftheSwedishwordused wouldbe‘means’,insteadof‘implies’.3Ifcongruencebetweenentities means that they are exactly similar and is thereby implying that they havealltheirinternalpropertiesincommon,theindicationofatris tinctionbeingmade,insteadofadistinction,isbarely,ifatall,visible. Congruenceisthennaturallythoughtofas beingthesameasexact similarity.

1Evidently,thisgivesexpressiontowhatwasnamed‘thesimilarityprinciple’ inchapterII. 2Segelberg1999/1945,p.38/29. 3TheSwedishwordis‘innebär’. 188CHAPTERIV

It should also be noted that the congruence which holds betweenmirrorcorrelatesdependsontherelationseachmirrorcorre latehastospace.Sincetheserelationsarenotinternalpropertiesof either mirror correlate, neither are they contents of them. Perhaps thatimpliesthatrelationaldifferencesareirrelevant.

4.3.3InternalandExternalRelations Let us return to the notions of internality and externality using a referencetoDavidHumeasanintroduction:

In The Treatise ,1 Hume divides relations into two classes: thosewhicharecompletelydependentonthe“ideas”we compare, and those that can be changed without the compared “ideas” changing. We call the first type of relationsimplya relation oran idealrelation ;thesecondtype a connection ora realrelation .2

Though inspired by Hume’s distinction, the one Segelberg has in mindisnotofsuchalimitedscopeastheformeroneatleastappears tobe.Idealrelationsdonothaveideasastheirexclusiverelata.

1Humesaysintheplacereferredto: These relations may be divided into two classes; into such as depend entirely on the ideas, which we compare together, and suchasmaybechang’dwithoutanychangeintheideas.(Hume Treatise ,Book1,Part3,Sect.1) As pointed out in Hochberg 1999, pp. 3367n, Segelberg may (mistakenly) believethatHumepartitionsallrelations as belongingtooneofthesetwo classes.Thisisnotsothough.Hume’sdistinctionappliestotheclassofwhat hecalls‘philosophicalrelations’. 2Segelberg1999/1945,p.41/32.WhereSwedishhas(atleast)threewords, Englishseemstohaveonlytwo.Theformerare‘relation’,‘förhållande’and ‘förbindelse’; the first of these being the most general. The English word ‘connection’ equals that of ‘förbindelse’ quite well. When it comes to ‘förhållande’,inthesenseusedbySegelberg,theterm‘idealrelation’seemsto bethebestalternative,despiteitsclumsiness.Touse‘relation’bothasaspe cificandageneraltermseemsrisky.Ihavethereforeinserted‘ideal’inafew places. MOMENTNOMINALISM189

Segelberg’sdefinitionofinternalrelation,underthename‘ideal relation’,reads:

If Risan[ideal]relation,thefollowingconditionsobtain. If xRy and x~x',1 where x, y and x' can be any objects, thenthereisanobject z,suchthat x'Rz and z~y.2

Arelationwhichsatisfiesthisconditionis(atleast)btypeideal.To earnthestatusofbeingatypeidealitmustalsosatisfythefollowing, somewhatstronger,condition:

Ifan[ideal]relation Risanarelation(aideal),ageneral implicationobtainsfrom xRy & x~x'to x'Ry .3

Examples of atype ideal relations are congruence and the mirror relation. The whole–part relation is an example of a btype ideal relation.4 AccordingtoSegelbergarelationanditsconverseareinfactthe samerelation.Giventhatthisisso,itisabitpuzzlinghowarelation 1The‘~’standsforcongruence. 2Segelberg1999/1945,p.41/32. 3Segelberg1999/1945,p.41/32. 4Unfortunately,therearetwomisprintsintheoriginaltext.Oneofthemstill remainsinthetranslation.Theparagraph,inSegelberg1999/1945,p.41/32, inwhichtheybothoccurreads: Examplesof[ideal]relations:(1) Congruence .If xiscongruentto y and x~x',thenthereisanobject z(forinstance y),suchthat x'is congruentto zand z~x[myremark:itshouldbe‘ z~y ’,insteadof ‘z~x ’;thisisthefirstmisprint].(2)The mirrorrelation .If xhasthe mirrorrelationto yand x~x',thereis anobject(forexample y itself), such that x' is a mirrorimage of z and z~y . (3) The relation of whole–part .If xhas y asapartand x~x',thereis an object zsuchthat x'has z[thetexthas x,trans.][myremark:this isthesecondmisprint]asapartand z~y . Assume for a moment that the rendering of the condition in (1) is not a misprint.Congruencestillsatisfiesit:( x~y & x~x')→∃z(x'~z & z~x )isa trueproposition.Thisconditionisnotthesameasthatof(2)and(3)though. Itmightturnoutthatcongruenceisthesinglerelationwhichsatisfiesit.Ifit isnotamisprint,atristinctionisbeingmadewithintheclassofidealrela tions. 190CHAPTERIV canbeinternalwhileitsconverseisnot.Segelbergcommentsonthis. Ilethimspeakforhimself.

Accordingtoourwayoflookingatit,[…]arelationand itsconverserelationarebasicallythesamethingseenfrom two points of view. That a is larger than b is exactly the samethingasthat bissmallerthan a.Thefact,whichboth statementssignify,hastheconstituents a, b,andtherela tion of comparison, and no other constituents. 1 On the otherhand,onecansaythatthereisadifferenceinmean ingbetweenthem,inthesensethattheunderstandingof theexperience,whichtheonestatementexpresses,differs inatypicalwayfromtheunderstandingoftheexperience whichtheotherstatementexpresses.Inthefirstcaseone beginsbythinkingabout a,whileinthesecondcaseone begins by thinking about b. What is it, then, that makes one use the expression ‘larger than’ in the one case, and ‘smallerthan’intheothercase,giventhatthemeaningis totally opposite when one chooses the relational expres sionsinreverse?Onecanputthematterinthefollowing way: The relation of comparison has two sides, a “plus side”anda“minusside”;inthestateofaffairs“aislarger than b”,theplussideisturnedto aandtheminussideto b;intheoppositestateofaffairstheminusside,instead,is turned to a and the plus side to b. We now use the expression‘largerthan’inordertoexpresstherelationin question, if the term of the relation which is thought of firstisunitedwiththeplussideoftherelation.However, whenthetermconceivedfirstisunitedwiththerelation’s minusside,weusetheexpression‘largerthan’.Whathas been said here about the relation “larger than” (“smaller than”) holds, mutatis mutandis , of all asymmetrical rela tions. 2

1BelowitwillbeseenthatBradley’sregressissupposedtoariseinconnec tionwithstatesofaffairs.Thereisnosignofthatherethough. 2Segelberg1999/1947, p.190/81.Isuspectthatthenonsymmetricalrela tionsareincludedintheclassofasymmetricalrelations. MOMENTNOMINALISM191

Thus,thereisonlyonestate ofaffairs,although it might look like therearetwo.Theappearanceoftwostatesofaffairsisduetosub jectivity; it is dependent on the order in which the relata are con sidered.Inthelightofthis,Segelbergnowsays:

Asitisdesirabletodefinetheconcept“internalrelation” without bringing in subjective factors, we should not definetheconceptsothatanasymmetricalrelationcanbe internal without its converse being internal. Rather, we should, instead, distinguish between two different con ceptions of internal . We speak therefore about unilaterally internal relationsand bilaterallyinternal relations. 1

Theuseof‘conceptions’in‘differentconceptionsof internal ’suggests thatadistinctionismadebetweenconceptsandconceptions.Inthe Swedishoriginal,however,justonesinglewordisused.Itsmeaningis that of ‘concept’. Thus, Segelberg’s intention is not to distinguish between the conceptofinternalrelation,ontheonehand,andvarious conceptions of it, on the other. Instead, what are distinguished are twoconceptsofinternalrelation.

Thatarelation R is internal means,wewillsay,that atleast one ofthefollowingstatementsholds: 1)If x hastherelation R to y,theneveryobjectcon gruentto x hastherelation Rtoatleastoneobjectcon gruentto y. 2)If x hastherelation R to y,theneveryobjectcon gruent to y has the converse of R toatleastoneobject congruentto x.2

If only one of the conditions (1) or (2) is satisfied, a relation R is unilaterally internal. If both conditions are satisfied, R is bilaterally internal.Tobeaninternalrelationistobeeitherunilaterallyinternal or bilaterallyinternal.Itakeitthatcongruenceandthemirrorrelation are both bilaterally internal; the whole–part relation is unilaterally internal. 1Segelberg1999/1947,p.190/82. 2Segelberg1999/1947,p.191/82. 192CHAPTERIV

Externalrelationsdonotfulfilanyofthetwoabovementioned conditions. To begin with, three examples of external relations are presented:

(1) Spatialcontact .If x liesspatiallynextto y and x~x' ,there neednotbeanobject z,congruentto y,whichliesnextto x' .(2) Temporal succession. Iftheevent x takesplacebefore theevent y andtheevent x isexactlysimilartotheevent x' ,thereneednotbeanevent z,congruentto y,suchthat x' occurred before z. (3) The relation between simultaneous experiencesinatotal consciousness. If x and y aresimultaneous experiencesinatotalconsciousnessandx~x' ,thereneed notbeanyexperience z,congruentto y,suchthat x' and z aresimultaneousmomentsinatotalconsciousness. 1

Connections and ideal relations form unities together with their relata.Inthestatesofaffairs“ xisspatiallynextto y”and“ xislarger than y”theunifiersareaconnectionandanidealrelationrespectively. Theterms‘connection’and‘idealrelation’arealsousedasdenomina tionsfortheirrespectiveunities. Whetheranasymmetricalrelationexistssinglyorinpairwitha converserelationisanintricateproblem.Asitappears,asymmetrical relationscomein pairsthough.Anobviousquestionisthen:which oneofthetwoisitthatreallyexists?IsupposethatSegelbergwould findthatquestioneasytoreplyto.Hisanswerwouldbethatthereis onlyonesincethetwoarethesame. If the asymmetrical relations do come in pairs, logical equi valence holds between atomic facts. Given that a relation holds, its conversealso holds between thesamerelata,intheoppositeorder. Hochberg suggests that there is a good reason to thinkthatasym metricalrelationscomeinpairs.

To recognize converse pairs is to recognize that, given a relation R, one does not introduce a further relational predicate‘ R*’by definition .Ratheroneholdsthatthereisa unique relation that is the converse of R. There may be

1Segelberg1999/1945,pp.412/323. MOMENTNOMINALISM193

other relations with the same extension as the converse, R*.Forneitherpropertiesnorrelationsareidentifiedwith theirextensions.Thismeansthatonecannottakethecon versetobe the relationrepresentedbyadefinedpredicate, asinthefamiliarsettheoreticalapproach: yR *x=df xRy . […] For this assumes that only one relation has the appropriateextension[…].Theassumptionisnotviable, ifthepredicatesrepresentrelations,notclasses.1

4.3.4ElementaryConnection ThefundamentalontologicalglueofSegelberg’sontologyistheele mentaryconnection.ItisacloserelativeofthatwhichWilliamscalls ‘concurrence’. The essential difference between these relations is of coursethatSegelberg’sconnectionisauniversal. Thefirstappearanceofelementaryconnectionisin Segelberg 1945. It is also there we find the most transparent and complete determinationofit.

A […] kind of connection is found in a homogenously colored surface. The color and the extension are here connected in a totally different way than, for example, parts of space in contact. If we wish to characterize the relationbetweencolorandextension,itisnaturaltospeak ofa“fusion”ofcolorandextensionortosaythatcolor and extension “permeate” each other or that the color “covers”theextension. We call this connection an elementaryconnection or e connection , since it should be evident that other kinds of connectionsarecompoundrelations,inwhichtheecon nectionisacomponent,andsincetheeconnectionitself doesnothaveanyotherconnectionasacomponent. 2

As it will turn out, the proposed definition of theelementarycon nectionismadeintermsofimmediateunionandbeingimmediately

1Hochberg1999,p.160. 2Segelberg1999/1945,p.54/45. 194CHAPTERIV united.Insteadoftryingtoaccountforthesetwonotions,IletSegel bergpresentthemhimself.

Assumethat xand yareimmediatelyunited,that xlacks content 1andthat yhasasolitarycontent z.Itiseasilyseen thattheimmediateunionbetweenxand ycanbeofdiffer entkinds.If xisimmediatelyunitedwith z, xis,thereby, immediatelyunitedwith y,butinadifferentwaythanif x isimmediatelyunitedwith ywithouttheintermediationof z.Weconsequentlyhavetodistinguishbetweena direct and an indirect immediate union. In the above example, the following cases of an immediate union between x and y canbeimagined:(1) xisdirectlyunitedwith ybutnotwith z; (2) x is directly united with z but not with y; (3) x is directlyunitedwithboth yand z.Ifoneconsidersseveral contentsof xand y,thenumberofalternativesofunion quicklygetslarger. 2

Thenotionofsolitarycontentseemstoplayanessential role here. Thedefinitionofitcanberendered:somethingisasolitarycontent of another entity if the latter does not have any content which is disparatefromtheformer. 3This,atfirst,givestheimpressionthata solitary content is simple, in some sense. This impression is rein forcedbyanexamplegivenindirectconnectionwiththedefinition. Itisfoundinthenextquotation,whichalsocontainsthedefinition itself.

Byasimpleunitywemeanaunitywhichdoesnothave several disparate contents.Thataunityissimpledoesnot

1Presumably, xlackingcontentdoesnotmeanthatitisempty.Itakeitthat itisasimpleentityandthisinastrongsense.Perhapswecanassumethatitis an atom, in the original sense of that word. Furthermore, although it is perhapsnotexplicitlysaidanywherethatonlymomentscanbeeconnected, thisseemstobeimplied.Thedescriptionofaneconnectionasbeingafu sionofentitiesandthatcolourandextensionareusedasexamplesofecon nectedentitiesarepartsofthecircumstantialevidence. 2Segelberg1999/1945,pp.56/467. 3Cf.Segelberg1999/1945,p.52/43. MOMENTNOMINALISM195

excludethatithasmanycontents,solongasthesearenot disparate.Asimpleunity xcanthuscontain y, zand u,for example, ycontains zand zcontains u.Here,itisassumed that xdoesnotcontainacontentthatisdisparatefromy, z or u.Ifanobject xcontainsanobject ywithouthavinga contentdisparatefrom y, yissaidtobea solitarycontent of x.1

There is another example of a solitary content: the general colour character,asitoccursinallcolours.Itisasolitarycontentofthem, sinceitisimpossibletofindanycontentinaspecificcolourwhichis disparatefrom thisgeneralcharacter.2Thereisafootnotemadein connectionwiththisexample,inwhichSegelbergcommentsonwhat iscalleda‘simplequality’.

Thegeneralconcept ofa“simplequality”doesnot cor respond exactly to the concept of “simple unity”, as a simple quality cannot contain another object. If, for example, red is a simple quality, red cannot contain the qualitycolor.On theotherhand,thisdoes notposeany obstacleifredisa“simpleunity”.Theconceptofasimple qualityseemstoinvolveacollectionisticoutlookasapsy chologicalpresupposition,thatistosay,anoutlookwhich doesnotallowforthepossibilityofsolitarycontents. 3

This of course adds to the impression that an entity which has a solitarycontentissimple,insomesense,although it is not that of beingabsolutelysimple. Inanother paragraph thereis moreinformation,which isalso new.Itbringsonarevisionofthefirstimpressionofwhathavinga solitarycontentamountsto.

Anespeciallyimportantcaseofasolitarycontentisthet collection[totalcollection]ofacomplexunity.If kisat collectionofacomplexunity a, kisasolitarycontentof a.

1Segelberg1999/1945,p.52/43. 2Segelberg1999/1945,pp.523/43. 3Segelberg1999/1945,p.124n/111n. 196CHAPTERIV

Ifacollection kisasolitarycontentof a, kisatcollection of a.1

Theimplicationtosimplicityiscompletelyabsenthere.Instead,the assertion is made that the tcollection of any complex unity is a solitarycontentofit.Sincetherearecomplexunitiesofinfinitecom plexity with regard to disparate contents, it turns out that the first example is misleading. The entity used as an example there just happenedtobeasimpleunity. Donotfailtonoticeanotherimplicationofthestatementmade in the last quotation: a tcollection of a complex unity is itself a content of that complex unity. This piece of information is in dependentofhowthenotionofsolitarycontentisdefined.Iamnot sure of whether the entity x, which plays a principal part in the determinationoftheelementaryconnection,hasasolitarycontentor not.Inthesecondquotationofthepresentsectionwewereinformed thatitlackscontent.Perhapsithasasolitarycontentinatrivialsense; i.e.,itisitsownsolitarycontent. A prerequisite to understanding Segelberg’s definition of ele mentaryconnectionisanunderstandingofwhatitmeansforsome thing to be immediately united with something else. An objection mightberaisedthatanallegeddistinctionbetweendirectandindirect immediate union is mistaken, since entities are either immediately unitedortheyarenot.Immediacydoesnotadmitofanyfurthergra dationonitsown.However,Segelbergwantstodistinguishbetween whathecalls‘directimmediateunity’,ontheonehand,and‘indirect immediateunity’,ontheother.Furthermore,hedefinesthenotionof elementaryconnectionintermsofdirectimmediateunity.Theactual definitionisfoundinthefourthparagraphofwhatfollows.

Incase 21thereisacomplex,whichwecall a,incase 2the complex b,incase 3thecomplex c.Alltheseunitiescanbe

1Segelberg1999/1945,p.53/43. 2 The three cases are those listed four quotations back — i.e., Case 1 : x is directlyunitedwith ybutnotwith z; Case2 : xisdirectlyunitedwith zbutnot with y; Case3 : xisdirectlyunitedwithboth yand z;andinallthesecases zis MOMENTNOMINALISM197

represented,inourschematicsymbolism,by‘ xy ’,sinceall have the collection x+y as a tcollection. But, obviously, theyarenotcongruent. Inthecomplex a, xisdirectlyimmediatelyunitedwith y. In b, x is indirectly immediately united with y, which impliesthat xisdirectlyimmediatelyunitedwithacontent of y,butnotdirectlyimmediatelyunitedwith yitself. Inthecomplex c, xisdirectlyimmediatelyunitedwith both y and z. Hence, c contains both a and b. Consequently,onecandistinguish,in c,aunityof xand y whichdoesnotcontainaunityofxand z,while ycontains z, and x is in fact immediately united with z. If one observesthis,onecangiveadefinitionoftheconceptele mentaryunity:Byan elementaryunityofxandy ismeantan immediate unity of x and y, which does not contain an immediate unity of x and some content of y or of a contentof xandacontentof y. Thecomplex aisthusanelementaryunityof xand y; thecomplex cisnotanelementaryunityof xand y,butit contains suchaunity;thecomplex b1neitherisnorcontains an elementary unity of x and y. If x and yformanele mentaryunity, xand yare elementarilyconnected .Inthecom plexes aand c, xand yarethuselementarilyconnected.2

Thus,thedefinitionofanelementaryunityis:

Elementaryunityof xand y= Df.Animmediateunityof xand y, (i) which does not contain an immediate unity of x and somecontentof y, (ii)which does not contain an immediate unity of y and somecontentof x,or

asolitarycontentof y.Cf.Segelberg1999/1945,p.56/47. 1Theoriginalhas‘ c’.Thismisprintiscorrectedinthetranslation. 2Segelberg1999/1945,p.56/47. 198CHAPTERIV

(iii)which does not contain a unityofacontentof xand acontentof y.

Sinceitisexplicitlyassertedthat xand yareeconnectedin c,thedefi nition should not be interpreted in such a way that an elementary unity of x and ymust notcontainanimmediateunity ofeitherof them with a content of the other or an immediate unity between contentsofeachofthem.Itmayinfactdoeitherofthosethings,but itmust also containadirectimmediateunityof xand ythemselves. Without the latter, x and y are not econnected with each other. Brieflysummingup,beingeconnectedisbeingdirectlyimmediately united. Notethattheterminologyusedinitiallyisslightlychangedinthe actualformulationofthedefinitionofeconnectedness.Initially,the content zisreferredtoasbeinga solitary contentof y.Thisisnotthe caseinthedefinitionathand,wherezisreferredtoasbeinga content of y. Whether zisasolitarycontent,orjustacontent,of yseemsto makeadifference.Takethecasewherethesolitary content of y is z1+z2+z3;i.e., z1+z2+z3isatcollectionof y.Now,tostartwith,what does it mean to say that x is directly, immediately united with this solitary content of y? Does it mean that x is directly, immediately united with each one of its three elements? Or, willitdoifitis directly, immediately united with just one of them? If the latter is sufficient, then it seems as if the direct immediate unity is with a content of y, and not a solitary content of it. If instead the former is necessary, it is somewhat difficult to grasp how that differs from beingdirectlyimmediatelyunitedwith yitself.Ifthereisadifference, how is it possible for x to be directly immediately united with y without being directly immediately united with at least one of its contents? Evidently, the last question touches on the essential one regardingtherelationsbetweenpartandwholeandviceversa . Itakeitthatirrespectiveofhowthequestionsoftheprevious paragraph are answered, it is important to note that xy can exist MOMENTNOMINALISM199 without xand ybeingeconnectedwitheachother.Inthecomplex unity b1theyarenotsoconnected.Instead, xiseconnectedwitha contentof y;thatissufficientfor xand ytoform xy .Ifeconnected nessbetween xand ywereaprerequisiteforthesymbolisation‘ xy ’, thelattercouldnotbeusedinthecaseof b.

4.3.5ElementaryIdealRelation The elementary connection is an external (or real) relation. In this section I discuss the notion of elementary ideal relation. When introducedinSegelberg1945,bothcongruenceandincongruenceare described as elementary concepts. 2 Later in the same work, when relationsingeneralarediscussed,itisstated:

Thephenomenologicalunity,whichexistswhenapairof objects stand in a relation to one another, we call a relational unity. A relational unity is either elementary or compound. Tosaythat xRy isacompoundrelationalunity meansthatitcanbeanalyzedinto xR'z& zR"yor xR'z∨ zR"y . It is to be noted that the concepts elementary and compound do not correspond to the concepts simple and complex,introducedearlier.Everyrelationalunity,evenan elementaryone,isacomplexunity.Therelationalunity“ x isapaternalauntof y”canserveasanexampleofacom poundrelationalunity.Itimpliesthatthereisanobject z, such that xisasisterof z and z is the father of y. The unities“ xisasisterof z”and“ zisthefatherof y”are,in turn,compoundunities.Thereisreasontobelieve,evenif itcannotbelogically proven, thateverycompound rela tionalunitycanbeanalyzedintoanumberofelementary relationalunities.So,if xRy isacompoundunity, R issaid tobea compoundrelation ;if xRy iselementary, R issaidtobe an elementary relation. 3

1Iamreferringtotheentity bappearinginthelastquotation. 2Cf.Segelberg1999/1945,p.38/29. 3Segelberg1999/1945,p.53/44. 200CHAPTERIV

Immediatelyafterthisquotationtherelationalunity“ xisincongruent to y”isdescribedasbeinganelementaryrelationalunity.Wearealso informedthatincongruenceisinitselfanelementaryrelation.After the proclamation of its being elementary, argumentation follows which is intended show that congruence cannot be elementary. Accordingtotheargument,incongruencemustholdbetweenatleast twoentities.Itdoesnotformaunitytogetherwithjustoneentityofa pair. Without any of the entities of the pair, there will be no in congruenceunity.Thus,nothingcanhaveanelementaryrelationto itself.Ifitcould,theelementaryrelationwouldneedtobereflexive. Sinceincongruenceiselementaryandirreflexive,therecannotbeany (other)elementaryrelationwhichisreflexive.Eachreflexiverelation isthereforecompound.Congruenceisreflexive.Therefore,itiscom pound. Itmightcomeasasurprisethatthecompoundrelationofthis pair is congruence and not incongruence. The reason it is not the other way round is because congruence is the negative one. No doubt,thisalsocomesasasurprise.Segelberggivesasortofargu mentforallthisinconnectionwiththeintroductionofthetwo.

Theconcept “incongruence”isthenegationofcongruence. Itisthennoteworthythatcongruence,ontologicallycon sidered, is the absence of incongruence. Incongruence is thepositive,congruencethenegative. 1Youcanconvince yourselfofthisbythefollowingconsideration:Thenega tive is not observable in the same sense in which the

1 Evidently, a distinction between the concept of incongruence, on the one hand,andthe concept ofcongruence,ontheother,ispresupposedhere.Judg ingfromwhatisstatedinthefirst,secondandthirdsentencestheconceptof incongruenceisthenegationofthatofcongruence.However,ontologicallyit is the other way round: congruence is the negation of incongruence. This meansthenthatinthesecondandthirdsentences‘congruence’and‘incon gruence’ do not refer to concepts. I take it that they refer to the two (universal)relations.Furthermore,inthetranslation‘concept’isinsertedafter ‘negative’; it is not there in the Swedish original. Since it annuls the pre supposeddistinctionbetweenconceptanduniversalrelation,Ihaveremoved it. MOMENTNOMINALISM201

positiveis:Ifwewishtodetermine,forexample,whether anobjectiswhiteornotwhite,welookfortheproperty “white”;weconsidertheobjecttobe“notwhite”ifwedo not find the property white. We do not look for the property “nonwhiteness” and explain the object’s being “white” in terms of our not coming across the negative property. Consequently, when we want to decide if an object has a certain negative property, we seek the cor responding positive property, and ascribe the negative propertytotheobjectifwedonotcomeacrosstheposi tiveproperty.Howdowethenproceedwhenwewantto decide whether x and y are congruent or incongruent? Obviously we look for incongruence (difference) and regard x and y as congruent, if we do not find any incongruence(difference).Incongruenceisapparentlythe positive,andcongruencethenegative.Thatthenegative 1 congruencehasacquiredapositivelinguisticexpressionis explainedbythefactthatcongruenceisamoreunusual andmoresignificantphenomenonthanincongruence. 2

Onemightgobattywhenlearningthatincongruenceispositiveand congruencenegative.Notethoughthatincongruencestillmeansdif ference;differencestillappearstobenegative.Itsbeingontologically positivedoesnotchangethat.Theargumentforitsbeingpositiveis thatwelookforitwhenitistobedecidedwhethertwoentitiesare congruentorincongruent.Theargumentforthis,inturn,isthatwe look for a positive property, not a negative one, when it is to be decidedwhetheranentityhasapropertyornot.Thishastheappear anceofbeinganepistemologicalargumentratherthananontological one.Ifthatisindeedthecase,hasitanybearingonontology?Ithink not. However that may be, the statement quoted in section 4.3.2,3 that both congruence and incongruence are elementary relations is

1Thetranslatorshaveinserted‘concept’after‘negative’.Ihaveremovedit, forthesamereasonasamomentago. 2Segelberg1999/1945,pp.3940/301. 3Iamreferringtothefollowingstatement. 202CHAPTERIV revisedthen.Accordingtothelatestnews,onlyincongruenceisele mentary.

4.3.6ObjectsofDifferentOrders Segelberg distinguishes between different orders of objects. While individualsareofthelowest(first)order,universalsoccupyahigher order.Eachobjectofthelowestorderislocatedinspaceandtime. Thehigherorderoneshavenosuchlocation.Anythingcontaininga universal—i.e.,arelation—isahigherorderobject.Thus,together with relations, 1 states of affairs and relational properties arehigher order objects. This is illustrated by what he asserts regarding the distinctionbetweenarectangleandastateofaffairs.

Comparearectangle H,consistingofthesquares aand b, tothefollowingstateofaffairs( S):thesquare aliesbeside b.Both Hand Sarecomplexescontaining aand b.What basically distinguishes H from S is that S contains, in additionto aand b,arelation.Itappearslikelythatevery complex unity (i.e. every complex that is not simply a collection)whichcontainsarelationiseithera stateofaffairs or a relational property . Objects of the lowest order never containrelations.Inanobjectofthelowestorderwhichis acomplex,arelationobtainsamongitscomponents,but therelationisnotacomponentoftheobject .If xisthecomplex yz andiftherelation Robtainsbetween yand z,then Ris

The concept congruence and its contradictory incongruence are ele mentary concepts, which cannot be defined by analysis. Their meaning can only be made clear by examples. (Segelberg 1999/1945,p.38/29) If I am right earlier in this section, that a distinction is made between the conceptsofcongruenceandincongruence,ontheonehand,andthe universal relations ofcongruenceandincongruence,ontheother,thentheassumption shouldbethatthesenseinwhich‘concept’and‘concepts’isusedhereisthe generalone,whichincludesalsouniversalrelations.Duetotheelusivenessof Segelberg’s use of ‘concept’, occurrences of the term are easily misinter preted.Iamsorrytosaythatthesameappliestomyownuseof‘notion’. 1Cf.Segelberg1999/1947,p.166/48. MOMENTNOMINALISM203

notacomponentof x;but Risacomponentofthestate ofaffairs yRz ,whichisanobjectofthesecondorder. 1

Partofthemessagehereobviouslyisthattherectangle Hwouldnot existifcertainrelationsdidnotholdbetweenthetwosquares aand b. Boththesesquaresarecontentsof H.Althoughtherelation R,which isoneoftherelationsholdingbetween aand b,isessentialfortheir forming H,itissupposednottobeacontentof H.Thisissomewhat obscuredbythefirsthalfofthepenultimatesentence:“Inanobject ofthelowestorderwhichisacomplex,arelationobtainsamongits components[…].”Theuseof‘in’heresuggeststhattherelationin factisacontentoftheobject.Therelationholdingamongthecom ponentsof Hisastateofaffairs;assuch,thelatterisahigherorder entity.Therefore,neither Rnor aRb isacomponentofthefirstorder object H. Incidentally,sincethetwosquares aand barefirstorderobjects themselves,neitherofthemcontainsanyrelation.However,asinthe casewiththerectangle H,therearerelationsthatholdbetweenthe constituentsofeachsquare.Theserelationsareconstitutiveoftheir statesofaffairs.Theyarealsonecessaryfortherebeingasquare aas wellasasquare b. Thestatedreasonfornotallowingrelationsamongthecontents offirstorderentitiesisthatiftheywere,itwouldresultinavicious regress.Theregressisanoldacquaintance.

Ifonesupposesthat Hcontainsthoserelationsthatobtain between a and b, one falls victim to Bradley’s infinite regress. Bradley is right in that there is a relation R between aand b,andthereisarelation R'between aand R, and so on. However, these relations are not compo nentsof H,butofcomplexesofhigherorder. 2

Iftheregresswouldensuegiventhatarelationwereacomponentof the rectangle and this is supposed to constitute a conclusive reason againstitsbeingacontentofthelatter,whyisthisnotequallysofor 1Segelberg1999/1947,pp.1656/478. 2Segelberg1999/1947,pp.221/1278. 204CHAPTERIV higher order objects? It is not obvious what Segelberg’s answer is. HerbertHochbergsuggeststhattheregressisconsideredtobeharm lesswhenoccurringinstatesofaffairs.

Segelberg’ssolution,acceptinganinfinitechainoffactsas nonproblematic, since the elements of the chain are merelydeductiveconsequencesoftheoriginalfact,asin thecaseoftheseriesofsentences(i)‘ p’,“ p’istrue’,‘“ pis true’istrue’,etc.[…]. 1

If the regress is to be harmless, it must be of the implicative sort; though I do not know for certain whether Segelberg believes that. Regrettably,Hochbergdoesnotgiveanyhintofwhattexttoconsult forcorroboration.Anyhow,hedoesnotagreewithwhathetakesto beSegelberg’sviewontheallegedregress.

WhenSegelbergtakesaninfiniteseriesofstatesofaffairs, beginningwith aRb ,tobeunproblematic,heignorestwo problems.First,atheorythatallowssuchagenerationof entities is prima facie implausible, though not paradoxical. Second,suchatheoryfailstoprovide,atanypointinthe series,theontologicalanalysisoftheoriginalfact.Hence, itfailstospecifyasufficient truthgroundforthe initial atomic sentence. A viable theory will neither recognize suchaninfiniteseriesoffactsnorfailtospecifythetruth grounds for atomic sentences. In short, a viable theory cannotpermitsuchinfiniteBradleytypeseries. 2

Fromwhatissaidwithregardtothesecondproblem, it is evident thatHochbergconsiderstheregresstobeananalyticalone.3 Ifoneconsidersananalyticregresstoberunningamokwhen everastateofaffairsissupposedtoexist,onemustacceptthatthe

1Hochberg1999,p.166.Thestepfrom‘ p’to“ p’istrue’hasasaprerequisite that pobtains.Theoriginalfactis p.Ifitdoesnotobtain,theregressdoesnot comeoff. 2Hochberg1999,pp.1656. 3Iamabitpuzzledbywhathesayswithregardtothefirstproblem.Ifthe regressisoftheanalyticsort,whyisSegelberg’sassumptionnotparadoxical? MOMENTNOMINALISM205 analysisofwhattheoriginalstateofaffairsconsistsinnevercomesto an end. For some reason, Segelberg thinks that the regress is un problematicwithregardtohigherorderentities.Thestrategyheuses for avoiding it in connection with the first order objects (where he thinks it is problematic) is to deny that they are contents of such objects.Aslongastheycanbeamongthecontentsofhigherorder objects,hethinkshehasgoteverythingheneeds.Thehigherorder objects take care of the laundering of (some of) 1 the first order objects,sotospeak. Besides the word ‘order’ Segelberg also uses ‘degree’, though notforthesamepurpose.

Onecanorderstatesofaffairsinahierarchyinthefollow ingway.Lowestarethosefactswhichare not factsabout facts,forexample,violetsbloominApril.Wewillcallsuch facts, facts of the first degree. One step higher are facts aboutfirstdegreefacts,forexample,[( a>b)&( b>c)]hasas a consequence ( a>c). If we go one step higher, we find factsaboutseconddegreefacts,andsoon. 2

Theterm‘degree’isonlyusedinconnectionwithstatesofaffairs.It should be fairly easy then not to confuse the notions of firstorder andfirstdegreeentities. Regrettably, ‘order’ is also used in a way which is somewhat problematic. We find it being used in this way in the following statement.

Relationsandotherobjectsofhigherorderarenotuniver salsinthesamesenseas,forexample,theconcept3“man” isuniversal.Whileuniversalobjectsofthefirstorderare logicalconstructions,thisisnottrueof(universal)objects of higher order. To universal objects of the first order,

1Thisinsertionismadebearinginmindthattheremightbesimpleentities completelylackinganyinternalstructure.Theseentitieswouldbetrueatoms. 2Segelberg1999/1947,p.165/47. 3Theimplicationhereseemstobethataconceptisnotahigherorderentity. Myguessisthatitisalogicalconstruction—mostlikely,asimilarityclass. 206CHAPTERIV

there correspond one or several instances. There are no instances corresponding to objects of higher order. The relation which obtains from a relational property to the objectwhichhastherelationalpropertyisarelationthatis totallydifferentfromthatwhichobtainsfromauniversal object of the first order to an instance corresponding to thatuniversal.TheuseinEnglishofthesameexpression —‘instanceof’—forthetworelations—thatfroman objecttoitsrelationalpropertiesandthatfromaninstance toauniversalobjectofthefirstorder 1—causesagreat dealofconfusion. 2

Thephrase‘universalobjectofthefirstorder’isabewilderingcom pound.Itevenlookslikeacontradictioninterms.Thoughitishardly a successful formulation, it need not be contradictory. As it occurs aboveitisa harbingerofSegelberg’sdoctrine onqualities. Amore transparentphrasetousewhenreferringtowhatiscalled‘universal’ herewouldbe‘surrogateforuniversal’where“universal”isaclassof moments.Suchaclassisconsideredtobeafirstorderobject. Anumberofordinaryobjectscanbethoughtofascombining tomakeupacomplexentity;anexampleofthiswouldbefourbooks whichconstituteapileofbooksandcanbeviewedasconstitutinga collection. In a collection, the ordering of the elements has no relevance. However, if the books are thought of as constituting a complexunityinstead,theorderingofthem,theirrelativepositions, areessential.

Whenonesaysthattheseperspectivesaredifferentways oflookingatthe same objects,onehas,however,expressed oneself inadequately. The pile of books abstracted from theorderingisadifferentobjectthanthepileofbooks in cluding theordering.Thecollectionofbooksisanabstract 1 The word used in the translation is ‘level’. I have changed it to ‘order’ though.MyjustificationisthatthewordusedbySegelberghereisthesame asthatwhichhasbeentranslatedinto‘order’earlier.Thetranslatorsalsouse ‘level’,insteadof‘order,inthe summaryofSegelberg1947.Thisisequally unmotivated.Cf.Segelberg1999/1947,p.228/137. 2Segelberg1999/1947,pp.166/489. MOMENTNOMINALISM207

component in the complex unity, which constitutes the concrete 1pileofbooks.Onecansaythatthecollectionof booksprovidesthe“buildingblocks”fortheconcretepile ofbooks.Onecaneasilyseethatthesamepile 2ofbooks can form several different concrete piles of books. If the booksare a, b, c,and donecanformpile abcd ,inwhich, a isonthetopand disonthebottom,thepile bacd ,andso on. Therefore, we must distinguish between, on the one hand, the collection a+b+c+d and, on the other hand, different wholes, for which this collection furnishes the buildingblocks,e.g. abcd , dcba ,andsoon. 3

In order for the books to form a complex unity together, none of themneedstobeeconnectedwithanother.Iamquitecertainthata bookcannotbeeconnectedtoanotherbook;onlymoments have thecapacitytobeconnectedwitheachotherinthatway. What is the pile of books including the ordering? Is it a first order object? According to the official doctrine, it cannot be since orderingisarelationalmatter.Itseemsnaturalthoughtothinkofa complex unity, of whatever order, as an entity with a qualitative contentaswellasarelationalcontent.Itsrelationsconnectthedis paratenonrelationalcontentsinaninternalstructure.Asonemight expect,Segelbergrejectsthis.

Onetendstopictureaconnectingrelationasacontentin thecomplexunitydisparatefromtheconnectedobjects.If xand yareconnectedintothecomplexunity xy,onethen thinks one can, in xy , distinguish a relation R, disparate from xand y,whichconnects xand yintotheunity.Itis obviousthataunionoftwoobjects, xand y,oftencon tainsmomentswhicharedisparatefrom xand y.But,itis amistaketothinkthat every unionof xand ymustcontain objectsdisparatefrom xand y.Suchanideaisdependent on a collectionist outlook: As the collection x+y and a 1Ithinkwecanassumethatneither‘abstract’nor‘concrete’isusedhereina technicalsense. 2Itwouldbebettertouse‘collection’here. 3Segelberg1999/1947,pp.1856/75. 208CHAPTERIV

unity xy bothcontain xand y,butarenotcongruent,from a collectionist point of view one of x+y and xy must containamomentwhichtheotherlacks.Sincethecollec tion x+y,bydefinition,doesnothaveacontentdisparate from xand y,the“differentiating”contentmustbelongto xy ,andsincesomesuchcontentcannotbeobservedin xy , an unobservable relationmoment 1 between x and y is simulated.Collectionismseekstounderstandeveryunion of xandyasacollectionof x, yandcertain“ties”,rela tions,whichunite xand yintoaunity.Thenotion,how ever, is absurd. A collection of x, y and one or more relations zcanneverbethesameasaunity xy . For, the collection x+y+zexistswhether x, yand zare“dispersed” orformaunity;but,theunity xy doesnotexistif x, yand zare“dispersed”. 2

Itisevidentthatacomplexunityisnotacollection,or viceversa .From thataloneitdoesnotfollowthoughthatacomplexunitycompletely lacks relational content. Relations are obviously essential for there being any complex unities at all. This is once again confirmed by Segelberghimselfwhenhesaysthatacomplexunity xy doesnotexist ifitscomponents, xand y,are“dispersed”.Iquoteyetanotherpass age to underline my point, which will be presented more explicitly afteritscontenthasbeendigested.

Even though the rectangle xyz 3is not[…]congruentto the collection x+y+z, one must not jump to the

1Hochbergtakesoccurrencesof‘moment’suchasthisone,andafewothers, toindicatethatSegelbergiscontemplatingindividualinstancesofrelations. Cf.e.g.Hochberg1999,p.45.Withthepossibleexceptionofoneoccurrence of it, ‘moment’ is not used in that book in the sense given to it later. ‘Moment’ is not a technical term in Segelberg 1945. Its sense in the three occurrences of it in the quotation above is more like that of ‘element’ or ‘constituent’.Theexceptionisoneplacewhere exemplars ofarelationRseem tobecontemplated.Cf.Segelberg1999/1945,p.53/44. 2Segelberg1999/1945,pp.55/456. 3Therectangleinquestionconsistsofthethreesquares x, yand z,suitably arranged. MOMENTNOMINALISM209

conclusionthattherectangle xyz isnotacollection.Ifan object kcontainsthemutuallydisparateobjects x, yand z, without being congruent to the collection x+y+z, there are,then,two possibilities:( a)Thereisanobject u,such that k is congruent with the collection x+y+z+u. — ( b) Thereisnotanobject u,suchthat kiscongruentwiththe collection x+y+z+u.Onlyinthelattercaseis kaunity. Does kcontainanobject u,disparatefrom x, yand z, andsuchthat kiscongruenttothecollection x+y+z+u? One can think of two possibilities here. ( a) One often assumesthatina spatial wholewecandistinguish,along withtheparts,separate“contactrelations”.Onecanthen imagine that u consists of such contact relations. This suggestion can immediately be rejected on the following grounds: ocancontain x, y, zandcontactrelationswithout having xincontactwith yand yincontactwith z.( b)The rectangle kcontains,besides x, yand z,atotalextension, t, in the shape of a rectangle. Is xyz congruent to the collection x+y+z+t? — No, because an object o can contain the objects x, y and z, as well as t, without o containingelementscombinedintotherectangle xyz .The rectangle xyz is therefore a different object from the collection x+y+z+t. Thereasoningcanbegeneralized.Iftherectangle xyz contains x, y, z andan arbitrary object u, disparate from these, one can always imagine a collection x+y+z+u, incongruentto xyz ,inwhich x, y, z,and udonotforma rectangle.Asthecollection x+y+z+uexists,whether x, y, z and u are “spread out” or form a rectangle xyz , the rectangle cannot be congruent with any collection. The rectangle xyz isthusaunity. 1

Evidently,asthetwonotionsaredefined,thereisnowayacollection and a complex unity can be congruous with each other. My im pression is that Segelberg takes the fact that no collection equals a complexunityasapretextfortherenotbeinganyrelationalcontent inacomplexunity.But,ofwhatrelevanceisthefactthatcollections 1Segelberg1999/1945,pp.4950/401. 210CHAPTERIV failtobecongruentwithcomplexunitiesasregardstheissueofthere beingrelationsamongthecontentsofthelatter?Theobviousanswer is:verylittle,ifanyatall.Thestrangethingthatseemstohappenhere is the following: one constituent of the complex unity is rejected becausethecomplexunityisconsiderednottobeacollection,i.e.,a mere sum, of its constituents. To reject the nonrelational con stituentsofthecomplexunityforthesamereasonwouldofcourse beevenmorestriking. Itseemsobviousthattherelevantdifferencebetweenacomplex unityandacollectionofitsqualitativecontentsistheresultofoneor morerelations, whichgivethecomplexunity whateverstructuresit has.Infact,Segelbergdoesnotreallydenythat.Hisstratagemisto submittheconnecting,whichisperformedbyrelations,tostatesof affairs that accompany the firstorder complex unities. Instead of lettingrelations,beingamongthecontentsofafirstordercomplex, connect its other constituents, he supplies the complex unity with servants,i.e.,statesofaffairs,whichtakecareofthatforit. My conclusion is that the threat of Bradley’s regress gives Segelbergreasonforpostulatingthatfirstorderobjectsdonothave anyrelationalcontents.Ifrelationsareallowedtoactinaccordance withtheirnature,whichistorelate,thenitisoflittlerelevancethata first order complex unity is not congruent with any collection, not even a tcollection of its contents. Note that if the analysis of a complex entity, having one or several relations as constituents, is carriedoutintermsofcollectionsofitsconstituents,thelackofcon gruence between the entity and a collection of its constituents is boundtobetakenasapretextfortheconclusionthatrelationsare notconstituentsofthecomplexinquestion.Theanalysesofcomplex unitiespresentedbyBradleyhimselfareamplecasesinpointofthis. In spite of his assumption that “relations are nothing if not con junctive,” 1heendsupwiththatarelationalcomplexcanbeanalysed withoutremainderastheclassofitsconstituents,includingitsstruc turing relations, although the relations are no longer conjunctive.2

1Cf.Bradley1970,p.642. 2‘Conjunctive’isanotherwordfor‘relating’. MOMENTNOMINALISM211

Andsincetheyarenotconjunctiveinthe analysans ,theycannotbeso inthe analysandum either.Thus,yetanotherrelationissupposedtobe neededtoperformtherelating.Ascanbeexpected,itmustsharethe fate of the first relation. At this point, the regress is rolling along nicely.

4.4QualitiesandQualityMoments

4.4.1Overview Inthetwofinalsectionsofthischapter,sections4.4.2and4.4.3,the qualitativesideofSegelberg’sontologyispresentedanddiscussed.It isherethathisnominalisticpersuasionsareprimarilymanifested.

4.4.2ThreePostulatesforaTheoryofQualities In Segelberg 1953 three assumptions are made with regard to momentsandwhatarecalled‘qualities’.

1. Every quality Qcorrespondstooneor morequality moments q′, q′′ , q′′′ ,etc. 2. Aquality Qisidenticaltotheclassofqualitymoments which Qcorrespondsto. 3. An individual object (of the first order)1 is either a qualitymomentoracomplexofqualitymoments. 2

Nothing is said explicitly in either of these postulates regarding similarity. Just before the presentation of the postulates a supple mentingassumptionsaremadethough.

Aqualityisnaturallysomethingotherthanacorrespond ing qualitymoment. We must, therefore, distinguish the

1 All individual objects are of the first order. Cf. Segelberg 1999/1947, p. 165/47.Inthetranslationtheword‘level’isused,insteadof‘order’.Sincethe Swedishword,whichisinlinewiththeterminologyintroducedearlier,isthat of‘order’,Ihavechanged‘level’into‘order’. 2Segelberg1999/1953,p.241/7. 212CHAPTERIV

following two relations, both of which hold, when two objects xand yhavethesamequality Q. 1) xhasarelation Rtoaqualitymoment q′and yhasa relation R to a qualitymoment q′′ , and q′ and q′′ are exactlyalike.(Therelation Risherea contentrelation .) 2)Theobject xstandsinarelation Ttothequality Q; y also stands in the relation T to Q. This relation is expressedbytheword‘has’(‘have’)inthesentences‘ xhas thequality Q’,‘ yhasthequality Q’,‘ xand yhavethesame quality’. Therelation Tisarelativeproductoftworelations:the firstistheabovementioned R.Thesecondwecall‘ S’.Itis arelationwhichholdsfromthequalitymoments q′and q′′ tothequality Q,andwhichwecanexpressbythesentence ‘q′and q′′ arecasesof Q’. 1

Thus,ananalysisoftwoobjects xand ybothhavingthequality Q, i.e.,Q(x)and Q(y),isperformed:2 (1)xTQ andyTQ ;where T= R/S,i.e.,( xRq′& q′SQ )and (yRq'' &q′′SQ ) (2)Q=Sim{ q' , q'' ,…} (3)xRq′and yRq'' R is a specific content relation. S is the relation expressed by the phrase‘isacaseof’,holdingfromamomenttoaquality,thelatter beingasimilarityclass.Itisnotcompletelyclearwhetherthatmeans that Sisaspecificcontentrelation,havingtheelementrelationasa constitutive part, nor is it evident exactly how the correspondence relationholdingbetweenaqualityanditscasesistobeinterpreted. Perhaps correspondence and being a case of are converses of each other. Qualitiesareidentifiedwithclassesofmoments.Inthesecond quotationweseethattheelementsofsuchaclassarethoughtofas being exactly similar to each other. Later, Segelberg says that they

1Segelberg1999/1953,p.240/7. 2TheorderinwhichIsummarise(someof)thecontentofthepostulatesand theaddendumisrandom. MOMENTNOMINALISM213 mightinsteadbejustrathersimilartoeachother,1thoughhedoesnot expand on that particular subject. But, judging from what he says concerning,e.g.,swans,itisevidentthatthesimilaritybetweenthem isnotexactsimilarity;theyarethoughtofasformingsimilarityclasses inawaywhichisnotdifferentinprinciplefromthe wayinwhich momentsdo. Evidently, an important issue is the role of (exact) similarity. Whatrelevancedoesithaveasfarasthequalitativecontentsofits relataareconcerned?Inthefollowingquotationnothingissaidwith regardtothatspecificissue.Though,hedoessaysomethingregard ingtheneedforuniversals:2

Whatisitwhich“unifies”thedifferentinstancesa1, a2,… of A into the group a? Naturally, it is the similarity between a1, a2,…,butwhatdoesitmeantoclaimthatthey aresimilar,ifnotthattheyhaveapropertyincommon? Andthecommonpropertyinquestionmustbeprecisely A. Husserl makes the claim that for this reason it is necessary to postulate the universal A.Asfaraswecan see,thisisnotcorrect.Onemustheredistinguishbetween twokindsofsimilarity: I)exactsimilarity,oraswewould rathersay,congruence; II )relativesimilarity,whichobtains betweendifferentobjectsthathavesomequality incommon . When we say that a universal object Aoccursin several instances; a1, a2,…,whichformtheset a,weconsequently mustdistinguishtwocases:1) a1, a2,…areexactlysimilar; theyforma congruencegroup ;2) a1, a2,…areonlyrelatively similar.Onlyinthelattercasedoessimilarityimplythat a1, a2,…haveacommonproperty.Supposethattheyhavea property Pincommon; Pthenoccurs,accordingtoStout’s position, in several instances p1, p2,…, and these are all congruent with each other. That which “unifies” the individualinstances x1, x2,…,ifthesearedistinctinstances

1Cf.Segelberg1999/1953,p.244/13. 2ThecontextofthisquotationisadiscussionofStout’sargumentsforthe existence of qualityinstances. I think it is clear though that Segelberg is expressinghisownview. 214CHAPTERIV

of the same object, is, consequently, either a congruence relation between x1, x2, etc. or a congruence relation betweenaqualityof x1andaqualityofeachoftheremain ingobjectsinthegroup x.Thereisnoneedtopostulatea universalhere. 1

Themessageofwhatisstatedhereregardingtheneedforuniversals isabitpuzzling.Thefirstimpressionisthattheyareneededincases ofrelativesimilarity butnotincasesofcongruence. Itwouldbea mistake to think that relative similarity requires relata to have uni versal content while congruence does not. An argument similar to thatusedinconnectionwiththeintellectualexperimentwithspheres as the only inhabitants of the universe can be usedhereaswell.It mightrunasfollows.Assumethattherearetwoentities which are (qualitatively)dissimilartoeachother.Assumealsothatoneofthem ischangingtobecomeexactlysimilartotheother.Now,whyisthere aneedforashareduniversalcontentwhenthetwoaredissimilarto eachother,allthewayfromalmostnosimilaritytoalmostexactsimi larity,butnonewhentheyareexactlysimilar?Ofcourse,Segelbergis not maintaining anything like that; he formulates himselfinamis leadingway.Thefinalpointmadeinthequotationmaybeinterpreted asrejectingthenotionthatthereisaneedforuniversalsevenincases of relative similarity. However, this stresses the need for getting a clear idea of whether the exact similarity has a founding role as regardsthequalitativecontentofitsrelata. ItisveryclearthatSegelberg’srelationofexactsimilarityisnot pseudoadditional; he shows no tendency to deny its existence. But whatroledoesitperform?AccordingtoHochberg,itperformstwo roles:

The realist’s exemplification connection only serves to connect particulars to universals to form states of affairs thatarethetruthmakersforatomicsentences:itconnects 1 Segelberg 1999/1947, pp. 152/289. Note the oscillation here between using the term ‘group’ and that of ‘set’. Although group and set are dis tinguishedbetweeninotherplaces,notsohere.Furthermore,Isuspectthat ‘set’and‘class’aresynonymswhenusedastechnicalterms. MOMENTNOMINALISM215

elements into complexes. The instance nominalist’s pur portedconnectionisnotjustsuchaconnection.Foritnot only [1] connects exactly similar quality instances into necessarysimilarityfacts,but,bysodoing,itisinvolvedin [2] connecting a qualitative content to an object. The realist’sconnectionmayormaynotobtain,giventheexist enceoftheelements—theparticularandthequality— thatareconstituentsofit.Thenominalist’ssimilarityfact necessarily obtains, given the elements that enter into it. Thus, the similarity connection may be said to be an “internal,”asopposedtoanexternalconnectionofexem plification,and,hence,whileitisa“universal”itisquite unliketheexemplificationconnection. 1

Theargumentputforwardhereisformulatedsosubtlythatitiseasily misunderstood, or missed. However, two roles are allegedly per formedbyexactsimilarity:

(1) Connectingexactlysimilarqualityinstancesintonecessary

similarityfacts;e.g.,□(m1~m2). (2) Connectingqualitativecontenttoqualityinstances.

InmyformulationofthesecondroleIdonotuseHochberg’sphrase ‘connectingaqualitativecontenttoanobject’.Sincethefirstroleis explicitly said to concern quality instances, the same presumably holdsforthesecondroleaswell.Itisthereforepotentiallymisleading touse‘object’insteadof‘qualityinstance’—or,‘moment’. Thesecondroleiswhatprimarilyinterestsushere.DoesSegel berg consider his universal relation of congruence to perform that role?Theansweris:no.Hemightbewrongthough.Infact,itcould bethatheisforcedtorecognisesomethinginlinewithwhatHoch bergsuggests.Iwouldsaythatheattemptstoavoidthequestionby noteveraskingit.Hepresupposesthatthereareindividualmoments andthattheyresembleeachotherinvariouswaysduetotheirindi vidualnatures.Similarityisconsideredtobeauniformphenomenon.

1Hochberg1999,p.46.AsfarasIcansee,Hochbergisrepeatinganargu mentwhichisalsostatedinHochberg1988. 216CHAPTERIV

Although there are various degrees of similarity, strictly speaking thereisjustonesimilarityrelation.Thatrelationisexactsimilarity.All theothersareaccountedforintermsofthat. 1

4.4.3QualityRelations Segelbergtakesintoaccountseveralqualityrelations that belong to thecontentrelations.Thelatterarerelationshavingwhathecalls‘the simple content relation’ as part. Schematically a content relation betweentworelata xand ycanbewritten‘ yIx & F’.Thefirstcon junctexpressesthesimplecontentrelation;the secondrepresentsa stateofaffairsabouttherelata. Before anything else is said about quality relations, Segelberg thinks that something should be said about the concept of quality (i.e.,moment). 2Themessageofthefollowingquotationisinteresting inmorewaysthanone.

Inordertobecharacterizedasaquality,anobjectmustbe simple. […] [Although] there is nothing to prevent a quality containing a multitude of mutually incongruent moments,ifonlythesearenotdisparate.Acertainshade ofpurplered,forexample,containscertainlythe general determinable red and indefinitely many other deter minablesintheseries—color:red:purplered. But, a lessgeneraldeterminableinthisseriescontainseachand everyofthemoregeneraldeterminables,hencethepurple redshadeisnotacomplexinwhichthedifferentdeter minablesarecomponents.Inregardtoaquality,onecan not just distinguish over and underdetermined contents, asitcanalsohavecontentsthatare,sotospeak,laterally ordered.Inthecaseofthepurpleredshade,onenotonly distinguishesastrainofred,butalso,withthat,astrainof 1IthasbeenseenearlierthatthesameshouldholdforWilliams.Itturnsout thatheisflirtingwithdifferentsortsofsimilarityrelationsthough,ofwhich neitherisreducibletoanyother. 2Theterminologyusing‘moment’asthepreferredterminsteadof‘quality’or ‘qualityinstance’hadnotbeensettledwhenthiswaspublished.Thathappens inSegelberg1953.ThequotationaboveisfromSegelberg1947. MOMENTNOMINALISM217

the laterally ordered determinable violet. But neither the rednorthevioletstrainsaredisparatecomponentsorthe purplered quality, as both have the general color deter minableincommon.1

Welearnherethatqualities(i.e.,moments)aresimples;thoughthat does not mean that they necessarily have just one component. A relativelylowdeterminateofthedeterminablecolourhaseveryhigher determinableascontent.AlthoughSegelbergperhapsdoesnotexpli citlysaysoanywhere,Ipresumethatwhereveracolourdeterminable ispresentallofitslowerdeterminatesarealsopresent.Thus,wecan notexpecttofindathingwhichiscolouredbutnotcolouredinany determinateway.Whatisreferredtoaboveusingtheterm‘purple red’ might be such a determinate. But, if it is not a lowest deter minate, it cannot occur without being the content of something whichisalowestdeterminate.Thatisthemessageofapproximately thefirsthalfofthequotation.Themessageofthesecondhalfisthat a colour (moment) can have contents which are laterally ordered. Purpleredissaidtobeanexampleofthat.Itdoesnotonlyhavethe contentoftheredseries;thereisalsoastraininitfroma laterally orderedcolourseries:violet.Allthesevariouscontentsdonotmake thequality(moment)acomplexentity.Itissimplesincenoneofits contentsaredisparatefromeveryother. Segelbergdistinguishesbetweenthreedifferentqualityrelations. Asapreludetothepresentationofthese,heasserts:

That an object o contains a quality q is not the same as o having thequality q.If,forexample, ohasayellowpart, o containsthequalityyellow,but odoesnot have thisquality; oisnotyellow.Inorderfor otohavethequality,some thing more is required than that o contains the quality. Whatisthis‘more’? 2

1Segelberg1999/1947,pp.218/1234. 2Segelberg1999/1947,p.219/124. 218CHAPTERIV

Thefirstqualityrelation Sowhatisthefirstqualityrelation?Itisthatwhich holds between onequality(moment)andanotherwhenthefirstcontainsthelatter. Theexamplegivenisapurpleredshade qwhichisred.Differently put,theformerhasthequalityred. Earlieritwassaidthat‘ xhasthequality Q’expressesarelative product,whichinthisparticularcasewouldbe: qRm & mSQ .Here m is a moment of redness. The relation S probably is the element relation,whichinthiscontextholdsfrommomentstoaclass,which inturnformthecongruenceclass Q.Finally, Risacontentrelation.I suspect that Segelberg’s characterisation of it is simply that it is, or involves,thesimplecontentrelationholdingbetweentwomoments. Thesecondqualityrelation

Example:‘Thesurface yisred’.Thesurface yisacertain complex,inwhich onecandistinguishextension ( u)ofa certain degree, a certain form ( f) and a certain color ( r). The collection u+f+r constitutes a total collection of the surface.Thiscontains,furthermore,apartialunitywiththe total collection u+r as a total collection, but no partial unity with f+r as a total collection. One can say that the extensionqualityformsacertain“center”ofthiscomplex. Thataunity xisa center inacomplex Ethenmeansthat thefollowingconditionsobtain: (1) E has a total collection x+y+z+… (2) Each and everyoneoftheelementsin E’stotalcollection(except) x) constitutes,togetherwith x,atotalcollectionofapartial unity of E. Expressed differently, x forms a dyadic ele mentarycomplextogetherwitheachandeveryoneofthe remainingmembersofthetotalcollection. 1

Judgingfromwhatisstipulatedinthesecondparagraph,thereshould beapartialunitywiththetcollection u+f.Isuspectthatithasbeen leftoutbymistake.Withoutthatpartialunity,uwillnotformadyadic elementarycomplex with each and every one of the remaining

1Segelberg1999/1947,pp.219/1245. MOMENTNOMINALISM219 membersofthetcollectionoftheentiresurface.NotethatSegelberg isineffectsayingthat fand rarenoteconnectedwitheachother. That is implied by there being no partial unity having f+r as t collection. Why is the extension moment the centre of the complex, i.e., thesurface?Whyistheformmoment,orthecolourmoment,notthe centre?Whyisthereacentreatall?Ipresumethatitisnotan adhoc stipulation that the extension moment is the centre. A special significance is ascribed to extension, but it is not explained why. Thereisroomforspeculationhere. Anyhow, a moment q having the second quality relation to a complex Hmeans:

1. Hcontains q. 2. Hhasacentre c. 3. q is either the center of H or q forms together with H’s centeratotalcollectionofapartialunityin H.1

Since each moment of the complex forms a partial unity with its centre,eachandeveryoneofthemomentsalsostandsinthesecond qualityrelationtothecomplexitself. Thethirdqualityrelation

Example: ‘The tonal series H has the melody quality g’. One has to distinguish between (1) the tonal series in cludingthegestaltquality;wecallthiscomplex H.(2)the tonalseriesminusthegestaltquality;wecallthiscomplex H′.2

Ifamoment ghasthethirdqualityrelationtoacomplex H,itmeans:

1. Hhasatotalcollection g+H′. 2. gisdirectlyconnectedwith H′.3

1Segelberg1999/1947,p.219/125. 2Segelberg1999/1947,pp.21920/125. 3Segelberg1999/1947,p.220/126.Itwouldbebettertouse‘united’here, 220CHAPTERIV

Whatthismeans enclair isthat gand H′areeconnected.Thisshould notbeconfusedwiththefactthatthesecondqualityrelationholds. Inthatcase,gwouldbethecentreofthecomplex;asitisnow,there isnopartialunityinthecomplexwhichhas g+H′astcollection. Thethirdqualityrelationbringsuptheissueofhowamoment can be econnected to a complex without being so connected with anyofitsconstitutingentitiessingly.Intheparticularcaseathandit is perhaps intuitively attractive that the moment g should be e connected with the rest of the complex, without being connected withanyofitsparts,since gisamelodyquality.Then,itisconvenient toassumethatthecompletetonalseriesmustbeeconnected with this particular g. Imagine though that the tonal series is interrupted halfway. Can g be econnected with what is just a segment of the complete tonal series? 1 This question will be dealt with after an excursusregardingtheinternalityofqualityrelations. Thequalityrelationsareinternalrelationsiftheyholdbetween individualentities.Thisfollowsfromthedefinitionofinternalrela tionpresentedearlier.Ifqualitymomentsarerecognised,thequality relationsareunilaterallyinternal,accordingtoSegelberg.Usingabit offormalismwhichheusesinparthimself,thismeansthataquality relationsatisfiesthefollowingcondition:

(I) (xRy → x′Ry′′ ) ∨(xRy → y′R*x′′ ). 2

Thefirstdisjunctisdeciphered:If xhas Rto y,then R obtainsfrom everyobjectcongruentto xtoatleastoneobjectcongruentwith y. Theseconddisjunctisdeciphered:If xhas Rto y,thentheconverse of Robtainsfromeveryobjectcongruentto y toatleastoneobject congruentwith x. Now,assumethatthethirdqualityrelationisunilaterallyinter nal.Canamelodyquality gbeeconnectedtoasegmentofthetonal

insteadof‘connected’. 1 I am simplifying the description of the situation. Evidently, neither the moment g, nor the tonal series H′, can be recycled and appear in other complexessimilarto H. 2Notethat‘ ′’and‘ ′′ ’areheavilyloadedwithinformation. MOMENTNOMINALISM221 series H′giventheotherpremisesofthedefinition?WhatSegelberg saysinthiscontextdoesnotsettlethis.However,inanotherplacehe asserts:

[A]ctually,weoftenexperiencemelodies—forexample, whenwerememberapieceofmusic—withoutevidently experiencing any sound qualities. This kind of appre hensioncanbecharacterizedasanexperienceofa“free standing”gestaltquality.Inthesameway,onecanremem ber a facial expression without visually experiencing the spatialandcolorqualitieswhichconstitutethesensedata corresponding to the face. On the whole, freestanding gestaltqualitiesseemtoplayasurprisinglylargeroleinso calledimageless(nonvisual,nonauditory,etc.)thought. 1

In the light of what is said here, g need not be econnected to any tonal series. Presumably, every tonal series congruent with H′ is connectedinthiswaytoagestaltqualitycongruentwith g. Notethateconnectedness,whichfiguresinthedeterminations ofthequalityrelations,isnotaqualityrelationinitself.Thetrivial reasonforthatisthatitisa connection ;ifitweretobeinternal,itwould havetobesoinaradicallydifferentsenseof‘internal’.

1Segelberg1999/1947,p.207/107. CHAPTERV

ModerateRealism

5.1Introduction ChapterIIcontainedananalysisofthemoderaterealismoftheyoung Donald Williams. After that followed discussions of versions of moderatenominalism.Inthepresentchapter,thecircleisclosedand moderaterealismisonceagainthesubject. Thetraditionofmoderaterealismgoesbackalongtimeinthe historyofphilosophy.TracesofitcanbefoundinPlato 1aswellasin Aristotle. 2 Some of the leading scholastic philosophers, including Thomas Aquinas 3 and John Duns Scotus, 4 are moderate realists. Beforethescholasticera,moderaterealismwasexpressedbyphilo sopherssuchas 5andAvicenna.6Thelatterhasformulated twoargumentsforparticularism,presentedbelow.Beingoneofthe leadingscientistsofhistime, 7AvicennaknewhisAristotlewell.Both ofhistwoargumentssetoutfrompremisesfoundinAristotle. Themajorityofthischapterdealswiththemoderaterealismof Donald Mertz. My discussion of it is based on Mertz 1993, 1996, 2001,2003and2006. 8Beingaversedscholarinphilosophyandits history,hisarticlesareveritablegoldminesofinformationandideas.

1Cf. Phaedo ,102be,and Theaetetus ,209ad. 2 Cf. Categories , 1a24b9, and Metaphysics , 1017b25, 1039b246, 1042a29, 1049a28ff,1057bff,1071a279. 3Cf.Aquinas1955,p.127. 4Cf.Harris1959,pp.945. 5Cf.Gracia1984,p.78. 6Cf.Morewedge1973,pp.334. 7Itisnoexaggerationtosaythatheisoneofthemosteminentscientistsof alltime. 8 Mertz 2006 is an anthology containing seven articles, six of which are publishedseparately. 224CHAPTERV

This chapter also includes an argument for the existence of instancesfromthepossibilityofsymmetricaluniverses.

5.2OnePartialandTwoMistakenArgumentsforParticularism

5.2.1Overview Presentations of Avicenna’s two arguments for particularism are giveninsections5.2.2and5.2.3.Boththeargumentsaremistakento the extent that they assume false premises. However, the second argumentinparticularisveryinteresting.Mymainreasonforpresent ingitisthatarefinedversionofitisdiscussedinsection5.3.3. Yetanotherargumentforparticularismispresentedinsection 5.2.4.Itisnotmorethanapartialargumentthough.Itassumesthe existenceofuniversalsandcombinesthatwiththepossibilityofthere beingSegelbergianBlackianuniverses.

5.2.2Avicenna’sFirstArgument Avicenna 1 (980–1037) presents two arguments for particularism.2 Oneofthese,whichwillbereferredtohereasthefirst,isstatedin hisTheBookofScientific .3Inthisargument,aswellasinthe second,transcendentrealism, orPlatonism,isrejected in favour of immanent realism.4 The first also takes a view on predication for granted: every property predicated of an individual substance is likewise predicated of its corresponding species and genus. If the assumption is made that predicates are the same throughout and combine it with this particular view on predication, the result is a

1Inhisownculturalspherethistruepolyhistorisknownbythename‘ibn Sina’,shortfor‘AbuAlialHusaynibnAbdAllahibnSina’. 2IrelyheavilyonMertz1993and1996inthissectionaswellasinsection 5.2.3. 3ThereisatranslationofitinMorewedge1973. 4Cf.Morewedge1973,p.33. MODERATEREALISM225 contradiction. The presupposed view on predication is ascribed to Aristotle .1 As everyone knows, Plato was a learned man. Meno, on the other hand, was not. Although they do not share the property of beinglearned,theyarebothmen.Sincetheyaremen(species),they areanimals(genus)aswell.Unfortunately,theresultofallthisisthat thespeciesandthegenusarenotjustlearnedbutignoranttoo.With thehelpofasimpleformalisationthiscanbeformulated:

Learned(Plato)→[Learned(Man)&Learned(Animal)] Ignorant(Meno)→[Ignorant(Man)&Ignorant(Animal)]

Theconjunctionofthesetwoimplicationsentailsthatbeingaman has contradictory properties; the same holds for being an animal. RegardingthisAvicennasays:

Theidenticalformofmanquamancannotbeaknower likePlatoandalsoanignoramuslikesomeoneotherthan Plato.Itisnotpossibleforknowledgetobeandnottobe inoneandthesamething.Neitherisitpossibleforone andthesamethingtocontainbothblacknessandwhite nesssimultaneously.Itissimilarlyimpossiblefortheuni versalanimaltobeaparticularrealanimal,forit would then have to be both walker and flyer, as well as not walkerandflyer,andbebothbipedandquadruped. 2

Sincenothingcanhavesuchasetofproperties,somethingmusthave gonewronghere.Avicenna’ssolutiontotheproblemistoconsider predicates as particulars. Using the same formalisation slightly changed,thisbecomes:

1Cf. Categories ,2b383a5.WhatAristotleexplicitlysaysis: When onethingis predicatedof another,allthatwhichis pre dicable of the predicate will be predicable also of the subject. Thus, ‘man’ is predicated of the individual man; but ‘animal’ is predicatedof‘man’;itwill,therefore,bepredicableoftheindi vidualmanalso:fortheindividualmanisboth‘man’andanimal’. IleaveopenwhetherAvicennahasinterpretedAristotlecorrectly. 2Morewedge1973,p.33. 226CHAPTERV

Learned 1(Plato)→[Learned 1(Man1)&Learned 1(Animal 1)] 1 Ignorant 1(Meno)→[Ignorant 1(Man 2)&Ignorant 1(Animal 2)]

Here,alloccurrencesofpropertiesareunitproperties,i.e.,particulars. Therefore,nocontrarypropertiesareascribedtothesamesubjects.

5.2.3Avicenna’sSecondArgument ThepremiseofAvicenna’sfirstargument,thatwhatispredicatedofa primarysubstanceisalsopredicatedofitsspeciesandgenus,isshaky. In Aristotle’s Metaphysics the doctrine is no longer the same; in it propertypredicatedofaprimarysubstanceispredicatedofacompo siteofmatterandform.Thus,accordingtothis,itis of such a composite that ignorance is predicated whenever it is predicatedofaparticularman,forexample,Meno. The second argument contains a questionable premise, that relationsarereducibletothemonadicattributesoftheirrelata.From antiquitytotheendofthenineteenthcentury,thiswasthemajority viewamongoccidentalphilosophers.2Itseemedtobesanctionedby Aristotle himself, whose description of relations as the “least of all things a kind of entity or substance” 3 was frequently referred to. Perhaps that description was nothing more than an unguarded remarkcasuallymade.Regardless,Avicennaisamongthosewhorely on the authority of the Philosopher. Additionally, the view has its proponents nowadays, especially among the trope theorists. Thanks totheargumentsputforwardbytheyoungBertrandRussellamong others, the premise has been on the defensive during the twentieth century.4 1Thesubscriptsindicatethattheentitiesareparticulars.Although‘Plato’and ‘Meno’lacksubscripts,theyofcoursealsorefertoparticulars 2Therehavebeenafewexceptionstothis.PeterAureoli(12801322)might beone.Acomplicationisthatheconsidersrelationsnottobeextramental. This is due to his . Cf. Henninger 1989, pp. 1534, 1823. It makeshisviewsimilartothatofJohnLocke,whothinksofrelationsasthe resultofcomparisons.Cf.,e.g., Essay ,bk.II,ch.25,par.8. 3Cf. Metaphysics ,1088a22. 4Cf.Russell1903,pp.221ff. MODERATEREALISM227

Avicenna presents his second argument in the book The Healing .1 I repeat that an essential premise of the argument is that relationsarereducibletopropertiesoftheirrelata.In thefollowing passage,thefathersonrelationshipisusedbywayofillustration.

Eachoftwothingshasinitselfanideawithrespecttothe other, which is not the idea the other has in itself with respecttothefirst.Thisisevidentinthingswhoserelated terms differ, as in the case of the father. Its relation to fatherhood,whichisadescriptionofitsexistence,isinthe fatheralone.[…]Thesameappliestothestateoftheson with respect to the father. There is nothing here at all whichisinbothofthem. 2

Theattributes(ideas)referredtointhefirstsentencearethe essead s oftherelevantessein softhetworelata,thefatherandhisson.The term‘essead’isthescholasticcounterpartoftheGreek‘το προξ τι ’.3 Bothcanbetranslated‘beingtowards’.Thescholasticterm‘essein’, having the meaning of ‘being in’, refers to the relevant monadic attributes of the relata. An esse ad is thought of as a secondorder attributeofan essein .Inthisparticularcase,therelevantessein sare the attributes being father and being son respectively. An English alternativeof‘essein’is‘relationproperty’. 4 The first formalisation 5 below is a preliminary version of the propertyreductionofarelationinthegeneralcase.Theessein softhe relataareR′ and R″respectively.TowardsxandTowardsy are the

1ThereisatranslationofitinMarmura1975. 2Marmura1975,pp.878. 3Aristotle’snameofthecategoryofrelationis‘προξ τι ’. 4Themeaningof‘relationproperty’isofcoursecloselyrelatedto,ifnotthe same as, that of ‘relational property’. Having a relation as constituent, a relational property is itself subjected to the propertyreduction. Likewise, a relationpropertyisboundtoinvolveanunreducedrelationalelement.How ever,thisseemstohavebeenrepressedbytheadherentsofthedoctrine. 5ItisproposedbyDonaldMertz.Sinceheisusingitwhenformulatinghis ownrefinedversionoftheargument,itispracticaltouseithereaswell. 228CHAPTERV essead s.Thecapital‘R’namestherelationtobereduced.Thecolonin frontofaformulaindicatesthatwhatevercomesafteritisafact.1

For any binary relation predicate ‘R’ and relata x and y, thereexistrelationpropertiesR′andR″suchthat‘R( x,y)is true ≡[:R′( x) •:Towardsy(R′) •:R″( y) •:Towardsx(R″)]2

Appliedtotheparticularcaseofthefatherandhisson:

‘a is the father of b’ is true ≡ :Fatherhood (a) • :Towardsb (Fatherhood) • :Sonship ( b) • :Towardsa (Sonship) 3

Theargumentforparticularismbeginstoshowitselfwhentheana lysisisappliedtoequivalencerelations.Avicenna’sexampleisbeing similaraswhiteto.Onewouldexpectthattherelevantessein isthe universalwhiteness.However,appearancesaredeceptive.

Ifsuchastateofaffairs[anequivalencerelationbetween two subjects] consists in the fact that each of the two [subjects]hasastate[relationproperty]withrespecttothe other, this is similar to the case of the swan and snow, eachofwhichiswhite.Noristhisstate[thewhiteofone subject]renderedidenticalbythefactthatitstands with respect to the other; for whatever belongs to each indi vidualwithrespecttotheotherbelongstothatindividual andnotthe other; butit possessesitwithrespectto the other. Ifyouhaveunderstoodthisfromwhatwehavegiven youbywayofexample,thenknowthattheidenticalstate ofaffairsobtainsintherestoftherelativesthat do not disagreeintheirtwoterms. 4

1 Colons are not used in Mertz 1993. They are part of Mertz’ considered formalismandusedinhislaterworks.Ihavethereforetakenthelibertyof insertingthemwhenitiswarranted. 2Mertz1993,p.197. 3Mertz1993,p.197. 4QuotedfromMarmura1975,p88.TheinsertsaremadebyMertz. MODERATEREALISM229

ThewayAvicennaexpresseshimselfhereissomewhatcompressed.It isquiteclearthoughwhathismessageis.Ifuniversalwhitenessisthe essein ,thereductionoftheequivalencerelationcan(preliminarily)be written,usingthesameformalismasabove:

‘a is similar as white to b’ is true ≡ :White ( a) • :Towardsb(White) •:White( b) •:Towardsa(White) 1

Itisevidentthatthiscanbenothingmorethanapreliminaryrender ingofthesituation.Thissincethewhitenesswhichisthe essein of a cannotbeidenticalwiththatof b.Therelevant essead s—Towardsb andTowardsarespectively —arecontrariesinthiscontext.There fore,theformalisationshouldbereformulated:

‘a is similar as white to b’ is true ≡ :White 1 ( a) • 2 :Towardsb1(White 1) •:White 2( b) •:Towardsa2(White 2)

The universal whiteness itself is not ascribed contrary esse ad s here. Instead, the contrary esse ad s are ascribed to separate instances of whiteness:White 1andWhite 2,respectively. Finally,ingeneralisedformthetraditionalpropertyreductionof binaryrelationslookslikethis:

For any formal binary relation predicate ‘ R’ and relata x

and y,thereexistrelationpropertiesR′iandR″jsuchthat ≡ • • • ‘R( x,y)’ is true [:R′i(x) :Towardsyk (R′i) :R″j ( y) 3 :Towardsxl(R″j)]

1Mertz1993,p.198.

2Mertz1993,p.198.Thesubscriptsin‘Towards b1’and‘Towards a2’belong tothepredicates aswholes.Moreperspicuousformulationswouldperhaps be‘(Towards b)1’and‘(Towards a)2’. 3Cf.Mertz1993,p.197, and1996,p.123.Inareduction carriedthrough completely,the essead sshouldofcoursealsobereduced.Ifnot,unreduced relational elements will be left over, not accounted for. An apposite speculationasregardsthe essead elementis: Perhaps, historically, the ‘towards’ aspect was not taken to be anotherrelationbecauseitwasconceivedtobeanalogoustothe actofpointingwhichachievesreferencetoanotherwithoutany 230CHAPTERV

Avicennaintendshissecondargumenttobecompletelygeneral.This isobviousfromhisadmonitionthat“[y]oumustneverthinkthatan accident,oneinnumber,existsintwosubstrata.” 1Inotherwords,the attributes of things are without exception particulars. This is more easilyseenifoneacceptsthenotionthatthingsresembleeachother in respect of whatever attribute they seemingly have in common. That means that there is an equivalence relation holding between them.Ithastheform:beingsimilarasPto.Andasthesecondargu mentshows,whatseemstobethesame essein will,duetocontrary essead s,bedifferent essein s.2 Mertz’s refined version of Avicenna’s second argument is dis cussedinsection5.3.3.Themaindifferencebetweenitanditsmodel isduetoMertz’srejectionofthemonadicreductionofpolyadicontic predicates.

5.2.4APartialArgumentfromSegelbergianBlackianUniverses TheintellectualexperimentputforwardinSegelberg1947isessen tiallythesameasthatofBlack1952.Inthepresentsection,thisexpe rimentprovidesthesettingforapartialargumentfortheexistenceof instancesofuniversals.Theimmediatepointofdepartureisneither

physical/causalconnection.Ofcourse,referenceitselfisanun reducedsemanticrelation,albeitofamoreimplicitandabstract kind. It is erroneous to think that polyadic relations are elimi natedcompletelyintermsofmonadicproperties.(Mertz1993,p. 197) 1Marmura1975,p.88. 2 In connection with Avicenna’s admonition Mertz makes an interesting reflection: [T]his admonition has come to be associated with Leibniz, in whoseworkitisstandardlyinterpretedtobebuttheinsistenceof the property reduction of relations […]. But Avicenna’s intent goesdeeper,andheusesthepropertyreductionofrelationsasa meansofdemonstratingthenonrepeatabilityofpropertyreducta themselves.(Mertz1996,p.125) Leibniz’sviewissubjectedtovariousinterpretations.However,noneofthese interpretsthereductivedoctrineassupplyingthepremisesforanargument likethatofAvicenna. MODERATEREALISM231

Segelberg 1947 nor Black 1952; instead, it is the discussion in RodriguezPereyra2004. Inthelatterwork,theauthoractsasspokesmanforarealistic versionofthebundletheory.1Itsfundamentalprinciplereads:

(BT) Necessarily,foreveryparticularxandeveryentity y, y constitutes x if and only if y is a universal and x instantiates y.2

The modal operator indicates that (BT) concerns itself with every concrete particular there is and might be. The term ‘particular’ is shortfor‘concreteparticular’. Constitution and instantiation are treated as reciprocal. An entityconstitutesorisamongtheconstituentsofaconcreteparticular ifandonlyifthelatterinstantiatesit.Furthermore, concrete parti cularsmusthaveconstituents. 3Onlyuniversalscanbeconstituents.4I 1 As reported earlier, RodriguezPereyra is not a realist of any kind. He describeshimselfasaresemblancenominalist.Cf.RodriguezPereyra2002.I takeitthatwhatheisdoinginRodriguezPereyra2004isdefendingaversion of realism, which he considers to be second best after his own version of resemblancenominalism.Iwouldsaythattheversionofrealismdefendedis amoderaterealism. 2RodriguezPereyra2004,p.72.Weareinformedthatthereisalsoanother versionofthebundletheory,accordingtowhichtropesconstituteconcrete particulars.Evidently,if(BT)issupposedtobeconstitutiveforthebundle theory, tropes must be interpreted according to some version of moderate realism.However,thatisnotwhatRodriguezPereyrahasinmind.Hetakes tropes to be nominalistic in nature. The following principle, which is not mentionedbyRodriguezPereyra,mightbeatropetheoreticalcounterpartof (BT). (Bt) Necessarily,foreveryparticular xandeveryentityy, yconstitutes xifandonlyif yisatropeand xinstantiates y. WhatIhaveinviewisaninterpretationof(BT)whichisinlinewithmoder aterealism.Inthatcontext(Bt)doesnotfitin. 3Cf.RodriguezPereyra2004,p.72. 4 Although RodriguezPereyra does not explicitly mention it, instantiation cannotitselfbeaconstituentofanyparticular.Ifitwere,itwouldhavetobe instantiated,accordingto(BT).Thatwouldimmediatelyresultinananalytical (vicious)regress. 232CHAPTERV wouldsaythatthedescriptionofconcreteparticularsasbundlesof universals,whichisusedinconnectionwiththepresentationof(BT), isahazardousone.Itsuggeststhatconcreteparticularslackinternal structure.(BT)isnotintendedtohavethatimplication. There is an alleged knockdown argument against the bundle theory.Itassumesthatitiscommittedtoafalseversionoftheprin ciple of the identity of indiscernibles. 1 The latter is rendered by RodriguezPereyra:

(PII) Necessarily, for all particulars x and y and every universal z, if z is instantiated by xifandonlyif z is instantiatedby y,then xisnumericallyidenticalwith y.2

MaxBlackputsforthhisintellectualexperimentasacounterexample of (PII).3 It is presented in the middle of a dialogue between two persons.Oneofthemisanadherentof(PII)andtheotherisnot.It isthelatterwhoisspeaking.

Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron,hadadiameterofonemile,thattheyhadthesame temperature, colour, and so on, and that nothing else existed.Theneveryqualityandrelationalcharacteristicof the one would also be a property of the other. Now if what I am describing is logically possible, it is not im

1Cf.e.g.Armstrong1978 a,p.91. 2 RodriguezPereyra 2004, p. 72. A trope version of the principle, not mentionedbyRodriguezPereyra,mightbe: (PIIt) Necessarily, for all (concrete) particulars x and y and every trope z,if zisinstantiatedby xifandonlyif zisinstantiatedby y,then xisnumericallyidenticalwith y. If we modify this principle by replacing ‘every trope z’ with ‘every Sim{ z1,…, zn}’,therevisedprinciple—callit‘(PIIt*)’—willmostcertainly befalse. 3TherefutationofthisprincipleisnotwhatSegelbergisaimingat.Onthe contrary,itseemstobea(tacit)premiseforhisapplicationoftheintellectual experiment. MODERATEREALISM233

possiblefortwothingstohavealltheirpropertiesincom mon.Thisseemstometo refute thePrinciple. 1

Earlierinthedialogue,theadherentof(PII)claimsthatitislogically impossible for two things to have all their properties in common. 2 Armedwiththeammunitionhebelievestheintellectualexperiment supplieshimwith,theotherthinkshecanrefutethat.Accordingto RodriguezPereyrathebundletheorydoesnotimply(PII);(BT)can evenbeusedtorefute(PII),sincethelattermaybefalsewhile(BT)is true. 3 Thereisanotherdefenceofthebundletheory.JohnO’Leary Hawthornearguesthatauniverse 4likeBlack’sdoesnotposeathreat to the theory. According to him, the description that the universe containstwoindiscernibleparticularsisnotadequate;strictlyspeaking itcontainsonlyoneentity,abundleofuniversals.Furthermore,thisis compatiblewith(PII).5Whattheintellectualexperimentdoesisthatit remindsusofaconsequenceofthebundletheory.Thisconsequence isthatabundleofuniversalscanbeatadistancefromitselfinthe samewayasasingleuniversalcanbeatadistancefromitself. 6The two spheres are but one single bundle of universals, which is fully presentattwoplaces. 7O’LearyHawthornefollowsthisupbysaying that a defender of (PII) should not appeal to relational differences whenconfrontedwithacaseof,forexample,twoindiscernibledrops ofwaterbecausewhatistwodropsofwater,looselyspeaking,isonly onedropfullypresentattwoplaces,strictlyspeaking,.8Rodriguez Pereyra’sverdictuponthisis:

1Black1952,p.156. 2Cf.Black1952,p.154.Theadherentof(PII)claimsthatifnotanythingelse separates the two, there are at least two properties that do: being identical withaandbeingidenticalwith brespectively—aand barethetwospheres. 3Cf.RodriguezPereyra2004,p.73. 4Thewordheactuallyusesis‘world’.SodoesRodriguezPereyra. 5O’LearyHawthorne1995,p.194. 6O’LearyHawthorne1995,p.196. 7O’LearyHawthorne1995,p.195. 8O’LearyHawthorne1995,p.194. 234CHAPTERV

[…]Hawthorne’sdefenceisnoteffective.Thepossibility thatallegedlyrefutestheBundleTheoryisthepossibility that there is a world with two indiscernible particulars. Hawthorneshowsneitherthatthisisnotagenuinepossi bilitynorthat theBundleTheorycanaccommodatethis possibility. What Hawthorne shows is that a world that apparentlycontainsindiscerniblesmayinsteadbeaworld containingamultiplylocatedbundleofuniversalsandno numerically distinct but indiscernible particulars. But for Hawthorne’sdefencetosucceedwhatneedstobeshown is that Black’s world is a world that contains a multiply located bundle of universals and no numerically distinct butindiscernibleparticulars.ForifBlack’sworldcontains two indiscerniblesthenitcannotbecorrectlydescribedasa world that contains no numerically distinct but indi scernible particulars. But Black’s world contains two indi scernible iron spheres, and so it cannot be correctly describedasnotcontainingtwoindiscernibleparticulars. 1

AnoverallclaimhereisthatBlack’suniverseispossible.Itcontainsa bundle of universals which is multiply located. However, it also containstwoindiscernibleironspheresandtheseareparticulars;each ofwhichissinglylocated.Theargumentshowingthecorrectnessof the overall claim is that there might be universes containing two almostindiscerniblespheres.

No one should deny the possibility of such worlds, and certainly there is nothing in them that a bundle theorist cannotaccept.Thatworldcontains two particularspheres, aand b.Butif ahasatemperatureTandadifferentparti cular b of the same kind as a has a temperature T* in finitesimallydifferentfromT,thenitispossiblefor ato have T*. Thus if the world with the almost indiscernible spheres is possible, so is another world in which the spheres are completely indiscernible. So Black’s world, which contains two indiscernible particulars, is possible. And, if so, Hawthorne’s defence fails, for Black’s world

1RodriguezPereyra2004,pp.734. MODERATEREALISM235

cannot be correctly described as a world not containing twoindiscernibleparticulars. 1

I suspect that this argument would not worry O’LearyHawthorne. Hisresponsetoitwouldprobablybethattheuniverse,whichisde scribedhereascontainingtwoalmostindiscerniblespheres,contains twobundleswithonelocationeach.Thereareotherthingsthatmight worryhim,though;Iwillsaysomethingaboutthosebelow. If (PII) is entailed by (BT), the bundle theory is incompatible with the possibility of there being a universe suchasthe onede scribed by Black, and Segelberg. Fortunately, (BT) does not entail Leibniz’sprinciple.

ForallBTassertsisthatparticularsareentirelyconstituted bytheuniversalstheyinstantiate.Thisentailsthatparticu lars instantiating the same universals have the same con stituents.ButthisiscompatiblewiththefalsityofPII— unlessparticularswiththesameconstituentsmustbenu mericallyidentical. 2

Itiseasytotakeitforgrantedthatcompletelysharingthe(universal) constituents with something else equals being numerically identical withit.However,toreachthatconclusionfrom(BT),anextrapre miseisneeded,forexample,thefollowing:

(PCI) 3 Necessarily,forallcomplexobjects xand yandevery entity z, if z is a constituent of xifandonlyif z is a constituentof y,then xisnumericallyidenticalwith y.4

Althoughthe needforanextraprincipletoreach(PII) from (BT) showsthatthelatterdoesnotimplytheformer,wewillremaincom mittedto(PII),giventhat(PCI)istrue.So,isittrue? 5Well,itistrue 1RodriguezPereyra2004,p.74. 2RodriguezPereyra2004,pp.756. 3Thedecodednameofthisprincipleis‘thePrincipleofConstituentIden tity’.ItisborrowedfromLoux1998,p.107. 4RodriguezPereyra2004,p.76. 5MichaelLouxthinksso.Accordingtohim,one“canprovide acomplete 236CHAPTERV for mereological sums and sets. RodriguezPereyra reminds us that ontologistswhorecogniseuniversalstendtodenythatmereological compositionistheonlymodeofcomposition.Statesofaffairsshould berecognisedaswell,butthesedonotobeymereologicalcomposi tion.Asaresult,anadherentofthebundletheoryhasreasontoreject (PCI).1 Arestrictedversionof(PCI)is(PCI*).Itconcernsparticulars, insteadofcomplexobjects,whichmakesitslightlyweakerthanthe former.

(PCI*) Necessarily,forallparticularsxand yandeveryentity z, if zisaconstituentof xifandonlyif zisaconstituent of y,then xisnumericallyidenticalwith y.2

Since PCI should not be recognised, independent reasons for recognisingPCI*areneeded.Theredoesnotseemtobeanythough.

[T]oaccept(PCI*)onewouldneedapreviousaccountof thekindofcomplexobjectsparticularsarethatcommits usto(PCI*).Butalthoughitmaynotbeclearwhatkindof complexobjectsparticularsare,theyarenotthosekindsof complex objects, like sets or mereological sums, that wouldrender(PCI*)true.Sothereseemtobenoreasons toaccept(PCI*). Thusthewayseemstobeopenforthebundletheorist toreject(PCI*).Byrejecting(PCI*)theBundleTheoryis liberated from its commitment to (PII). So by rejecting

“recipe”forcomplexthingsbyidentifyingtheitemsthatcountastheircon stituents.”(Loux1998,p.156)InSegelberg’sterminology,byidentifyingthe tcollection of a complex, one provides a complete recipe for it. Segelberg wouldnotagreewiththis. 1Iwouldsaythatthisoncemoreillustratesthattheterm‘bundle’isnota particularly successful one. It suggests that the complexes referred to are extensionallydetermined,likesetsandmereologicalsums. 2RodriguezPereyra2004,p.77. MODERATEREALISM237

(PCI*) the Bundle Theory can accommodate Black’s world. 1

Asindicatedabove,particulars’beingentirelyconstitutedbyuniver sals does not entail their being identical with bundles of universals. RodriguezPereyraproposesthatwedistinguishbetweenabundleof universals, on the one hand, and instances of it, on the other. Althoughaninstanceofabundleofuniversalsisentirelyconstituted by the bundle, the two are distinct entities. 2 What holds for the former need not do so for the latter, and vice versa . An instance is uniquely located, while a bundle might be simultaneously multiply located.Abundleislocatedatthesameplacesas its instances are located,butaninstanceneednotbelocatedwhereverthebundleis located.So,whereveraninstanceofabundleisfound,thebundleis therealso,butnottheotherwayround.

So when a bundle of universals has more than one in stance,therearesomenumericallydistinctparticularswith exactly the sameconstituents. Soitisnotincoherentfor thebundletheoristtoreject(PCI*). Notonlythat.Byclaimingthatparticularsareinstances of bundles, the bundle theorist must reject (PCI*). For bundles can be in more than one place at once. So a bundlecanhavemorethanoneinstance.Sotherecanbe numericallydistinctparticularswithexactlythesamecon stituents.So(PCI*)isfalse. 3

ReferringtotheterminologyofchapterII,abundleofuniversalsisa concrete universal since it exhausts the universal content of a con creteparticular,orseveralconcreteparticulars.Now,ifnodistinction ismadebetweenabundleandtheinstancesofit,therewillbeafew oddresultswithregardtotheirlocations. Assumerelationism aboutspace.Thelocationofanentityisthen causedbyitsspatialrelationstootherentities.Spaceisconstitutedby

1RodriguezPereyra2004,p.77. 2Cf.RodriguezPereyra2004,p.78. 3RodriguezPereyra2004,p.78. 238CHAPTERV thespatialinterrelatednessofentities.Apeculiarconsequenceofthe premises of a bundle theorist such as O’LearyHawthorne’s is that there need not be a difference between a case where a bundle is locatedintwoplacesandoneinwhichitislocatedinthreeplaces. Further,itscircumstancesmustofcourseberatherspecial.Imaginea universe with two exactly similar spheres separated by a certain distance. Compare this with another universe with three exactly similarspheres whichareseparatedbythesamedistance as in the former universe. Together, these form an equilateral triangle. Since thereisnodistinctionmadebetweenbundlesandinstances,thereis no relational difference between these two cases. However, if instancesofthebundlewereallowedfor,thatwouldresultinadiffer ence.Therewouldbetwospheresinthefirstuniverseandthreein the latter. O’LearyHawthorne should, and perhaps even would, be impressedbythis.Anindiciumofthatisthesuggestion,madebyhim andJanCover,thatthedifferencebetweenthetwosituationsisthata triadicdistancerelationisapplicableinonecasebutnotinanother.

Consider some sphere s. There is one possible world W containing s wherethesoleoccupantsarewhatweordi narilydescribeasspheresinrelationalspacefivefeetapart. ThereisanotherpossibleworldW ′containing s wherethe sole occupants are what we ordinarily describe as three spheresinarelationalspace,eachfivefeetfromeachother (thus making up an equilateral triangle). How can the bundle theorist distinguish these worlds? Clearly, if the bundle theorist restricts himself to dyadic facts, he will struggle.Iftherelataofdyadicfactsareimmanentuniver sals,itishardtofindadyadicfactinstantiatedbyoneof WorW ′butnottheother.But,onceagain,unlessthereis some obligation to restrict oneself to dyadic facts or to insistthatalltriadicfactssuperveneondyadicones, the TriplicationProblemisnoobjectiontotheBundleTheory perse .1

1O’LearyHawthorne&Cover1998,p.214. MODERATEREALISM239

Since O’LearyHawthorne obviously wants there to be a difference between the two situations, it should worry him that his ontology cannotaccountforit.Infact,inthecaseathanditcannot.Thetri adicrelationdoesnotdeliverthedifferencehebelievesisthere. If absolutism aboutspaceisassumedinstead,theoutcomeiseven morecounterintuitive.Sinceallplacesarethesameplace,according to the premises of the bundle theory in question, each spatially locatedentityisinthesameplaceaseveryotherentity.Theassump tionisherethatspaceisasetofpoints.Further,ifuniversalpoint hood is recognised, but not instances of it, there will only be one singlepointtooccupy.1This,bytheway,indicatesthatanabsolute spacemustbeparticular, not justuniversal.2 Obviously, the notion thateachbundleofuniversalshavingspatiallocationwouldhavethe samelocationaseveryotherbundlethatisidenticalto ordifferent fromitisnothingshortofanabsurdity. The problems referred to in the two previous paragraphs are remedied if instances of bundles are recognised. The problems in connectionwithrelationismaremetifthelocationsofinstancesare prior to those of the universals they are instances of. Then, the bundleswillbelocatedduetotheirinstancesbeinglocatedwhilethe latterarelocatedduetothespatialrelationsholdingbetweenthem. Furthermore,theproblemsconnectedwithabsolutismevaporate.It isinstancesofbundlesofuniversalswhichhavelocationsprimarily; theplacestheyoccupyareinstancesthemselves.Placesareinstances ofauniversalwemightcall‘pointhood’.Sincetheinstancesofpoint hoodareseparatefromeachother,theinstancesofotheruniversals occupydifferentpoints.Inbothofthesealternatives,thenumberof spheresequalsthenumberofinstances. What has been pointed out here constitutes a more or less conclusive reason for there being instances. Given that there are universals, the absurdities which result from recognising them and bundlesofthem,butnottheirinstances,showthatinstancesshould

1Cf.RodriguezPereyra2004,p.75. 2Cf.Johansson1989,p.147,wheretheparticularityanduniversalityaspects ofabsolutespace(containerspace,inJohansson’sterminology)arediscussed. 240CHAPTERV be recognised as well. An account of instantiation remains; to that end,theanalyticontologyproposedbyDonaldMertzisdiscussedin section5.3.

5.3TheModerateRealismofD.W.Mertz

5.3.1Overview According to Donald Mertz, Avicenna’s second argument is poten tiallyaconclusiveargumentforparticularism.InMertz’sownrefined version of it, he claims that its potentiality has become actual. An analysisoftherefinedversionisfoundinsection5.3.3.Beforethat, theprinciplesdefiningMertz’sownmoderaterealismarepresentedin section5.3.2. Section 5.3.4 details the notion of unit attributes, describing howeachunitattributeisconsideredtohavetwoaspects.Insection 5.3.5,oneoftheseaspectsisexaminedmorecloselywithregardto whether it is a simple or complex entity. Section 5.3.6 defines con tinuouscompositesandconsiderstheissueofwhetherunitattributes arecontinuouscomposites.Thepredicativeaspectofunitattributesis thesubjectofsection5.3.7.Finally,insection5.3.8ashortpresenta tionisgivenofhowunitattributesformnetworkstructures.

5.3.2PrinciplesofModerateRealism Areasonfornotusingtheterm‘trope’asacomprehensivetermisits strong association with nominalistic particularism. There are other terms which can better fulfil that role. Among these are ‘property instance’, ‘attribute instance’, or just ‘instance’, as well as ‘unit pro perty’and‘unitattribute’.Mertzusesallofthem.Inaddition,heuses thepair‘relationinstance’and‘unitrelation’.Asregardsthetwolatter terms,itshouldbenotedthatitisnotjustthatheconsidersrelations tooccurasparticulars.Moreimportantly,hedoesnotthinkthatthe distinctionbetweenmonadiconticpredicates,ontheonehand,and polyadic ones, on the other, should be assigned any importance of principle. Ontic predicates, irrespective of their adicities, should be MODERATEREALISM241 recognisedasformingonesinglecategory.Whatisessentialisthatan onticpredicatehasadicity,notofwhatdegreetheadicityis. Ontologicalparticularismatitsminimumissaidtosatisfytwo principles.Thesetwoprinciplesare:

n n n ForinstancesR iandR j,ofthesame nplacerelationR , Principleofsubjectuniqueness(SU): n n If:R i (a1,a2,…,an)and:R i (b1,b2,…,bn),then a1= b1,…,a n= bn , and Principleofinstanceuniqueness(IU): n n n n 1 If:R i(a1,a2,…,an)and:R j(a1,a2,…,an),thenR i=R j.

Sincethesetwoprinciplessupposedlyconstitutetheminimumcon tent of particularism, the phrase ‘of the same nplace relation R n’ shouldbeneutralbetweenrealisticandnominalisticinterpretationsof thegeneralparticularisticdoctrine.Keepthatinmindwhenreading thefollowing.

As subjectunique (SU), no relation instance can have morethanonedistinct ntupleofrelata.Itisnotthecase, forexample,thatRed 1inheresasnumericallythesamein both apple a and distinct apple b, for otherwise Red 1 would have the nature of a universal and not an un repeatable instance. The principle of instanceuniqueness (IU) formalizes the nonredundancy thesis: for example, that apple a cannot have (at the same time and corre spondingtothesamespatialregion)numericallydifferent instances of the property Red. The doctrine of instance uniqueness can be supported not only by an argument fromonticeconomy(‘Ockham’srazor’),butalsoanargu

1Mertz1996,p.10.Again,Ihavetakenthelibertyofinsertingthecolons. While the superscript of ‘Rni’ indicates adicity, the subscript indicates individuality.Quiteoftena simplifiednotationisused,omittingsuperand subscript. In this practice, ‘R’ sometimes stands for either a relation or an instanceofit.Thismoreambiguoususecanmakeitquitedifficulttointer pretwhattheintendedsenseis. 242CHAPTERV

ment from the identity of indiscernibles: 1 namely, that there is simply nothing that could serve to intrinsically differentiatetworelationinstancesiftheyhavenumerically thesamerelata ntupleandareofthesamerelationcon stantR n.Thecentralproblemforparticularismistopro ducecogentargumentsfortheexistenceofinstancesthat satisfytherequirementofsubjectuniquenessSU. 2

In chapter III we saw that Maurin is not entirely out of sympathy withtheideathattropesarerecyclable. 3However,(SU)rulesthatout. One may ponder upon whether this means that (SU) should be revisedinsomewaysothatherviewfitsinorifsheshouldrecon siderherposition.Anyhow,since(SU)and(IU)aredeclaredtobethe commoncontentofallversionsofparticularism,whatcategorythe referentof‘R’belongstoshouldbeleftopen.Forexample,itmust notbepresupposedthatitdesignatesauniversal.Theuseoftheterm ‘’ in the quotation probably offends that provision since ‘intension’ and ‘universal’ are synonymous in Mertz’s own termino logy. Evidently,ifuniversalsaretohaveanyroletoplayinthiscon text,thisistobestipulatedbyyetanotherprinciple,whichhastobe addedtotheminimumprinciples.Thefollowingissuchanadditional principle:

1Cf.Mertz1996,pp.148ff,mentionssomeofLeibniz’sownonthe principle. Among other things, he considers it to be a metaphysical, not a logical,principle.Whileitislogicallypossiblethat∃x∃y[( x≠ y)& ∀P[P( x)↔ P( y)]],itisinconsistentwithGod’swisdomandthereforeinconsistentwith the way things must be. Cf. Leibniz 1969, p. 699. I do not know to what extentMertzreliesonGod’swisdomhere. 2Mertz1996,p.11. 3 Her compresence tropes cannot be recycled. Presumably, the same holds for all the other external relations. A wellfounded suspicion is that the predicativityofrelationsmakesallthedifferencehere. MODERATEREALISM243

Principleofimmanentinstancerealism(IR): n n FordistinctrelationinstancesR i,R j,…thereexistsandentity Rn which is a numerically identical aspect of each of the n n 1 instancesR i,R j,…

Therearequiteafewadherentsof(IR).Aninexhaustiveenumeration of is: Boethius, 2 Avicenna, 3 Thomas Aquinas, 4 John Duns Scotus, 5 John Cook Wilson, 6 Edmund Husserl,7 Nicholas Wolterstorff 8 and PeterStrawson. 9ItisquitepossiblethatPlato 10 andAristotle 11 also belongtothislist. 12 1Mertz1996,p.11.(IR)isnotintendedtoimplythatonlyextraconceptually instantiated universals exist. Universals which are merely conceptually in stantiatedarealsorecognised.Cf.Mertz2006,p.39. 2Cf.Gracia1984,p.78. 3Cf.Morewedge1973,pp.334. 4Cf.Aquinas1955,p.127. 5Cf.Harris1959,pp.945. 6Cf.CookWilson1926,Vol.I,pp.171,187,199,2078,233;Vol.II,pp. 665,6701,713. 7Cf.Husserl1970,Vol.I,pp.3767. 8Cf.Wolterstorff1970,pp.90ff. 9Cf.Strawson1971,pp.1689,footnote1. 10 Cf. Phaedo ,102be,and Theaetetus ,209ad. 11 Cf. Categories , 1a24b9, and Metaphysics , 1017b25, 1039b246, 1042a29, 1049a28ff,1057bff,1071a279. 12 FranciscoSuarezisnotonthelist.Heseemstobeanominalistofsome sort.Cf.Suarez1964,pp.30,36,478.However,heisclassifiedasaparti cularist.Tosomeextent,thatfactunderminesthestatusof(IU)asanecess aryconditionofparticularism.RegardingSuarezand(IU)Mertzsays: […] Suarez maintains that an entity is its own principle of in dividuation […]. […] But, if accidents are not individuated by theirsubjects,itisimpropertoexplaintheindividualityofacci dents,whichissomethingintrinsicandtiedtotheirverynatures, bysomethingextrinsic[…].Hethusgoesontoassertthatthere isnoapparentreasoninprinciplewhymultipleinstancesofthe same accident cannot be simultaneously in the same subject (a denialoftheprincipleofinstanceuniqueness,IU),though,asa matter of fact, no such duplicated inherence occurs naturally […].(Mertz1996,pp.1289) 244CHAPTERV

Mertz is scanty with own arguments for realism. He mainly referstoargumentspresentedbyothers,inparticularthoseofArthur Pap, David Armstrong, Reinhardt Grossmann, Herbert Hochberg andFrankJackson. 1Sincenoneoftheseisaparticularist,theirargu mentssupportrealismingeneral.Heisofcourserightthatthephilo sopherslistedprobablyhavesuppliedthebestargumentsforrealism whichcanbefound. Moderatenominalismsdonotsatisfy(IR).Dependingonwhich moderate nominalism we are dealing with, the stipulated substitute principle will vary. Take for example G. F. Stout’s moderate nominalism.Hisunitattributesarethesametypebecausetheyallbe longtoacertainclass.Belongingtothisclassiswhatgivesthemtheir qualitativecontent. 2Thismakeshisontologyaversionofclassnomi nalism. Neither should (SU) and (IU) involve any particular view on predicativity.Thequalitytropesofmany,ifnotall,moderatenomina lisms are not predicative entities. The quality tropes of Campbell constituteacaseinpoint.Anappositedescriptionofthemis:

[T]ropes are not ontically predicative , they do not exist as ‘inhering’ in a subject, but rather ‘freefloat’, as it were. Thegroupingoftropes(e.g.,bald 2,snubnose 5,white 1,etc.) whichconstitutesordinaryindividuals(e.g.,Socrates)isa functionoftheunique compresence relation. 3

IsupposethatSuarez’sclaimthatduplicationinfactneveroccurs explains whyheis onthelistofparticularists.Bytheway,itisstatedhere thatthe individuality of unit attributes is in some way dependent on their subjects. This is not part of either principle (SU) or (IU). It is a consequence of Mertz’sownviewonpredication. 1Mertz1996and2001mention:Pap1959,Armstrong1978and1989,Gross mann1983,Hochberg1988andJackson1977. 2 Cf. Stout 1930, Essay XVII. Caution is called for here. Stout’s notion of classmayverywelldifferfromthatwhichisusednowadays. 3Mertz1993,p.190. MODERATEREALISM245

Earlier Campbell often said that instances of compresence should alsobereducedtotheirrelata.1Heseemstohavechangedhismind in recent years though.2The goal he used to try to attainwas the reduction of all polyadic attributes. The former were supposed to supervene on their relata. Compresence was no exception to this. Usingabitofpicturesquelanguage,theallegedcementofacomplex waslookeduponasnothinginadditiontothebricksofthecomplex inquestion.3Inthisvisionofrealitynothingispredicative.Incontra distinctiontothatview,Maurinhasrecognisedunreduciblepredica tiveinstancesofcompresencefromthestart,thoughherqualitytro pestotallylackpredicativity.4 Inadditionto(SU),(IU)and(IR),Mertzrecognisestwoother principles:

Principleofinstancepredicates(IP): n Only unrepeatable relation instances, R i , are ontic predicates — that is, exist as predicative among specific subject ntuples, the universalR nisnotonticallypredicative. 5

1Cf.Campbell1990,pp.40ff. 2Cf.Campbell2003. 3Cf.Campbell1990,pp.130ff. 4 For some reason both she and Campbell refer to quality tropes as being monadic. It would be more apposite to describe them as monads. Not necessarilyinterpretedidealistically,althoughthehistoryoftheterm‘monad’ suggeststhat. 5ThatuniversalsarenotpredicableiscontrarytoAristotle’sview,thoughthe notion that particulars (instances of universals) are predicable need not be. Thiscanbeseenfromhisdefinitionsofuniversalandparticular,in DeInter pretatione ,17a3840: Somethingsareuniversal,otherindividual.Bytheterm‘univer sal’Imeanthatwhichisofsuchanatureastobepredicatedof manysubjects,by‘individual’thatwhichisnotthuspredicated. Thisallowsfortwodifferentinterpretations: either thatparticularsarenotpre dicableatall or thattheyarenotpredicableofmanysubjects. 246CHAPTERV

Principleofrelatalinking(RL): n No nadicrelationinstanceR iexistsexceptasontically predicative among, and hence necessarily presupposing, some ntuple of entitieswhichassuchitrelates. 1

Theintroductionofthesetwoprinciplescorroboratestheimpression thatpredicativityisnotsupposedtobeapartofthecontentofanyof thethreeformerprinciples.Itisthanksto(IP)thatrelationinstances arepredicativeandthatuniversalsarenot.Sincethesecondhalfofit isnegative,Isupposeanominalistcouldinprincipleconcurwithitin its entirety. However that may be, the predicative entities are unit attributes and are characterised as being ontoglial .2 Their ontoglial natureismanifestedthus:monadiconticpredicates link to subjects; polyadic ontic predicates link among subjects. 3The subjectsofontic predicates may be other ontic predicates. On the lowest level of realitytheymustbesincesubstrataarerepudiated.Freefloatingunit attributesarealsorepudiated,by(RL). Mertz’spreferrednameforhisownanalyticontologyis‘moder aterealism’. 4Hedoesnotintenditasanexclusivenameforhisown particularversionofparticularismthough. 1Mertz1996,p.26.Althoughunitrelationsonlyexistasactuallyrelatingenti ties,thereareuniversalswhicharenotinstantiated. [I]ntensionsexistforwhichtherearenocorrespondingonticpre dicatesandsofacts,e.g.,Unicorn 1,Phlogiston 1[…].(Mertz2006, p.107) Also mentioned are the Spouse 2 and Employer 2, as exiting in a universereducedtooneextanthumanbeingwhohasretainedtheseinten sionsbyabstraction.Withregardtotheissueofuninstantiateduniversals,the twolatterareevidentlyirrelevant.Thetwoformeraremoreinteresting.Isus pectthatneitherofthemisatotallyfreecreationofthemind.Presumably, theyaresynthesisedfromintensionalmaterialgainedfromexperience. 2Cf.Mertz1996,p.25.Theterm‘ontoglial’isderivedfrom theglueofbeing in Greek. Unfortunately, Mertz wavers a bit concerning which entity is the actualglue.InMertz1996,p.25,theimplicationisthatitistheunitattributes. InMertz2006,p.25,itissaidtobethepredicationalaspectsofunitattri butes. 3Cf.Mertz1996,p.24. 4Analternativedenominationis‘networkinstancerealism’,itsuggeststhat MODERATEREALISM247

The conjunction of Principles SU, IU, and IR, with R restrictedtothelimitingcaseofmonadicproperties,con stitutesthe ModerateRealism ofAvicennaandtheChristian scholastics,andrepresentsamedianbetweentheextremes ofPlatonicrealismontheonehandandnominalism on theother. 1

ThedoctrinewhichrestrictsRtomonadicattributesistheonemen tionedinsection5.2.3.Initsclassicalformitdecreespolyadicpredi catestobereducibletomonadiconesincombinationwithapeculiar characteristicofpointing.PerhapsitoriginatesfromPlato. 2

5.3.3ARefinedVersionofAvicenna’sSecondArgument Earlier, we saw certain secondorder attributes being essential for Avicenna’s arguments. It holds correspondingly for Mertz’s refined versionofthesecondargument.Thisisevidentfromthefollowing conciseaccountofit:

LikeAvicenna’sarguments,thefollowingturnsuponthe factthatarelationRasitoccursinthecomplexes aRband bRahasdistinctandincompatiblesecondorderproperties. Inparticular,letitbethecasethatbothfacts aRband bRa obtain,whereRisanonsymmetricrelation,forinstance, xloves y.3Wehaveinthiscasetwodistinctcomplexes,or facts, composed of apparently exactly the same parts. Of course, this is impossible. The standard and intuitive observationisthatthereisanorderinwhichRrelatesits relataandthisorderisdistinctforthetwocomplexes.In

instances form networks together. Among the networks are the ordinary objects.Thenetworkaspectisworkedout,e.g.,inMertz2004. 1Mertz1993,p.193. 2Cf.Cavarnos1975,pp.1725,foranaccountofPlato’sview.Althoughthis doctrineisfoundinthewritingofPlato,heneednotbeitsoriginator.Forall weknow,itmayoriginatefromancientEgypt. 3Sincelovingisanintentionalrelation,itmighthappenthatanexistingsub jectlovesanonexistingrelatum,andsurprisinglyoftenactuallydoesso.The inverseisyettohappen.ItakeitthatJohnandMarybothexist. 248CHAPTERV

thefactthatMarylovesJohn,thelovingisfromMaryto John,andnottheotherwayaround.Thelatterwouldbea separatearrangementwhichmayormaynotobtain.The distinctionbetweenthetwocomplexes, aRband bRa,isa function of the relation, and specifically of its ordering connectedness among its relata. In aRb, R relates atob andnot btoa,whereasin bRa,Rrelates btoaandnot a tob.Butthen,ifRisnumericallyidenticalinbothcom plexes,thenRpossessescontrarynextlevelproperties.We mustconcludethatRisnumericallydistinctinits occur rencesacrossthesecomplexes. 1

Throughoutthisquotationtheterm‘R’isused.What‘R’,or‘relation’, n indicates is a relation instance of the form ‘R i’. In fact, there is supposedtobetwosuchinstances;theargumentcanbesummedup as follows. If one and the same relation instance is supposed to obtain in one fact as well as in another, where it is holding in the opposite direction, it has contrary properties. This is impossible. Therefore,therelatingentitiesofthetwofactscannotbenumerically identical with each other. The two contrary properties, which are relevantinthisparticularexample,arerelatingatobandrelatingb toarespectively. Evidently,Leibniz’slawisinvokedhere.2Thecontraryproper ties indicate that there cannot be the same relating entity in both cases. Thus, the two facts should be rendered aR1b and b R2a res 2 pectively.Or,moreinlinewiththecanonicalnotation::R 1(a,b)and 2 :R 2(b,a).Heretherelatingentitiesareparticulars,notuniversals. ItisimportanttonotethatthereisauniversalR2involvedhere andthatitmakesadifference.

ThereisasenseinwhichRisthesameinbothcomplexes (asintensionR—e.g.,Loves);yet,asrelatingdistinctspe cific relata and thus establishing a specific order among

them, R is particularized (as instances R i and R j). If one failstomakeadistinctionbetweentheintensionofarela

1Mertz1993,p.199. 2Cf.Mertz1996,p.184. MODERATEREALISM249

tion and the actual relating or linking that is unique to a specificordered ntupleofrelata,thentheaboveargument doesawaywithrelationuniversals,andweendupatbest with trope nominalism. The combinatorial state con stitutingoneordered ntupleisnotthecombinatorialstate ofadifferentlyordered ntuple.Yettheintensionsunder whichallrelatingmusttakeplacearerepeatable. 1

Oneproblemwhichclassicalrealismhasfailedtosolveissatisfactory explanation of the role of universals. The regress, named after Bradley,canbeseenasanillustrationofthat.AlthoughMertz,strictly speaking,agreeswiththe(tacit)premiseoftheregressargument,that (universal) relations do not relate, he does not agree with the conclusion of the argument. The conclusion being that there is no such thing as a relating. The entities which actuallyrelaterelataare unitrelations,whicharenumericallydistinctfromeachother.Thatis what is supposed to be shown by the arguments for particularism. WhileAvicennaandthetraditionofferanalysesin terms of esse ins and essead s,whatisproposedhereisananalysisinwhichaunitattri buteisan esseinter ;i.e.,afullyrealinterconnective. 2Forrelations,to beistobond. 3Ihastentoaddthatisinstancesofrelationsthatare supposedtobond,notrelationsthemselves. What about the secondorder attributes appearing in the pre sentedargumentforparticularism?Thedirectionofaunitrelationis said to be a secondorder attribute, or at least that it founds one. Furthermore,itisduetothatsecondorderattributethattheunitrela tionisnotthesameasanother.Theformofthesecondorderattri butementionedis:beingfromatob.Whichformulacanbeusedto adequatelyexpressthattheunitrelationofthefacthasthissecond 3 2 order attribute? Is it perhaps ‘:R 2(R 1,a,b)’? In this rendering it is a 2 triadicunitrelationholdingbetweenR 1, aand b.Aregressmayliein waithere.Ifthatisinfactthecase,whichkindisit?Ifitisanalytical, 4 3 R 3willneedtodotherelatingofR 2totherest;thenextstepafter

1Mertz1996,p.185. 2Cf.Mertz2001,p.55,and2006,p.26. 3Cf.Mertz1996,p.187. 250CHAPTERV

5 4 thatistheneedofR 4todotherelatingofR 3andrest;etc.Mertz wouldmostcertainlynotadmitthatananalyticalregressisinherent here.Ifthereisaregresshere,perhapsitisanimplicativeone. Onecouldalsodenythatthereisanyregresshereatall.Partof thatdenialwouldbethatthefirststepintheproposedrenderingof 3 2 the situation — i.e., ‘:R 2(R 1,a,b)’ — is a misrepresentation. The secondorder property is expressed in the relative order the con 2 stituentshaveintheformula‘:R 1(a,b)’,particularlythatof‘ a’and‘ b’ . 2 ThissincethepredicationalaspectofR 1isspecificforthepair aand bandnoother.1 Theargumentfromconversesecondorderpropertieshasbeen questioned. One objection is made by Reinhardt Grossmann. The particularversionoftheargumentfromwhichhestartsisfoundin AlexiusMeinong.2Meinongmaintainsthatthetriangularityofapar ticulartriangle,A,isnotthesameasthatofanothertriangle,B.The reasonforthatisthatthetwohavedifferentproperties: being the triangularity of Aand beingthetriangularityof B, respectively.3 In ordertoshowthatthisisdeceptive,Grossmanninvokesananalogy.

[T]hisargumentisofthesameformasthefollowingfalla cious argument. The son of John cannot be the son of Mary;fortheformerhasthepropertyofbeingthesonof Johnwhilethelatterdoesnot.[…]But,ofcourse,Tom— theonlysonofJohnandMary—hasbothproperties;he isboththesonofJohnaswellasofMary.Andso,too, thepropertyofbeingatrianglehasboththepropertyof being the triangularity of A as well as that of being the triangularityof B.4

Itakeitthatthecounterargumenthereisasfollows:Iftheargument fromconversepropertiesissound,Tomcannotbethesonofboth

1Usinganuglyformula::R 21(a,b)→ ∀x∀y[(:R21(x,y)↔(( x= a)&( y= b ))]. 2 According to Grossmann, the same kind of argument can be found in Wolterstorff1970,p.139,andCookWilson1926,vol.I,pp.346,394.He mightberightaboutthat.However,inbothcasesitisratherimplicit. 3Cf.Meinong196878,vol.1,p.75. 4Grossmann1983,p.109. MODERATEREALISM251

JohnandMary.Ifhewere,hewouldhavetwopropertieswhichare conversesofeachother:beingthesonofJohnandbeingthesonof Mary.However,sinceTominfactistheirson,hecansimultaneously havetheseproperties.Hence,theargumentisnotsound. Classification of the two relational properties mentioned as beingconversesofeachotherisdubious.Nevermind that though. ContemplateinsteadtheremarkthatGrossmann’scounterargument misses the point. The criticised argument does not rule out that a personcanhavetwoparents.Whatitismeanttoshowisthatthereis notjustonebuttwoinstancesoftheparentrelationinvolved.Oneof theseholdsbetweenthefatherandtheson.Theotherholdsbetween themotherandtheson.Theclaimisthatifitwerethesamerelating entity, it would have two properties which it cannot have simul taneously: holdingfromJohntoTom and holdingfromMaryto Tom.However,inGrossmann’srenderingoftheargumentwhathe takestoberelevantisthatthesonhasconverseproperties:beingthe sonofJohn and beingthesonofMary. Evidently, that is a mis representationoftheargument. Ifthereisarelationintheexamplewiththetwotriangles,being theanalogueoftheparentrelation,itwouldbeinstantiation.Now,is it the same relating obtaining in both triangles? If instantiation is supposedtobearelationjustlikeanyother,aparticularistwouldgive anegativeanswer.Thereasonforthatisthesameasinthecasewith theparentsandtheirson.Ifweinsteadconcentrateonthetriangu larityofthetwotriangles,itisofcourselessevidentthattherearein facttwoinstancesofit:onein Aandanotherin B.Meinong’sclaim, that they are two since they have different properties, is taken by Grossmanntobenomorethananassertion. Aswillbeseenbelow,Mertzdoesnotthinkthatthereareany instancesofaninstantiationrelation.Further,sincethereisnosuch relation, there can be no instances of it. However, he has a notion whichcanbesaidtocorrespondtoinstantiation.Itiscalled‘predi cationalaspect’amongotherthings. It will beseeninwhat follows thatsinceit perdefinitionem isparticular,thetriangularityof Aisnot identicalwith that of B.Whatissaidinthe previoussentenceisof 252CHAPTERV coursenotavalidinference.Afewmorepremisesareneeded.They aresuppliedbelow.

5.3.4UnitAttributes:Preliminaries EveryunitattributehastwoaspectsaccordingtoMertz.Oneofthese he refers to using denominations such as ‘universal aspect’, ‘inten sionalaspect’orsimply‘universal’or‘intension’.Theotheraspecthas several alternative names, some of which are: ‘predicational aspect’, ‘predicational tie’ or just ‘predication’ or ‘tie’, ‘unification under an intension’orjust‘unification’,‘relatingunderanintension’,‘relating aspect’ or just ‘relating’, ‘combinatorial aspect’, ‘agent unifier’, ‘uni fying’,‘agentcombinator’,etc. 1Sincetheintensionalaspectis a universal, it is shareable. The predicational aspect, on the other hand,isnotshareable.Consequently,itisaparticular,or,itisatleast particular(adjective).FortherestofthischapterIwillbeusingmost ofthedenominationsmentioned,andalsoafewinadditiontothese. TwoargumentsarefrequentlyadducedbyMertz.Botharein tendedtoshowthatthepredicationalaspectunderanintensionmust beaparticular.Aversionofoneofthesereads:

[T]herelatingunderRisuniqueandunrepeatabletoeach fact because the existence sustaining unification under R among one set of relata can obtain while the like uni ficationunderRamongtheother(oranyother)setofre lataceasestoexist.[]Restatedasa reductio ,ifitwereone and numerically the same unification under R sustaining theexistenceofeachfact,justasforrealistsitisnumeri callythesameintensionR‘in’eachfactwithonticpredi 1Whilethetermsofthefirstgroupareusedunivocally,someofthesecond are used equivocally. E.g., by ‘agentcombinator’ is often meant an entire onticpredicate.But,equallyoftenismeantjustitspredicationalaspect.The sameistrueofaphraselike‘relatingunderanintension’.Oneofitspossible sensesisthatof‘instanceofanintension’.Anotheristhatof‘predicational aspect’.Thereisevenathirdsense,whichisanintermediateoftheformer two.Thus, atristinctionisindicated:(i)instanceofanintension,(ii)predi cationunderanintension,and(iii)predication.Thedistinctionbetweenthe intermediateandeitheroftheothertwoiseasilyblurred. MODERATEREALISM253

cateR,[…]allsuchfactswouldobtainorceaseto exist simultaneously. A content or intension R might persist, but all of its relatings, being identical (numerically one), wouldcomeintoandgooutofexistencetogether.Allof thisiscounterfactual.AnintensionRcanbeshared,buta unionunderitamongaspecificrelatasetcannot. 1

Thus,iftheassumptionismadethatthesamespecificpredicational aspectistheunifierofdistinctfacts;allthesefacts must go out of existencewheneveroneofthemceasestoexistsinceallthesefacts have identically the same predicational aspect. However, this is counterfactual.Theassumptionmustberepudiated.Whentheinten sionLoveisinvolved,werealisethatJohn’sloveforMarycanobtain evenwhenherloveforhimceasestoexist,and viceversa .Thesame appliestothepredicationalaspectsofmonadicpredicates.Whenone oftheapplesofapairofredapplesceasestobered,theotherdoes not automatically stop being red. Since one and the same predica tionalaspectcannotbehavedifferentlyfromitself, it cannot be the samepredicationalaspecteverywheredoingthat.Instead,thereareas many particular predicational aspects under a specific intension as thereareinstancesofit. Ageneralisationoftheargumentwouldbethatitcannotbethe samepredicationalaspectthatisdoingthejobineveryobtainingfact, irrespectiveofintension.Giventhatassumption,whenonefactgoes outofexistence,everyotherfactmustalsoceasetoexistsincethe relatingaspectinallfactsisidentical. The other argument is the one from contrary secondorder properties.InoneofhisformulationsofitMertzreferstoaprinciple which he calls ‘the constituent analogue of the identity of indiscernibles’:

(CII) Entitieshavingexactlythesameconstituentsareidenti cal,i.e.,

1Mertz2001,p.556. 254CHAPTERV

(x)( y)[( z)( zisaconstituentof x≡zisaconstituentof y) ⊃x= y]. 1

While the original version of the principle of the identity of indiscernibles—with‘universals’insteadof‘constituents’—iscon troversial, Mertz considers (CII) to be fairly uncontroversial.2 It is said to be intuitive and consequential,3 similar to the principle, or axiom,offorsettheory. Thesecondargumentcannowbestatedquitebriefly.

[I]ftherelatingunderRbetween aand bwerenumerically oneandthesameinallofitsfacts,then,becauseR, aand barealsonumericallythesameinallthesefacts,underCII itwouldbethecasethat:R( a,b)=:R(b,a). 4

1Mertz2001,p.49.TheprincipleisfoundinMoreland1998,p.252,whereit isstatedthat“[i]tishardtoseehowtwoentitiescouldshareliterally all their constituentsincommonandstillbetwo.” 2Cf.Mertz2006,p.15.(CII)isrejectedbyArmstrong.Cf.Armstrong1986, pp. 858; 1989, p. 90; 1997, pp.11821. According to him, the differences betweenentitieshavingthesameconstituentsareduetodifferencesinhow the constituents are organised. The implication is then that organisation is separatedfromtheconstituents.Thus,:R( a,b)and:R( b,a)aredifferentdueto differencewithregardtoorganisation,notconstituents.Aslightlymisleading wayofspecifyingthesense‘constituent’hasinMertz’terminologyistosay that organisation is an aspect of the constituents. This illustrates the importance of keeping track of how ‘constituent’ is being used. Cf. the followingfootnote. 3 The inversion of (CII) might be called ‘the constituent analogue of the indiscernibilityofidenticals’(CII*): (CII*) Entitiesbeingidenticalhaveexactlythesameconstituents,i.e., (x)( y)( z)[( x= y)⊃(zisaconstituentof x≡zisaconstituentof y)]. Thisprinciple,justas(CII),isintuitiveandconsequential.Thisholdsgood also when ‘constituent’ is replaced by ‘universal’ in (PCI*). In contrast to Leibniz’s principle, Leibniz’s law is considered valid by most philosophers. Now,IwouldsaythatgiventhesenseinwhichMertzisusing‘constituent’, thesignificantdifferencebetweenLeibniz’sprincipleandlawismadetrivial. 4Mertz2001,p.55.Iremindof(PCI),presentedinsection5.2.4: (PCI) Necessarily,forallcomplexobjectsxand yandeveryentity z,if MODERATEREALISM255

Sincetherelatingaspect,accordingtotheassumption,isnumerically thesamein:R( a,b)and:R( b,a),ithasthesamesecondorderunitpro pertyinbothfacts.Thatwouldbeone,butnotboth,ofthefollowing two:fromatoborfrombtoa.However,thatisimpossible. Whatnowofthedistinctionbetweenthetwoaspectsofaunit attribute?Adecisionhastobemadewithregardtoanalysis.There seemstobeonlytwoalternatives.Accordingtooneofthese,apre abstractionrealcomplexityexistswithintheunitattribute.According totheother,thereisonlyapostabstractiondistinctionbetweenpar tialandincompleteaspectsofwhatisitselfasimpleentity. 1 Mertz considers the first analysis to be untenable. If it is accepted,oneoutoftwoabsurditiesmustalsobeaccepted.Oneof theseabsurditiesisaviciousregress.Theotheristhenonrelational tietheory. Letusseefirsthowtheregresssupposedlyarises.

[A]ssumeanalysis1),i.e.,thatafactoftheform:R( a,b)has asrealanddistinctconstituentsrelata aand b,intensionR, andthelatter’spredicationaltie.Soconstrued,thepredica tional tie under R will have R as an additional term or relatum.Thisissosincethetie,tobea tie andtobeR’stie, mustdotheconnectingofRto aand b.Now,clearlythe tie cannot itself be an additional and full relation 2 (a tie

zisaconstituentof xifandonlyif zisaconstituentof y,then xisnumericallyidenticalwith y. Thisprincipleissimilarto(CII).However,Itakeitthattheintendedsenseof ‘constituent’in(PCI)isnotthesameasthatof(CII).InMertz’interpretation oftheprinciple(CII)thepredicationalaspectsofconstituentsareincluded. (PCI)doesnotincludecorrespondinginstantiationamongtheconstituents. An objection to this might be that constitution and instantiation are reci procal in the sense that what is a constituent is instantiated and what is instantiated is a constituent. However, the notion of instantiation, which seemstobepresupposedbyRodriguezPereyra,doesnotruleoutthepossi bilitythattheconstituentsofacomplexarearrangeddifferentlyinanother complex. 1Cf.Mertz2001,p.57. 2Theterm‘fullrelation’hasnotbeenusedbefore.Itmeansthesameas‘unit relation’. 256CHAPTERV

withitsownintension)R',forotherwiseR'wouldbethe firststepinBradley’sviciousregressoffurtherandfurther relations.Ineffect,theoriginalfact:R( a,b)wouldturnup onthisanalysistobeidenticaltothefact:R'(R,a,b).But,of course,thelatterfactisexactlythesamekindofentityas the original fact and so would itself dissipate upon the presentanalysisintothefurtherfact:R "(R',R, a,b),andso on,evaporatingintotheoblivionofanendlessregress. 1

The overall assumption of this reductio is that the predicational and intensionalaspectsofwhatappearstobetherelatingentityof:R( a,b) aredistinctfromeachother.Thatmeansthatthereferentof‘R’isnot doing the relating in the fact. Instead, R is one of the relata of the relating entity, which is the predicational aspect ofR.Now,ifthis predicational aspect is itself a unit relation, its predicational aspect mustalsobeaunitrelation.Assuch,ithasanintensionalaspectas well as a predicational aspect. That predicational aspect is a unit relationinitself,withanintensionalaspectandapredicationalaspect. Bynow,weseehowtheregressisprogressing.But,whyshouldwe admit that the predicational aspect of the first unit relation in this seriesisaunitrelationitself?Theansweristhatthisisoneoftwo possibilities.Theotherpossibilityisthatitisnothingmorethanthe predicationaltieitself;itisnotaunitrelationinitself.Thenext reductio involvesthelatterassumption. Letusmoveonthentothatreductio .Nowtheassumptionisthat thepredicationalaspect ofa unitrelationisabare tie. Part of the argumentreads:

Failing on this analysis [i.e., the previous one], we will assumethealternative—thatthepredicationaltieinthe fact :R( a,b) is bare, i.e., has no content or intension. So under the present assumption, for a fact with an nadic intension R, the predicational linking is characterised as bothablanktie,ameretogetherness,andonethatis n+1 adic, e.g., for dyadic intension Love, its tie in fact :Love(a,b)mustbetriadic,orfortriadicintensionBetween,

1Mertz2001,p.57. MODERATEREALISM257

its tie in fact :Between(a,b,c) must be fourterm. Now I note first that this latter characteristic should render the presentassayimplausibleonthefaceofit.For,itdeclares tobeapervasiveillusionwhatweunderstandwhenweare cognisant of a property or relation — that the nsubject specificationthatconstitutespartoftheveryapprehension ofanyintensionRisalwaysfalsebyoneterm.Aninten sioncarriesits nadicityasapartofitsverymeaning.To understand the intension is to grasp the number of sub jectsthecorrespondingpredicatecanhave.Yetthepresent assumptionrendersthisunderstandingfalseineverycase. 1

An objection to this might be that the analysis brings us new knowledge. We thought we had correctly understood the adicity of the relating entity of the fact. Unfortunately, wewere wrong. What seemedtobetherelatingentityturnedoutnottobethatentity.Asa consequence we were mistaken regarding the adicity of the proper relatingentity.Nowweknowbetter. Therestoftheargumentrunslikethis:

Beyondthisisthefurtherand,Icontend,compellingcri tiquederivingfromtheuntenabilityoftheverynotionofa barelinking.Herethefact :R( a,b) is supposed to resolve intothreesubjects,R, a,and b,heldtogetherbyatiethat itselfhasnocontent(nointensionR'),itscontenthaving been separated out as R. This is the ‘nonrelational tie’ theory that some ontologists contend is the proper con clusioninthefaceofBradley’sregress.Butifthis is the case,[…]itimpliesthattheunityamongR, a,and binthe fact :R( a,b) is no different in kind than the unity among them as elements of the set {R, a,b}. On a blank asso ciationtheunificationbetweenthetermsisconditionedon nothingbuttheirexistence,thenaturesandcharacteristics of the terms are irrelevant. In particular, no ordering amongthetermsisspecified. 2

1Mertz2001,p.57. 2Mertz2001,p.57. 258CHAPTERV

Intheformer reductio itwaspartoftheassumptionthatthepredica tionalaspectofaunitattributeisaunitattribute.Theassumptionof thepresentreductio isinsteadthatitisabarelinking.Theconclusion ofthelatteristhattheunityamongtheconstituentsof:R( a,b)isnot moreintimatethanitisamongthesameentitieswhentheycombine toformaset.Inotherwords:{R, a,b}=:R( a,b).Evidently,thatisan absurdity.Furthermore,sincethereisnocontrollingintensionalinput toabarelinking,everyfactwillhavethesamemodalcharacter.Pre sumably,theywillallbecontingent.Thisconstitutesareductio onits own.1 Thereareonlytwoconceivableanalysesofthe“relationship” between thetwoaspectsofa unitattribute.Oneof these hasbeen dealt with in the previous paragraphs. It turned out to be abortive. Theconclusionisthatwhatunderliesthedistinctionbetweenthem cannotbeapreabstractionrealcomplexity.Whatisleftthenisthe other alternative, according to which there is no ontic distance between the two aspects. This being so, what we have is a post abstraction distinction. According to this second analysis, the true picture of the situation is that although a unit attribute is a simple entity, there is a real foundation within it for making a distinction betweentwoaspects.2 Theanalysishintedatinthesecondpartofthepreviouspara graphisdifficulttospelloutandtounderstand.Insection5.3.5,the twoaspectsofaunitattributearediscussed.Mertz’sproposedana lysisoftheirunionisexaminedafterthat.Butfirst,preliminarydeter minationsofsimplicityandcomplexityareintroduced. Thekindsofsimplicitysupposedtoinhereinunitattributesare defined in terms of its opposites, which are two notions of com plexity.Oneofthesekindsofcomplexity,inturn,isdefinedinterms ofhavingpredicativestructure.Anentityiscomplexinthissenseifat leastoneofitsconstituents,oraspects,ispredicatedofanotherofits constituentsoraspects.Since facts perdefinitionem involve onticpre dicates’ linking to subjects, or linking between subjects, facts are

1Cf.Mertz2001,p.58. 2Cf.Mertz2001,p.58. MODERATEREALISM259 complex entities in this sense. Evidently, ordinary objects are also complex entities. With this kind of complexity, comes what Mertz calls‘onticdistance’:“Relationsas‘actuallyrelating’ maintain ‘ontic distance’ among their relata — a real distinction in the containing entity(i.e.,factorstateofaffairs).” 1 Ifsetsandsumsareconditionedbynothingelsethantheexist enceoftheirelementsormembers,perhapstheyaresimpleentitiesin thesensehintedatinthepreviousparagraph?Theelementsormem bersmayofcoursebecomplexentitiesinthemselves.Forexample, thesetofallhumanbeingsobviouslyinvolvescomplexitysinceeach humanbeingisacomplexentitybyitself.However,thecomplexity of the set depends primarily on whether there is any set forming (unit)relation;likewisewithregardtomereologicalsums.Iwouldsay thatitisreasonabletoassumethatthereisasetformingrelation,as wellasasumformingonesincesettheoryhasitselementofrelation and mereology its partof relation, governed by axioms which are nonarbitrary.2Therefore,neithersetsnorsumsaresimpleentitiesin thesensehintedathere. Thewayunitattributesaretalkedaboutsuggeststhattheyhave a nature. Perhaps that is unavoidable. It is difficult to say anything withoutatleastformallypredicatingsomething.Thatisalsotrueof unitattributes.Whatispredicatedofaunitattributeis,amongother things,thatitissimpleandunrepeatable.Doesthisimplythatithas two unit attributes as some sort of constituents? The predicational aspects are talked about in a similar way. They are said to be un repeatableandunique.Presumably,ifthesepredicatesreallyareontic predicatesoftheirrespectivesubjects,theyareof their essence. At leastinoneplace,thescholasticprinciplethatwhatisoftheessence ofanentitymustbeaconstituentofitisreferredtoapprovinglyby Mertz.3

1Mertz2001,p.47. 2Cf.Mertz2006,p.25,whereitispointedoutthattheelementofandpart ofrelationsareinprincipleunreducibletoextensionalsurrogatesofanykind withintheirrespectivetheories. 3Cf.Mertz2006,p.14. 260CHAPTERV

Itmayseempettytomakeafussaboutattributessuchassim plicity,unrepeatability,uniquenessandthelike.Theyseemawkward anyhow. However, the impression is given that Mertz takes them seriously.Infact,heseemstobeusingthemasammunition when shooting at the notion of a bare particular. 1 But, since it is hard to makeheadsortailsofallthis,Ileaveitatthat. 2

5.3.5IntensionalAspect:SimpleorComplex? Interpretationaleffortsareneededtofigureoutwhatthestructureof aunitattributeis.Allegedly,useof‘structure’hereiscontradictory, strictlyspeakingsinceaunitattributecannot perdefinitionem havean internal structure. If it had, it would be complex in a sense which Mertzcannotpermit.Anyhow,aspreparationforadiscussionofthe “structure”ofaunitattribute,Iwillbrieflydiscuss theconstituents or,ashepreferstosay,aspectsofunitattributes. Thereisakindofsimplicitywhichwemightcall‘absolutesim plicity’.AccordingtoMertz,anonticpredicateinitsentiretyisnotan

1 Cf. Mertz 2001, pp. 50f, where, among other things, the following is asserted. [B]are particulars do have properties, and moreover they have themnecessarily,e.g.,thepropertiesofunrepeatabilityandsim plicity,thepropertyofnothavingproperties(insomesense),and thepropertyofbeingtheconstituentofatmostoneobjectata giventime. Iwouldsaythatthesearedoubtfulcasesofproperties,especiallyiftheyare supposedtobeconstituentsofentities.Cf.alsoMertz2003. 2ItshouldbepointedoutthatwhatIhaveclumsilyexpressedinthelasttwo paragraphsmightprovetobeafailuresinceMertzalsosays: [A]llpredicatesare external totheirsubjectsinthesensethatwhat ispredicableofasubject(orsubjects)isnotaconstituentofthe subject(s),contrarytothepopularcontainmentmodelofpredi cation.”(Mertz2006,p.31) Whatisstatedhereisnotintendedtoruleoutthepossibilitythatanentity might be a complex as a result of having ontic predicates as constituents. Predicatesbeingexternal,intheintendedsense,totheirsubjectsisaresultof Mertz’networkmodelforcomplexes. MODERATEREALISM261 absolute simple. Though, he is inclined to considereachoneofits aspectstobesimpleintheabsolutesense.

[A]nonticpredicatenowidentifiedasarelationinstance n R i is a composite continuous simple, whereas its con stituentcombinatorialactUisabsolutelysimple,asisits intensionR ninsome(e.g.,Red 1),ifnotinallcases. 1

Iwilldwellupontheallegedabsolutesimplicityofrednessandother intensionsforamoment.Thedeterminationofthenotionofabso lutesimplicityitselfwillhavetobeintuitive.Irely,asMertzseemsto do,onaninarticulateintuitionofabsolutesimplicity. Note first that instances of redness are said to resemble each other.Thepreviousquotationsuggeststhattheyresembleeachother exactly evenly. Furthermore, this is explained by their sharing the sameintension,whichisredness.

The fact that there are multiply exactly resembling in stances of a ‘kind’ […] is, in this ontology, the result of numericallythesameintensioncontentbeingaconstituent of each such instance, i.e., exactly resembling instances share as their sole qualitative content one and the same universal[…]. 2

Thus,exactresemblanceisexplainedintermsofqualitativeidentity. Now,isrednessabsolutelysimple?Letusassumethatwhatismeant by‘redness’isadeterminate,alowestdeterminateeven.Assumealso that ‘yellowness’ denotes another lowest determinate. 3 Now, what wouldMertzsayoftheresemblancethatholdsbetweenaninstance oftheformerandaninstanceofthelatter?Iftheyaresimilartoeach other, which he would say that they are, the explanation cannot be that they are exactly similar to each other. It presents itself im mediatelythatthereissomethingineachwhichmakesthempartially

1Mertz2006,p.112. 2Mertz2006,p.v. 3Whetherthesetwoarelowestdeterminatesisnotdecisive.Whatisdecisive isthattheyarenothighestdeterminables. 262CHAPTERV similartoeach other.Reasonably,thissomethingisadeterminable theyshare.Thiswouldcauseresemblancebetweeninstancestohave a uniform explanation. On the other hand, if less than exact resemblancebetween instancesisnottobeexplainedintermsofa commoncontent,butexactresemblanceis,resemblanceistreatedas a heterogeneous phenomenon. What would the explanation of less thanexactresemblancelooklike?AsfarasMertzisconcerned,itcan beruledoutthatlessthanexactresemblanceisprimitiveinrelation tothequalitativecontentsofinstances.Thatwouldbetoinvitesome formofresemblancenominalism.Herejectsallformsofnominalism, includingversionsofresemblancenominalism. 1Sinceitisdifficultto seewhatotheralternativestherecanbeleftforhim,thechancesare thathewouldaccepttheexplanationhintedathere.Thus,rednessis notabsolutelysimple.Neitherisyellowness. Iwouldsaythat whatissaid regardingnoninstantiatedinten sionsalso suppliescircumstantialevidenceforthe claim that inten sionsarenotabsolutelysimple.Ponderupontheimplicationsofthe followingstatement.

Intensions and combinatorial acts when separated in abstraction from any relation instance have a conceptual existence only, as do any constructed noninstantiated intensions,e.g.,Unicorn,Phlogiston[…]. 2

Whatisinterestinghereisthattheintensionsmentionedaresaidto beconstructed.Itakeitthatanoninstantiatedintensioniseithera part of an instantiated intension or it is a combination of several instantiatedintensions.Intheformercase,theinstantiatedintension isnotabsolutelysimple.Inthelatter,thenoninstantiatedintensionis not absolutely simple. What I have in mind here might be called ‘intension’.Itisthroughoursensesthatwegetacquainted with intensions. By means of various intellectual tools these inten sionsaremanipulatedinvariousways.Amongtheproductsofthese manipulations is the intension of being a unicorn. It is not pre

1Cf.Mertz1996,pp.13,635,149,157. 2Mertz2006,p.vii. MODERATEREALISM263 requisite here that intension empiricism is the only conceivable option.Presumably,complexintensionswouldbeconstructiblefrom other intensions irrespective of whether the latter are empirically obtained or innate. The existence of innate intensions would mean thatintensionistobeseriouslyreckonedwith.However, itdoesnotchangeanythinginprincipleasregardsthepossibilityof therebeingcomplexintensions. Anotherindiciumthatspeaksagainstthenotionthatintensions areabsolutelysimpleistheamountofinformationtheyaresupposed tocontain.Themessageofthefollowingthreequotationsindicates whatIamreferringto.

Rasanontic predicate is not simply intension R, it is more; it is the linking of specific relata under the con comitant controlling content of R, the latter determining thenature,number,andorderoftheformercombination. 1

Theintensionisthesource(i.e.,isthecauseof)thenum ber, order, and compatibility/admissibility of the linked relata,and,moreglobally,oftherelation’sformal/logical properties.Thisisthemoreobviousthehighertheadicity. Forexample,inthefact:Between( a,b,c),whichisthelinear spatialarrangement ofobjects bbetweenobjects aand c, thereistheunificationofthreeobjectsundertheintension Between. The intension specifies the secondorder attri butesoftriadicity,the a–b–corder,andthelogicalproper ties such as the triadic version of symmetry, i.e., if :Between( a,b,c )obtainsthensodoes:Between( c,b,a).2

[C]onsiderfirstthatthoughanyarbitraryentitieswhatso ever are said to form a set or sum, only certain limited combinationsofonticpredicatesandsubject ntuplesform afact.Thisissobecausetheunityofafactdependsupon thenonarbitrarymatchorcontentdeterminedmutualre levance or qualitative agreement between the predicate’s specificintensionR nandthedeterminatenaturesof(and 1Mertz2001,pp.534. 2Mertz2006,p.31. 264CHAPTERV

ordering among, if any) the entities in the ntuple. The dyadicpredicateexpressed,forexample,by‘isafatherof’, 2 i.e., Fatherof (x1,x2), delimits as its extension pairs in cluding,butnot<4,5> or. 1

Weseeherethatintensionsdetermineanumberofthings. Among thesearesuchthingsasthenature,numberandorderoftheentities whicharepossiblesubjectsoftheonticpredicatesofwhichtheinten sionsaretheintensionalaspects.Addtothattheformalpropertiesof theonticpredicates.Inthelightofthis,myrhetoricalquestionsare: Can intensions really be absolutely simple in general? Can even an intensionsuchasrednessbeabsolutelysimple?Theanswersshould be:noandno.

5.3.6UnitAttributes:ContinuousComposites Thefollowinglistprovidesanotherselectionofdescriptivenamesof unit attributes, supplementing the one which was given earlier: composite simple, 2 continuous composite, 3 composite continuous simple, 4continuouswhole 5ornonstandardcomposite. 6Thesedeno minationshaveinviewthepeculiarstructureofunitattributes. Whenadefinitionofsimplicityissoughtfor,theimmediatere flexistotakesimplicitytobetheoppositeofcomplexity.Thelatter, inturn,isnaturallythoughtofashavingparts;putmoreprecisely,as havingproperparts.Thatwhichisactuallyundividedandpotentially indivisibleissimple.Anotherangleistothinkofsimplicityinterms ofcategorialdivisibility,thus,asimpleentityissomethingwhichcan notbedividedintoentitiesbelongingtodifferentcategories.Inthe chapterIIIwesawsimplicitybeingdefinedinthatway.However,the

1Mertz2006,pp.1067. 2Cf.Mertz2006,p.83. 3Cf.Mertz2006,p.85. 4Cf.Mertz2006,p.112. 5Cf.Mertz2006,p.86. 6Cf.Mertz2006,p.91. MODERATEREALISM265 notion of simplicity invoked there is a different one that approxi matestheintuitivenotionofabsolutesimplicity. Thenotionofhavinginternalpredicativestructureisthenotion ofcomplexitythatisrelevantforthenotionofacontinuoussimple. According to Mertz, unit attributes lack this kind of complexity; therefore,theyaresimpleinthecorrespondingsense,notinthesense ofnotbeingcategoriallycomplex.Eachandeveryoneofthemhasa universalaspect(itsintension)aswellasaparticularone(itspredica tionalaspect).Infact,aprerequisiteforanentity’sbeingacomposite simple seems to be that its constituents belong to different cate gories.1SupposethatIamrightinmyclaimfromsection5.3.5where I said that not every intension is absolutely simple. In that case, if Mertz is right, that does not automatically imply that they have an internalpredicativestructure.Thus,anentitybeingcategoriallysimple whilebeingcomplexinanothersensedoesnotimplythattheentityis anarticulatedcomplex.Beinganarticulatedcomplexisthesameas havinginternalpredicativestructure;havingsuchastructurerulesout itsbeingacompositesimple. Afterthesepreliminaries,letustrytocometogrips with the somewhat bewildering notion of a continuous simple. As shown in the previous paragraphs, unit attributes are continuous simples. Analysisoftheserevealsthenatureofthiskindofentity.

Aclarifyingthesisargued[…]isthatontology’sbasicpar ticulars are ontic predicates themselves, where each is a unionofwhataretheformallydistinctaspectsofaqualita tiveintensionandacombinatorial/unifyingactamongan ntuple of subjects, the latter being as such unrepeatable, i.e., an individuating aspect. Out of the related analysis therewillariseaclarificationofourprecriticalconceptsof thesimple,complex,andcomposite. 2

Thus, the unit attributes are in a sense the fundamental entities of reality.Thequalification‘inasense’isinsertedbecauseunitattributes

1Cf.Mertz2006,p.111. 2Mertz2006,p.83. 266CHAPTERV haveaspects.Itakeitthatthelatterareevenmorefundamentalthan theformer.Althoughthetwoaspectsarefundamental,itiscrucialto realise that they are nonidentical constituents of the unit attribute withouttherebeingarealdivisionbetweenthem.Thisexplainswhy Mertzconsiderstheentireunitattributetobethefundamentalentity ofreality. AccordingtoWilliamofOckham(c.1288–c.1347),“[a]llthings whicharedistinctarereallydistinctandtherefore,differentthings.” 1 The apparent claim here is that entities which are distinct are also discrete.Irrespectiveof their beingconstituentsofthesamewhole, theyareseparatefromeachother. 2Thus,Ockham’sviewisthatevery composite involves real internal differentiation between its constituents,irrespectiveofwhatitspartsmightbe.Furthermore,we canexpecthimtoclaimthatallentitiesonalllevelsofanalysisare particulars.Thelatterisa,ifnotthe,definingthesisofnominalism. Mertz’sdescriptionofOckham’sviewisthatheconsidersalldistinc tions to presuppose ontic distance between what is being dis tinguished.Lackofonticdistancemeansthatthereisinfactnoreal distinction.Ifthereis noreal distinctionbetweentwoentities,they areinfactidenticalwitheachother.Iftheyareidentical,thereisno realcomposition. John Duns Scotus (1265/6–1308) is an ally of Mertz. His famousformaldistinctionistheoneMertzhasinviewbetweenthe aspectsofaunitattribute,orcomesclosetoit.DunsScotus’nameof the distinction is ‘distinctio formalis a parte rei’. As the name indi cates,thereissupposedtobeadifferenceinreality.Theformaldis tinction is an intermediate between a real distinction, on the one hand,andamerelyconceptualdistinction,ontheother. The latter has no extraconceptual basis. 3 Duns Scotus applied the formal distinctiontotheunionof natura and haecceitas ..Whilethe natura is 1WilliamofOckham1974,p.84. 2Cf.Mertz2006,p.81. 3Amerelyconceptualdistinctioniscalledbythescholastics‘distinctioratio nis ratiocinantis’. It can be translated ‘distinction of the reasoning reason’. DunsScotus’formaldistinctionisalsocalled‘distinctiorationisratiocinatae’. InEnglish:‘distinctionofthereasonedreason’.Cf.Suarez1947,p.18. MODERATEREALISM267 universal,the haecceitas isparticular;itiswhatcombineswiththe natura to compose a substance.1 I confine myself to this extremely brief account of Duns Scotus’s doctrine. It is very subtle. It was not for nothingthathiscontemporariescalledhimbythenickname‘Doctor Subtilis’. Now, note that the notion of a continuous simple, or con tinuouscomposite,istheoreticallynecessitated.Mertzexplicitlysays sohimself. 2Rememberwhatwassaidtobethefirstconceivablealter native concerning the relationship between the intensionalandpre dicationalaspectsofaunitattribute:apreabstractionrealcomplexity existswithintheunitattribute.Thatproposalturnedouttobewrong. Thereasonforthatisthatitgivesrisetooneoutoftwoabsurdities:a viciousregressorthenonrelationaltieviewonpredication. 3Whatis leftthenisitsalternative:thereisonlyapostabstractiondistinction between partial and incomplete aspects of what is itself a simple entity. Ponderuponthefollowingstatement.

[W]emustgiveupthenaivedefinition: xissimple= df x has no proper parts. Observed in the limiting case of monadic properties as far back as scholastic ontology, a n relationinstanceR iofanyadicityisnecessarilyassayedas a continuouscomposite ofcognitivelydistinguishablebutnot discrete constituents, the latter being the correlative as pects ofanunrepeatablecombinatorialagency(indicated by the subscript ‘ i’) and a specific and delimiting inten sionalcontent,R n(thesubscriptindicatingthenumberof subjectsrequiredjointlyfortheintensiontocharacterize, what is specified by the intension itself). The uniqueness oftheunifyingactofarelationinstanceaspredicableofits relata is precisely the ‘thisness’ ( haecceitas ) aspect dis tinguishedbutunexplainableintraditionalontology.Inthe followingitwillbeexplainedhowitmustbethecasethat, though such a whole is internally undifferentiated, the 1Cf.JohnDunsScotus, OrdinatioII ,d.3,part.1,pp.16. 2Cf.Mertz2006,p.83. 3Cf.section5.3.4. 268CHAPTERV

identities of each of the constituents as constituents are maintainedintheirfullandessencespecific, and so the whole is properly a composite. In other words, thoughsuchawholeisnotapluralityofarticulatedparts, neither is it homogenous — it is not the same through out. 1

Iwouldliketocallattentiontoafewthingswhicharesaidorimplied here.Notethateachconstituentofarelationinstanceissaidtohave itsownessencespecificreality.Further,itisbecauseoftheseessence specificrealitiestheinstanceisacomposite.Oneoftheconstituents oftheinstanceisanintension.Presumably,sinceitisauniversal,it constitutes its own essence. The predicational aspect, on the other hand,isnotauniversal;itisaparticularwhichcannotconstituteits own essence. Since no contrary information has been given, it suggestsitselfthatitsessenceissuppliedbyoneorseveraluniversals. Accordingtothedescriptionofit,itisacombinatorialagency.Itake it that that is a serious determination of its nature, or essence. The moralofthisisthatthepredicationalaspectofaninstanceissome thinginitself;itisnota nothing.Thenotionofabareparticular,the perennial nudist of ontology, 2 is rejected by Mertz. Among his reasonsisthatthedeterminationmakesitintopreciselythat—i.e.,a nothing. 3 Towhatisassertedinthelastquotationwithregardtothepar ticularpredicationalaspectofaninstancewecanaddthefollowing quoteconcerningparticulars.

Everyindividualisofoneormorekinds(types,catego ries),F,G,H,…,anditisasanindividualthatitisdistinct fromeveryotherindividualofanykind,andbeingofkind Fitisinsomesensethe‘sameas’,andsogroupedaslike,

1Mertz2006,pp.856. 2Armstrong,perhapsowingtoprudishness,feelsmorecomfortablewiththe designation‘thinparticular’forhisownversionofit. 3 Mertz 2006, p. 89. Cf. also Mertz 2006, pp. 1323. Another of Mertz’s reasonsforrejectingbareparticularsisthathisnetworkdoctrinemakesthem unneeded.Moreissaidaboutthenetworksinsection5.3.8. MODERATEREALISM269

everyotherindividual ofkindFbutdistinctfrom every otherindividualofkindGcontrarytoG.Thatweunder stand this implies that we can at least cognitively dis tinguishbetweenwhatisanindividuatingaspectandone ormorequalitativecontentsorintensionalaspectsofindi vidualentities.Thequestioniswhetherthereisarealand extraconceptual distinction in the particular that corre spondstothisdistinctionbetweenabstractions?Essential totheirpositions,realistsarerequiredtoadmitsuchreal distinctions a parte rei , whereas nominalists cannot allow them. 1

Thus,totheextentthatthepredicationalaspectofaunitattributeisa particular, or individual, it is of one or more kinds. It also has an individuating aspect. In light of this, it seems that a predicational aspectdoeshaveanintensionalaspectaswellasanindividuatingone. Itisperhapsacompositesimple? Theessenceofthepredicationalaspectcanbeapproachedfrom anotherangle. Mertz oftenassertsthat ifthe predicationalaspectis notcontrolledbyanyintension,itwillbeablanktie,barelinking,free association,etc.Tothis,itisfrequentlyaddedthatassuchitcanonly producealist,setormereologicalsumoftheentitieslinked. 2Thatin itselfindicatesthatitisofakind:linking. Iwillcomebacktothenotionofpredicationinsection5.3.7. Butbeforethat,letusseewhatmoreissaidabout the notion ofa continuouscomposite. What is essential for continuous composites is that they lack internal predicativestructure.Inaquotationearlierit wassaidthat suchawholeisinternallyundifferentiated.Itsbeingundifferentiated mustnotbeexaggerated.Afterall,itisnothomogenous.Thisisalso indicatedinthesamequotation.Therearealsocomplexeswhichare notcontinuouscomposites;thesearethestandardcompositeswhich 1Mertz2006,p.88. 2Itishardtoevaluatetherelevanceoftheclaimthatablanktieisthesame asasetformingunitrelationsinceitissaidonoccasionthatasetforming unitrelationiscontrolledbyaspecificintension.Anotherspecificintension wouldbetheoneofasumformingunitrelation. 270CHAPTERV

Mertzlikestocall‘articulatedcomposites’.Hehintsatthecausefor thisdescriptivenamelikethis:

Acomplexis‘articulated’atrelata,the‘joints’,wherethe relation instances, the ‘connecting rods’, meet. Directed externally,relationinstanceshavetheonticroleofeffect ing unityatadistance, i.e., unity among the yet discrete. Thisanalysisexplainsthefactofstructure[…]. 1

Thecontinuouscompositesarenotinternallyarticulated.Particularly, n the intensional aspect of an ontic predicate R i(x1,x2,…, xn) is not predicated of the predicational aspect of the same ontic predicate. Allegedly,thereisnounifierbetweenthetwoaspectsofanonticpre dicate. This makes it, and all the other ontic predicates, to non standardcomposites. 2Yetanotherdescriptionofthesecompositesis thattheyareinternallynondifferentiatedwholes.3 Now,thenotionofsimplicitywhichcomesoutofthisisthatof lackinginternalpredicativestructure.Thus,thisnotionofsimplicity can be defined as absence of division. An entity is simple, in this sense, if and only if it has no constituent which is a predicate of anotherofitsconstituents.Thisis the promisedclarificationofthe precriticalconceptofthesimple.Supposedly,itcanreplacewhatwas pejorativelydescribedearlierasthenaivedefinitionofsimplicity;i.e. xissimple= df xhasnoproperparts.Thecorrespondingnotionof complexityisthatofhavinginternalpredicativestructure.Thisisthe characterisationofanarticulatedcomposite.Togethertheseformthe disjunctivenotionofacompound. 4 Insteadofhavinganinternalpredicativestructure,theunitattri buteisseamless.MertzreferstoFranciscoSuarez,whodescribesthe unionofaquantityanditsinherenceinasubstanceasfollows.

[I]n quantity, for example, which inheres in a substance, twoaspectsmaybeconsidered:oneistheentityofquanti 1Mertz2006,p.84. 2Cf.Mertz2006,p.91. 3Cf.Mertz2006,p.83. 4Cf.Mertz2006,p.118. MODERATEREALISM271

tyitself,theotheristheunionoractualinherenceofthis quantityinthesubstance. 1

Whatisreferredtoastheactualinherenceisperhapsbetterknown underthedenomination‘modeofinherence’. 2Itturnsupinoneof the names of the distinction exemplified here: ‘modal distinction’. Though it was an appropriate one four hundred years ago, that denomination is more or less impossible to use in ourtime.Itdis tinguishesbetweenwhatexistsintherealorderbutitislessthana realdistinction.Whatisdistinguisheddoesnotexistastwoseparate things. 3MertzrecognisesinSuarezwhathehimselfiscontemplating inthecaseofcontinuouscomposites.

That this union between an entity and its mode is very similartothatofacontinuouscompositeascharacterized aboveisevidentfromSuarez’sdescription:“[A]mode is not,properlyspeaking,athingorentity.Itsimperfectionis clearly brought out by the fact that it must invariably be affixedtosomethingelsetowhichitis perse anddirectly joined without the medium of another mode, as, for instance, sitting is joined the sitter, union to the things united,andsoofothercases….” 4Specifically,then,fora propertyintension 5andits‘modeofinherence’in(i.e.,its ontic predicativity of) a subject, they are distinct but ‘directlyjoinedwithoutthemediumofanothermode’,i.e., withoutafurthermodeofwhatwouldbehereatleasta dyadic(relational)‘inherence’.Suarezalsoatleastimplies

1Suarez1947,p.28. 2TheLatinterm‘modus’isusedbySuarez. 3Cf.Suarez1947,p.97. 4ThisisquotedfromSuarez1947,p.31. 5Touse‘intension’hereispotentiallymisleading.InMertz’sterminologyitis synonymous with ‘universal’. Suarez is a nominalist. Therefore, its realistic connotationsshouldbeignored.Bytheway,beinganominalistSuarezcon sidersboththequantityanditsmodeofinherenceinthesubjecttobeparti culars.AccordingtoMertz,oneoftheconstituentsinacontinuouscompo sitemustbeauniversal.Mertz2006,p.111. 272CHAPTERV

that if it were otherwise then Bradley’s Regress would result. 1

Ifthequantityanditsmodeofinherencewerereallydistinct,there wouldbeaneedforanonticpredicatetounitethem.Moreover,the unionwouldthenbeanarticulatedcompositeandnotacontinuous one. But, as it is now, the two are joined without there being any mediumwhichjoinsthem. As statedafewtimespreviously,thenotionofacontinuous composite is theoretically necessitated. That might beso.But,isit truethataunitattributeisutterlydevoidofinternalpredicativestruc ture? According to Mertz, the intensional aspect of a unit attribute n 2 R i(x1,x2,…, xn) controls or delimits itspredicationalaspect. Theuseof eitherofthesetwoverbssuggeststhattheunitattributehasaninter nal predicative structure. If either of these two had been used in almostanyothercontext,onecouldbecertainthatMertzwouldhave consideredthemtoexpressrelationalintensions.Though,notinthis context.However,whenreadingpassagessuchasthefollowing,itis quiteeasytoforgetwhatissupposedtobethecase.

[I]f an ontic predicate has no qualitative constituent or intension determining/delimiting the range and ordering ofitsunifyingcausation,thenitwouldbea‘bareunifier’, analoguestoandasillegitimateasa‘bareparticular’. An intensionlessunifierwouldbeabsolutelyuncontrolledand withoutlimitationinitsagency,bothlocallyinthesenseof allowing anything to be unified to anything else, and globallyin thesenseofrequiringeithernothing orabso 1Mertz2006,p.97.Isuspectthatthetwofollowingsentencesarerelevant when Mertz says that Suarez at least implies that Bradley’s regress would result: Thatinherencedoesnotaddapropernewentitycanscarcelybe doubted.Ifitwereanaltogethernewentity,itcouldnotbethe actualunionbetweenquantityanditssubject,butwouldrequire somemediumforunionwithsubjectandquantity,justasquanti tyitselfrequiresaninherencewherebyitisunitedtoitssubject. (Suarez1947,p.29) 2Cf.e.g.Metz2006,p.90. MODERATEREALISM273

lutelyeverythingtobeunifiedatonce—totalreality— withoutdifferentiationintoanysubwholesofsets,facts, orcomplexes. 1

Whatisofinteresthereisthatintensionsaresupposedtocontrolthe predicationalaspectsofunitattributeswithoutgivingrisetointernal predicativestructureintheunitattributes. Letusforamomentdisregardwhatistheoreticallymotivated. Instead,rehearseoneofMertz’sstandardarguments.Assumethatthe intensionRncontrolsthepredicativeaspectoftheonticpredicateof n n :R i(a1,a2,…, an)aswellasthatof:R j(b1,b2,…, bn).Assumealsothatthe firstfactceasestoobtain;thenthelattermustalsodo so sincethe same entity is the controller in both cases. When this argument is usedagainstrealistswhotakeuniversalstobetheonticpredicatesof facts, the conclusion is that the predicates must be individuated. However,ifwetrythesamemoveinthecaseathand,itdoesnot preventtheonticpredicatesfromnotbeingcontinuouscomposites. n n Theunitattributescontrol kandcontrol lgiverisetointernalpredica tivestructuresintheirrespectivewholes.To blockthis, the control performedbyRnisdeclaredtobeanonpredicativeone.

5.3.7Predication Traditionally,instantiation,orexemplification,hasbeenlookedupon asarelation.Thewellknownproblemsthisgivesrisetohavebeen handledinaccordancewithdifferentstrategies.Oneofthestrategies isonewhichcanbeexpectedfromthelegendaryostrich:pretendthat thereisnoproblem.Anotheristostipulatethattheinstantiationrela tiondoesnotbehavethesamewayotherrelationsdo.Incontrastto alltheothers,isitneitherinstantiatednorisitinneedofbeingin stantiated.Itisstillarelationthough. When discussing his own ontology, Mertz does not use ‘instantiation’.However,predication,whichistraditionallyconsidered tobetheconverseofinstantiation,appearstobeconstantlypresent inthatitisanaspectofeachunitattribute.Whatdoeshesaycon

1Mertz2006,p.107. 274CHAPTERV cerning there being a relation of predication? Not much explicitly. Amongthefewplaceswhereheaddressestheissueincleartermsis thefollowing.

[…]Inotethatonticpredicationcannotbeidentifiedwith anyparticularrelation(s),forallrelations(includingmona dicproperties)ofwhateverintensionsareallequallycases ofonticpredication,andtootherwisemakethisreduction istoidentifyanaspectofeveryrelationwiththewholeof a particular relation (or relations). The plausibility of this identificationturnsonthefactthatthechosenrelation(s) exercises that very aspect that was to be explained in all relations — a combinatorial act guided by an intension, i.e., ontic predication. In other words, the unsuccessful strategyhereistoexplicatesomethingexhibitedbyevery elementinaclassbyidentifyingitwithoneoftheexhibit tingelementsintheclass,aformofviciouscircularity. 1

AsignificantdifferencebetweenMertz’sunitattributesandthetropes of many a trope theorist is that the former are ontic predicates. Tropesaresubstancesinthesensethattheylackpredicativity.Asa consequencethereistheneedforacompresencerelation.Thanksto instancesofthiscompresencerelation,tropesarebundledtogether, formingcomplexes.Withouttheinstancesofcompresence,therewill not be any complex entities of that kind. Exactly what the con stitutingrelationsofsetsandsumsareisseldom,ifever,dealtwith explicitly. Mertzcharacterisespredicationasanintensiondetermineduni fying agency. 2 In his later works, four principles are stated which jointlyexplicateonticpredication.Theyrehearsewhathasbeenstated inhisearlierworks.Iquotethemherewiththepurposeofpointing outafewdetails.

1Mertz2006,pp.1145. 2Cf.Mertz2006,p.98. MODERATEREALISM275

PrincipleI: n Constitutiveofeveryfact:R i(a1,a2,…,a n),for n≥1,isan n onticpredicate, R i(x1,x2,…,x n),thatistheagent/causeof thecharacterizingpredicableunityofitselfwithitsrelata,

a1, a2,…,a n,aunificationwhosetypeistoresultinafact, asopposedtoalist,set,ormereologicalsum.

PrincipleII: n EveryonticpredicateR i(x1,x2,…,x n)hasasaconstituenta single universal intension R n whose ontic role is that of delimiting or determining nonarbitrarily the possible n n tuplesofrelata< a1,a2,…,a n>,thatpredicateR i(x1,x2,…,x n) canunifyintoafact.However,anintensionR nofitselfhas nocausalagencywhatsoeverasaunifier(itis‘predicably inert’or‘substancelike’).

PrincipleIII: InadditiontoanddistinctfromintensionR n,thereiscon n 1 stitutiveofonticpredicateR i(x1,x2,…,x n)itsactualmode ofunion,itscombinatorialor linkingagency,amongand toitsparticular ntuple ofsubjects.Thelinkingaspect of n predicateR i(x1,x2,…,x n)isitselfnotafurtherintensionin additionto R n,buta causalactofunification thatis‘joined’ withintensionR nthatcontrolsitseffects. Thisjoiningis the unity of a continuous composite , i.e., a union of two distinctentitieswithouttheagencyofafurtherinterposing ontic predicate or act of unification. Of fundamental importance,theunifyingactofan onticpredicate is un repeatable and particular, rendering the containing predi cate an individual, i.e., a unit attribute (hence the sub scripts,e.g.,‘i’).

PrincipleIV: Theunifyingactamongan ntupleofsubjectsisuniqueto that ntuple.Hence,aninstanceonticpredicatesubsuming this act is unique to this ntuple of subjects, i.e., if n 2 n :R i(a1,a2,…,a n) and :R i(b1,b2,…,b n), then a1 = b1, a2 = 1Theuseof‘mode’hereisofcourseinspiredbySuarez. 2Ihavetakenthelibertyofinsertingthecolonshereandintheotherthree 276CHAPTERV

b2,…, an= bn.Intheoppositeway,onticeconomyrequires thatno ntupleofsubjectshavemorethanoneinstanceof n n the same intension R , i.e., if :R i(a1,a2,…,a n) and n n n :R j(a1,a2,…,a n),thenR i=R j.Also,becauseitisintrinsic toaninstanceonticpredicatetobeanagentunifierofan ntuple of subjects, it cannot exist independent of this n tupleexceptcognitivelyinselectiveabstraction. 1

Ofparticularinterestiswhatisstatedinthesecond principle. The same principle is stated, with a slightly different wording, in Mertz 2004 a. In both versions the same claim is expressed: the predicate n R i(x1,x2,…,x n) can have more than one ntuple as relata. Note the phrase ‘the possible ntuples of relata < a1,a2,…,a n>, that predicate n R i(x1,x2,…,x n)canunifyintoafact’.Ifthepluralusedhere,aswellas inMertz2004 a,isnotaslipofthepen,whatwearepresentedwithis a universal ontic predicate. If in fact entities of this kind are con templated,thewaytoobtainthemishintedatinthefollowingquota tion.

The process of abstraction from fact to contained agent onticpredicate,andfromthelattertocontainedagentless intension,aremarkedbyvariationsonwordsandphrases inEnglish.Wecanabstractfromastateofaffairsorfact, e.g., :Red 1(a)2, :Loves 2(b,c), :Fatherof 2(e,f), or :Similar to 2(g,h),expressedrespectivelyby‘ aisred’,‘ bloves c’,‘ eis thefatherof f’,and‘ gissimilarto h’,intensionsexpressed by abstract nouns, e.g., ‘red’ or ‘redness’, ‘love’, ‘father hood’, and ‘similarity’, that have in themselves no com binatorial nuance or ‘mode’ in the scholastic sense, and that stand in contrast to the intermediate abstractions of

formulaswiththesameform. 1Mertz2006,p.140.ThisquotationisfromwhatoriginallyisMertz2004 b. TogetherwithMertz20004 aandfiveotherarticlesitconstitutesMertz2006. InMertz2004 athesubscriptsofthepredicateareomitted.Thisis unfortunatesinceitcomplicatestheinterpretationofwhatisbeingasserted. 2Inthisformula,aswellasinthefollowingonesinthisquotation,thesub script is omitted. As was remarked in the previous footnote, this is un fortunate. MODERATEREALISM277

1 2 ontic predicates proper, e.g., Red (x1), Loves (x1,x2), 2 2 Fatherof (x1,x2), and Similarto (x1,x2), expressed in the verbphrases,respectively,as‘isred’,‘isinlovewith’,‘isa fatherof’,and‘issimilarto’. 1

n Thus, the process of abstraction starts from a fact: :R i(a1,a2,…, an). n From this an ontic predicate is abstracted: R i(x1,x2,…, xn). Next, an intension abstracted: R n according to the message of the quotation. Now, the plural form of ‘ ntuples of relata’ suggests that there is another abstracted entity, one which is to be found between the n n abstracted entities R i(x1,x2,…, xn) and R .Theformulaexpressingit n would then be: R (x1,x2,…, xn). Here, the omission of the subscript n marks the significant difference. While R i(x1,x2,…, xn) is an ontic predicate which can only have one single ntuple as its relatum, n R (x1,x2,…, xn)isauniversalonticpredicate.Whiletheformerisaone timeoccurrence,thelatterwouldbearepeatableentity. Althoughthisdiscussionmightemanatefromamisprint,which occurstwice,itactualisestheissueofthestatusofpredicativity.The traditional pattern of predication might be rendered: n+1 n n Pred (U (a1,a2,…, an)).HereU isauniversalwhichispredicatedof the ntuple< a1,a2,…, an>.Sincethepredicationrelationissupposedto betheunifier,itsadicityshouldbe n+1,giventhattheadicityofthe universal, which it predicates of the tuple, is n. It is of course in appropriatetodescribethelatterashavingadicity.Strictlyspeaking, onlyPredhasadicity.Furthermore,it seemsasif this model must postulateonepredicationrelationperadicity. ThepatternofMertz’smodelismoredifficulttoformalisesince auniversal,R n,issupposedtooperateonwhatisdescribedasapre dicational aspect. In turn, the predicational aspect, as controlled by Rn, is what operates on an ntuple. Judging from what Mertz often sayswithregardtotheformingofaset/sum,itmightbethepredica tional aspect which operates on an ntuple. Furthermore, since the predicational aspect is described as a linking, it is a bare linking in caseswherethereisnointensioncontrollingit.Perhapsthelastcase might be rendered: Predasp i(a1,a2,…, an). An implication here might 1Mertz2006,pp.1078. 278CHAPTERV thenbethattheremustbepredicationalaspectswithdifferentadici ties.Afterall,thecardinalitiesofsets/sumsvary. Enoughofthesespeculationsfornow.Instead,Iwillsaysome thing about Mertz’ network theory. That concludes, for now, my discussionabouthismoderaterealism.

5.3.8NetworksofUnitAttributes Mertzpresentshisnetworkmodelasanalternativetothetraditional doctrines of complex entities. Crudely put, realists have tended to analyse complexes either as bundles of universals or as universals predicatedofoneorseveralbareparticular(s).Aversionofthelatter viewisthatsomeuniversalsarepredicatedofthe combinations of bare particulars and universals. Equipped with the notion of a net workofunitattributes,wecandispensewithbundlesofuniversalsas wellasuniversalspredicatedofbareparticulars. Whatthephilosophercando,andwhatMertzhasdone,isto offeramodelforhowthe structuresofrealitycan be constructed given that instances of attributes are the only buildingstonesavail able.TheprinciplesIIV,quotedinsection5.3.7,characterisethese buildingstones. At the lowest level of spatiotemporal reality, networks are formedbyunitattributeslinkingtoeachother. 1Thus,atthislowest level,therelataandtheunitattributesareinstances.Undoubtedly,it isanempiricalquestionwhat instancesexistatthislevel,aswellas practically every other level. It cannot be answered at the writing desk, at least not the writingdesk of a philosopher. However, a matterofprinciplewhichthephilosopherMertzventurestoclaimis foundinthefollowingquotation.

Here we have the closed chain of three dyadic facts 2 2 2 2 2 2 2 2 2 :J i(K j,L k), :K j(L k,J i), :L k(J i,K j). It is easily seen that

1 A similar, if not the same, idea is expressed by Ernst Cassirer. He takes quantum entities to be points of intersections of certain relations. He also demonstrateshowtheycanbemutualintersectionsofindividuatedrelations. Cf.Cassirer1956,p.180. MODERATEREALISM279

this scheme of mutually sustaining instances can be extended logically to networks composed of any number of relation instances and of any mixture of adicities, as longaseachinstancehasassubjectsinitsrelata ntuple onlyotherinstancesofthenetwork.Theonlyconstraints intheseregardswouldbeviatheintensionofeachcom posinginstanceandwhatitallowsastothenaturesofand theorderingamongitsrelata. 1

Theclaim Iamreferringtoisexpressedin thelast sentence. The intensionsofthecomposinginstancessetthelimitsforwhatcanbe combined.Inviewofthis,adescriptivetermmaybecoined:‘inten sional determinism’. 2 Depending on to what degree the intensions allow their instances to form complexes with others, the degree of intensionaldeterminismwillvary.Atoneextremethereisnoelbow room;atanotheritmightbelimitless.Therepeatedlymadereference to bare linking might be the latter extreme. The intension which determineswhatcanmakeupasetorsumingeneral,ifthereissuch an intension, does not set any limits whatsoever. This constitutes a state of intensional in determinism. At the other extreme we might find various mathematical structures. Intensional determinism will thenbetheprerequisiteofthewithwhichthesestructurescan beinvestigatedbymeansofdeductivereasoning. 3 Two principles of network composition are discerned: hori zontalandverticalcompositionrespectively.Thesetwoconstitutea 1Mertz2006,pp.1545.MertzmentionstheTrinityasanexampleofatriad ofunitrelationsformingaclosednetwork: SinceeachPersonisanindividual,thiswouldpresumablyrequire that the respective relations be individuated — that is, be instances. So understood, they would together constitute the interlinking, selfcontained whole described discursively as :Father 1(Son 1,Spirit 1), :Son 1(Father 1,Spirit 1), and :Spirit 1(Father 1, Son 1).(Mertz1996,p.77) An obvious comment on this is that the three predicate names used here cannothavetheirordinarymeanings. 2ThistermisnotusedbyMertz;Ihaveinventeditmyself. 3NothingofthisisexplicitlyassertedbyMertz.However,Ithinkthatitis impliedbywhathedoesassert. 280CHAPTERV partition;theyexhaustallthepossibilities.Thedefinitionsofthemare formulatedinafifthprinciple:

Principle V: All plural unity — and thus plural wholes (complexesorstructures)—isbythefollowing: n a) ArelationinstanceR i predicableofan ntupleofre lata,< a1,a2,…, an>,isthecauseofanindividualplural n n whole, viz., the fact :R i(a1,a2,…, an), having R i , a1, a2,…, an,asitsonlyconstituents. n n b) IfR iisaconstituentofapluralwhole xandS jisa n n constituentofapluralwhole y,andR iandS j ,share oneormorerelata,thenthereisanindividualplural whole zthathasasconstituentsallandonlythecom binedconstituentsof xand y(horizontalcomposition). n c) For any fact :R i(a1,a2,…, an),iffor1≤ j ≤ n, aj is a plural whole, then there exists an individual plural wholewhoseconstituentsareallandonlytheconsti

tuentsofthefactandconstituentsof aj(verticalcom position). 1

Thesignificantdifferencebetweenthetwocompositionprinciplesis thatinverticalcompositionentirestructuresaretreatedasrelata.This isnotsoinhorizontalcomposition. Oneofthegainswiththismodelisthattheneedforasubstra tumisgone.Sinceunitattributesofvariousadicitiesformnetworks, thereisnofirst“point”whereeverythinghastostartwithaproperty beingpredicatedofwhatitselfisnotpredicableofanything. Emergentunit propertiescan beunderstoodintermsof hori zontalcomposition.Anemergentunitpropertyisonewhichispre dicatedofanentirestructure.In otherwords,itdoesnot haveany particularconstituentincludedinthestructureasitssubject. Mertzsaysthisregardingthesubject:

Now,itiseasytoconceivehowthisverticalcompounding could be continued indefinitely up through further and furtherlevels,andhowatcertainlevelstherecouldbepro perties and relations, say U 3, whose instances emerge sui 1Mertz2006,p.145. MODERATEREALISM281

generis ,i.e.,donotoccuratlowerlevelsandpresupposeas atleastsomeoftheirrelatacertaintypesofsubstructures. This fits the bill precisely for an ontology of ordinary objects […]: ordinary objects are immense though finite hierarchiesofhorizontallyandverticallycomposedstruc tures generated upwardly from what science determines aretheultimatesubatomicentities.Similarly,oncealerted tothesetwoformsofcompositiononecanseetheiritera tionsexemplifiedincognitive,mathematical,logical,social, etc.,structures. 1

Evidently,thisistrulyacomprehensivemodel,giventhattheexpec tationsarousedbydescriptionslikethiscanberedeemed.

1Mertz2006,p.144. References

Adams, R. (1979). “Primitive Thisness and Primitive Identity.” The Journal of Philosophy , Vol. 76, No. 1 (Jan.), pp. 5-26. Aquinas, T. (1955). Summa Contra Gentiles . A. Pegis (transl.), Garden City, N.Y.: Doubleday. Armstrong. D. M. (1978 a). Universals and , vol. I. Cam- bridge: Cambridge University Press. — (1978 b). Universals and Scientific Realism, vol. II. Cambridge: Cam- bridge University Press. — (1986). “In Defence of Structural Universals.” Australasian Journal of Philosophy , Vol. 64, No. 1 (March), pp. 85-8. — (1989). Universals: An Opinionated Introduction . Boulder: Westview Press. — (1991). “Arda Denkel’s Resemblance Nominalism.” The Philoso- phical Quarterly , Vol. 41, No. 165 (Oct.), pp. 478-82. — (1997). A World of States of Affairs . Cambridge: Cambridge Uni- versity Press. Avicenna (1495). Metaphysica . Venice: Bernardinus Venetus, de Vitali- bus, for Hieronymus de Durantibus. Bacon, J. (1989). “A Single Primitive Trope Relation.” Journal of Philo- sophical Logic , No. 18, pp. 141-154. Barnes, J. (1987). Early Greek Philosophy. London: Penguin Books. Black, M. (1952). “The Identity of Indiscernibles.” Mind , Vol. 61, No. 242 (April), pp. 154-64. Bradley, F. H. (1908). Appearance and Reality. Second edition, London: The Macmillan Company. Broad, C. D. (1925). The Mind and Its Place in Nature. London: Routledge & Keegan Paul. Campbell, K. (1990). Abstract Particulars. Oxford: Basil Blackwell Ltd. — (2002). “Unit Properties, Relations, and Spatio-Temporal Natura- lism.” The Modern Schoolman , Vol. 79, Nos. 2 & 3 (January/ March), pp. 151-162. — (2003). “The Place of Relations in a Trope Philosophy.” Proceedings of the Colloque International de Philosophie de Grenoble: La Structure du Monde; Objets, Propriétés, Etats de Choses , in Recherches sur la Philoso- phie et le Langage , Grenoble : Université Pierre Mendes France. 284

Cassirer, E. (1956). Determinism and Indeterminism in Modern Physics . New Haven: Yale University Press. Cavarnos, C. (1975). The Classical Theory of Relations. A Study in the Meta- physics of Plato, Aristotle and . Belmont, Mass.: Institute for Byzantine and Modern Greek Studies. Clatterbaugh, K. (1973). Leibniz’s Doctrine of Individual Accidents. In Studia Leibnitiana , special issue No. 4, Wiesbaden: Steiner. Cook Wilson, J. (1926). Statement and Inference, Vols. I-II . Oxford: Cla- rendon Press. Cornelius, H. (1900). “Über Gestaltqualitäten.” Zeitschrift für Psychologie und Physiologie der Sinnesorganen , Bd. 22, pp. 101-21. Daly, C. (1997). “Tropes.” In D. H. Mellor & A. Oliver (eds.), Proper- ties . Oxford: Oxford University Press. Ewing, A. C. (1934). . A Critical Survey. London: Methuen & Co. Ltd. Funkhouser, E. (2004). Review: Anna-Sofia Maurin, If Tropes . Notre Dame Philosophical Reviews , http://ndpr.icaap.org/archives/ 2004/2/funkhouser-maurin.html . Goodman, N. (1951). The Structure of Appearance. Cambridge, Mass.: Harvard University Press. Gracia, J. J. E. (1982). Suárez on Individuation . Milwaukee: Marquette University Press. — (1984). Introduction to the Problem of Individuation in the Early . Washington: Catholic University Press. Grossmann, R. (1983). The Categorial Structure of the World . Blooming- ton: Indiana University Press. Harris, C. R. S. (1959). , Vol. 2 . New York: Humanities Press. Henninger, M. (1989). Relations: Medieval Theories, 1250-1325 . Oxford: Clarendon Press. Hochberg, H. (1969). “Moore and Russell on Particulars, Relations, and Identity.” In E. D. Klempke (ed.), Studies in the Philosophy of G. E. Moore . Chicago: Quadrangle Books. — (1988). “A Refutation of Moderate Nominalism.” Australasian Journal of Philosophy , Vol. 66, No. 2 (June), pp. 188-207. — (1999). Complexes and Consciousness . Library of Theoria No. 26, Stockholm: Thales. — (2002). “Individuation and Individual Properties: A Study of Metaphysical Futility.” The Modern Schoolman , Vol. 79, Nos. 2 & 3 (January/March), pp. 107-136. 285

— (2004). “Relations, Properties and Predicates.” In H. Hochberg and K. Mulligan (eds.), Relations and Predicates , Heusenstamm: Ontos Verlag. Hochberg, H. & Mulligan, K. (eds.)(2004). Relations and Predicates . Frankfurt & Lancaster: Ontos Verlag. Hourani, G. (ed.)(1975). Essays on and Science . Albany: SUNY Press. Hume, D. ( Treatise ). A Treatise of Human Nature . Second edition, Selby- Bigge, L. Al (ed.), Oxford: Clarendon Press, 1978. Husserl, E. (1900-1901). Logische Untersuchungen . Halle: Niemeyer. — (1970). Logical Investigations, Vol. I. J. Findlay (transl.), New York: Humanities Press. Jackson, F. (1977). “Statements about Universals.” Mind , Vol. 86, No. 343 (July), pp. 427-9. John Duns Scotus ( Ordinatio ). Ordinatio II . Translation in Spade 1994. Johansson, I. (1986). “Externa, interna och andra relationer.” In Logic and Abstraction . Essays Dedicated to Per Lindström on His Fiftieth Birthday . Göteborg: Acta Unversitatis Gothoburgensis. — (1989). Ontological Investigations. An into the Categories of Nature, Man and Society . London: Routledge. — (2000). “Determinables as Universals.” The Monist , Vol. 83, No. 1 (January), pp. 101-22. Johnson, E. W. (1921). Logic. Part I. Cambridge: Cambridge University Press. Johnston, M. (2006). “Hylomorphism.” The Journal of Philosophy , Vol. 103, No. 12 (December), pp. 652-698. Kemp-Smith, N. (1927). “The Nature of Universals: III.” Mind , Vol. 36, No. 144, pp. 393-422. Keynes, J. M. (1921). A Treatise on Probability. London: Macmillan. Küng, G. (1964). “Concrete and Abstract Properties.” Notre Dame Journal of Philosophy , Vol. 5, No. 1 (January), pp. 31-6. — (1967). Ontology and the Logistic Analysis of language. Dordrecht: D. Reidel Publishing Company. Leibniz, G. W. (1969). Philosophical Papers and Letters . Second edition, L. Loemker (ed.), Dordrecht: Reidel. Leonard, H. & Goodman, N. (1940). “The Calculus of Individuals and Its Use.” The Journal of Symbolic Logic , Vol. 5, No. 2 (June), pp. 45-55. Lewis, D. (1986 b). Counterfactuals . Oxford: Blackwell. — (1990). Parts of Classes. Cambridge: Basil Blackwell. 286

Locke, J. ( Essay ). An Essay Concerning Human Understanding . Oxford: Clarendon Press, 1975. Loux, M. J. (1978). Substance and Attribute. Dordrecht: D. Reidel Publishing Company. — (1998). Metaphysics. A Contemporary Introduction . London: Routledge. Lowe, E. J. (1989). Kinds of Being. A Study of Individuation, Identity and the Logic of Terms . Oxford: Basil Blackwell. MacBride, F. (2004). “Whence the Particular-Universal Distinction.” Grazer Philosophische Studien , Vol. 67, pp. 181-94. McTaggart, J. McT. E. (1921). The Nature of Existence, Vol. I. Cam- bridge: Cambridge University Press. Marc-Wogau, K. (1945). Die Theorie der Sinnesdaten. Probleme der Neueren Erkenntnistheorie in England . Uppsala: Lundequistska bokhandeln. Marmura, M. (1975). “Avicenna’s Chapter, ‘On the Relative,’ in Meta- physics of the Shifa .” In Hourani 1975. Martin, C. B. (1980). “Substance Substantiated.” Australasian Journal of Philosophy , Vol. 58, No. 1 (March), pp. 3-10. Maurin, A-S. (2002). If Tropes. Dordrecht: Kluwer Academic Pub- lishers. — (2005). “Same but Different.” Metaphysica , Vol. 6, No. 1, pp. 129- 46. — (2007). “Infinite Regress – Virtue or Vice?” In Hommage à Wlodek. Philosophical Papers Dedicated to Wlodek Rabinowicz. T. Rønnow- Rasmussen, B. Petersson, J. Josefsson & D. Egonsson (eds.), www.fil.lu.se/hommageawlodek . Meinong, A. (1968-78). Gesamtausgabe . 7 vols., R. Haller & R. Kind- inger (eds.), Graz: Ak. Druck und Verlagsanstalt Graz. Mertz, D. W. (1993). “Instance Ontology and Avicenna’s Argu- ments.” The Modern Schoolman , Vol. 70 (March), pp. 189-99. — (1996). Moderate Realism and Its Logic. New Haven: Yale University Press. — (2001). “Individuation and Instance Ontology.” Australasian Journal of Philosophy , Vol. 79, No. 1 (March), pp. 45-61. — (2003). “Against Bare Particulars. A Response to Moreland and Pickavance.” Australasian Journal of Philosophy , Vol. 81, No. 1 (March), pp. 14-20. — (2004 a). “The Nature and Necessity of Composite Simples, E.g., Ontic Predicates.” Metaphysica: International Journal for Ontology & Metaphysics , Vol. 4, No. 1, pp. 89-133. 287

— (2004 b). “Objects as Hierarchical Structures: A Comprehensive Ontology.” In Hochberg & Mulligan (2004), pp. 113-48. — (2006). Essays on Realist Instance Ontology and Its Logic. Predication, Structure, and Identity . Frankfurt: Ontos Verlag. Mill, J. S. (1843). A System of Logic Ratiocinative and Inductive. London: Longmans. Moore, G. E. (1922). “External and Internal Relations.” In Philoso- phical Studies. London: Routledge and Keegan Paul, pp. 276-309. First printed in Proceedings of the Aristotelian Society , 1919-20. Moreland, J. P. (1985). Universals, Qualities and Quality Instances: A Defence of Realism . Lanham: University Press of America. — (1998). “Theories of Individuation: A Reconsideration of Bare Particulars.” Pacific Philosophical Quarterly . Vol. 79, pp. 251-63. — (2001). Universals. Chesham: Acumen Publishing Limited. Moreland, J. P. & Pickavance, T. (1998). “Bare Particulars and Individuation. Reply to Mertz.” Australasian Journal of Philosophy , Vol. 81, No. 1 (March), pp. 1-13. Morewedge, P. (1973). The Metaphysica of Avicenna . New York: Columbia University Press. Mulligan, K., Simons P. & Smith, B. (1984). “Truth-Makers.” Philo- sophy and Phenomenological Research , Vol. 44, No. 3 (March), pp. 287-321. Nerlich, G. (1994). Shape of Space . 2nd revised edition, Cambridge: Cambridge University Press. Nozick, R. (1981). Philosophical . Oxford: Clarendon Press. O’Leary-Hawthorne, J. (1995). “The Bundle Theory of Substance and the Identity of Indiscernibles.” Analysis , Vol. 55, No. 3 (July), pp. 191-6. O’Leary-Hawthorne, J. & Cover, J. (1998). “A World of Universals.” Philosophical Studies , No. 91, pp. 205-19. Pap, A. (1959). “Nominalism, Empiricism, and Universals.” Philoso- phical Quarterly , Vol. 9, No. 38 (Oct.), pp. 330-40. Read, S. (2000). “Truthmakers and the Disjunction Thesis.” Mind , Vol. 109, No. 433, pp. 67-79. Restall, G. (1996). “Truthmakers, Entailment and Necessity.” Austra- lasian Journal of Philosophy , Vol. 74, No. 2, pp. 331-40. Rodriguez-Pereyra, G. (2004). “The Bundle Theory Is Compatible with Distinct but Indiscernible Particulars.” Analysis , Vol. 64, No. 1 (January), pp. 72-81. 288

— (2002). Resemblance Nominalism. A Solution to the Problem of Universals . Oxford: Clarendon Press. — (2004). “The Bundle Theory Is Compatible with Distinct but Indiscernible Particulars.” Analysis , Vol. 64, No. 1 (January), pp. 72-81. Russell, B. (1903). The Principles of Mathematics . Cambridge: Cambridge University Press. — (1911). “On the Relations of Universals and Particulars.” Pro- ceedings of the Aristotelian Society , Vol. 11-12, pp. 1-24. — (1912). The Problems of Philosophy . Oxford: Oxford University Press. — (1922). Our Knowledge of the External World: As a Field for Scientific Method in Philosophy. London: George Allen & Unwin. — (1948). Human Knowledge. Its Scope and Limits. London: Allen & Unwin. Seargent, D. A. J. (1985). Plurality and Continuity. An Essay in G. F. Stout’s Theory of Universals. Dordrecht: Kluwer Academic Pub- lishers. Segelberg, I. (1945). Zenons paradoxer. En fenomenologisk studie . Stock- holm: Natur och Kultur. — (1947). Begreppet egenskap. Några synpunkter . Stockholm: Svenska Tryckeriaktiebolaget. — (1953). Studier över medvetandet och jagidén . Stockholm: Svenska Tryckeriaktiebolaget. — (1999). Three Essays in Phenomenology and Ontology. H. Hochberg & S. Hochberg Ringström (transl.), Library of Theoria No. 25, Stockholm: Thales. Sellars, W. (1957). “Substance and Form in Aristotle.” The Journal of Philosophy , Vol. 54, No. 22 (December), pp. 688-699. Simons, P. (1992). “ and Its Ontological Refine- ment: A Defence.” In K. Mulligan (ed.): Language, Truth and Ontology . Dordrecht: Kluwer Academic Publishers. — (1994). “Particulars in Particular Clothing: Three Trope Theories of Substance.” Philosophy and Phenomenological Research , Vol. 54, No. 3 (Sept.), pp. 553-75. — (1998). “How the World Can Make Propositions True: A Celebra- tion of Logical Atomism.” In M. Omaly (ed.): Sklonnosci Meta- fizyszna . Warsaw: Warsaw University. — (2006). “Real Wholes, Real Parts: Mereology without Algebra.” The Journal of Philosophy , Vol. 103, No. 12 (December), pp. 597-613. 289

Spade, P. (1994). Five Texts on the Mediaeval Problem of Universals . Indianapolis: Hacket Publishing Co. Stjernberg, F. (2003). “An Argument Against the Trope Theory.” Erkenntnis , Vol. 59, pp. 37-46. Stout, G. F. (1921). “The Nature of Universals and Propositions.” Proceedings of the British Academy , Vol. 10. Reprinted in Stout 1930, pp. 384-403. — (1923). “Are the Characteristics of Particular Things Universal or Particular?” Proceedings of the Aristotelian Society , Suppl. Vol. 3, pp. 114-122. — (1930). Studies in Philosophy and Psychology. London: Macmillan. — (1952). God and Nature. Stout, A. H. (ed.), Cambridge: Cambridge University Press. Strawson, P. (1971). Individuals. An Essay in Descriptive Metaphysics . London: Methuen & Co. Ltd. Suarez, F. (1947). On the Various Kinds of Distinctions (Disputationes Metaphysicae, Disputatio VII, De Variis Distinctionum Generibus ). C. Vollert (transl.), Milwaukee: Marquette University Press. — (1964). On Formal and Universal Unity (Disputationes Metaphysicae, Disputatio VI, De Unitate Formali et Universali ). J. F. Ross (transl.), Milwaukee: Marquette University Press. van Cleve, J. (1986). “Mereological , Mereological Conjunctivism and Identity Through Time.” Studies in Essentia- lism, Midwest Studies in Philosophy , vol. 11, P. French, T. Uehling & H. Wettstein (eds.), Minneapolis: University of Minnesota Press. van Steenburgh, E. W. (1974). “The Problem of Simple Resemb- lance.” Philosophical Studies , Vol. 25, pp. 337-46. Weinberg, J. R. (1965). Abstraction, Relation, and Induction: Three Essays in the History of Thought. Madison: The University of Wisconsin Press. Whitehead, A. N. (1916). “La théorie relationniste de l’espace.” Revue de Metaphysique et de Morale , Vol. 23, pp. 423-454. — (1919). An Enquiry Concerning the Principles of Natural Knowledge. New York: Cambridge University Press. — (1926). The Concept of Nature. Cambridge: Cambridge University Press (1974). The Summa Logicae. Part I . Published as M. Loux (transl.), Ockham’s Theory of Terms , Notre Dame: University of Notre Dame Press. 290

Williams, D. C. (1931). “The Nature of Universals and of Abstrac- tions.” The Monist , Vol. 41, pp. 583-593. — (1951). “The Myth of Passage.” The Journal of Philosophy , Vol. 48, No. 15 (July), pp. 457-472. — (1953 a). “On the Elements of Being: I.” The Review of Metaphysics , Vol. 7, No. 1 (Sept.), pp. 3-18. — (1953 b). “On the Elements of Being: II.” The Review of Metaphysics , Vol. 7, No. 2 (Dec.), pp. 171-192. — (1963). “Necessary Facts.” The Review of Metaphysics , Vol. 16, No. 4 (June), pp. 601-626. — (1986). “Universals and Existents.” Australasian Journal of Philosophy , Vol. 64, No. 1 (March), pp. 1-14. Wittgenstein, L. (1961). Tractatus Logico-Philosophicus . London: Rout- ledge & Kegan Paul. Wolterstorff, N. (1970). On Universals . Chicago: University of Chicago Press.