Contemporary Aristotelian Metaphysics

C on t e m por a ry A r is tot e l i a n M e ta ph ysic s

Aristotelian (or neo-Aristotelian) metaphysics is currently undergoing something of a renaissance. This volume brings together ­fourteen new essays from leading philosophers who are sympathetic to this conception of metaphysics, which takes its cue from the idea that metaphysics is the first philosophy. The primary input from Aristotle is methodological, but many themes familiar from his metaphysics will be discussed, including ontological ­categories, the role and interpretation of the existential quantifier, essence, ­substance, natural kinds, powers, potential, and the development of life. The volume mounts a strong challenge to the type of ­ontological deflationism which has recently gained a strong foothold in analytic metaphysics. It will be a useful resource for scholars and advanced students who are interested in the foundations and development of philosophy. t uom a s e . t a h k o is a postdoctoral researcher at the University of Helsinki. He has published a number of articles on metaphysics and its methodology.

Con t e m por a ry A r is tot e l i a n M e ta ph ysic s E di t e d b y Tuom a s E . Ta h ko

c a mbr idge u ni v er sit y pr e ss Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge c b 2 8r u, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781107000643 © Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Contemporary Aristotelian metaphysics / edited by Tuomas E. Tahko. p.   cm. Includes bibliographical references and index. i s b n 978-1-107-00064-3 1. Aristotle.  2. Metaphysics.  3. Aristotle. Metaphysics. I. Tahko, Tuomas E., 1982– II. Title. b491.m4c67  2011 110–dc23    2011039355 i s b n 978-1-107-00064-3 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

For Jonathan

Contents

List of contributors Preface

page ix xi

Introduction

1

1 What is metaphysics?

8

Tuomas E. Tahko Kit Fine

2 In defence of Aristotelian metaphysics

26

3 Existence and quantification reconsidered

44

4 Identity, quantification, and number

66

5 Ontological categories

83

6 Are any kinds ontologically fundamental?

94

7 Are four categories two too many?

105

8 Four categories – and more

126

9 Neo-Aristotelianism and substance

140

10 Developmental potential

156

Tuomas E. Tahko Tim Crane

Eric T. Olson

Gary Rosenkrantz Alexander Bird John Heil

Peter Simons

Joshua Hoffman

Louis M. Guenin

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Contents

11 The origin of life and the definition of life

174

12 Essence, necessity, and explanation

187

13 No potency without actuality: the case of graph theory

207

14 A neo-Aristotelian substance ontology: neither relational nor constituent

229

References Index

249 259

Storrs McCall

Kathrin Koslicki

David S. Oderberg

E. J. Lowe

Contributors

A l e x a n de r Bi r d is professor of philosophy at the University of Bristol T i m C r a n e is Knightbridge Professor of Philosophy at the University of Cambridge, and a fellow of Peterhouse K i t F i n e is professor of philosophy and mathematics at New York University L ou i s M. Gu e n i n is lecturer on ethics in science at Harvard Medical School Joh n H e i l is professor of philosophy at Washington University in St Louis and honorary research associate at Monash University Jo s h ua Hof f m a n is professor of philosophy at the University of North Carolina at Greensboro K at h r i n Ko s l ic k i is associate professor in philosophy at the University of Colorado at Boulder E . J. L ow e is professor of philosophy at Durham University S t or r s Mc c a l l is professor of philosophy at McGill University Dav i d S. Ode r be rg is professor of philosophy at the University of Reading E r ic T. Ol s on is professor of philosophy at the University of Sheffield G a r y Ro s e n k r a n t z is professor and head at Department of Philosophy, University of North Carolina at Greensboro Pe t e r S i mons is professor of philosophy at Trinity College Dublin, where he holds the Chair of Moral Philosophy T uom a s E . Ta h ko is postdoctoral researcher in philosophy at the University of Helsinki ix

Preface

For Aristotle, metaphysics was the most important form of rational inquiry, the first philosophy. Aristotelian metaphysics is the study of the fundamental structure of reality; it examines the preconditions of scientific knowledge. It is in the so-called ‘neo-Aristotelian’ tradition where this understanding of metaphysics has thrived and where discussion of traditional metaphysical concepts prevails. This collection anticipates the renaissance of Aristotelian metaphysics and brings together some of its most prominent defenders. The contributions provide both an analysis of metaphysics understood in this fashion as well as a detailed look into some of the most important themes of neo-Aristotelian metaphysics. Four chapters in this volume (those by Olson, Rosenkrantz, Heil, and Hoffman) are based on presentations given at a conference, ‘The Metaphysics of E. J. Lowe’, at the State University of New York at Buffalo, 8–9 April 2006. I am grateful to the organizers for their permission to use material presented at the conference in this volume. All contributions, including these four, are published here for the first time.

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Introduction Tuomas E. Tahko

One might raise the question whether the science of being qua being is to be regarded as universal or not. Each of the mathematical sciences deals with some one determinate class of things, but universal mathematics applies alike to all. Now if natural substances are the first of existing things, natural science must be the first of sciences; but if there is another entity and substance, separable and unmovable, the science of it must be different and prior to natural science, and universal because it is prior. (Aristotle, Metaphysics 1064b6–13)

The expression ‘Aristotelian metaphysics’ suggests a commitment to the view that there is a study that is different and prior to natural science. Metaphysics is ‘first philosophy’, the core and beginning of any and all philosophical and rational inquiry into the world. The task of metaphysics is not to serve science or to clear conceptual muddles, but to study being and the fundamental structure of reality at the most general level. This view competes with recent deflationary conception about the methods and aims of metaphysics. One approach that has a strong foothold in this field could be called ‘Quinean’. According to a Quinean, ‘naturalized’ conception, metaphysics is continuous with science in its methods and aims. Questions about the nature of reality are to be answered by application of ‘regimented theory’. Philosophers such as the contributors to this volume, who in various respects may be described as ‘neo-Aristotelian’, continue to regard metaphysics as an inquiry distinct from natural science. They deploy what they regard as distinctly philosophical, often a priori, methods to discuss metaphysical concepts like essence, substance, dependence, potential, ground, and other categories of being and relations among beings described by language that is not purely extensional. We may also contrast Aristotelian metaphysics with Kantian metaphysics: categories are central to both, but in Aristotelian metaphysics they are categories of being whereas in Kantian metaphysics they are categories of understanding. 1

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There has recently arisen a discussion of ‘metametaphysics’, a discussion of the methods and foundations of metaphysical inquiry. The best example is the anthology edited by Chalmers, Manley, and Wasserman (2009), but James Ladyman and Don Ross (2007) as well as Timothy Williamson (2007) have also made influential contributions to the topic. One important theme in this recent literature, highlighted especially in Ladyman and Ross (2007), is the relationship between science and metaphysics. There is a growing concern that metaphysics fails to take into account recent developments in science or does so in a misguided manner. Understandably, this is something that philosophers sympathetic to the Quinean conception of metaphysics will find alarming. I think that Aristotelian metaphysicians should also be concerned, but the underlying assumption that is sometimes found in this approach is equally troubling, namely, that metaphysics needs to be naturalized, and that metaphysical inquiry is secondary to empirical inquiry. One effect of some contributions to this volume is to question that assumption and to suggest an alternative methodology inspired by Aristotle. Only some of the contributions deal with methodological matters explicitly, but the volume as a whole exemplifies the work of philosophers whose approach to metaphysics is broadly Aristotelian. The chapters have been organized in a loosely thematic manner, beginning with a general methodological discussion preceding more specific topics. Chapters 1 to 3 serve to contrast how the methodological approach endorsed by many contributors to this volume differs from a Quinean or deflationary understanding of metaphysics. Topics that are relevant here include the theory of quantification, ontological commitment, and the relationship between metaphysics and science. Chapter 4 examines some applications emerging from the theories of quantification and identity, after which follow five chapters dealing with questions deriving from the important topic of ontological categories. These are discussed both in general and in terms of specific accounts of categories. Chapters 10 and 11 discuss the notions of potential and life, both of which were extremely important for Aristotle, and the remaining three chapters concern essence, powers, and substance, respectively. In what follows, I provide a brief summary of each chapter. Kit Fine’s chapter ‘What is metaphysics?’ attempts to characterize the discipline of metaphysics. He suggests that five key elements distinguish traditional metaphysics from other disciplines: the aprioricity of its methods; the generality of its subject-matter; the transparency or ‘non-opacity’ of its concepts; its eidicity or concern with the nature of things; and its

Introduction

3

role as a foundation for how things are. Fine examines each of these elements and their role in metaphysics as well as how they come together in metaphysical inquiry. The present writer’s ‘In defence of Aristotelian metaphysics’ is also concerned with the methodology of metaphysics and specifically with how ‘Aristotelian metaphysics’ differs from ‘Quinean metaphysics’. I discuss two challenges to Aristotelian metaphysics: one which suggests that its methods are esoteric and inaccessible, and one which calls for naturalized metaphysics. The first is due to Thomas Hofweber and concerns especially the interpretation of the existential quantifier; the second is familiar from the work of James Ladyman and Don Ross. I argue that both of these challenges can be met. This can be done by giving up the Quinean understanding of ontological commitment and by explicating the relationship between science and metaphysics. Finally, a methodological account which addresses the two challenges is sketched. Tim Crane continues the topic of existence and quantification in his chapter ‘Existence and quantification reconsidered’. Crane is dissatisfied with the usual way of understanding the connection between the notion of existence, the natural language quantifiers, and the logical formalization of these things. He contrasts two approaches to formalization, a ‘descriptive’ and a ‘revisionary’ approach. The first takes formalization to be concerned with the actual workings of natural language, whereas the second is the approach familiar from Quine; it is not concerned with the actual semantics of the way we speak, but rather with creating a precise language for scientific purposes. Crane is interested in the descriptive approach and specifically the problems that emerge with regard to the representation of the non-existent: how do we make sense of claims and thoughts about things which do not exist? The solution, Crane suggests, requires us to change our conception of a domain of quantification: it should be thought of as a universe of discourse considered as a collection of objects of thought. However, he argues that this gives us no reason to change the standard way of understanding the semantics of quantifiers. Eric T. Olson’s ‘Identity, quantification, and number’ deals with quantification from a slightly different point of view. Olson considers a group of principles, which he calls the quantification principle, the identity principles and the uncountability thesis. The first can be expressed as follows: ‘Something is F if and only if at least one thing is F.’ The identity principles state that for this and that to be identical is for them to be one, and that for them to be distinct or non-identical is for them to be two. Finally, according to the uncountability thesis there are things that we

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cannot even begin to count – things to which the concept of number does not apply. Olson explains that the uncountability thesis is not compatible with the other principles and defends the others against the objections of those who advocate the uncountability thesis. He considers a number of examples, such as ‘gunk’, and through them attempts to clarify what it would mean if the uncountability thesis were true or false. Gary Rosenkrantz opens a series of chapters on the important topic of categories with his ‘Ontological categories’. As Rosenkrantz points out, an ‘ontological category’ is a much narrower notion than ‘category’ in general. The first refers to categories of being as identified by Aristotle. Typical examples include substance, event, time, place, absence, boundary, property, relation, proposition, set, and number. Rather than discussing any of the numerous taxonomies that have been suggested in the literature or focusing on the details of any specific category, Rosenkrantz pursues the logically necessary conditions that a predicate must adhere to if it is properly to express an ontological category. He identifies ten such necessary conditions that together offer an illuminating analysis of an ontological category in terms of logical, modal, semantic, and epistemic notions. Alexander Bird’s chapter ‘Are any kinds ontologically fundamental?’ examines the ontological basis of kinds and categories, and specifically whether the category of kinds is a fundamental category of being. Bird examines E. J. Lowe’s four-category ontology in this regard. For Lowe, the category of kinds is one of the four fundamental categories, but Bird argues that, in addition to particulars, all we need is universals: kinds are not ontologically fundamental. Bird’s case is based on an analysis of the laws of nature in Lowe’s ontology, which may appear to require the existence of kinds. Lowe claims an advantage over David Armstrong’s account of the laws of nature, but Bird is not convinced: Lowe’s account of laws does not avoid the problems that Armstong’s account faces and hence does not constitute a reason to adopt the category of natural kinds. Bird concludes that although Lowe’s four-category ontology is appealing, it can do without the category of natural kinds. John Heil is also interested in the fundamentality of ontological categories. In his ‘Are four categories two too many?’ Heil investigates Lowe’s four-category ontology, according to which there are four fundamental ontological categories, and suggests that there may be a reading of Lowe’s work according to which two of those four categories can be abandoned. Heil is especially suspicious of universals, but less so about modes (or tropes) and substances. He considers a number of ways to understand what universals are, but is ultimately dissatisfied. However, Heil finds

Introduction

5

reasons to think that Lowe’s account bears some similarity to that of D. C. Williams, who is best known as a proponent of one-category trope ontology. According to Heil, this is not quite correct, for Williams does have an account of universals comparable to John Locke’s. If Heil is correct in his suggestion that Lowe’s account of universals can be regarded as a Williams-type trope-kind theory, the upshot is that universals and kinds would not constitute fundamental ontological categories, and we would be back to two-category ontology. Peter Simons moves in the other direction with his ‘Four categories – and more’, arguing that the four categories familiar from Lowe’s work may not be enough. Simons begins with a brief historical study of disputes concerning categories and clarifies that he is interested in ontic categories in Aristotle’s sense rather than Kantian categories. A detailed study of the grounds for making categorial distinctions follows. We learn that from the Aristotelian point of view there are eighty-one categories of object emerging from Kant’s scheme, and that Kant’s twelve categories do not concern kinds of object but the factors that are used to differentiate categories. Simons goes on to examine what kind of ‘factor families’ may be legitimately used to make categorial distinctions and concludes with some methodological remarks about the study of ontology. Joshua Hoffman’s chapter ‘Neo-Aristotelianism and substance’ wraps up the discussion of ontological categories. As the title suggests, Hoffman’s primary interest is the category of substance, and he provides a systematic case study of this particular category of being. Hoffman begins with an analysis of Aristotle’s two accounts of individual substance and goes on to list three necessary conditions for a neo-Aristotelian theory of substance. Next, he examines three contemporary accounts of substance that could be called neo-Aristotelian; these are familiar from the work of Roderick Chisholm, Lowe, and Hoffman and Rosenkrantz. The upshot is that all three of these accounts satisfy the three necessary conditions for a neoAristotelian theory of substance, even though each account differs with regard to certain inessential conditions. Louis M. Guenin’s ‘Developmental potential’ harkens to Aristotle as it tackles the elucidation of an organism’s potential to develop into an individual of its kind. Guenin introduces developmental potential as a probabilistic disposition consisting in a capacity to develop a capacity. Construing ‘dispositional’ as a type of predicate for purposes of the construction, he shows how one may individuate an organism’s situationdependent potentials and then construct a probabilistic model of manifestation of all the potentials. By reference to a probability distribution,

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the set of such potentials may be said to be bounded. The analysis defends this account against a Quinean attack on de re modality and referential opacity of the dispositional idiom. The account is presented as countenanceable not only within ontological views that recognize potentials, but also within views that regard references to potentials as grammatical devices for describing regularities in events. The analysis ends by posing the question whether developmental potential is irreducibly probabilistic. Storrs McCall also deals with biology in his chapter ‘The origin of life and the definition of life’. Aristotle had a clear idea about the origin of life, according to which it emerged in a piecemeal fashion proceeding from lifeless nature to animal life in such a way that the boundary between the two remains vague. Modern biology and especially the discovery of DNA may seem to go against this view. McCall takes this as a starting point, but argues that although the conditions imposed by DNA may be necessary for the development of an organism, they may not be sufficient. He speculates that there may be a different kind of information that is not DNA-based and which plays a role in this process, in which case a definition of life strictly in terms of the genetic code would not be correct. With the help of examples, McCall proposes a combination of digital genetic information and analog pattern information in the regeneration and development of organisms, concluding that digital genetic information on its own, although necessary, is not sufficient to define life without an analog component in the form of pattern control. Kathrin Koslicki’s chapter ‘Essence, necessity, and explanation’ discusses Aristotelian essentialism. Koslicki examines the view according to which essence does not reduce to modality but rather the other way around. This, she suggests, is how Aristotle views essence, although nowadays the view is perhaps more familiar from the work of Fine and Lowe. Koslicki compares the views of Aristotle and Fine on essence and especially the distinction between what is part of the essence of an object and what merely follows from it. She suggests that we should follow Aristotle in tracing the explanatory power of definitions to the causal powers of essences, as this may help to explain how the necessary features of an object are related to its essential features. David S. Oderberg’s ‘No Potency without Actuality: The case of graph theory’ concerns dispositional essentialism. A good example of a dispositional property is solubility; in Oderberg’s words: ‘any solid, liquid or gas that has the disposition of solubility in a liquid L will, when inserted into L, dissolve to form a homogeneous solution with L’. Dispositions are a hotly debated topic in contemporary metaphysics and Oderberg is

Introduction

7

interested in Alexander Bird’s influential account of them, according to which all properties have dispositional essences. This view is motivated by the idea that the fundamental level is that of properties with ‘nonredundant causal powers’, a world of pure powers. There is a well-known regress-circularity objection to this account, developed for instance by Lowe. Bird has replied to this objection with the help of the formalism of mathematical graph theory. Oderberg argues that this reply does not help to save a world of pure powers and that the regress-­circularity objection can be maintained. E. J. Lowe concludes the volume with his chapter ‘A neo-Aristotelian substance ontology: neither relational nor constituent’. Lowe discusses a topic that has recently gained considerable attention in contemporary metaphysics, namely, the distinction between relational and constituent ontologies. The distinction is already present in Aristotle, but the terminology derives from Wolterstoff. Here is how Michael Loux (2006: 208) puts it: Those who endorse what Wolterstoff calls the constituent approach tell us that the items from which familiar particulars derive their character are constituents or components of sensible things; they are something like ingredients or parts of those things. On what Wolterstoff calls the relational approach, by contrast, the items from which familiar sensibles derive their character are not ‘immanent in’ those sensibles.

Now, Aristotle’s substance ontology is generally thought to be a constituent ontology, whereas for instance Plato’s ontology is of the relational kind. Accordingly, one would think that any neo-Aristotelian substance ontology will be constituent as well. Lowe however argues that, based on his own four-category ontology, we can have a neo-Aristotelian substance ontology that is not constituent. Further, Lowe argues that the four­category ontology is not relational either, and hence cannot be classified in terms of the constituent–relational distinction.

ch apter 1

What is metaphysics? Kit Fine

There are, I believe, five main features that serve to distinguish traditional metaphysics from other forms of enquiry. These are: the aprioricity of its methods; the generality of its subject-matter; the transparency or ‘­non-opacity’ of its concepts; its eidicity or concern with the nature of things; and its role as a foundation for what there is. In claiming that these are distinguishing features, I do not mean to suggest that no other forms of enquiry possess any of them. Rather, in metaphysics these features come together in a single package and it is the package as a whole rather than any of the individual features that serves to distinguish metaphysics from other forms of enquiry. It is the aim of this chapter to give an account of these individual features and to explain how they might come together to form a single reasonably unified form of enquiry. I shall begin by giving a rough and ready description of the various features and then go into more detail about what they are and how they are related. Metaphysics is concerned, first and foremost, with the nature of reality. But it is not by any means the only subject with this concern. Physics deals with the nature of physical reality, epistemology with the nature of knowledge, and aesthetics with the nature of beauty. How then is metaphysics to be distinguished from these other subjects?1 1 The material of this paper was originally written in the early 2000s as the first chapter of a book on metaphysics that is still to be completed. It should become clear that my conception of metaphysics is broadly Aristotelian in character though I make no real attempt to relate my views to historical or contemporary sources. Still, I should mention that my position is very similar to views on the nature of philosophy set out by George Bealer in his paper of 1987 and developed in some of his subsequent work. We both believe in the ‘autonomy’ of philosophy and metaphysics and trace its source to the distinctive character of the concepts that they employ. Perhaps two key points of difference in our approaches is that I have preferred to work within an essentialist rather than a modal framework and I have been less inclined to place much weight on general arguments in defence of the a priori. I should like to thank Ruth Chang and the participants at the 2010 Petaf conference in Geneva for many helpful comments on an earlier version of the paper.

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What is metaphysics?

9

It is distinguished, in part, from physics and other branches of science by the a priori character of its methods. The claims of science rest on observation; the claims of metaphysics do not, except perhaps incidentally. Its findings issue from the study rather than from the laboratory. Some philosophers have thought that the distinction between the a priori and the a posteriori is not absolute but one of degree. I am not of their view. But philosophers of this persuasion would presumably be happy to take metaphysics to be relatively a priori to the same degree, and perhaps in much the same way, as logic or pure mathematics. And with this qualification in place, a large part, though not all, of what I want to say will still go through. Metaphysics is also distinguished from other branches of philosophy, not by the aprioricity of its methods but by the generality of its concerns. Other branches of philosophy deal with this or that aspect of reality  – with justice and well-being, for example, or with feeling and thought. Metaphysics, on the other hand, deals with the most general traits of reality – with value, say, or mind. The concepts of metaphysics are also distinguished by their transparency. Roughly speaking, a concept is transparent if there is no significant gap between the concept and what it is a concept of. Thus there is a significant gap between the concept water and the substance H2O of which it is a concept but no significant gap between the concept identity and the identity relation of which it is a concept. The thought then is that the concepts of metaphysics are more akin to the concept of identity than that of water. Metaphysics as so characterized might be a somewhat anemic discipline – there might be very little for it to do. But it has also been thought that metaphysics might play an important foundational role. It is not merely one form of enquiry among others but one that is capable of providing some kind of basis or underpinning for other forms of enquiry. In some sense that remains to be determined, claims from these other forms of enquiry have a basis in the claims of metaphysics. Let us now discuss each of these features in turn. 1.1  F ou n dat ion a l a i m s of m e ta ph y s ic s There are perhaps two principal ways in which metaphysics might serve as a foundation. One, which has received considerable attention of late, is as a foundation for the whole of reality. Some facts are more fundamental or ‘real’ than others; and metaphysics, on this conception, attempts to

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characterize the most fundamental facts which are the ‘ground’ for the other facts or from which they somehow derive. It is important to appreciate that metaphysics, on this conception, will not be interested in stating the fundamental facts – the physical facts, say, on a physicalist view or the mental facts on an idealist view – but in stating that they are the fundamental facts. Its concern will be in the foundational relationships and not in the fundamental facts as such. But important as this conception of metaphysics may be, there is, it seems to me, another conception that is even more central to our understanding of what metaphysics is and that would remain even if the other foundational project that is centred on the notion of ground were to be abandoned. Metaphysics, on this alternative conception, serves as a foundation, not for reality as such, but for the nature of reality. It provides us with the most basic account, not of things – of how they are – but of the nature of things – of what they are.2 In order to understand this conception better, we need to get clearer on the relata, on what is a foundation for what, and on the relation, in what way the one relatum is a foundation for the other. As a step towards answering the first question, let us distinguish between two different ways in which a statement might be said to concern the nature of reality. It might, on the one hand, be a statement like: Water is H2O,

which describes the nature of water but involves no reference, either ­explicit or implicit, to the nature of water; or it might be a statement like: Water is by its nature H2O,

which does involve a reference, either explicit or implicit, to the nature of water. Let us call a statement that is concerned with the nature of reality eidictic, from the Greek word eidos for form; and let us call statements of the former sort eidictic as to status and those of the latter sort eidictic as to content. We shall take a broad view of the latter – not only will they include such statements as that water is by its nature H2O, but also such statements as that if water is H2O then it is by its nature H2O. As long as there is some reference to nature, the statement will count as eidictic as to content. 2 I have discussed the ground-theoretic approach to metaphysics in ‘The Question of Realism’ (Fine 2001) and the essentialist approach in ‘Essence and Modality’ (Fine 1994). There is an interesting question of their relationship which I shall not discuss.

What is metaphysics?

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What I have in mind by way of an answer to the first question, concerning the relata, is that metaphysics should attempt to provide a foundation for all truths eidictic as to content; and what then provides the foundation are the metaphysical truths that are eidictic as to content, along with the possible addition of other ‘auxiliary’ truths that are not eidictic as to content. Thus given the non-eidictic truths, the eidictic truths of metaphysics will provide a foundation for all other eidictic truths. Note that, in contrast to the previous foundational project, it is the fundamental facts themselves, rather than the foundational relationships, that are properly taken to belong to the province of metaphysics. A minimal answer to the second question, concerning the relation, is that the metaphysical eidictic truths (along with the auxiliary non-eidictic truths) should provide a logical basis for the other eidictic truths; the latter should follow logically from the former. One might want to insist, of course, on something more than a logical basis; it might be required, for example, that the eidictic truths of metaphysics should provide some kind of explanation for the other eidictic truths. But the notion of explanation here is somewhat obscure; and my suspicion is that, for all practical purposes, it will be sufficient to insist upon a logical basis – that anyone who succeeds in finding a logical basis will also succeed in finding an explanation in so far as an explanation can be found. Thus again, in contrast to the previous case, there is no need, in making sense of the foundational enterprise, to appeal to a distinctive form of explanation or ‘ground’. Part of what has made the idea of an a priori foundation for eidictic truth seem so attractive is the thought that there should be a priori bridge principles connecting the non-eidictic facts to the eidictic truths. Consider, for example, the earlier claim that water is by its nature H2O. This is an eidictic claim that does not belong to metaphysics, both because it is not a priori and because it is not sufficiently general. However, it might be taken to be a consequence of the following two claims: Any substance with a given composition is by its nature of that composition; Water is a substance whose composition is H2O.

The first of these is a statement of metaphysics, while the second is noneidictic (as to content). And it might be thought that, in a similar way, any eidictic truth could be ‘factored out’ into a purely metaphysical component, on the one hand, and a purely non-eidictic component, on the other.3 3 It has been supposed in the same way that all necessary truths might have their source in a priori necessary laws or that all moral truths might have their source in a priori moral principles.

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Unfortunately, the above example is by no means typical and other cases are far less tractable. How, for example, are we to ‘factor out’ the claim that an electron by its nature has a negative charge? One might propose a factoring along the following lines: Electrons have a negative charge; If electrons have a negative charge then they have negative charge by their very nature,

where the first statement is non-eidictic (as to content) and the second is to be eidictic and a priori. However, it is far from clear that the second statement is a priori, for it is not true, in general, that something with a negative charge has a negative charge by its very nature and so why, in particular, should this be an a priori truth concerning electrons? Perhaps there is some ingenious argument that the claim is a priori in the case of electrons. But still, cases such as these make it far more difficult to see how factoring might always be achieved. In the light of such difficulties, we might think of dividing our grand foundational aim into two more modest aims. The first is to provide a basis for the a posteriori eidictic truths (such as that water is by its nature H2O) within the realm of the a priori. Thus ultimately the nature of things will be seen to have an a priori source (such as that water is by its nature H2O if it is H2O). The second is to provide a basis for all a priori eidictic truths within the realm of metaphysics. Thus ultimately the a priori nature of things will be seen to have a metaphysical source. Consider, for example, the a priori eidictic claim that red and green are by their nature incompatible. This is not itself a claim of metaphysics, since it is lacking in the appropriate level of generality. But it may be derived from the following three claims: (1) red and green are two distinct determinates of the determinable color (2) distinct determinates of a determinable are incompatible (3) if distinct determinates of a determinable are incompatible then they are by their very natures incompatible The first two are plausibly taken to be a priori and non-eidictic (as to content), while the third is plausibly taken to be an eidictic principle of metaphysics. Thus it appears that the same kind of ‘factoring’ that was used to span the a posteriori/a priori divide can also be used, within the realm of the a priori, to span the metaphysical/non-metaphysical divide.

What is metaphysics?

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My suspicion is that the second of the two more modest aims might be somewhat easier to achieve and, if this is so and some a posteriori eidictic truths resist ‘apriorification’, then there is something to be said for focusing more attention on the a priori realm. But even here there may be difficulties. Consider, for example, the claim that it lies in the nature of any set to have the members that it does. This is presumably an a priori eidictic claim that, on account of its lack of generality, does not belong to metaphysics. But just as in the electron case, it is somewhat hard to see how it might be derived from the more general eidictic claims of metaphysics (though my own view is that it can be so derived). 1.2   S u bj e c t-m at t e r Before considering the question of the subject-matter of metaphysics, let us make some general remarks on subject-matter. I feel that these remarks could be situated within an even more general study of the nature of different fields of enquiry and of how they are related to one another. But this is not an aspect of the question that I shall pursue. Any field of enquiry deals with certain propositions, those that lie within its purview and whose truth it seeks to investigate.4 Thus mathematics deals with mathematical propositions, logic with logical propositions, and so on. We might call the set of propositions with which a field of enquiry deals its domain of enquiry (to be distinguished, of course, from its domain of quantification). Any proposition has a certain subject-matter. Thus the proposition that Socrates is a philosopher has as its subject-matter the man Socrates and the property of being a philosopher. We construe the subject-matter broadly so that the proposition that Socrates is not a philosopher might also be taken to have the operation of negation as part of its subject-matter, but we do not construe it so broadly that the proposition that every philosopher is wise also has each individual philosopher as part of its subjectmatter, in addition to the property of being wise and the quantifier every philosopher. On a structural conception of propositions, we might take the subject-matter of a proposition to be constituted by the constituents from which it is formed, though it might also be possible to arrive at a conception of the subject-matter of propositions on a less refined conception of what they are. 4 My interest in what follows is in pure fields of enquiry, such as pure mathematics, and not in their application to other fields of enquiry.

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We may distinguish between the elements of the subject-matter that occur predicatively within the proposition and those that occur objectually or non-predicatively. Elements of the first sort might be said to constitute the ontology of the proposition and elements of the second sort its ideology. Thus the property of being wise occurs predicatively in the proposition that Socrates is wise and so belongs to its ontology and the man Socrates occurs objectually in the proposition and so belongs to its ideology. A property may occur objectually in a proposition, as in the proposition that the property of being wise is a property, and it may even occur both objectually and predicatively, as in the proposition that the property of being a property is a property, and hence belong both to the ontology and the ideology of the proposition.5 Each field will have a certain subject-matter through the association with its domain of enquiry, the subject-matter of the field being the subject-matters of the propositions within its domain. Thus given that the propositions 2 + 2 = 4 and 9 > 7 are part of the domain of arithmetic, the numbers 2, 4, 7, and 9, the relations of identity and of being greater than, and the operation of addition will all be part of the subject-matter of arithmetic. The subject-matter of a field will be ascertainable in this way from its domain of enquiry but, in general, the domain of enquiry will not be ascertainable from the subject-matter. If we put together different elements of the subject-matter of the field to form a proposition, we will not always get a proposition from its domain of enquiry. Identity and existential quantification, for example, are logical elements, they are part of the subject-matter of logic; but the proposition that there is something (∃x(x = x)) is not a logical proposition, one whose truth-value it is the job of logic to ascertain. The subject-matter of a field, as we have defined it, might be called the broad or overall subject-matter. But there is also a narrower notion of subject-matter that might be defined. For there appears to be a sense in which certain elements of subject-matter are distinctive to a field  – a sense in which an element is distinctively mathematical, say, or distinctively metaphysical, or distinctively physical. Consider the metaphysical 5 The ontology/ideology distinction in this sense should be distinguished from Quine’s distinction of the same name. For Quine, the ontology of physics will include elementary particles since these are included within its domain of quantification. But for me, they will not be included in the ontology since physics has no interest in any particular elementary particle. The distinction is analogous to Frege’s distinction between ‘saturated’ and ‘unsaturated’ but is differently drawn.

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proposition that two things are the same whenever they are parts of one another. Its constituents are part, universality, conjunction, and identity. But only the first is distinctively metaphysical. The rest are logical. Or consider the physical proposition that E = mc2. Its constituents are energy, mass, the speed of light, product, square, and identity. But only the first three are distinctively physical. The next two are mathematical rather than physical and the last is logical. An element of subject-matter distinctive to a given field somehow has its home in the field. It may appear in the propositions of other fields but only as the result of having been exported from its home; and, by the same token, other elements of subject-matter may appear in the propositions of the given field but only as the result of having been imported from their homes. The overall subject-matter of a field will in general be broader than its distinctive subject-matter. Many elements will appear in the propositions of the field that are not distinctive to the field. What then is it for an element of subject-matter to be distinctive to a given field? From among all of the elements that may occur in its propositions, how do we tell which are distinctive? It is tempting to answer this question along the following lines. One field of enquiry may presuppose or be built upon the subject-matter from other fields. In order to state the propositions of interest to the given field, we may need to make use of subject-matter from these other fields, even though strictly extraneous to the field itself. The clearest case is with logic. There is hardly a field (with the possible exception of fields simply concerned with the tabulation of data) in which logical elements are not required in order to state its propositions. And other fields may have other presuppositions. As we have seen, mathematics is required to state the propositions of physics; geographical locales are required to state the propositions of history; and numerous naturalistic properties and relations are required to state the propositions of aesthetics and ethics. Let us suppose that we can make sense of one field of enquiry presupposing another. Then we might say that the distinctive elements of a field are those that occur in its propositions but are not distinctive of any presupposed field of enquiry.6 Thus logical elements will not be distinctive of 6 The hope is that this may serve as an inductive definition. Thus as long as the hierarchy of fields, as ordered by the relation of presupposition, is well-founded, the notion of distinctive subjectmatter will be well-defined.

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any field of enquiry but logic, given that any non-logical field presupposes logic or makes no use of logic; and if pure mathematics only presupposes logic, then the constituents of its propositions will either be logical or distinctively mathematical. Under an ideal organization of theoretical enquiry, one might hope that each element of subject-matter had a single home and that each field of enquiry was home to some element of subject-matter. Different fields could then be distinguished by their subject-matter. But even without such an ideal organization, it is still plausible that many of the fields of enquiry of interest to us can properly be said to have their own subjectmatter. 1.3   G e n e r a l i t y When we survey the subject-matter of metaphysics, there appear to be elements of it that are distinctively metaphysical. The properties of existence, material thing, or event are examples of such elements, as are the relations of part to whole and of determinate to determinable or the notions of nature and necessity. It is, of course, possible for such elements to appear in non-metaphysical contexts. I can say that my car is missing a part or that I observed a surprising event. But still, the elements part and event appear to be distinctive of metaphysics in a way in which car and surprise or and and some are not. These distinctively metaphysical elements have a striking characteristic in common. They all operate at a high level of generality. We do not talk of cats and dogs or of electrons and protons but of material particulars; and we do not talk of thunder and lightning or of wars and battles but of events. But what is it for one element of subject-matter to be more general in this sense than another? The traditional view is that metaphysics deals with kinds or categories of the broadest possible sort; and the generality of a metaphysical kind will therefore lie in the breadth of its application. But whatever merit this idea might have in regard to kinds (and even here I have my doubts), it has little plausibility in regard to the other subjectmatter of metaphysics. Any case of part, for example, is a case of overlap, though not vice versa, but part is not on this account less general in the relevant sense than overlap. Or, again, any case of identity is a case of part, though not vice versa, but identity is not on this account less general in the relevant sense than part.

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Another suggestion is that generality is a matter of how broadly the element is employed in other fields of enquiry. This suggestion is related to the idea that logic is topic-neutral, since the topic-neutrality of logic can be taken to consist in the wide or universal presence of logical subject-matter within other fields of enquiry. However, the correctness of this account depends critically upon what one takes the other fields of enquiry to be; and it is hard to avoid the thought that, in so far as the account yields correct results, it is because it has already been taken to be definitive of the relevant fields of enquiry that they should contain the logical elements. The relevant notion of generality has more to do, I believe, with descriptive content. The more general or ‘abstract’ an element of subject-matter, on this conception, the less its descriptive content. Thus what is determinative of the generality of an element is not the breadth of its application or employment but the extent to which it is sensitive to the descriptive character of the items to which it applies  – with the more general elements being less sensitive to descriptive differences and the less general elements more sensitive. So, for example, the relation of identity will be highly general on this conception since its application to objects x and y is merely sensitive to whether they are one or two, while the relation of part to whole will be less general since its application will also be sensitive to the mereological relationships between the objects. But what is descriptive character? And how might we measure the degree of descriptive content? We can make a start in understanding these notions by appealing to the concept of invariance. For simplicity, consider the special case of a relation in its application to actual objects and suppose that a, b, c, … is a list of objects to which the relation can meaningfully be said to apply. The relation will then induce a certain pattern of application on these objects – holding of a, b, say, but not b, a, of b, c and c, b, and so on. Let us now reorder the objects as a′, b′, c′, … with a′ taking the place of a, b′ of b, c′ of c, and so on. We may then ask whether the relation still induces the same pattern of application, holding now of a′, b′ but not b′, a′, of b′, c′ and c′, b′, and so on. If it does, then it is not ­sensitive to the difference in descriptive character between the objects a, b, c, … and the objects a′, b′, c′, … and otherwise it is. So by going through all of the different re-orderings or permutations of the objects a, b, c, … , we can obtain a measure of the degree to which the relation is sensitive to descriptive character. But such an account will only take us so far. It will not deliver the result that event or universal, for example, are more general than dog since,

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from a purely formal point of view, permutations that preserve eventhood or universality are no less sensitive to descriptive character than those that preserve doghood. Still, we have a strong sense that they are less sensitive to descriptive character. There are, of course, hard cases. Are dog and cat equally general? Or is one more general? Or is perhaps neither one as general as the other? However, such cases may not be involved in delimiting the subject-matter of metaphysics. For since dog and cat are each less general than animal, we may decide that the generality of metaphysics requires that it contain animal in preference to either dog or cat. In this way, a partial handle on the comparative generality of different elements may give us something close to a complete handle on the subject-matter of metaphysics. But a question remains. For where exactly within the scale of generality is the distinctive subject-matter of metaphysics to be located? We cannot say that its elements are the most general of all (with invariance under all permutations) since that distinction properly belongs to logic. But it is not implausible that the elements of metaphysics should be next in generality to those of logic  – the only elements more general than them being either metaphysical or logical. Logical and metaphysical elements will be neighbours, so to speak, with the logical elements lying on the ‘formal’ side of the divide and the metaphysical elements on the ‘material’ side. It is also not implausible that any element that is neither logical nor metaphysical will be less general than some metaphysical element. Thus the elements of metaphysics, on this picture, will provide a buffer between the logical elements, on the one hand, and all of the remaining elements, on the other hand, the only neighbours to the logical elements being the metaphysical elements. This picture still leaves open how far down within the space of subjectmatters the metaphysical elements will extend. How specific can such an element be and yet still be sufficiently general to have its ‘home’ in metaphysics? The most straightforward answer is that the elements of metaphysics are those of penultimate generality, next in generality to the logical elements. Thus anything more general than a metaphysical element will be logical and anything less general will be neither metaphysical nor logical. If we were to think of logic as relating to the structure of thought and of metaphysics as relating to the structure of reality, then logic would provide us with the most general traits of thought and metaphysics with the most general traits of reality.

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This gives us a pretty picture – with logic at the top, metaphysics immediately below it and everything else below them. Some may think that it too pretty to be true. One problem, which we have already mentioned, is that, even if there is a sufficiently clear notion of comparative generality to enable us to make sense of the idea of an element at an ultimate level of generality, it may not be sufficiently clear to enable us to make sense of the idea of an element at a penultimate level. It might also be thought that, even if there is well-defined idea of penultimate generality, there is no reason to think that there always will be elements at this level intervening between the elements of ultimate generality and the others. I am not sure how seriously to take either of these misgivings, for the idea of an element at a penultimate level of generality appears to be tolerably well-defined and nor is it clear that there are any actual cases in which elements at this level of generality will not exist. In any case, to the extent that we can make sense of some traits of reality being more general than others, we can get some grip on the idea that metaphysics should aim towards generality, even if this aim can never be fully realized. 1. 4   E i dic i t y Let us return to the topic of eidicity and consider more closely the way in which metaphysics might be concerned with the nature of reality, with how things are by their very nature. As already mentioned, metaphysics is not by any means the only field of enquiry with this concern. Thus logic is concerned with the nature of logical form, physics with the nature of the physical universe, and the various branches of philosophy with the nature of this or that aspect of reality. We might call fields of enquiry of this sort eidictic; and we should consider how metaphysics is like other eidictic fields of enquiry and how it is different. We might, as a first step, take a field of enquiry to be eidictic if its truths are all and only those propositions true in virtue of its subject-matter.7 Thus the truths of an eidictic field, on this conception, will flow from the very nature of the items with which it deals – the truths of logic from the nature of the logical elements, the truths of mathematics from the nature of the mathematical elements, and so on; and it is the combination of the particular subject-matter and the requirement of eidicity that will serve to characterize the propositions of the given field. If the domain of enquiry is not closed under negation, then we should add that its falsehoods are all and only those propositions that are false in virtue of its subject-matter. 7

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But what is meant here by the subject-matter? Is it the overall subjectmatter or the distinctive subject-matter? Neither answer seems to give the correct results. Take the overall subject-matter first. The logical elements of identity and universal quantification are part of the overall subjectmatter of mathematics and the Law of Identity (∀x(x = x)) is true in virtue of the nature of these elements; and yet the Law is a proposition of logic rather than of mathematics. Take now distinctive subject-matter. That 2 + 2 = 4 is a true proposition of mathematics and yet not true in virtue of its distinctively mathematical subject-matter (since the nature of the relation of identity is also involved). A more refined account is required. What I would like to suggest is that the truths of an eidictic field should be taken to be those that are distinctively true in virtue of its overall subject-matter, i.e. they are those that are true in virtue of its overall subject-matter but not true in virtue of its non-distinctive subject-matter, that part of its overall subject-matter that is not distinctive to the field. This then has the desired results. The Law of Identity (∀x(x = x)), for example, is not a truth of mathematics since it is true in virtue of its non-distinctive subject-matter and that 2 + 2 = 4 is a truth of mathematics since it is true in virtue of its broadly mathematical subject-matter but not in virtue of purely logical subject-matter. We might state the definition in terms of the different species of necessity. With each eidictic field of enquiry E might be associated a species of necessity, where E-necessity is a matter of being true in virtue of the nature of the (overall) subject-matter of E. Take now a field of enquiry E and let E′ be the union of the fields of enquiry E1, E2, … presupposed by E. Then under plausible assumptions, the truths of E will be the E-necessities that are not also E′-necessities; they are, that is to say, the distinctive necessities of the field. Thus the truths of metaphysics will be the distinctively metaphysical necessities, the metaphysical necessities that are not also logical necessities; and similarly for mathematics and physics and the like.8 It is important to observe that the present definition only requires that a proposition should be true in virtue of the nature of the subject-matter of the field to which it belongs, not that it should be true in virtue of its very own subject-matter. In certain cases, this distinction can be important. Consider again the proposition that there is something (∃x(x = x)). This is not true in virtue of the nature of its own subject-matter since there is nothing in the nature of existential quantification or the relation 8 Metaphysical necessity in this subject-oriented sense is to be distinguished from the usual notion of metaphysical necessity, which is indifferent as to source.

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of identity which demands that there be something.9 However, it is true in virtue of the nature of the subject-matter of mathematics, since it follows from the nature of the number 0 that it exists. Thus this proposition is correctly classified by our definition as a truth of mathematics rather than of logic, despite the fact that it has a purely logical formulation. We have seen that metaphysics is distinguished from other eidictic fields partly by the aprioricity of its methods and partly by the generality of its subject-matter. But there appears to be another significant distinction, perhaps arising from the latter. For the notion of eidicity, of being true in virtue of the nature of certain elements, is itself part of the subject-matter of metaphysics. Thus the propositions with which metaphysics deals will include not only propositions eidictic in status but also propositions eidictic in content. Indeed, any metaphysical truth T that is eidictic + as to status will follow from a metaphysical truth T  that is eidictic as to content. For if T is a metaphysical truth, it will be true in virtue of the nature of various general ‘traits’ of reality (including perhaps some logical + traits). Let T  be the proposition that T is true in virtue of the nature of + those traits. Then T  will also be true in virtue of the nature of general traits of reality (viz., those by means of which T is true plus perhaps the + eidicity trait); and so T  will also be a truth of metaphysics. Given that this is so, we may confine our attention to simple eidictic truths of the form ‘it is true in virtue of such and such traits that so and so’. For instead of asking ‘is S the case?’, for some suitable metaphysical sentence S, we may ask ‘is S the case in virtue of the nature of the general traits of reality?’ Put somewhat grandiosely, we might say that ‘□FS’ for suitable F is the general form of a metaphysical claim and that the task of metaphysics will have been completed once we have a complete inventory of the F (the general traits of reality) and of the truths of the form □FS (to the effect that S is true in virtue of the nature of the F). It is not altogether clear to me whether, or to what extent, other eidictic fields have an interest in truths eidictic as to content in addition to truths eidictic as to status. Take logic. It is concerned to state the logical truths, those true in virtue of the nature of the logical elements. But logic is not also concerned to state that these truths are the logical truths. Similarly in the case of mathematics. We want to get at the mathematical truths, but not at their being the mathematical truths. The various different branches 9 It is here important to distinguish between ideology and ontology. We may say (treating identity objectually) that it lies in its nature to exist but not (treating identity and existential quantification predicatively) that it lies in their nature that something should exist.

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of philosophy, such as epistemology or ethics, seem to have an explicit interest in the nature of certain items – such as knowledge or obligation. But even here the interest seems incidental to the interest in the ‘low-level’ eidictic truths (in knowledge being true justified belief, say, rather than in its being by its nature true justified belief); and if the foundational aims of metaphysics can indeed be achieved, then separate consideration of the corresponding ‘high-level’ eidictic truths will not in fact be required. 1.5   T r a nspa r e nc y a n d a pr ior ic i t y Our concern so far has been with the propositions and subject-matter of an eidictic field. But what of its sentences and terms? What kind of sentences or terms can be used in logic, say, or in mathematics or metaphysics? One might think that the answer to this question was obvious. A sentence will be mathematical, say, iff it expresses a mathematical proposition and a term will be mathematical iff it signifies a mathematical item. However, this view can hardly be sustained. For suppose we use the description ‘the number of planets’ to fix the reference of the term ‘nop’. Then the sentences ‘9 > 7’ and ‘nop > 7’ will express the very same proposition and yet the first is clearly mathematical while the second clearly not. This is a somewhat artificial case and depends upon doctrines within the philosophy of language which not everyone will accept. But there are also more natural and less contentious cases. The term ‘the number of sides of a triangle,’ for example, signifies the number 3 and yet is not a suitable term of arithmetic and ‘here’ signifies a locale and yet is not a suitable term of geography. Thus it appears that a field of enquiry comes with a built-in restriction not only on its propositions but also on how those propositions may properly be expressed. But what are these further restrictions? Let us not attempt to answer this question in full generality (even if this were possible) but only in relation to an a priori eidictic field, such as metaphysics or logic. If we wish a field to be a priori, then we should so choose its vocabulary that it provides us with a priori access to its truths. Let us be a little more precise. Suppose that the subject-matter of the field is given by the elements t1, t2, …; and let t1, t2, … be corresponding terms for t1, t2, … Then we want every sentence ‘S’ formulated by means of the terms t1, t2, … to be such that: (*) if ‘S’ expresses a necessary truth then it is a priori that S.

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We may also want that every one of the sentences ‘S’ be such that: (**) it is a priori that if S then it is a priori that S.10

We might say that a vocabulary constituted by the terms t1, t2, … is epistemically transparent if case (*) is satisfied and that it is strongly epistemically transparent if (**) is also satisfied. It is then a natural requirement on an a priori eidictic field that it should have an epistemically – or strongly epistemically – transparent vocabulary. The transparency requirement might also be formulated in terms of concepts.11 Roughly speaking, the concept signified by a term is what we grasp in understanding the term; and our intention is that terms signifying the same concept should not differ in their epistemic status – that claims about what we can know should be indifferent to the use of one such term as opposed to another. Let τ1, τ2, … be concepts for the elements t1, t2, … Then we want every statement Σ formulated by means of the concepts τ1, τ2, … to be such that: (*)′ if the statement Σ signifies a necessary truth then it is a priori that Σ.

And similarly for the analogue of (**). Epistemic transparency, whether for terms or for concepts, is both a global and an epistemic phenomenon. But it might be thought to have a basis in the local and modal features of the individual concepts and terms themselves. Consider Kripke’s famous example of water being H2O. This statement signifies a necessary truth and yet is a posteriori. Why? It might be thought that this is because of the character of the concept of water (and perhaps also of H2O). For what the concept is a concept of is hostage to the empirical facts. In this world it is a concept of H2O but in another world, in which XYZ falls from the sky and fills the oceans etc., it will be a concept of XYZ. Say that a concept of x is modally transparent if it is necessarily a concept of x and that otherwise it is modally opaque. Thus the concept of identity will be modally transparent since it is necessarily a concept of identity while the concept of water will not be modally transparent since it will not necessarily be a concept of water (i.e. of H2O). The thought then is that the modal transparency of individual concepts will be sufficient to guarantee their epistemic transparency and that it is only because 10 We may want to weaken the requirement that S be a priori to the requirement that it be a priori if knowable. 11 There are difficulties in taking each term to correspond to a concept which I hope, for the purposes of the present discussion, may be ignored.

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of the presence of a modally opaque concept (such as water in water is H2O) that a necessary truth might fail to be a priori.12 An alternative, eidictic, notion of transparency might be defined. Given a concept τ of x and a field F, let us say that τ is strictly transparent in F if it lies in the nature of the subject-matter of the field F that τ is a concept of x.13 Any strictly transparent concept will, of course, be modally transparent; if the concept τ is a concept of x by the nature of some subject-matter then the concept will necessarily be a concept of x. So strict transparency will also be sufficient for epistemic transparency given the sufficiency of modal transparency. However, the converse connection need not hold; a concept may be modally transparent without being strictly transparent. For consider our previous example of the concept of the number of sides of a triangle. It is necessarily a concept of 3 but it might be argued that it is not by its nature and the nature of the subject-matter of arithmetic a concept of 3; something about the nature of triangle and side is also required. Given that the truths of an eidictic field turn on the nature of its subject-matter, it seems to be especially appropriate that the objects picked out by its concepts should also turn on the nature of its subject-matter; and so, by using the strict criterion in place of the modal criterion, we may get a better grip on what the concepts of various eidictic fields should be. 1.6  T h e p o s s i bi l i t y of m e ta ph y s ic s We have characterized the traditional conception of metaphysics in terms of a range of desirable features. Metaphysics should be concerned with the nature of reality; it should operate at a high level of generality; its method of enquiry should be a priori and its means of expression transparent; and it should be capable of providing a foundation for all other enquiry into the nature of reality. But can all of these desiderata be captured within a single field of enquiry? Might there not be a conflict between the demand to know the nature of reality, for example, and the desire for a prioricity? Or between 12 Under the ‘two-dimensional’ semantics – favoured by Chalmers (1996), Jackson (1998) and others – a term will be transparent in this sense if its intension remains the same under any variation in the ‘world’ or ‘scenario’ considered as actual. The notion of semantic stability in Bealer (1999) plays a somewhat similar role, as does the homonymous distinction of Foster (1982: 62–3). 13 A related notion is that of a concept which by its very nature signifies what it does. The concept contains within itself, so to speak, what it is a concept of. In so far as we can be expected to have a priori knowledge of the nature of a concept we can also be expected to have a priori knowledge of the nature of its object for concepts of this sort.

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the demand for generality and the desire to achieve the foundational aims? And should the traditional conception of metaphysics as a unified field of enquiry perhaps be abandoned in favour of a multitude of different fields of enquiry, each emphasizing this or that aspect of the traditional conception? The answer to this question is by no means clear, but there is at least some reason to think that these various desiderata can all be captured within a single field of enquiry. For suppose we start off with the desire to find an explanation for eidictic truth. Then, as a rule, we can expect there to be an elevation in the generality of the subject-matter as we move from a given eidictic truth to its explanans. The example concerning water is typical in this regard, since substance is more general than water and composition more general than the molecular form of composition involved in H2O; and so one might hope that, in the limits of eidictic explanation, the elements of subject-matter will be of a high, and perhaps even of a penultimate, degree of generality. Once we have achieved the desired level of generality, it is not so hard to see how we might secure modal (or eidictic) transparency. For, as a rule, the more general an element of subject-matter – the more ‘cut off’ it is from the world – the easier it is to secure transparent reference. Thus it is that we have the sense of greater transparency as we move from cat to animal, say, or from animal to living thing; and so, again, one might hope that in the limits of eidictic explanation, the generality of the subjectmatter of metaphysics will be sufficient, as it is in logic, to secure the transparency of its concepts. Finally, with the combination of necessity (or eidicity) and transparency comes the possibility of a priori knowledge. One major obstacle to achieving a priori knowledge is removed; and perhaps no other obstacle stands in its way. Thus if all goes well, eidictic explanation will terminate in the general a priori truths of metaphysics.

ch apter 2

In defence of Aristotelian metaphysics Tuomas E. Tahko

2 .1   I n t roduc t ion When I say that my conception of metaphysics is Aristotelian, or neo-Aristotelian, this has more to do with Aristotle’s philosophical methodology than his metaphysics, but, as I see it, the core of this Aristotelian conception of metaphysics is the idea that metaphysics is the first philosophy. In what follows I will attempt to clarify what this conception of metaphysics amounts to in the context of recent discussion on the methodology of metaphysics (e.g. Chalmers et al. 2009, Ladyman and Ross 2007). There is a lot of hostility towards the Aristotelian conception of metaphysics in this literature: for instance, the majority of the contributors to the Metametaphysics anthology by Chalmers et al. assume a rather deflationary approach towards metaphysics. In the process of replying to the criticisms towards Aristotelian metaphysics put forward in recent literature I will also identify some methodological issues concerning the foundations of Aristotelian metaphysics which deserve more attention and ought to be addressed in future research. In Section 2.2 I will compare the Aristotelian and what could be called a ‘Quinean’ conception of metaphysics. According to the Quinean approach, the key questions of metaphysics concern the existence of different kinds of things, whereas the Aristotelian approach focuses on the natures or essences of these things. A somewhat different attack towards Aristotelian metaphysics can be found in Ladyman and Ross (2007), who group it under the label of ‘neo-scholastic metaphysics’  – a term which This paper was written while I was a Visiting Research Fellow at Durham University; this was made possible by a grant from the Academy of Finland. I would like to express my gratitude to the Academy of Finland, to my colleagues in Durham, and most of all to Jonathan Lowe, the supervisor of my doctoral dissertation at Durham, whose work has done so much by way of developing and defending Aristotelian metaphysics. I would also like to thank Richard Stopford for helpful comments on an earlier draft of the paper.

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they use in a strictly pejorative sense: if metaphysics is not supported by current physics, then it has no value. In Section 2.3 I will consider the approach emerging from the critique by Ladyman and Ross; it aims to naturalize metaphysics. I contend that the call for naturalization is deeply mistaken: not only is Aristotelian metaphysics already naturalized, it is also a necessary precursor of all scientific activities. Finally, I will hint towards a programme for a rigorous methodology of Aristotelian metaphysics inspired by E. J. Lowe’s (e.g. 1998) work. According to this line of thought, metaphysics is primarily concerned with metaphysical possibility, which is grounded in essence. I will reply to the critique that Ladyman and Ross (2007) developed against this view and suggest that it is fully consistent with science, and that the theoretical work in science is in fact also based on this very methodology. 2 .2   S hoe s a n d s h i p s, a n d s e a l i ng wa x The view that the central task of metaphysics is to determine ‘what there is’ was popularized by Quine’s well-known paper, ‘On What There Is’ (1948). But it would be a rather crude simplification to claim that the Quinean conception of metaphysics is simply to list the things that exist: shoes and ships, and sealing wax. Rather, the Quinean metaphysician is interested in ontological commitment, namely, what sorts of things are we committed to in our ontology? Shoes and ships, and sealing wax are not the most interesting types of entities in this regard, but pigs with wings are. Consider the following argument: (1) The number of winged pigs is zero. (2) There is such a thing as the number of winged pigs. (3) Hence, there are numbers. Now, this argument does not aim to establish the existence of pigs with wings, but rather the existence of numbers. However, if it is valid, the implication is that anything that we quantify over in the manner that numbers are quantified over in this argument can be subjected to a similar argument. This includes winged pigs. Arguments of this type have recently received a lot of attention, unduly, in my opinion. The idea behind the argument is that we can formulate existence questions in terms of the existential quantifier: ‘∃x(x is a number)?’ (cf. Fine 2009: 157). But if we can settle these existence questions with the help of arguments such as the one above, then metaphysics does not seem like a very interesting endeavour. While some deflationists about metaphysics would

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welcome this result, I am more inclined to think that we are not in fact dealing with a very typical metaphysical question here. Another worry is that if most metaphysical questions are really existence questions of this type, then these questions are not only trivial, but already addressed by special sciences such as mathematics and, in the case of existence questions concerning material objects, physics. It may be of some comfort that many existence questions are obviously non-trivial. For instance, ‘Does the Higgs boson exist?’ appears to be a very important and non-trivial existence question. Of course, it has nothing to do with metaphysics. This is not to say that metaphysicians should not be interested in existence questions of this type, but they are certainly not what metaphysics is centrally concerned with. Perhaps this is not a fair reading of what the Quinean tradition takes metaphysics to be about. After all, existence questions such as the one about numbers have a certain ambiguity about them, and even if we formulate them in the manner suggested above, i.e. ‘∃x(x is a number)?’, there is still the question of how we should interpret the existential quantifier. We have several options in this regard, but here I will focus on Thomas Hofweber’s (2005, 2009) suggestion, according to which we can distinguish between the internal and the external reading of the existential quantifier.1 Let me borrow some examples from Hofweber (2009: 276 ff.) to illustrate this distinction. Consider the following statement: ‘Everything exists.’ The first reaction to this statement is that it is trivial, as naturally everything in the world exists. But then again there would appear to be some things, such as Sherlock Holmes, that do not exist, and hence not everything exists. In this sense, the statement is apparently false. These two senses are supposed to correspond with the external and the internal readings of the existential quantifier, respectively. Essentially, the external reading concerns objects within the domain of the quantifier, whereas the internal reading concerns the inferential role of the quantifier, i.e., the role that the quantifier has in linking quantified statements to quantifier free statements. Hofweber illustrates the distinction with sentences such as ‘Someone kicked me’, where the natural reading of the quantifier is external since whoever it is that kicked me is surely within the domain of the quantifier ‘someone’. But the same quantifier can have a different interpretation in sentences such as ‘There is someone we both admire’, where the reading is internal when I have forgotten who it is that we both 1 I will not discuss the differences between the objectual and the substitutional reading of the existential quantifier here, but see Crane (this volume) for further options.

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admire. In this case I just want to say that there is some X that we both admire, but I cannot remember who X is. A quantifier is needed in this case as well, but we would not want it to range over what the world contains: if it happens to be Sherlock Holmes that we both admire, then X would not be contained in the world at all. So, the internal reading remains neutral about the domain; we want to be able to replace it with any term, whether or not that term refers to something that exists in the world. This distinction is motivated by Carnap’s internal–external distinction, but the historical details are unimportant for my purposes. What Hofweber hopes to cash out with this distinction  – and I suspect that many contemporary metaphysicians would be sympathetic to the move – is a way to address the apparent problems that existence questions pose for metaphysics. The upshot is that we have two ways to go regarding our talk about a given metaphysical problem, such as the one concerning the existence of numbers: internalism and externalism. Internalism is the view that quantification over things like number terms is non-referential in ordinary uses (it does not aim to refer to some domain of entities) and externalism is the view that it is commonly referential (it refers to a domain of entities). Hofweber (2009: 284) suggests that the question ‘Are there numbers?’ is underspecified because it has both an internal and an external reading. The argument for the existence of numbers that opened this section relies on the internal reading, and on this reading the existence of numbers seems to be trivially true. However, with an external reading the question is not trivial, and furthermore, Hofweber thinks that mathematics does not provide an answer to the external reading. Accordingly, perhaps it is the external reading of the question that metaphysics is concerned with: it is not trivial, nor is it answered by the special sciences. This is the middle way between esoteric and deflationist metaphysics that Hofweber proposes: metaphysics attempts to settle what there is, but this question is neither trivial nor settled by the special sciences. So, according to Hofweber, metaphysics is interested in the external reading of questions such as ‘Are there numbers?’. But the correct answer to this question still depends on whether internalism or externalism is true about numbers, that is, whether our ordinary talk about numbers is such that it aims to refer to some domain of entities, ‘numbers’, or does not. The task of metaphysics is now supposed to be to answer this question. In the case of numbers, Hofweber argues that internalism is the most plausible choice, as it seems that talk about numbers does not aim to refer to a particular domain of entities; in this sense numbers words are like the words ‘some’ and ‘many’ (2009: 286). Since numbers are ­non-referential,

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there is nothing in the world that they pick out and hence no such things as numbers. In general, Hofweber suggests that internalism settles many of the problematic external ontological questions, and that the task of metaphysics is merely to decide whether internalism or externalism is true regarding these external questions: There is no distinct metaphysical method to address ontological questions. To find the answer we have to decide between internalism and externalism, which is done with the methods employed in the study of language, and related issues. (Hofweber 2009: 287)

This is Hofweber’s ambitious, yet modest, metaphysics. However, I do not see how it differs from the deflationist approach; by the looks of it, metaphysics turns out to be a rather trivial and uninteresting endeavour, its only task being to determine whether internalism or externalism is true in given cases. In fact, even this task is delegated to the special sciences, since Hofweber states that it is by using the methods ‘employed in the study of language, and related issues’ that we determine whether internalism or externalism is true (2009: 287). Metaphysics, it turns out, is really nothing but linguistics. I do not think that this result is particularly surprising. If existence questions are considered to be the core questions of metaphysics, then something has gone wrong to begin with. It is true that numbers, for instance, have received considerable attention in metaphysics, however, the form of the metaphysical question concerning numbers ought not to be whether there in fact are any such things, but rather what is the nature of these things. But what is this other question, the question about the nature of numbers? Well, if we acknowledge that metaphysics does not concern the existence of numbers but we nevertheless think that there are some important and interesting metaphysical questions about numbers, then the questions must concern the status or type of these entities. The way Kit Fine puts this is that the question is about whether numbers are real: The realist and anti-realist about natural numbers, for example, will most likely take themselves to be disagreeing on the reality of each of the natural numbers – 0, 1, 2, …; and this would not be possible unless each of them supposed that there were the numbers 0, 1, 2, … It is only if the existence of these objects is already acknowledged that there can be debate as to whether they are real (Quine’s error, we might say to continue the joke, arose from his being unwilling to grasp Plato by the beard). (Fine 2009: 169)

Indeed, Fine suggests that existence should be considered as a predicate: if we wish to ask whether integers exist, we should not formulate the

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question like this: ‘∃xIx?’, where ‘I’ refers to integers, but rather like this: ‘∀x(Ix ⊃ Ex)?’, where ‘E’ is the predicate for existence – the question is not whether some integer exists, but whether every integer does (Fine 2009: 167). In fact, many existence questions are for the most part only interesting to scientists, or mathematicians in the case of numbers. Accordingly, Fine takes the realism/anti-realism debate to concern the reality of objects, and in order to have a debate about this in the first place realism in the usual sense has to be assumed. The upshot of this line of thought is that the realism/anti-realism debate in the usual sense is a non-starter, because either we are all realists, or there is no discussion to be had. Although I am very sympathetic to the line that Fine takes, there are some problems that remain to be solved, for we are now on our way towards what Hofweber has scornfully dubbed ‘esoteric metaphysics’. The folly of esoteric metaphysics, as Hofweber defines it, is that metaphysical questions should be answered with metaphysical terminology, and an understanding of metaphysics is needed for one to even be able to understand metaphysical questions (Hofweber 2009: 266 ff.). This bears some similarity to the idea that there is a specific ‘ontology room’ where we can sensibly doubt the existence of tables, or a particular language of metaphysics where questions such as this make sense. The obvious problem with this approach is that it seems particularly mysterious in the light of a metametaphysical analysis: it may save metaphysics, but it does not help in clarifying what metaphysics is about. Indeed, I do not think that this is the way to go. Metaphysics is already mysterious enough for the layman, and to say that we are talking in a ‘metaphysical sense’ that ‘ordinary’ people cannot understand when we inquire into the existence of tables will surely be the end of what little funding still finds its way towards the study of metaphysics. There are more sophisticated versions of so-called ‘esoteric’ metaphysics however, such as the ones proposed by Kit Fine (2001, 2009, this volume) and Jonathan Schaffer (2009). Central to both of these approaches are certain core concepts such as GROUND and PRIORITY, capitalized to separate them from the ordinary usage of these terms (following Hofweber 2009). I do not wish to go into the details of either view, but both of these approaches hold that a central part of metaphysics is the study of ontological dependence: certain things depend on other things for their existence and identity and metaphysics is interested in these dependency relations (cf. Fine 1995a, Correia 2008). Hofweber’s main concern with these approaches is that they take certain notions as primitive and that seems to make metaphysics dangerously inaccessible:

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As far as I understand Fine’s view, it is a sophisticated version of esoteric metaphysics: metaphysics is supposed to find out what is GROUNDED in REALITY, in a special metaphysical sense of these terms. To know what this sense is gives you entrance into the discipline, but it takes a metaphysician to know this sense. Esoteric metaphysics never sounded so exclusive. (Hofweber 2009: 270)

After a similar analysis of Schaffer’s views, Hofweber concludes as follows: Esoteric metaphysics appeals to those, I conjecture, who deep down hold that philosophy is the queen of the sciences after all, since it investigates what the world is REALLY like. The sciences only find out what the world is like, but what philosophy finds out is more revealing of reality and what it is R EALLY like. (Hofweber 2009: 273)

Hofweber continues to pour scorn on esoteric metaphysics by suggesting that it opens the door to views such as the one familiar from Thales: everything is ultimately water. But this is just a straw man; the real problem is whether metaphysical questions can be formulated in the manner that is commonly assumed in contemporary analytic metaphysics. The answer that Fine offers is a resounding ‘no’, and I am inclined to agree with him. Still, Hofweber is right to ask for more, as it is true that this type of approach to metaphysics is not particularly well developed. It is, however, difficult to develop a view which is not taken seriously to begin with. Unfortunately, the Quinean interpretation of ontological questions is very deep-rooted in contemporary metaphysics. The distinction between (neo-)Aristotelian and Quinean metaphysics should now be somewhat clearer, and we have already identified some aspects of Aristotelian metaphysics that need to be developed. But before we attempt to engage with the problems that have been identified so far, let us turn to another critique of Aristotelian metaphysics – potential lines of development will be discussed in the final section. 2 .3   N at u r a l i z i ng A r i s t o t e l i a n m e ta ph y s ic s I think that philosophy is indeed the queen of the sciences. However, this in no way entails that one needs to be educated in metaphysics to be able to pursue metaphysical questions or to gain access to metaphysical truths  – there is no doubt that it will help, but it is not necessary. Moreover, I do not think that philosophy is the queen of the sciences because it is concerned with what reality is REALLY like: I think that both philosophy and science are concerned with reality in this capitalized

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sense. In fact, this is why I take metaphysics and science to be continuous. It should be emphasized here that when I say that metaphysics and science are continuous, I do not mean it in the sense that they would both have exactly the same agenda. Rather, I mean that we could not really engage in one without the other, that is, we could not get very far in our inquiry into the nature of reality with just one of these disciplines. Because of this, it might be better to say that metaphysics and science complement each other (cf. Lowe 2011). This idea is compatible with Aristotle’s writings about the relationship between the study of ‘being qua being’, i.e., metaphysics, and the special sciences: There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature. Now this is not the same as any of the so-called special sciences; for none of these others deals generally with being as being. They cut off a part of being and investigate the attributes of this part – this is what mathematical sciences for instance do. Now since we are seeking the first principles and the highest causes, clearly there must be some thing to which these belong in virtue of its own nature. (Metaphysics 1003a22–28)

Thus, Aristotelian metaphysics is the study of being as it is in itself, whereas the special sciences investigate only a part of that being. But how well does this view sit with the modern scientific view? Not very well, if Ladyman and Ross (2007) are right. They begin their book, Every Thing Must Go with a brief critique of metaphysics which sweeps over Aristotle’s metaphysics as well as contemporary analytic metaphysics. Their primary criticism is that metaphysics suffers from a lack of scientific rigour and is in fact very badly informed of the latest developments in science. The result is a domestication of certain aspects of contemporary science at best, pseudo-scientific mumbo-jumbo at worst. Instead, Ladyman and Ross call for naturalized metaphysics – metaphysics which is based on science. Can we reconcile Aristotelian metaphysics with this idea of naturalized metaphysics? The main problem that Ladyman and Ross raise for the prospect of reconciling metaphysics  – understood in the Aristotelian sense  – with natural science is that this type of ‘neo-scholastic metaphysics’, as they call it, gives priority to a priori, armchair intuitions, and ignores the fact that recent empirical results show the natural world to be much more complicated than our armchair intuitions might suggest. It is difficult to deny this: if we consider Aristotle’s ideas in his Physics for instance, most

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of them seem rather obsolete. No philosopher in Aristotle’s time could have realized just how small and strange the world of subatomic particles is, or indeed how vast and old the universe is. Having said that, the manner in which Ladyman and Ross characterize ‘neo-scholastic metaphysics’ is almost as misinformed about the nature of Aristotelian metaphysics as Aristotle perhaps was about natural science. Let us start with armchair intuitions. Ladyman and Ross (2007: 10–15) give a number of examples of metaphysical, armchair intuitions which seem to be blatantly incorrect from a scientific point of view. Indeed, it is easy to find such examples, in metaphysics and science alike – just consider the repeatedly stated yet later falsified intuition that we have reached the fundamental level of reality when a new microparticle is found. Intuitions are clearly not very trustworthy, but does this mean that armchair reasoning is completely worthless? Even Ladyman and Ross do not go as far as to claim this, for they admit that it is often said of a good physicist ‘that he or she has sound physical intuition’ (2007: 15). But the use of the word ‘intuition’ is supposedly different in this case, as it refers to ‘the experienced practitioner’s trained ability to see at a glance how their abstract theoretical structure probably – in advance of essential careful checking  – maps onto a problem space’ (2007: 15). There is an ongoing debate in metaphysics about the nature and role of intuitions (e.g. Booth and Rowbottom forthcoming), but I believe that this description is entirely accurate for the metaphysician’s use of the term as well, contrary to what Ladyman and Ross claim. Is it not the case that a metaphysician’s intuition is exactly a preliminary judgement about how a certain abstract theoretical structure probably maps onto a problem space? Ladyman and Ross further distance metaphysicians’ intuitions from those of scientists by pointing out that the former are often taken as evidence whereas the latter are only heuristically valuable, but this is certainly not a commonly accepted view. In fact, my own view is that intuitions are, for the most part, misleading, exactly because the problem space is generally much more complicated than one first assumes. Regardless, certain very experienced practitioners both in science and in metaphysics may use intuitions as a good heuristic tool. The intuitions themselves are at best only prima facie evidence: careful study, or in some cases empirical research, is required before they can be accepted. But it is certainly a naϊve view of metaphysics to assume that metaphysicians simply take their intuitions at face value and leave it at that – generally a book-length study follows!

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Since intuitions are a controversial subject in any case, perhaps we would be better off talking about a priori inquiry in general, as most proponents of (neo-)Aristotelian metaphysics at least contend that some kind of a priori inquiry is possible. One account about the role of this inquiry comes from Lowe (1998), who suggests that metaphysics studies the realm of metaphysical possibility – the space of the possible fundamental structures of reality – but we also need empirical science to determine which of the possible structures corresponds with the actual world. This is one way to understand the Aristotelian conception of metaphysics: the first philosophy studies the fundamental structure of reality, possibility strictly in virtue of being qua being, but we need the second philosophy, the special sciences, to determine how this structure is reflected in the actual world. Ladyman and Ross are aware of this general understanding of metaphysics and in fact claim to endorse the idea that the goal of metaphysics is to unify the special sciences, but: [W]e differ with Lowe on how this task is to be accomplished, because we deny that a priori inquiry can reveal what is metaphysically possible. Philosophers have often regarded as impossible states of affairs that science has come to entertain. For example, metaphysicians confidently pronounced that non-Euclidean geometry is impossible as a model of physical space, that it is impossible that there not be deterministic causation, that non-absolute time is impossible, and so on. Physicists learned to be comfortable with each of these ideas, along with others that confound the expectations of common sense more profoundly. (Ladyman and Ross 2007: 16–17)

This is all that Ladyman and Ross say against the possibility of a priori inquiry into metaphysical possibility, so it is this critique that we must repel if we hope to defend Aristotelian metaphysics. However, I think that what we have here is a very uncharitable interpretation of Lowe’s conception of the methodology of metaphysics. This is because Ladyman and Ross seem to assume that our epistemic access to metaphysical possibility has to be infallible. While the infallibility of a priori inquiry may have been a doctrine of Cartesian metaphysics, it is most certainly not a doctrine of Aristotelian metaphysics. Hence, it is true that metaphysicians, like scientists, make mistakes. Kant held that non-Euclidean geometry is impossible, but physics soon showed that not only is it possible, but actual. In fact, in non-Euclidean geometry we have a good case study about how a priori inquiry can indeed reveal what is metaphysically possible. For if we look at the historical facts, it was not empirical inquiry that revealed the possibility of non-Euclidean geometry, but mathematical

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and thus, we might argue, a priori inquiry: the mathematicians Gauss, Lobachevski, and Riemann developed alternative, non-Euclidean geometries which replaced the controversial parallel postulate of Euclidean geometry with an alternative axiom. This way we get a number of possible geometries, although we know that only one of them can be actual. Kant did indeed make a mistake, but the mistake was not due to a flaw in the methodology of a priori inquiry, but rather a failure to grasp the possibility of alternative geometries. The lesson that we should take from this is that the space of metaphysical possibilities reached by a priori means is revisable, quite similarly to empirical results which can be revised in the light of new empirical data. In fact, the methodological similarities between science and metaphysics are much greater than this. Recall the discussion about intuitions above. As we saw, Ladyman and Ross acknowledge that something like intuitions are used in science as well, although merely as a heuristic tool. Let us imagine a situation where a scientist uses her intuition to come up with a scenario that might explain some empirical data, a new model about, say, gravity. The first thing that she is likely to do is to formulate the model suggested by her intuition with mathematical rigour, which will enable her to determine whether the model is consistent. Sometimes models based on such ‘hunches’ turn out to be inconsistent, but if this is the case, the error can be spotted early on, certainly before any empirical tests need to be performed. So far, this story is not very far from how a metaphysician would proceed. The metaphysician is perhaps unlikely to use mathematics to model the insight in question, but logic and other means of careful analysis would certainly be in the metaphysician’s toolbox. To me, both of these activities seem to be a priori activities, since no empirical elements are present, but I do not want to dwell on the question of whether mathematics is a priori or not. It is sufficient to note that the scientist and the metaphysician proceed from intuitions to detailed models in a similar manner – both use their intuitions merely as a heuristic tool, and both acknowledge the fallibility of this heuristic tool. It is the next stage of the story which one might expect to demonstrate the superiority of empirical science over armchair metaphysics, namely, the empirical experiments which the scientist can design and use to test the validity of the original intuition. The model, if it is consistent, will only provide proof of the possibility of a correspondence with the actual reality, and only an empirical experiment can reveal which model reflects the actual structure of reality. Of course, this

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empirical element is also available for the metaphysician, but only insofar as her model makes testable predictions. Because metaphysics in the Aristotelian tradition rarely makes such predictions, Ladyman and Ross think that it should not be taken seriously. In fact, they think that the value of metaphysical claims is very limited indeed: Any new metaphysical claim that is to be taken seriously should be motivated by, and only by, the service it would perform, if true, in showing how two or more specific scientific hypotheses jointly explain more than the sum of what is explained by the two hypotheses taken separately, where a ‘scientific hypothesis’ is understood as an hypothesis that is taken seriously by institutionally bona fide current science. (Ladyman and Ross 2007: 30)

This ‘Principle of Naturalistic Closure’ would seem to reduce metaphysics merely to the task of unifying scientific hypotheses. But this ignores a crucial element of the story: metaphysical inquiry is required in order to produce scientific hypotheses in the first place. We have seen that, on the face of it, the process by which metaphysicians and scientists proceed from intuitions to models of reality is rather similar. Specifically, it appears to be non-empirical. Moreover, these models ought to be not just formally consistent, but also consistent with the current empirical data. In the spirit of the Aristotelian tradition, a metaphysician should be familiar with this empirical data – Aristotle certainly seems to have had a good knowledge of the (rather limited) empirical data of his time; in fact he engaged in some empirical research himself, especially in biology. In any case, the core of the matter concerns the nature of the reasoning process which leads to the formulation of a scientific hypothesis. This process is fallible, but it fulfils all the essential elements of metaphysical inquiry. If this is correct, then our attention should not be directed towards the question of whether Aristotelian metaphysics can be naturalized, but rather what the metaphysical foundations of natural science are. 2 . 4  T h e m e t hod ol o g y of A r i s t o t e l i a n m e ta ph y s ic s Although the analysis of the methodology of Aristotelian metaphysics suggested by Ladyman and Ross is flawed in its requirement for infallibilism, it does raise a point that must be addressed. This point concerns the epistemology of metaphysics. Ladyman and Ross (2007: 16) refer to Ted Sider disapprovingly in this connection and point out that Sider’s strategy to defend a priori metaphysics by claiming that the epistemological foundations of science and mathematics are equally mysterious is not convincing. Indeed, although I think that there will be an important overlap

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between the epistemological foundations of science and metaphysics, the problem seems to be more pressing for the latter, since the empirical elements of science give it a rather more effective tool to spot errors than anything we have in metaphysics. So, I acknowledge that there is more work to be done on the foundations of (neo-Aristotelian) metaphysics. Specifically, I think that we need an account of modal epistemology: how can we reliably inquire into the realm of metaphysical possibility given that we sometimes make mistakes? This problem is analogous to a more general debate in modal epistemology, namely the one concerning the link between conceivability and metaphysical possibility (cf. Gendler and Hawthorne 2002). Conceivability arguments are a familiar tool in metaphysics, but one problem is that it seems to be easy to conceive of metaphysically impossible things as well. In any case, it appears that for something to be possible, it must also be conceivable (at least by an ideal conceiver), but although this is a necessary requirement for possibility, it is not sufficient. We seem to have a similar situation with regard to a priori access to metaphysical possibility. In fact, it may appear that these are one and the same problem, since conceivability is sometimes defined in terms of a priori reasoning. I think that this is misleading: it is a short step from conceivability to conceptual analysis, which is another typical way to understand what conceivability means  – imaginability in terms of the definitions of concepts – but a priori access to metaphysical possibility cannot be based strictly on conceptual analysis because concepts do not give us access to being qua being; they concern merely a part of being, not the nature of reality in general. Unfortunately Ladyman and Ross make the mistake of identifying metaphysical a priori inquiry with conceptual analysis. They claim that Lowe follows Frank Jackson and others ‘in advocating the familiar methodology of reflecting on our concepts (conceptual analysis)’ (2007: 16), and immediately ask how conceptual analysis could possibly reveal anything about the structure of reality. Well, this is a concern that a proponent of Aristotelian metaphysics shares. Moreover, it is the very reason why metaphysical a priori inquiry cannot be identified with conceptual analysis. It should also be noted that far from following Jackson, I believe that Lowe would be as critical of Jackson’s project as Ladyman and Ross themselves are. It is a mystery to me where they get the impression that metaphysics in this tradition has anything to do with conceptual analysis. Nevertheless, we do have to face the problem of modal epistemology. The groundwork for an appropriate account of modality is due to Kit

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Fine’s article ‘Essence and Modality’ (1994), which helped to rejuvenate the Aristotelian idea that the notion of essence is more fundamental than that of modality and that the latter is grounded in the former. Kathrin Koslicki’s contribution to this volume also deals with this topic. It is not possible to discuss all the details concerning this issue here, so instead I will attempt to motivate one of the underlying ideas, namely, that possibility precedes actuality. This is effectively what Ladyman and Ross deny, as they are opposed to the idea that metaphysical a priori inquiry could reveal what is possible in advance of empirical research. The idea of possibility preceding actuality is central especially in Lowe’s work, as it forms the basis for the possibility of metaphysics: ‘In short, metaphysics itself is possible  – indeed necessary  – as a form of rational human inquiry because metaphysical possibility is an inescapable determinant of actuality’ (Lowe 1998: 9).2 So, metaphysics deals with possibilities – metaphysical possibilities – but is not able to determine what is actual without the help of empirical research. However, it is crucial for this account that empirical knowledge in itself is not able to determine what is actual either, for a priori inquiry is needed to delimit the space of possibilities from which the actual structure of reality can be identified by empirical means. Consequently, a priori inquiry is necessary and prior to knowledge about actuality, because without this metaphysical delimitation of what is possible, the space of possibilities would be too vast to handle. So, it is this a priori delimitation of the space of possibilities which enables us to pick out just the genuine metaphysical possibilities from the enormous space of conceivable yet metaphysically impossible things. Consider the following statement, which is commonly thought to be metaphysically necessary: ‘Gold is the element with the atomic number 79.’ If this statement is indeed metaphysically necessary, the necessity must be due to the nature of elementhood, that is, the atomic number is, by metaphysical necessity, associated with one and only one element (cf. Tahko 2009b). However, it is certainly conceivable that a different organization of subatomic particles would produce exactly the same characteristics that gold has, and indeed be gold to all ends and purposes. Examples like this are familiar from Putnam’s Twin Earth scenarios, but they are generally considered not to entail metaphysical possibility. In any case, there is nothing contradictory in the scenario where the element 2 It should be noted though that what follows is my own conception of the methodology of neoAristotelian metaphysics. It is inspired by the work of Fine and Lowe, but is not necessarily entirely faithful to either. See also the contributions of Fine and Lowe in this volume.

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with atomic number 78, for instance, has the characteristics that gold has instead of the ones that platinum has. Whether or not this element would be gold is the question that the Twin Earth scenarios are supposed to raise and the correct answer is typically considered to be that it would not be gold. Regardless of this, we can easily imagine a completely different organization of the fundamental physical constants and the laws of physics that would enable this possibility. The usual conclusion is that whatever the resulting element would be, it would not be gold as we know it. At best, it is an epistemic possibility that this element would be gold, but we would be making a metaphysical error if we thought that it could be the same gold that we know and value highly. In fact, there are infinitely many such conceivable scenarios, which are nevertheless metaphysically impossible. Due to our limited rational capabilities, it is impossible for us to consider all of these alternative scenarios – we have to delimit this space of possibilities somehow if we wish to make any progress in science. This is where a priori inquiry is required: the conclusion that the atomic number is a part of the essence of elements is the result of a combination of empirical research and a philosophical, a priori analysis of the different possible ways to interpret the empirical data.3 There is more to be said about the relationship between metaphysical a priori inquiry and empirical data. To emphasize that a priori inquiry is needed before empirical data becomes intelligible, let us consider another example, namely the basic thesis of the identity theory: brain states are mental states. This is an a posteriori identity claim and its status, I take it, is currently unsettled. Now, the question is: what sort of empirical information could verify this identity claim? We certainly have ample information about what happens in our brains, yet few physicalists would claim that this is by any means enough to settle the debate. In fact, I think that it is fair to say that no amount of purely empirical information could settle the debate by itself, for otherwise the debate would perhaps be over already.4 I do not wish to go into the literature about the ‘explanatory gap’ here, but the idea is that we lack sufficient information about the underlying a priori identity, namely, we do not know whether this identity holds or not. Note once again though that the understanding 3 Although the atomic number is commonly accepted to be a part of the essence of elements, the issue is not as simple as it might seem; alternative accounts have been suggested. These different accounts may all be consistent and a priori, but only one of them, at most, is actual. See Hendry (2006) for further discussion about elementhood, specifically for one alternative account. 4 Admittedly, some physicalists especially may think that the debate is indeed over, but given the number of articles and books that continue to be published on the issue, it appears that far from being over, the debate is in fact only heating up.

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of aprioricity at hand here is not synonymous with conceptual analysis – this view is familiar from the work of Frank Jackson and others, but from an Aristotelian point of view the identification of a priori inquiry with conceptual analysis is a watered-down conception of the nature of a priori inquiry. So, although a central theme in the literature on the explanatory gap concerns the role of a priori conceptual analysis which is required to settle the status of the identity theory, this is not the idea that I am advocating. In fact, I think that the role of the a priori part in the mind–brain identity thesis is exactly the same as in the matter–energy (or better: mass–energy) identity thesis, to use an example also familiar from the explanatory gap literature. The a priori work required in the latter case does not concern an analysis of the concepts of ‘mass’ and ‘energy’, but rather the natures of mass and energy. Einstein’s insight was that really we are only talking about the nature of one thing, namely energy; mass energy, which we observe as matter, is just one of many forms of energy. In the terminology of Aristotelian metaphysics, it would appear to be a part of the essence of energy that it can exist in many forms, one of them being mass energy. Now, it is worth emphasizing here that when Einstein formulated special relativity, one consequence of which is the mass–energy equivalence, he certainly did not do this experimentally, but rather by carefully considering the different possibilities of the behaviour of objects travelling at speeds approaching the speed of light. Much of this work is mathematical, but whether or not we consider mathematics to constitute a priori work, there must be something that this mathematical work is based on as well – perhaps it could be described as an intuition in the sense that was introduced in the previous section. Returning to the case of mind–brain identity, the upshot would seem to be that even the possibility of mind–brain identity has not been sufficiently characterized, nor has the possibility of mind–brain duality. The stalemate in contemporary philosophy of mind amounts to just this: the a priori delimitation of the different possibilities available in explaining consciousness has not been completed, at least not in sufficient detail to convince the majority of philosophers. Many philosophers are convinced that it is impossible to explain consciousness in terms of the physical, whereas others think that this is the only possible explanation. But since it seems to be very difficult to come to an agreement about which of these possibilities are genuine, the result is that we do not even know what sort of empirical information could verify or falsify the identity claim in question. It is possible that we already possess this empirical information,

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but as the a priori work concerning this debate has not been completed, the empirical information is of little use to us. The same, I think, is true of many other a posteriori identity claims, perhaps even of our previous example about elementhood. More generally, this methodological picture suggests that the way in which we interpret and analyse empirical information is dependent on an a priori delimitation of what is possible. In some cases the a priori work has been done long ago, whereas some cases seem to elude definite a priori characterization rather effectively. There are plenty of examples of this in science as well: for instance, it appears that no amount of empirical information will settle the most important and most difficult questions concerning quantum mechanics, such as whether the wavefunction has an objective existence or whether it is merely a mathematical convenience, or how the role of the observer should be accounted for in the universal wavefunction, or whether a realist or an anti-realist interpretation of quantum mechanics is correct; any attempt to address issues such as these will have to start from metaphysics. Some difficult questions about the epistemic role of a priori inquiry remain. From what has been said above, it may still seem that we are dealing with some sort of mysterious rational intuition, since a priori inquiry provides the parameters for any interpretation of empirical data while also being self-correcting. Even given fallibilism, there remains a problem concerning the justification of the criteria used to evaluate a priori propositions. But here as well I believe that Aristotelian metaphysics has a long tradition of research, for the Aristotelian categories are central to the task of determining the criteria by which we judge both empirical and rational information. Several chapters in this volume discuss either the categorical structure of reality in general or specific categories; this is exactly the type of research needed to examine the foundations of metaphysics. It should be emphasized though that this research goes hand in hand with empirical research: there is a bootstrapping relationship between a priori and a posteriori inquiry, and we cannot engage in one without the other (Tahko 2008). Certain a priori principles, such as the ones emerging from the categorical structure of reality, may be more fundamental, and it is perhaps with these principles that the bootstrapping begins. One of the obvious candidates for such a fundamental principle – one that Aristotle certainly considered to be fundamental – is the law of non-contradiction. Perhaps the law of non-contradiction could be self-evident enough to act as a foundational a priori principle, although even this is a question that

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requires further research.5 These are questions that will have to be settled elsewhere, but many chapters in this volume serve as steps towards answering them. To conclude, the role of (neo-)Aristotelian metaphysics as I understand it is to provide a mapping of the initial limitations of any kind of rational inquiry, because without such a mapping it would be impossible to choose which of the infinitely many potential lines of research are feasible in the first place.

  See my (2009a) for discussion on the role of the law of non-contradiction.

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ch apter 3

Existence and quantification reconsidered Tim Crane

3.1  I n t roduc t ion The currently standard philosophical conception of existence makes a connection between three things: certain ways of talking about existence and being in natural language; certain natural language idioms of quantification; and the formal representation of these in logical languages. Thus a claim like ‘Prime numbers exist’ is treated as equivalent to ‘There is at least one prime number’ and this is in turn equivalent to ‘Some thing is a prime number.’ The verb ‘exist’, the verb phrase ‘there is’, and the quantifier ‘some’ are treated as all playing similar roles, and these roles are made explicit in the standard common formalization of all three sentences by a single formula of first-order logic: ‘(∃x)[P(x) & N(x)]’, where ‘P(x)’ abbreviates ‘x is prime’ and ‘N(x)’ abbreviates ‘x is a number’. The logical quantifier ‘∃’ accordingly symbolizes in context the role played by the English words ‘exists’, ‘some’, and ‘there is.’ This view about how to represent or regiment these kinds of sentences will be familiar to philosophers; so familiar, in fact, that for many it will be taken as an established result. I think it should not be taken in this way, and my aim in this paper is to disentangle a number of different claims contained in this standard view, and to dispute some of them. Before doing this, I must first distinguish between two ways in which these kinds of formalization can be understood. On one understanding, they are taken as representing the underlying logical form (or maybe the For comments and discussion of these topics, I am grateful to audiences in Bristol, Cambridge, Canberra, Glasgow, Melbourne, Paris, and especially to Tim Button, Katalin Farkas, Fraser Macbride, Graham Priest, Greg Restall, Barry C. Smith, and Richard Woodward. For comments on an earlier version I am indebted to Hanoch Ben-Yami and Lee Walters. A more general thanks is due to Jonathan Lowe, my first teacher in philosophy: my reconsideration of the standard position on existence was sparked off by some characteristically insightful remarks he made in a conversation some years ago.

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semantic structure, if that is the same thing) of sentences like ‘there are prime numbers’ or ‘prime numbers exist’. This treats formalization as part of a systematic account of the actual workings of natural language, and such attempts should be assessed by their adequacy in accounting for the structure of as much of the way we actually speak as possible. I will call this the ‘descriptive’ approach. The second way of understanding formalizations like this is as a proposed revision of the way we talk, for certain scientific or philosophical purposes. The aim here is not to capture the actual underlying ‘logical form’ or ‘semantic structure’ of the way we speak, but rather to create a more rigorous representation of our theories of the world, by removing ambiguities, unclarities, and misleading idioms. This is the approach championed by Quine (1969). Quine’s aim was not to give a systematic semantics of natural language, but to create a language in which we can express, in as precise a way as possible, our best theory of the world. I will call this the ‘revisionary’ approach. The two approaches to formalization are very different. The descriptive approach is concerned to get as much of our natural language right as possible, and it is evaluated against the considered linguistic judgements (‘intuitions’) of native speakers. The revisionary approach is prepared to disregard these judgements or explain them away, if they are not required to express what we independently believe to be our best theory of the world. My concern here will be with the descriptive approach, and to that extent I will not take issue with Quine’s revisionary project. I will dispute the connection made between verbs of existence and natural language quantifiers, as claims about the meaning or semantic role of these words. My reason for doing this is that there are natural language sentences which seem to be straightforwardly true, but which are incompatible with the standard approach to existence, understood semantically. These are sentences which we use to talk about – and apparently ‘quantify over’ – things that do not exist. I will argue that if we are to give an adequate semantic account of these claims, then we cannot treat ‘some things are F’ and ‘Fs exist’ as equivalent in meaning. The claims which I will focus on are claims like, ‘some things we think about do not exist’ or ‘some characters in the Bible did not exist’ or ‘some characters in War and Peace existed, and some did not’. My interest in these claims derives from the phenomenon of intentionality: the mind’s direction upon its objects. A definitive feature of intentionality is that intentional mental states can concern or be about things that do not exist:

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we can think about characters in fictions and myths, and about things mistakenly supposed to exist, like gods or entities postulated by false scientific theories. Moreover, our language seems to behave in similar ways whether or not the things we are talking about exist. We can use names and other referring expressions to talk about these things, and it seems that we can generalize from these uses and quantify over these things too. Unless we can make clear sense of these intentional phenomena, then we can have no adequate general account of intentionality. Part of making sense of these phenomena, I believe, is a matter of showing how claims like those just quoted are true. The standard semantic approach to existence and quantification does not allow them to be true; so the standard approach must be rejected. Fortunately there are reasons, independent of any particular theory of intentionality, to reject the standard approach. Or so I will argue. My underlying motivation would not move someone like Quine, because he does not think that it is possible to make scientific sense of intentionality or the semantics of attributions of intentionality. In Word and Object, Quine famously talked of the ‘baselessness of intentional idioms and the emptiness of a science of intention’ (Quine 1960: 221). He agrees that we have more or less precise ways of talking about intentionality in ordinary speech, and for practical purposes (in the ‘market place’) we can talk as if there are thoughts, desires, intentions, and so on. But when we are ‘limning the true and ultimate structure of reality’, we will not find intentionality there. So the regimentation of our ordinary talk which is required for formulating our best theory will not need to account for the phenomenon of thought about the non-existent. Our best theory of the world will not need to talk about thoughts, and a fortiori it will not need to talk about thoughts about the non-existent. I reject Quine’s attitude to the mental and to intentionality, and I am sceptical of his conception of what the best theory is. The arguments of this chapter, however, are not addressed to these issues, but to the semantics of our actual talk of existence and quantification. Quineans who look for a revisionary approach will not be moved by the arguments presented below. This chapter is addressed to those who want to make sense of our ordinary claims, and not to those whose concern is with the construction of a new language for expressing the best theory of the world. However, to the extent that someone (like e.g. van Inwagen 2003) thinks that Quine’s view gets something right about natural language quantification, this chapter is addressed to them.

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3.2   T h e probl e m When thinking or talking about, say, characters in the Bible, we might reason as follows. Abraham, Moses, Solomon, and Jesus are all characters in the Bible. We have good reason to think that Solomon and Jesus existed; but less reason to think that Abraham and Moses did. From this we might generalize to the claim I call (S): (S) Some characters in the Bible existed and some did not.

This seems like a straightforward use of quantification (‘some …’) as a device of generalization. Compare this case with the following. We might be thinking about the history of England, and contemplating the ways in which various kings of England met their deaths. Edward II and Richard III died violently; Henry VII and Charles II did not. So we can generalize to the claim I call (K): (K) Some kings of England died violently and some did not.

This claim looks somewhat similar in its syntax to (S). (K) combines a quantified noun phrase with a verb phrase, and the second quantifier ‘some’ is elliptical for ‘some kings of England’. (S) likewise combines a quantified noun phrase with a verb, the only syntactic difference being that in (K) the verb is modified by an adverb and in (S) it isn’t. If we approached these sentences without any knowledge of philosophical and logical history of discussions of existence, then we might say the following. Intuitively, what both these sentences do is to pick out or identify a group of things (characters in the bible, kings of England) and say something about some of them (existing, dying violently) while denying it about the others. But while we might be able to say this about (K), the standard approach will not let us say this about (S). This is because it holds that ‘Some Fs are Gs’ is equivalent to ‘There exist Fs which are Gs.’ So, with the ellipsis spelt out, (S) is equivalent to: (S1) There exist characters in the Bible which exist and there exist characters in the Bible which do not exist.

And the second conjunct of (S1) is a contradiction, assuming that ‘… does not exist’ is equivalent to ‘it’s not the case that … exists’. Given that contradictions are not true, then (S) cannot be true, because it is equivalent to a contradiction. Yet we previously found good reasons to think that (S) is true, since it seemed to be an generalization from some simple truths about characters in the Bible.

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If the standard approach is right, then we cannot think of ‘some Fs’ as picking out a collection of things independently of whether they exist. And so we cannot then go on to predicate existence of some of them but not of others. This is because ‘some’ already introduces, implies or otherwise contains the idea of existence. A defender of the standard view might say that this is the reason that the symbol used to represent ‘some’ in the predicate calculus (‘∃’) is called the existential quantifier. There is another reason why the orthodoxy cannot think of what (S) says in the intuitive way described above. The intuitive description was that a quantified sentence ‘some Fs are Gs’ first picks out the Fs and then predicates G-ness of some of them. On the standard account, this is a perfectly acceptable way of thinking of a sentence like (K), for example. One starts with a domain of quantification, where this is thought of as a domain of objects, real things. Either the domain contains everything, and (K) says that some things in the domain are both kings of England and died violently. Or we restrict the domain to the kings of England, and we identify some objects in the domain as those who died violently. But on both approaches, it is usually assumed that the domain contains only real – and that means existing – things. So (S) cannot be true because its domain of quantification cannot include those characters in the Bible that exist and those that do not exist: no domain can include things that do not exist. This problem  – about real or apparent ‘quantification over nonexistents’ – is, of course, well-known and has received extensive discussion. I am not pretending that I have discovered a new problem. But many responses to the problem have either denied that these sentences are true, or tried to modify the normal logic of quantification. My aim here, by contrast, is to develop a way of understanding sentences like (S) which preserves their intuitive truth-value and keeps the basic ideas of the logic of quantification intact. In what follows I will not, I believe, take issue with any major claim of contemporary logic. Instead, I will argue that we can keep logic pretty much as it is (with a few minor modifications), and yet make sense of the idea that some things do not exist. The truth or falsehood of this claim is not a matter of logic. Rather what I will challenge is the philosophical interpretation of some logical ideas, and how this interpretation has shaped a conception of the meaning of claims like (S) which makes intentionality hard to understand. 3.3  T wo i r r e l e va n t i de a s In order to make progress in understanding (S) and related claims, we need to put to one side two ideas which are often introduced in this context.

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It is sometimes said that the essence of the standard view of existence is that the verb ‘exists’ is not a ‘logical’ predicate, or not a ‘first-level’ ­predicate.1 It is also said that the essence of the standard view is that there is no conceptual or ontological distinction between being and existence, implying that anyone who rejects the standard view has to accept such a distinction between being and existence. It turns out that neither of these ideas is central to the standard view as I conceive of it – i.e. to the view that makes sentences like (S) contradictory. What is central to this view is the connection between existence and certain kinds of quantification (the quantification we express in the vernacular with ‘some’). But one can accept this connection while also accepting that ‘exists’ functions as a first-level predicate. So it cannot be essential to the standard view that ‘exists’ is not a first-level predicate. Likewise, as I shall explain below, one can accept the standard view and still hold some kind of distinction between being and existence. Or one can deny the standard view and hold that there is no interesting such distinction. I will take these two ideas – ‘exists’ as a predicate, and the distinction between being and existence – in turn. A vast amount has been written about this thesis that ‘exists’ does not function logically as a first-level predicate (and about its historical origins) – too much than can be reasonably surveyed here. What I will do is explain briefly why this thesis is independent of the standard view. Firstlevel predicates are defined by Dummett as ‘incomplete expressions which result from a sentence by the removal of one or more occurrences of a single “proper name” [i.e. referring expression]’ (Dummett 1981: 37–8). If this is all it takes for a predicate to be first-level, then ‘exists’ is a firstlevel predicate. We can construct the predicate ‘x exists’ from the sentence ‘Vladimir exists’ by removing the name ‘Vladimir’ and replacing it with the free variable ‘x’ to mark its incompleteness. Furthermore, this way of representing the form of this sentence makes it clear how we can also represent, in a simple way, the form of sentences like ‘everything exists’ and ‘something exists’ (see Mackie 1976). Those who think that ‘exists’ is not really a first-level predicate treat this fact as superficial and as misleading as to the real logical structure of the sentence ‘Vladimir exists.’ I need not rehearse their reasons here, which are well-known.2 The point I want to make here is only that it is 1 Of course, when I say general things about the meaning of the English word ‘exists’ I mean this to apply to its cognates in other languages. 2 But see Wiggins (1995) for a spirited defence of this position.

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not essential to what I am calling the standard view that it accept this view about the logical role of ‘exists’. The essence of the standard view is that a use of a quantified sentence of the form ‘some Fs are G’ expresses a belief in the existence of Fs. If you think ‘exists’ is not a first-level predicate you will probably take ‘some Fs exist’ to be of the form ‘(∃x)(Fx)’. But the fact that your use of ‘some’ commits you to the existence of the things you are quantifying over does not prevent you from treating ‘exists’ as one-place predicate, if you have other reasons to treat it in this way. If you did this, you would treat ‘some Fs exist’ as having the form ‘(∃x)(Fx & Ex)’ where ‘Ex’ is your first-level existence predicate. This is in effect the view taken by Gareth Evans, who argues that there are linguistic reasons for treating ‘exists’ as a first-level predicate (Evans 1982: 346–7; he appeals also to Mackie (1976) in defence of this view). But in arguing for this, Evans does not depart from the standard view, since he thinks that the sense of the first-level existence predicate E ‘is precisely fixed by saying that it is true of everything’ (1982: 348). He adds that the sense of ‘E’ is ‘shown’ by the formula: ‘(x)(x satisfies ‘E’)’. Since this formula is equivalent to ‘¬(∃x)¬(x satisfies ‘E’)’ it is clear that the standard connection between existence and quantification is maintained on Evans’s view. If ‘E’ is true of everything, then it cannot be that some things do not exist. I think Evans, Mackie, and others are right that we should treat ‘exists’ as a first-level predicate, and that there are no overwhelming logical or semantic objections to such a thesis. But my aim here is not to argue for this thesis, but to emphasize that the thesis does not suffice to refute the standard view, since it is perfectly compatible with the standard view. The standard view is about the relationship between existence and quantification, not about the logical form of ‘exists’. The second irrelevant idea I need to discuss is that there is no significant (non-verbal) distinction between being and existence, and that this is the essence of the standard view. The idea is this: those who say ‘there are things that do not exist’ are distinguishing between what there is and what exists. So they are distinguishing between being and existence. But once we recognize that the distinction between being and existence is merely verbal, then we will see why, properly understood, a sentence like (S) is genuinely contradictory: for either it implies that there are things which there are not, or that there exist things which do not exist. This line of thought is derived from Quine (1948), and the idea that there is no non-verbal difference between being and existence is described

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by Peter van Inwagen as ‘the essence of Quine’s philosophy of being and existence’ (2008: 37). But it seems to me that the distinction between being and existence is largely irrelevant to the question posed by (S). Someone who rejects the standard view of quantification and existence can agree with the Quinean that there is no interesting distinction between being and existence. To see why this is so, we need to look a little more closely at what the distinction is supposed to be. The Quinean critic no doubt has in mind the view expressed in this famous passage from Russell’s The Principles of Mathematics: There is only one kind of being, namely being simpliciter, and only one kind of existence, namely, existence simpliciter. Being is that which belongs to every conceivable term, to every possible object of thought … Numbers, the Homeric gods, relations, chimeras, and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them … For what does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent. (1903b: §427)

Russell here distinguishes between being and existence and says that things that do not exist nonetheless have being. To apply Russell’s idea to our problem: since every object of thought has being, so all biblical characters have being, even if not all of them exist. Since being and existence are so different, there is no contradiction in saying that there are some biblical characters which do not exist: the things that there are (those that have being) are one thing, and the things that exist quite another. Elsewhere Russell (1959: 64) attributed this view to Meinong. But in fact, Meinong’s view was quite different from Russell’s 1903 view. Meinong (1904) did draw a distinction between being and existence, and held that only spatiotemporal things exist. Non-spatiotemporal things – like numbers, propositions (‘objectives’ in Meinong’s terminology) – do not exist. Rather, they have a different mode of being, which Meinong called subsistence. But in addition to these entities, there are also things that have no being at all, neither existence nor subsistence. These are the objects of thought which are ‘beyond being’ (Meinong 1904; see also Priest 2005). So Meinong’s view is not Russell’s 1903 view. Meinong’s view that not everything we think about (not every object of thought) has being is surely more plausible than Russell’s.3 Of the many things that can be said about the concept of being, one obvious 3 As Russell later acknowledged, apparently without recognizing that he was agreeing with Meinong here: see Russell 1919: 169–70.

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connection is with the idea of reality: what has being is what is real, it is an inhabitant or part of reality. Not everything we think about is part of reality, despite what Russell says: the Homeric gods are not. Neither are non-existent biblical characters. Not only do they not exist, but they also have no reality, they are not beings. Whatever we want to say about the vexed questions of being, this at least seems obvious. So we should reject Russell’s 1903 view. If we can think about things that have no being at all, then the problem posed by (S) remains. Distinguishing between being and existence does not help in solving the problem posed by (S). On this the Quineans are right. But rejecting the distinction in the way just indicated does not make the problem disappear either. For the problem arose because (S) seemed to be a straightforward generalization from ‘Abraham did not exist, Jesus did’ etc. And yet (S) expresses a contradiction. Insisting that there is no distinction between being and existence does not show us how to avoid this contradiction. The distinction (S) makes between things that exist and things that do not should not be expressed in terms of the distinction between being and existence. But this does not mean that there is no interesting distinction that can be made between being and existence – it’s just that this distinction is not relevant to our problem. However, since the distinction is often appealed to in discussions of non-existence, it is worth getting clear what might be at issue here. Meinong’s distinction is intended to express the idea that there are different kinds of ways or modes of being. Although contemporary philosophers occasionally ridicule the idea that there are different modes of being  – associating it with rejected ideas like ‘degrees of reality’  – the phrase has a perfectly unexceptional reading, and the idea it expresses should be accepted by everybody. Some of those who believe in events, for example, consider them to be entities which are temporally extended over time, and which have temporal parts. This is the mode of being of events, as opposed to the mode of being of material objects, which have no temporal parts. Those who reject this kind of distinction – e.g. fourdimensionalists about objects – can say that events and objects have the same mode of being. But they can still say that four-dimensional entities have a different mode of being from abstract entities (if they believe in such things). At least with regard to the distinction between being and existence, then, Meinong’s view is only terminologically different from the Quinean

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view. For the Quinean can distinguish between concrete and abstract objects, just as the Meinongian can distinguish between existing and subsisting objects. Each of them will agree that there are such objects, but the Quinean will say that the abstract objects exist as much as the concrete ones do. The Quinean and the Meinongian can agree about what has being, they just disagree about how to use the word ‘exist’. There should, therefore, be no dispute between the Quinean and the Meinongian about whether there are different modes or kinds of being. The only dispute is whether different modes of being are described in terms of (say) the contrast between existence and subsistence, or in some other way. And this might indeed be a verbal dispute. The real point of disagreement between the Quinean and the Meinongian is over whether there are some objects with no being whatsoever, or whether it is true that some objects have no being whatsoever. In order to say what this means, and what this disagreement amounts to, we need to understand what quantifiers like ‘some’ mean. I will turn to this in the next section. But before leaving the topic of being and existence, I need to make two final points. First, a possible reason for thinking that ‘there are things that do not exist’ introduces a distinction between being and existence is that the expression ‘there is’ contains the third-person present tense form of the English verb ‘to be’. But we should not move too quickly here. The mere presence of this verb is not in itself a sign that we are talking about being. (Consider: ‘there are things that have no being’ is not an obvious formal contradiction.) As is well-known, the verb ‘to be’ has many uses which have no simple connection to being. The English verb is used to express the copula too, and there is no inference from this use to predications of being or existence. The fact that the word ‘is’ occurs in ‘Pegasus is a mythological horse’ implies nothing, of course, about whether Pegasus has being. Second, it is sometimes said (e.g. by van Inwagen 2003) that ‘there are things which do not exist’ involves two quantifiers: a committing one (associated with existence) and a non-committing one (associated with being). I will not discuss this view in detail, for two reasons. The first is that it is implausible to regard claims about what has being to be ‘noncommitting’. If you really want a non-committing quantifier – and I shall argue below that our quantifiers are non-committing  – then it should commit us neither to the existence nor to the being of something. The second reason is that ‘there is’ is not, on the face of it, a natural language

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quantifier phrase. So we need good reasons for seeing it as ‘really’ a quantifier. So this just raises the question, to which I now turn: what is a quantifier? 3. 4  Qua n t i f ic at ion i n n at u r a l l a nguag e The general answer is that a quantifier is a term which specifies the quantity of things being talked about. Philosophers are most familiar with the quantifiers ‘some’ and ‘all’ and their treatment in predicate logic. These quantifiers are normally called the existential and the universal quantifiers, and symbolized by ‘∃’ and ‘∀’ respectively. But natural languages contain many other ways of quantifying: that is, of specifying the quantity of things being talked about. As well as ‘some’ and ‘all’, we have ‘few’, ‘most’, ‘many’, ‘at least one’, and so on. Syntactically, these expressions are determiners: expressions that combine with a noun to create a noun phrase. Noun phrases created by quantifiers and nouns (possibly modified by adjectives) are known as quantified noun phrases. Thus ‘some’ combines with ‘pigs’ to make the quantified noun phrase ‘some pigs’. Quantified noun phrases combine with verb phrases to make sentences; so ‘some pigs’ combines with ‘swim’ to create the sentence ‘some pigs swim’.4 In Frege’s logic, quantifiers are treated as second-level function­expressions (‘concept-words’). They take first-level function-expressions (such as those we these days might represent as ‘Pig(x)’) as arguments and yield truth or falsehood as values. Frege treated the quantifiers as unary: that is, they can create a sentence by taking one first-level functionexpression as argument. For example, the formula ‘∀x(Pig(x))’ says that everything is a pig. On the Fregean understanding, this formula says that the concept ‘Pig(x)’ yields the value true for all objects in the domain. Thus quantifiers are unary function-expressions which combine with one open sentence to make a closed sentence. On Frege’s logical analysis, ‘some pigs’ is not a syntactic constituent of the logical form of the sentence ‘some pigs swim’. Rather, ‘some’ is a variable binding operator and the logical role of ‘pigs’ is as a unary first-level function-expression (or open sentence). This contrasts with the apparent syntax of ‘some pigs’ in English (and other languages: see BenYami 2009). The English sentence ‘Some pigs swim’ seems to combine 4 For authoritative accounts of natural language quantification and their relations to logic, see Westerståhl (2007), Peters and Westerståhl (2006).

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the determiner ‘some’ with two expressions (‘pigs’ and ‘swim’) to create a sentence. But the determiner ‘some’ cannot combine with ‘pigs’ to make a sentence, unlike the way the quantifier ‘∃x’ and ‘pig(x)’ can make the sentence ‘∃x(pig(x)).’ So as far as apparent natural language syntax is concerned, quantifiers are binary: they combine with two expressions (either verb phrases, noun phrases or adjectives) to make a sentence. Frege’s (1879) view was that apparently binary quantifiers could be defined in terms of unary quantifiers plus sentential connectives. Thus ‘some pigs swim’ has the form ‘∃x(pig(x) & swims(x)).’ The sentence says that some things in the domain of quantification are pigs that swim. (More precisely, the first-level concept-word ‘pig(x)’ yields the value true for some objects in the domain and the first-level concept-word ‘swims(x)’ also yields the value true for those objects.) This was for many decades the standard approach to the syntax and semantics of quantifiers, and this is still the way that students of logic are taught the syntax and semantics of the two quantifiers of elementary first-order logic. But it has been widely recognized for some time that not all natural language quantifiers can be represented by unary quantifiers and connectives.5 ‘Most pigs swim’, for example, cannot be represented by saying that most things in the domain are such that they are pigs and they swim; nor by saying that most things in the domain are such that if they are pigs they swim. The former is obviously not what is meant by ‘most pigs swim’, and the latter is rendered true by the fact that since most things in the world are not pigs, then most things are such that if they are pigs they swim. But if the original claim is true, then surely it is not true because of this! ‘Most’ does not have a formalization in classical first-order logic.6 The objection here is not to Frege’s view of quantifiers as second-level function-expressions as such. We can preserve this view yet say that the quantifiers are binary: the semantic value of a quantifier is a function from a pair of first-level function-expressions to truth-values (Evans 1982: 58). But treating quantifiers as binary does bring them closer to surface syntax than Frege’s analysis does. For example, we can represent ‘some pigs swim’ as ‘[some x: pigs x](swim x)’ where the material in the square brackets corresponds to the quantified noun phrase ‘some pigs,’ and ‘swim(x)’ corresponds to the verb phrase. The quantifiers are still treated 5 For an authoritative account, see Barwise and Cooper (1981); the idea of generalized quantifiers appealed to there derives from the work of Mostowski and Lindström. 6 This point is usually credited to Rescher (1962). For more details, see Wiggins (1980) and Neale (1990).

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as binding variables, and we can still treat the semantic value of the quantifier as a second-level function-expression which takes first-level function expressions (‘pig(x)’ and ‘swim(x)’) as arguments.7 But the formalization preserves the syntactic unity of ‘some pigs’ and other quantified noun phrases, and therefore facilitates a unified semantic and syntactic account of all natural language quantifiers. What is appealing about this approach is that it gives a lucid representation of the idea that whether or not ‘some pigs swim’ depends on how things are with the pigs in the domain. For this reason, many treat natural language quantifiers as restricted quantifiers: the role of quantified noun phrase is to pick out some things from the domain of pigs, and the role of the second open sentence is to predicate something of them. Assuming the intelligibility of an existence predicate, ‘some biblical characters exist’ can be represented as: ‘[some x: biblical character x](exist x).’ And on the face of it, its semantics can be understood in the same way as that of ‘some pigs swim’. The quantified noun phrase identifies some things in the domain of biblical characters and the second open sentence predicates existence of them. We can also identify some biblical characters in the domain and predicate non-existence of them. It is natural, and orthodox, to think of quantifiers as describing a relationship between two sets. So in this case, the set of existing things will intersect with the set of biblical characters: the set of existing biblical characters is a subset of the set of biblical characters. What is wrong with taking this simple face-value view? The immediate objection is that existence is implied as soon as we start talking about domains of quantification. When evaluating a quantified sentence for truth or falsehood, we assume a domain of quantification, where this is normally understood as a set of entities (but see Stanley and Szabó 2000: 252). The members of the domain must be entities. For if they were not entities, we cannot make sense of the semantics of quantification. So we cannot say that there are non-existent objects in the domain of quantification. I do not think that non-existent biblical characters are entities of any sort, for the reasons given above (see Section 3.3). So in order to justify my face-value interpretation of (S) I have to say something else about This is not say that we have to construe the semantics in Frege’s way; the more usual approach is to treat the semantic values of the quantifiers as sets of subsets: see Westerståhl (2007). For an exceptionally lucid introduction to the issues here, see Neale (1990). 7

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domains of quantification. This will be my central point of disagreement with the standard view. 3.5  D om a i ns of qua n t i f ic at ion a n d u n i v e r s e s of di s c ou r s e To understand what is going on here, we have to return to the phenomena we started with: our ordinary talk about the world. I am assuming as an undeniable fact that our ordinary talk about the world contains terms which refer, and terms which do not. Some names do not refer (‘Pegasus’) and some predicates neither refer nor are true of anything (‘x is phlogiston’). If we are to obtain a satisfactory account of our language as it actually is, we have to accommodate these facts. We can talk about all these things and we can think about them. So just as we can use the term ‘object of thought’ to refer to anything we can think about (whether or not it exists) we can also use the term ‘object of discourse’ to refer to anything we can talk about (whether or not it exists). ‘Object’ here does not mean entity, any more than ‘object of thought’ means ‘entity of thought’ (see Crane 2001). Just as we can use referring terms or predicates in similar ways whether or not they refer to anything, so we can generalize about objects of discourse whether or not they exist. Quantifying is generalizing: it is talking about a quantity of things and predicating things of them. A domain of quantification contains all the things which are relevant to evaluating the quantified claim. Sometimes we quantify unrestrictedly, as when we want to talk about absolutely everything. But, as noted above, it is more usual in ordinary discourse to assume some restriction on the domain of quantification (see Stanley and Szabó 2000). In a traditional terminology, the domain of quantification was called the universe of discourse. This term gives a hint as to how we should understand quantification if we are going to make literal sense of sentences like (S). The universe of discourse contains all the items we assume or stipulate to be relevant to our discourse. An item here is simply something which can be thought or spoken about: an object of thought or discourse, in the sense I introduced above. The domain of quantification consists of just those objects of thought relevant to the truth or falsehood of the quantified claim. Objects of thought are not, as such, entities. An object of thought is just anything which is thought about, in the most general sense of that term. Some objects of thought exist, and some do not. But to say this is

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not to assume that there is an ontological or quasi-ontological category of ‘objects of thought’ to which all these things belong. When an object of thought exists – for example, when I think about the planet Neptune – then the object of thought simply is the thing itself (Neptune itself). When the object of thought does not exist, it is nothing at all (cf. Husserl 1900–01: 99). I am assuming that quantifying over things is a way of talking about them, in an intuitive sense. It is true, as Frege famously pointed out (1884: 60), that one can quantify over some entities without being able to think or talk about them individually. Thus one can say that all men are mortal without being able to judge of each man individually that he is mortal – since no-one is capable of forming a judgement about each man individually. There are men about whom we know nothing. But this does not stop my thought being about – in a perfectly ordinary sense – all men. So we can quantify over all the things we are talking about, and this is a way of talking about them too. All the things we are talking about are all the things we are thinking about: we can quantify over objects of thought. It might be objected, however, that thinking of the members of a domain of quantification as objects of thought gives rise to paradox. An object of thought is just something thought about. But surely we can quantify over things that have never been thought about: for example, we can say ‘some things have never been thought about’. This surely must be true. But if so, how can the domain of quantification consist of objects of thought?8 This apparent paradox is avoidable, so long as we state our thesis clearly enough. I am using the idea of what is ‘talked about’ and ‘thought about’ in a very general way, to apply to any thing that is what we might call the subject-matter of thought or discourse. So, in particular, I do not understand such ‘aboutness’ in the sense of reference. Reference – the relation in which singular terms stand to objects, or plural terms stand to pluralities of objects – is one way in which words can be about things, but it is only one way. Predication, too, is a way in which words can be about things. When I say that some pigs swim what I am saying is about swimming just as much as it is about pigs. ‘All men are mortal’ is about mortality as much as it is about all men. But it is perfectly natural to think of the sentence as being about all men too, in this very general sense of ‘about’. So I can use a quantified noun phrase to ‘talk about’ things, even if those things cannot be talked about in other ways. It might seem

  I am indebted here to discussions with Makoto Suzuki and Stephan Leuenberger.

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paradoxical to say ‘some things have never been talked about’, but if we agree that quantified noun phrases are ways of talking about things, then we should understand this as conveying the following: some things have never been talked about except by being talked about in this way. This is comparable to what one should say to Berkeley when he says that one cannot conceive of an unconceived tree. Of course, by conceiving of a tree as unconceived, what one means is that it is not conceived in any way other than in this act. If there is a paradox here, it is not one which is specific to the view of quantification defended here. A related clarification is needed about the idea of aboutness. When I say that ‘all men are mortal’ is a way of talking about all men, I do not mean that there is some peculiar thing ‘all men’ which is the ‘logical subject’ of this sentence, any more than ‘no men’ is the peculiar logical subject of ‘no men are immortal’. ‘All men’, I claim, is a quantified noun phrase and in a perfectly ordinary sense is the syntactic subject of the sentence. This is expressed clearly in the binary quantifier notation ‘[all x: men(x)] (mortal(x))’. It is consistent with this to define the truth-conditions of this sentence in (e.g.) Russell’s way, where one does not employ anything like ‘all men’ as a ‘logical subject’. I am not questioning the conventional wisdom about logical subjects. All I want to insist on is that ‘all men are mortal’ is about all men. What a sentence is about is not the same as the logical subject of the sentence. What does it mean, then, to quantify over non-existent objects? It is to have non-existent objects of thought in the universe of discourse, where a universe of discourse is a specific generalization of the idea of an object of thought: viz. all the things relevant to what we are talking about. So to have an object of thought in the universe of discourse is to have it among the things relevant to what we are talking about. These things can be ‘values’ of the variables bound by the quantifiers, just in the sense that things can be true or false of these objects of thought. So, when evaluating ‘some biblical characters did not exist’ we look for something in the domain (biblical characters) of which we can predicate non-existence. And lo! We find one: Abraham. Abraham is, then, a value of the variable.9 I suspect that to many philosophers, this way of thinking of a domain of quantification will seem either obscure or unexplanatory. But when we look at the ways in which philosophers typically use the idioms of quantification, when they are not explicitly talking about ontology, we find that I am therefore committed to the idea that there can be true simple predications of non-existent objects. I plan to say more about this in future work. 9

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they are very relaxed about quantifying over entities in whose existence they do not believe, and that their actual way of talking conforms very nicely to what I have just said. One case is when philosophers talk of possible worlds to illuminate other important concepts, like the concept of representation. Here is an especially lucid example from Frank Jackson: A sentence represents by making a partition in the space of possible worlds, a partition in logical space. For such a sentence, S, there is a function from S to a set of possible worlds. Each world in that set is a complete way things might be consistent with how the sentence represents things to be. Each world in this set is a complete way things might be in the sense that every ‘i’ is dotted, every ‘t’ is crossed. In understanding S, we are able, in principle, to know which worlds are in this set and which are not. To know that some given world w is in the set, we don’t, however, have to be able to discriminate w from any other world in thought (which is anyway impossible, for there are infinitely many possible worlds, whereas we are finite beings). Typically we know that w is in the set in the sense that we know that any world that is thus and so is in the set, where indefinitely many worlds fall under ‘thus and so,’ and we know that w is thus and so. (Jackson 2010: 45; my emphasis)

The italicized phrases are the quantified noun phrases which make reference to possible worlds. So Jackson is perfectly happy to quantify over possible worlds. Yet Jackson does not believe that possible worlds exist, and so he cannot believe that the domain of quantification really is a set of existing possible worlds. It will be replied that Jackson will adopt some reductionist analysis of possible worlds, of the kind David Lewis called ‘ersatzist’. One such analysis is to treat worlds as ‘recombinations’ of actual properties and objects (Armstrong 1989). Another is to treat ‘worlds’ as maximally consistent sets of sentences or propositions (Stalnaker 1984). But each of these approaches must appeal to representation in explaining what talk of worlds really is. This is especially obvious in the case of propositions, which are representations, if anything is. It is slightly less obvious in the case of ‘combinatorial’ theories: but one only needs to reflect on the fact that on these theories, nothing is actually recombined, and everything is actual. So what is really going on is that combinations of actual things are represented (maybe by being an abstract object). Quantifying over possible worlds, on these ersatzist views, either assumes a domain of propositions or a domain of representations of re-combined actual entities.

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The approach defended in the present chapter assumes the idea of representation too, by assuming the idea of an object of thought. An object of thought is anything which can be thought about, in the broadest sense of ‘object’ and ‘thought about’. Thinking about is a form of representation. So I am assuming the idea of representation in explaining the idea of a domain of quantification. This is one way to describe my departure from the standard view: for many who hold the standard view want to explain representation in terms of an antecedent conception of domains of quantification, and relations defined on these domains. However, if what I have argued above is right, many ersatzists about modality are also thinking in my way: they explain quantification over possibilities ultimately in terms of representation. This does not invalidate their talk of sets of possible worlds or quantification over worlds; on the contrary, for any actualist, it makes good sense of it. The use by actualists of quantification over possible worlds as an example of how natural it is to use quantifiers to talk about things even if one is not assuming a domain of existing objects. Whether it is acceptable to take the notion of representation as fundamental or basic in this way, is a question for another occasion. 3.6  E x i s t e n t i a l s e n t e nc e s: ‘t h e r e’ Having said how I think we should understand, in the most general terms, natural language quantification, I now need to say something about the relationship between the relevant natural language quantifiers and the English verb phrases ‘there is’/‘there are’. What I have to say here is somewhat provisional, but I believe it is on the right lines. Philosophers are used to explaining the symbol ‘∃’ variously as ‘some’ and ‘there is’. This is entirely natural, for (pace Ben-Yami 2004) ‘some F is G’ is equivalent to ‘there is an F which is G’. But ‘there is’ can also be used to express belief in the existence of something (‘there is a God!’ is, after all, a way of saying ‘God exists!’). If this is so, then how can I separate ‘some F is G’ from ‘an F which is G exists’ in the way I have tried to? Syntactically speaking, ‘there is’ is not a quantifier. ‘There’ functions as what linguists call an expletive – a word that fills a syntactic gap but has no semantic function – and ‘is’ is the third-person singular present tense form of the verb to be. Linguists call sentences beginning ‘there is …’ existential sentences (see McNally in press; Moro 2007; Sawyer 1973). This title, and the occurrence of the verb to be in these sentences

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might suggest that the function of these sentences is purely to say that something exists (or is, or has being). If this were so, then my attempts to say that ‘Some biblical characters did not exist’ is not contradictory are doomed from the outset! For ‘Some biblical characters did not exist’ entails ‘there are biblical characters who did not exist’ and this is an ‘existential sentence’. And if the function of existential sentences is to say that something exists, then my sentence is close to an explicit contradiction. In fact, matters are not quite that simple. Existential sentences in some other languages use verbs other than the equivalent of the verb to be: German existentials begin Es gibt … and French Il y a … Since these languages do not reach for the cognate of to be when expressing what in English we express with ‘there is’ constructions, we should not rush to assume any deep semantic or metaphysical connection with the idea of being. And in any case, as noted above (Section 3.3), the presence of the verb to be in English is not always an indicator of ‘being’ in an ontological sense. As for the fact that these sentences are called ‘existential’, this is of little significance. Although some analyses of the semantic structure of existentials introduce an ‘exists’ predicate into the underlying structure (Barwise and Cooper 1981), other theorists are more circumspect. In a recent survey, Louise McNally expresses doubts as to ‘whether a uniform semantics and discourse function can be given for everything that looks formally like an existential sentence, or whether in reality there are several subtypes of existential sentence, perhaps with distinct semantics and pragmatics’ (McNally in press, Section 1.2). Indeed, when looking for a general mark of existential sentences, the one thing which seems to emerge is not directly connected to the idea of existence: Although it is unlikely that one single semantics and discourse function can be assigned to existential sentences cross-linguistically, certain semantic and discourse functional properties are consistently associated with these sentences across languages. Perhaps the most important of these is the intuition that existential sentences serve primarily to introduce a novel referent into the discourse  – one fitting the description provided by the pivot nominal. (McNally in press, section 1.2; my emphasis)

‘Introducing a novel referent (or referents) into the discourse’ is a good description of what happens when you say ‘There were some Kings of England who died violent deaths’ or ‘There are some characters in the Bible who did not exist.’ And a related idea which has had some currency

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in the literature on existential sentences is that ‘there’ in many of these sentences serves to introduce new information as the ‘theme’ of a discourse (see Allan 1971: 6–7). 10 One terminological clarification: I would rather say ‘object of thought/ object of discourse/object of discussion’ than ‘referent’, since in my terminology a referent must exist (this is a stipulation, but one which follows the usual philosophers’ practice of calling names like ‘Pegasus’ non-­referring). Some linguists would use the term ‘discourse referent’  – a term that derives from Discourse Representation Theory: see Geurts and Beaver (2007). A discourse referent in their sense is just an object of discourse in my sense.11 But apart from this terminological difference, McNally’s description of one central role of the existential ‘there is …’ is perfectly consistent with the account of quantification given here. The subject requires a detailed treatment, of course; there are many kinds of existential sentences and certainly some of them (‘There is a God!’) should be understood as attributing existence. For present purposes my aim is only to show that the non-contradictoriness of ‘Some biblical characters did not exist’ is not undermined by the fact that it entails ‘There are biblical characters which did not exist.’ 3.7  C onc lus ion: l o g ic a n d on t ol o g y In this chapter I have been talking about how to understand quantifiers in natural language, and the thoughts expressed by using these words. In particular, I have been talking about the meaning of ‘some’ and how its semantics should be understood, and how the semantics of quantification relate to predications of existence. The standard view was stated in Section 3.1; the problem that intentionality poses for this view was given in Section 3.2. In Section 3.3 I 10 In a textbook account of English grammar, David Crystal writes ‘What the “there” construction does is highlight a clause as a whole, presenting it to the listener or reader as if everything in it is a new piece of information. It gives the entire clause a fresh status. In this respect, existential sentences are very different from the other ways of varying information structure, which focus on individual elements inside a clause’ (Crystal 2004: 354). 11 According to Geurts and Beaver (2007: section 3.1), ‘A discourse representation structure (DRS) is a mental representation built up by the hearer as the discourse unfolds. A DRS consists of two parts: a universe of so-called “discourse referents”, which represent the objects under discussion, and a set of DRS-conditions which encode the information that has accumulated on these discourse referents.’ The emphasis is mine: but I do not think it is accidental that the universe of discourse referents represent the objects discussed; this is the same idea as my claim that a universe of discourse is a representation of all those things relevant to what is talked about.

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distinguished this problem from problems about whether ‘existence is a predicate’ and about whether there is a distinction between being and existence. In Section 3.4 I described what seems to me the current state of play about quantification, and in Section 3.5 I argued that representation of the non-existent should not give us reason to change the standard way of understanding the semantics of quantifiers. What we need to change is the conception of what a domain is: a domain should be thought of as a universe of discourse, a collection of objects of thought. However, I argued that my way of understanding domains is not as unfamiliar to philosophers as it might at first seem, given their unreflective appeal to quantification over such non-entities as possible worlds. Finally in Section 3.6 I sketched how this interpretation should fit with an understanding of so-called ‘existential’ sentences. So the question remains: how should we represent ‘some’ and ‘exists’ in a formal language? If we want to account for our initial data (e.g. sentences like (S)), we have a choice. We could translate ‘some’ as ‘∃’ in the usual way. But in this case, we should not understand ‘∃’ as ‘there exists’; we should express existence in another way. Or we could translate ‘there exists’ using ‘∃’, in accordance with Quine’s claim that ‘existence is what the existential quantifier expresses’ (1969: 166). But in this case, we should not understand ‘∃’ as ‘some’; we need another quantifier symbol for ‘some’. Which should we choose? Unlike words in a natural language, the meanings of symbols like ‘∃’ are not something for us to discover, but something for us to decide. As long as we make it explicit the semantic distinction between ‘exists’/‘there exists’ and ‘some’, and have enough symbols for the distinct notions, it is not a substantial matter what meaning we give to the symbol ‘∃’. Of course, these considerations will not move those who adopt the revisionary approach described in Section 4.1. On the Quinean revisionary view, no distinction is made between quantification and existence, because the machinery of quantification is the best way of representing the ontological commitment of a theory. The ontological commitments of a theory, according to Quine, are the objects that are the values of the theory’s bound variables if the theory is to be true: ‘to be is to be the value of a variable’ (Quine 1939: 708). What I have said in this chapter does not directly challenge the revisionary view. But it does challenge it indirectly. What I have argued here is that if we aim to give a systematic account of our actual thought and

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language, then we have to make room for quantification over the nonexistent. So if this is our aim, then we cannot accept that to be is to be the value of a variable. How we should think about ontological commitment, then, remains an open question.

ch apter 4

Identity, quantification, and number Eric T. Olson

4 .1  T h e qua n t i f ic at ion a n d i de n t i t y pr i nc i pl e s When I was a student I was taught that there were intimate connections between identity, quantification, and number. First quantification and number. I was taught that for there to be something – anything at all – is for there to be at least one such thing. For there to be an F, or for there to be Fs, or for something to be F, is for there to be at least one thing or entity that is F. (I don’t mean anything special by ‘thing’. Everything is a thing – ‘thing’ is for me just a completely general count noun.) We might put this by saying that for any kind to be instantiated is for there to be at least one thing that instantiates it. But the claim is not meant to require the existence of kinds or other universals. Nor is it meant to allow the possibility of nonkinds that could be instantiated without being instantiated by at least one thing. (Being red might be a nonkind.) So it might be better to appeal to a schema: Something is F if and only if at least one thing is F.

The claim is that every possible instance of this schema is true. Call this the quantification principle. As for identity and number, I was taught that for this and that to be identical is for them to be one, and that for them to be distinct or nonidentical is for them to be two: x=y if and only if x and y are one. x≠y if and only if x and y are two.

It is because of this connection between identity and number, my teachers said, that we call the relation here expressed by the ‘=’ sign ‘numerical identity’. And I appeal to these principles in explaining to my own students the difference between numerical and qualitative identity. I don’t know of any other way of explaining it. Call them the identity principles. 66

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Exactly how these three principles relate is a nice question, but they show definite affinities. The two identity principles look inseparable. If being identical is being one, it’s hard to see how being non-identical could be anything other than being two. And if being non-identical is being two, how could being identical not amount to being one? If identity implies anything at all about number, both principles must be true. There are also connections between the quantification and identity principles, though they are less neat. Suppose this thing and that thing were identical and yet not one, falsifying the first identity principle left to right. Then presumably this thing would not be one on its own. So there would be something identical to that thing without there being one such thing. Nor would there be more than one of them. It follows that there would be something identical to that thing, yet not at least one such thing, contrary to the quantification principle. So the quantification principle appears to entail the first identity principle left to right. We can almost derive the left-to-right component of the second identity principle from the quantification principle. Suppose something is F here and something is F there. By the quantification principle it follows that we have at least one F thing here and at least one there. Now suppose further that one of the F things here is distinct from one of the F things there. So we have at least one F thing and we have at least one other F thing non-identical to it. Does it not follow by simple addition that there are at least two F things? To put it the other way round: suppose this and that were non-identical yet not two, so that the second identity principle were false left to right. Then it could not be that there is at least one such thing as this and at least one such thing as that. Yet there would be such a thing as this and such a thing as that. Hence, there would be something without there being at least one such thing. Or again, suppose there is something, x, that is F. Given that everything is self-identical, x = x. Then by the first identity principle x and x are one. Does it not follow that at least one thing is F? So the first identity principle provides an argument for the left-to-right component of the quantification principle. (And its right-to-left component is, to my knowledge, wholly uncontroversial: if at least one thing is F, then something is F.) 4 .2  T h e u nc ou n ta bi l i t y t h e s i s Because I was taught these principles at an impressionable age, perhaps, they seem true to me. Indeed, they sound like platitudes. But some

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philosophers think I was taught wrongly. Geach and Dummett, for example, say there are things that we cannot even begin to count. And if we cannot even begin to count them, we cannot say that there is at least one, contrary to the quantification principle (Geach 1980: 63; Dummett 1981: 547). Henry Laycock says things that at least appear inconsistent with both the quantification principle and the second identity principle.1 But their most outspoken opponent is E. J. Lowe, who explicitly denies all three. To say that there is something of a certain sort, Lowe claims, is not by itself to say or imply anything about how many there are – not even that there is at least one; so the quantification principle is false. Further, things can be identical without being one, and distinct without being two. Identity and non-identity, by themselves, imply nothing about number. Lowe puts this by saying that things might have ‘determinate identity but not determinate countability’ (Lowe 1998: 72). In fact Lowe claims that the identity principles hold neither left to right nor right to left: this and that might be one without being identical (or at least without being definitely identical), or two without being (definitely) non-identical. Number need not imply anything (or at least anything definite) about identity or non-identity: in Lowe’s terms, things might have ‘determinate countability but not determinate identity’ (1998: 62). I won’t discuss this claim here, and will consider only the left-to-right components of the principles. How could there be something without there being at least one such thing? And how could things be identical without being one, or distinct without being two? It looks as if the answer can only be that some things simply do not admit of number. The concept of number, or of how many, does not apply to them. They are, in the strongest possible sense, uncountable. The claim is not that some things are uncountable in the sense that there are too many to count. If we try to count the real numbers, for instance, by assigning one of the counting numbers 1, 2, 3, … to each of them, we find that when all the counting numbers have been used up there are still real numbers left over. But even though we cannot count them all, we can count any finite subset of them. We can at least begin 1 He denies that ‘if and when we speak of this F, that F or the other F, we speak in each and every case of just one F’ (1975: 416), which seems to amount to rejecting the quantification principle. And this passage sounds like a rejection of the second identity principle: ‘There is no natural way of thinking of the water in two distinct bottles as two distinct things and thus no way of thinking of the water in one bottle as one distinct thing’ (1972: 31).

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counting them. In fact we can say exactly how many real numbers there are in total. Nor is the claim that some things are so many as to be beyond the reach even of transfinite cardinals. Most mathematical logicians agree that for every number there is a set with more members than that number. One way of showing it is to suppose that numbers are sets: specifically, each number is the set of sets with that number of members. Thus, 0 is the empty set, 1 is the set of singletons, 2 is the set of pairs, and so on. Then for every number there is at least one set with that number of members. But every set has a power set – the set of all its subsets – and the power set of any set has more members than the original set has. It follows that for any number there is a set with more than that number of members. And so for any number there are more things than that number. Hence there cannot be a number of things. But this does not prevent us from saying how many things there are: there are more than any number can capture. In fact this would seem to be a completely precise answer to the question of how many there are. The claim is not merely that some things are not countable under a certain concept or predicate. Someone might argue that there’s no saying how many red things there are, insofar as there is no principled way of counting red things as such – the concept red thing provides no way of distinguishing one red thing from another. Still, the uncountability of red things qua red things would not entail their uncountability simpliciter. We can count roses, pillar boxes, and copies of The Thoughts of Chairman Mao, among other things. And it may be that every red thing is countable under some concept or other. The claim in question is that some things are not countable under any concept. They are uncountable simpliciter: there is no saying how many of anything they are. The claim is not that certain things have no number because identity is always relative to a sortal concept.2 In that case something x and something y might be the same F and not the same G, but there would be no question of whether they are identical or distinct without qualification. Assuming a sortal-relative analogue of the identity principles, x and y would then be one F and two Gs; but there would be no question of whether they are one or two simpliciter. So we could ask how many Fs there are or how many Gs, but not how many things. There would be no such thing as number simpliciter, but only number under a sortal. But this is not what Lowe has in mind. In fact he rejects the relativity of identity.

  In this paragraph and the next I follow van Inwagen (2002).

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Nor, finally, is the claim that certain things have no precise number owing to vagueness. It may be that identity can be vague: there can be things that are neither definitely identical nor definitely not identical. Consider a simple case: there is something x and something y such that it is indeterminate whether x is y, and nothing is determinately distinct from x or from y. Then it will be indeterminate whether the number of things is one or two, and every other number will determinately not be the number of things. And that will be all the answer there is to the question of how many things there are. But it is still a perfectly meaningful answer – supposing, anyway, that the notion of vague identity is intelligible. Lowe’s view is that some things simply do not admit of number or of numerical description. ‘It makes no sense even to inquire how many there are’ (1998: 74; see also 33, 50). Such things ‘cannot be assigned numbers – neither the number one nor any greater number’ (2009a: 50). Dummett seems to mean the same when he says, ‘it simply makes no sense to speak of the number’ of some things. ‘There are some questions “How many?”’, he continues, ‘which can only be rejected, not answered’ (1981: 547). Such things exist, but we cannot say that there is at least one of them. Nor can we say that there is more than one. We cannot say that their number is between m and n, or that there are more of them than any number can capture. We cannot say anything at all about how many there are. So it is an understatement to say that such things merely lack determinate countability. They have no countability at all, determinate or otherwise. The concept of number has no application to them. Call such things strongly uncountable. And call the claim that there could be strongly uncountable things the uncountability thesis. Lowe concedes that the thesis sounds paradoxical. The word ‘things’ is plural, and plurality implies more than one. That seems to make it impossible for there to be things without there being more than one of them; and if we can say that there is more than one thing of a certain sort, such things are not strongly uncountable. The grammar of the English language (and of every other language I am familiar with) makes the claim ‘there are uncountable things’ hard to state. This may show that the first speakers of Indo-European languages at least tacitly accepted the quantification and identity principles. Perhaps they too were taught wrongly. I hope this grammatical obstacle will not render my discussion unintelligible. The precise relation between the uncountability thesis and the quantification and identity principles is not easy to establish. The falsity of any

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of the three principles would appear to entail the uncountability thesis. Suppose the thesis were false, so that for any things whatever, it were always possible to say how many there are, even if it were something like ‘an indenumerable infinity’ or ‘more than zero but not more than two’. Then there being something that is F would entail there being at least one F thing: any numerical description other than ‘zero’, be it vague or precise, entails ‘at least one’. The quantification principle would be true. And if there were any numerical description of x and y, surely x’s being identical or non-identical to y would entail that x and y are one or two, respectively, as the identity principles say: the quantification and identity principles would seem to be true of any entities that admit of number at all. If everything admitted of number – if the uncountability thesis were false – the quantification and identity principles would be true. But it is less clear whether the converse entailment holds. Geach and Dummett suggest not only that red things are strongly uncountable and do not admit of number, but that they do not admit of identity or diversity either. In that case their existence would be consistent with the identity principles. Some things might be strongly uncountable for reasons other than the falsity of the identity principles. If so, establishing the identity principles does not suffice to refute the uncountability thesis. But the quantification principle would appear to be true if and only if the uncountability thesis is false. 4 .3  P or t ions of s t u f f As examples of strongly uncountable things Lowe mentions tropes and facts: they exist, but we can say nothing about how many there are  – not even that there is at least one. Geach and Dummett, following Frege, speak of red things (though to my knowledge Frege himself never endorsed the uncountability thesis). I will set aside tropes and facts and consider instead a case that both Lowe and Laycock appeal to: portions of stuff. (I will return to red things later.) Suppose there is water in the glass. Then, says Lowe, we can ask how much water there is, but not how many (1998: 74; see also 2009a: 49–51). The point is not merely that grammar forbids the question ‘How many water are there?’ It likewise forbids the question ‘How many Aristotle are there?’; yet Aristotle is not uncountable: there is exactly one thing that is Aristotle (Chappell 1970: 64 makes a similar point). As far as that goes, grammar forbids the statement ‘it makes no sense even to inquire how many water there are’. In order to state Lowe’s view about water and the like, we need a count noun

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of which the water in the glass, as well as the water in this part of the glass and the water in that part of it, are instances. Let us call such things portions. (‘Part’, ‘parcel’, ‘mass’, and ‘quantity’ are sometimes pressed into use for the same purpose.) Then the view is that portions of stuff – of water, or gold, or matter generally – are strongly uncountable. Although there are such things, it makes no sense even to inquire how many there are. Nor is there any answer to the question – not even an imprecise answer such as ‘at least one’. They are beyond numerical description. For something to be a portion of stuff is different from its being what Lowe calls a piece of stuff. Drops of water, chunks of ice, and grains of sand are pieces. They contrast with their surroundings and have non­arbitrary boundaries. (More precisely, the entire boundary of a piece is nonarbitrary: the matter in the upper half of a certain grain of sand would be a portion but not a piece. Lowe’s definition of ‘piece’ at 1998: 73 is different from mine, but we can ignore the difference for present purposes.) Lowe accepts that pieces are countable: we can ask how many drops of water or grains of sand there are. Portions of stuff, however, need not contrast in any way with their surroundings, and can have arbitrary boundaries. I find it hard to see how portions of water could be strongly uncountable.3 They are composed of water molecules,4 and water molecules are countable if anything is: even if there is no finite number of them, or no precise number owing to vagueness, we can ask how many there are. (They are ‘pieces’ in Lowe’s sense.) And surely no water molecules can compose more than one portion of water at once. Given these facts, the number of portions ought to be a function of the number and arrangement of molecules. What function it is depends on two factors, both of which are disputable. The first is the circumstances in which water molecules compose something – where some things, the xs, compose something y if and only if each of the xs is a part of y, none of the xs share a part, and every part of y shares a part with one or more of the xs. That determines how many things composed of water molecules – call them aggregates – there are. The second factor is what is required for an aggregate to count as a portion of water. Maybe a lone molecule could not be a portion of water because it cannot be in a liquid state; maybe similar facts prevent an aggregate of many molecules from being a portion of water if they are too far apart. 3 Lowe in fact shows some hesitation about whether portions of actual stuff are uncountable (1998: 72), though Laycock (1975: 418) does not. 4 In reality the microstructure of water is more complicated, but the point is unaffected.

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Then the number of portions of water is the number of aggregates that satisfy the conditions necessary for being a portion of water. Thus, if any water molecules whatever compose something – if there is universal composition for water molecules – then the number of aggregates is the number of non-empty subsets of the set of water molecules – 2n – 1 if there are n molecules. If some water molecules but not others compose something, the number of aggregates will be something between n and 2n – 1. Either way, subtracting from the number of aggregates the number that don’t count as a portion of water will yield the number of portions of water. Or maybe water molecules never compose anything no matter how they are arranged. In that case the number of portions of water will be equal to the number of water molecules if an individual water molecule counts as a portion of water and zero if not. Suppose for the sake of illustration that there are exactly three water molecules. If composition is universal and any aggregate of water molecules counts as a portion of water, then the number of portions of water is seven. If no portion of water can be composed of fewer than four molecules, there are none. Other assumptions will yield numbers between zero and seven. But in each case and for any number of molecules there will be a number, even if not a precise one, of portions of water. Lowe is unconcerned about all this because he is convinced that there could be homogeneous stuffs, every portion of which is composed of smaller portions of the same stuff. The number of portions of such stuff could not be a function of the number of molecules or atoms or any other natural unit of it, because there would be no such units of which all portions of it are composed. David Lewis called such stuff atomless gunk. I doubt whether Lowe has any right to be confident that atomless gunk is metaphysically possible. But suppose it is. If it existed, he says, there would be portions of it, but we could not say or even ask how many. In that case there would be portions of gunk, but there would be no number of them. There would not even be at least one, contrary to the quantification principle. If there were gunk in England and gunk in France (and a gunk-free zone in between), the English gunk would be different from the French gunk – maybe not qualitatively different, but, if we may so speak, numerically different. But there would not be at least two things that are gunk, contrary to the identity principles. Portions of gunk, Lowe says, would have determinate identity but not determinate (or even indeterminate) countability: for any portions x and y, either x is y or x is not y; but x’s being y does not entail that x and y are one, and x’s not being y does not imply that x and y are two.

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4 . 4  A rgu m e n t s f or t h e u nc ou n ta bi l i t y of p or t ions Why suppose that portions of any sort of stuff would be uncountable? Here is a common line of argument: When we say that water surrounds our island, or that the water surrounding our island is clear, our discourse is not singular discourse (about an individual) and is not plural discourse (about some individuals); we have no single individual or any identified individuals that we refer to when we use ‘water.’ We are talking about some stuff, not a thing or some things … (McKay 2008: 311)

To say that water surrounds the island, the argument goes, is not to say that a certain thing surrounds the island as a reef might, or that certain things collectively surround it as a lot of jellyfish might. It would be wrong to analyse the sentence ‘water surrounds the island’ in such terms. That’s not what it means. The meaning of the word ‘water’ does not imply that it is made up of bits. In this respect it differs from such mass terms as ‘sand’ or ‘snow’: it is part of their meaning that whatever they apply to must be made up of smallest portions of sand or snow. ‘Water’ has, in Laycock’s apt phrase, no ‘semantic atoms’ (2006: 52). Semantic analysis of sentences about water cannot eliminate mass nouns in favour of count nouns. Talk of water is not talk about countable things. It must therefore be talk about something uncountable. But it is still a fact, even if not a semantic one, that water is made up of smallest bits, and that for water to surround an island is for such bits to surround it. And those bits – molecules or elementary particles – are countable. Gunk, of course, is not made up of smallest bits. But it may still be a metaphysical fact that for gunk to surround an island is for a certain number of portions of gunk to surround it, even if this fact does not obtain by virtue of the meaning of the word ‘gunk’. Peter Simons has proposed an argument suggesting that the truth conditions of certain sentences must appeal to uncountable things (1987: 155  – though as far as I know he does not endorse the uncountability thesis). Imagine that most of the world’s gunk has yet to be mined. How could we give truth conditions for this in terms of countable things? It’s no good saying that most of the discrete pieces of gunk have yet to be mined: we may have dug up most of them even though most of the gunk remains underground. Contrariwise we may have dug up most of the gunk even though most of the pieces of it are unmined. And if portions of gunk are countable (that is, not strongly uncountable), it’s no good saying that most of the world’s portions of gunk have yet to be mined either,

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for if there is any number of unmined portions it will be the same as the number of mined ones: some transfinite cardinal, presumably 2c. But if a statement could be true, and its truth conditions cannot be given in terms of countable things, then they must be given in terms of uncountable things. It must therefore be possible for there to be uncountable things. Well, these truth conditions look right, and are consistent with the countability of portions of gunk: There are two sets of portions of gunk S1 and S2 such that

i. no member of either set overlaps any other member of either set; ii. every portion of the world’s gunk overlaps a member of one of the sets; iii. all the members of S1 have been mined; iv. none of the members of S2 have been mined; and v. the sum of the masses of the members of S2 exceeds the sum of the masses of the members of S1 (where portions overlap if and only if some portion is a part of both). Those suspicious about sets could no doubt devise something analogous in terms of plural quantification. There may, of course, be statements about gunk that resist truth conditions in terms of countable entities; but that has yet to be shown. Lowe’s argument for the uncountability of portions of gunk is that because they are infinitely divisible into smaller such portions, they lack a ‘principle of individuation’ (1998: 74–6). This means that nothing could count as one portion of gunk, as opposed to two or some other number. And if nothing could count as one, nothing could count as any other number either. Let me explain how I think the argument goes. In order for things to have a number, it must be possible to count them, or at least the members of any finite subset of them. And for things to be counted, each must be picked out uniquely and distinguished from all others: it must be, as Lowe says, individuated. Otherwise something may get left out or counted twice. But this is impossible for portions of gunk. A portion of water, by contrast, is composed of water molecules; and because a water molecule is not itself infinitely divisible into further water molecules, it can be picked out uniquely. We know what counts as one of them. Given that no water molecules can compose more than one portion of water at once, it seems possible to individuate and count portions of water as sums of molecules. It is even possible to individuate and count some portions of gunk, namely those that make up material objects

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that contrast with their surroundings (‘pieces’ in Lowe’s terminology). If I have a ring made of gunk, I can refer uniquely to the gunk making it up (which Lowe thinks is distinct from the ring itself). But not all portions of gunk can be referred to in this way: some are mere arbitrary portions. Such a thing could only be individuated as a portion of gunk. And that, Lowe says, cannot be done. Here is what he says about why not (where a ‘part’ is what I have been calling a portion): Parts of stuff have no unity merely in so far as they are parts of stuff, one consequence of this being that we cannot make direct reference to a part of stuff using a demonstrative noun phrase of the form ‘that part of S,’ where ‘S’ is a mass term denoting the kind of stuff in question. If I point in the direction of some gold and say, ‘That part of gold weighs one ounce,’ for example, then I have failed to express a determinate proposition, because I have failed to pick out a determinate object of reference … The problem, once again, is that whenever I point in the direction of some gold, there is never just one part of gold that I could be taken to be demonstrating because, as we have seen, any part of gold is always divisible into other parts of gold (once again adopting the fiction that gold is a homogen­ eous stuff). Nothing whatever counts as ‘just one’ part of gold, simpliciter, in the way that something counts as just one gold ring … (1998: 76; see also 2003: 78)

When he says that portions of stuff have no ‘unity’, Lowe means that their parts need not be arranged in any special way: any portions of gunk whatever make up a larger portion. Because of this, and because they are infinitely divisible into smaller portions of gunk, their boundaries are arbitrary and they need not contrast in any way with their surroundings. That prevents us from picking out any one arbitrary portion of gunk as such: no matter how precisely we point, there will never be just one portion of gunk there. This argument is puzzling in a number of ways. For one thing, the reason we can never point at just one arbitrary portion of gunk would seem to be that wherever we point there will always be many such portions amongst which our pointing does not discriminate – that is, more than one. But ‘more than one’ is a numerical description: if we can say that whenever we point at gunk we point at more than one arbitrary portion of gunk, then such portions are not strongly uncountable. The deeper question the argument raises is why our inability to refer uniquely to an arbitrary portion of gunk should imply or even suggest that there is no number of such portions. This inability would seem to be due merely to our limited powers of discrimination – which ought to be irrelevant, seeing as the existence and metaphysical nature of portions of

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gunk is not supposed to depend on the powers of human beings. Lowe evidently thinks that the inability is not merely contingent, and that no being could pick out one arbitrary portion of gunk uniquely. Not even God could do it. You might think that it must be within the power of an omnipotent being to pick out a precise gunk-filled region of space. And there would have to be exactly one portion of gunk occupying such a region. Thus, a being with infinite discriminatory powers could count portions of gunk by counting gunk-filled regions. But Lowe says that regions cannot be individuated either – not even by God. Nothing could count as just one region of space, or as any other number. Lowe says little about why regions of space should be strongly uncountable. But here is a way of arguing for it. What would it take to individuate a region of space? To make things simple, think of a two-dimensional region. You could pick one out by doing something analogous to drawing a closed figure on a sheet of paper. Because of the thickness of the line and the vagueness of its boundaries, however, that will not succeed in picking out any one region. Beings with superior discriminatory powers could draw sharper lines. But one could pick out a unique region only by drawing an infinitely sharp line, and maybe not even God could do that. Perhaps God’s power could only consist in this: for any line that could be drawn, he can draw a sharper one. His powers of discrimination could be unlimited, but not infinite. Or one could pick out a region by choosing a point and specifying its boundaries in terms of their precise distance from it. But if God cannot draw an infinitely sharp line, he won’t be able to pick out a unique point either. At most he might have this power: for any extended region, he can choose a smaller one.5 But this reasoning relies on two controversial assumptions: that infinite discriminatory powers are impossible, and that if no being could count things of a certain sort, there is no number of them. I don’t know how to support these claims. Without further argument, then, the case for the uncountability of portions of gunk is inconclusive. 4 .5   T h e c ou n ta bi l i t y of p or t ions I think we can go further and argue that portions of gunk would be countable. 5 One might expect Lowe to say that points are uncountable because they cannot be individuated. In fact he denies that there are any points, and understands talk of a point in terms of the limit of a sequence of ever-smaller regions (1998: 75).

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We can certainly ask how many pieces of gunk there are – how many discrete portions with non-arbitrary boundaries. Suppose I have a cubical piece of gunk, and no other gunk, on my desk. Then there is exactly one piece of gunk there. If I also have a spherical piece of gunk on the floor, then I have two pieces of gunk. The idea that I might have a cubical piece of gunk on my desk and a spherical piece on the floor without having at least two pieces of gunk looks unintelligible. So pieces are countable. And a piece is a special sort of portion. It follows that at least some portions of gunk, namely those that are pieces, are countable after all. If I have two pieces of gunk, I have at least two portions. We can say something about how many portions there are: at least as many as there are pieces. We can begin counting the portions, even if we can never finish the job. They are not beyond numerical description. One may reply that if portions of gunk are countable, that is only because a special subclass of them – the pieces – are countable. Arbitrary portions  – those that are not pieces  – remain uncountable, confirming the uncountability thesis. But the objection can be pressed further. It seems possible for something to be a piece of gunk at one time and a mere arbitrary portion at another. If we break a piece of gunk in two, it looks as if each of the resulting smaller pieces was previously a mere arbitrary portion. Arbitrary portions can be made into discrete pieces by detaching the surrounding gunk. Likewise, it seems that a piece of gunk can cease to be a piece and become a mere arbitrary portion by being fused with another piece. Suppose I start with ten pieces of gunk, then squash them together so that they cease to be pieces and become arbitrary portions. If there were initially ten pieces, and none has ceased to exist or ceased to be a portion, does it not follow that there are still at least ten portions? And if each of them is now an arbitrary portion, are there not now at least ten arbitrary portions? It certainly seems so. A thing’s countability could hardly be a mere temporary feature of it: a thing cannot be countable at one time and not countable at another. But in that case even some arbitrary portions of gunk would admit of numerical description. It is hard to see how even permanently arbitrary portions – those that are never discrete pieces – could be uncountable. Whatever is potentially or possibly countable would seem to be actually countable. Suppose that in one possible situation there are exactly n items of a certain sort. Now consider any other possible situation in which all those items exist and are of that sort and there are no other items of that sort. Then there must be n items of that sort in the second situation too. Nothing could be

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only contingently uncountable. But any arbitrary portion of stuff could have been a piece: it could be made into a piece by removing the surrounding stuff of the same kind, even if this never actually happens. So every portion is possibly countable. It follows that every portion is in fact countable. One might try to defend the uncountability of portions by denying that any arbitrary portion could come to be a discrete piece, or that any piece could be made into an arbitrary portion. It is a necessary truth that every arbitrary portion is essentially arbitrary and every piece is essentially non-arbitrary. Arbitrary and non-arbitrary portions of gunk are different fundamental metaphysical kinds. This would mean that if we take a piece of gunk and break it in two, we create two non-arbitrary portions that did not exist before. And we destroy the original portions whose places the new ones take (but these are not two original portions, since arbitrary portions are uncountable). If we fuse two pieces of gunk to make a larger piece, then again the two smaller pieces do not become arbitrary portions, but cease to exist and are replaced by new portions (though again, not two of them). It is metaphysically impossible for a piece of gunk to survive the process of having another piece of gunk fused to it – if it did, it would change from a countable piece to an uncountable arbitrary portion, which is itself impossible. Nor can an arbitrary mass of gunk survive the removal of the gunk surrounding it. But I doubt whether anyone would actually say this. If we know anything about what it takes for gunk to persist, we know that the result of breaking a piece of gunk in half is that some of the original gunk goes into one of the two pieces and the rest of it goes into the other piece. We have merely separated one from the other. We haven’t destroyed or created any gunk, but only reconfigured the gunk we already had. And if we have the same gunk, how could we not have the same portion of gunk? A portion of stuff is by definition nothing other than some particular stuff. As long as no gunk is destroyed in the process, then, breaking a piece of gunk in two cannot destroy any portion of gunk. These arguments rely on the assumption that pieces of gunk, which are countable, are portions of a certain sort. Lowe has recently said that pieces are not portions: a piece of matter is distinct from the portion of matter that makes it up or constitutes it (2009a: 50). But this is a mere change of vocabulary. As long as we take ‘piece’ to mean ‘discrete portion with non-arbitrary boundaries’ as originally defined, the arguments are unaffected.

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I have argued against the claim that portions of gunk would be strongly uncountable  – though I have not shown that the uncountability thesis is false, or even that there is no reason to accept it. I will conclude with some remarks about the uncountability thesis in general. What would it mean if the thesis were true? It might not mean very much. Suppose we grant for the sake of argument that there really are things to which no numerical description applies. That would not by itself prevent us from defining ‘quasinumerical’ descriptions like this: At least *one* thing is F =df something is F. Exactly *one* thing is F =df something is F and everything that is F is ­identical to it. Exactly *two* things are F =df something is F and something distinct from it is F and everything that is F is identical to one or the other of them.

And so on. In that case we could say that there is a *number* of Fs if and only if there is *one* F or there are *two* Fs or …, and so on – that is, if and only if one of these quasinumerical statements is true.6 Lowe says that for some values of F there is no number of things that are F – for instance, there is no number of portions of gunk – but he does not deny that there is a *number* of such portions. Nor does he deny that we can sensibly ask *how many* portions there are, where this is understood as a request for a quasinumerical description. And the result of replacing the numerical terms of the quantification and identity principles with the corresponding quasinumerical terms would seem to be principles that are not only true, but consistent with the uncountability thesis. There being uncountable things would not rule out the claim that everything is *countable*. And that might lead us to doubt whether the uncountability thesis is as interesting as it appears, or even whether it is intelligible. If the definitions of the quasinumerical descriptions make sense, there could be a population of beings who spoke a language identical to ours except that they use quasinumerical terms where we use genuine numerical ones: when they say ‘one’ or ‘two’ or ‘number’, they mean *one* or *two* or *number*. That would make it a serious question whether we ourselves are such beings: whether our own words ‘one’, ‘two’, ‘number’, 6 Or at least not definitely false, to allow for vagueness. Defining quasinumerical analogues of transfinite numerical descriptions introduces complications that I must set aside, but I doubt whether it is impossible.

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and so on are numerical or only quasinumerical. Maybe the reason some of us find the uncountability thesis so baffling is that we mean nothing more by ‘one’ and ‘two’ than *one* and *two*, even if others mean something else. In that case there would be no real disagreement between those who say that portions of gunk would be uncountable and the rest of us. There would be no proposition that they accept and we deny or vice versa: they can accept that portions of gunk are *countable*, and we quasinumerates need not affirm that everything is countable in Lowe’s sense. We might even wonder why we quasinumerates should care whether everything is countable in Lowe’s sense – supposing we can even understand it – as long as it’s countable in ours. Uncountabilists may reply that some things are not even *countable*: it is impossible to ask not only how many there are, but even whether they are the same or different. Such things would not admit even of identity or non-identity, never mind number. The claim would have to be not only that such things are sometimes neither definitely identical not definitely distinct, but that the concept of identity has no application to them whatever: it makes no sense even to inquire whether they are identical. But I cannot explore this idea here. 4 .7   T h e n u m be r of t h i ng s Let us now ask what it would mean if the uncountability thesis were false. What if necessarily everything were countable? What if the existence of something were necessarily the existence of some number of such things, or at least always implied some numerical description of them? It would follow that there is a number of things or entities in general. Or at least it would make sense to ask how many there are; and the question would have an answer, even if it did not take the form of a number. As we noted in Section 4.2, it may be that there is no precise number of things owing to vagueness; or it may be that for any number, finite or transfinite, there are more things than that. But the question, ‘How many things are there?’ would have a unique right answer. If there is a number of things, then there is a number of red things (though probably not a precise number), contrary to the claims of Geach and Dummett. Of all the things there are, some are red and some are not (indeterminate cases aside). If there is a number of things in general, there would have to be a number of them that are red. Likewise, there would have to be a number of soft things, and a number of things that are not tigers.

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This would not mean that the concept red thing determined a principle of individuation and a criterion of identity that would enable us to count red things as such. Even if red things are not countable as red things, each of them would be countable as something or other – under some sortal concept. The number of red things would be determined by two factors: what things there are, and what it is for a thing to be red. Suppose, to take a simple case, that the only concrete things are material objects. (I assume that only a concrete thing could be red.) And suppose that all material objects are composed of elementary particles. Then the number of mate­ rial objects will be a function of the number of particles  – though for reasons discussed in Section 4.3 there is room for debate about what function it is. And the number of red things will be the number of material objects that are red. There will no doubt be a good deal of vagueness and observer-relativity about what it is for a material object to be red, and this will infect the question of how many red things are there, much as it infects the question of how many bald men there are in London. But that does not make the question unaskable or unanswerable. The ontology of concrete objects may be more complicated: for instance the red things might include not only material objects composed of elementary particles but also portions of gunk, surfaces, beams of electromagnetic radiation, or mental images. Then the answer to the question of how many red things there are will be more complicated too. But a complicated answer is still an answer.7 For comments on earlier versions of this paper I am grateful to Bob Hale, Nils Kurbis, Jonathan Lowe, and Tuomas Tahko. 7

ch apter 5

Ontological categories Gary Rosenkrantz

5.1  M e ta ph y s ic s a n d c at e g or i e s Aristotle famously described metaphysics as ‘First Philosophy’ or ‘first science’. In a similar vein, E. J. Lowe has described metaphysics as ‘the systematic study of the most fundamental structure of reality’ (1998: 2). As such, metaphysics examines the more general categories of being, and the more general ways in which entities are related to one another. Accordingly, metaphysics includes ontology, the science of being, concerned with the categorization of what exists, and cosmology, the science of reality as an orderly whole, concerned with characterization of reality as an ordered law-governed system.1 It should be noted that these ontological and cosmological enterprises are intertwined with one another. In one very broad sense of ‘category’, any predicate which denotes a non-empty class, or which (holding its actual meaning constant) could or might denote such a class, expresses a category. In this weak sense of ‘kind’ or ‘category’, predicates such as ‘sweet’, ‘red sock’, ‘horned horse’, ‘cube’, ‘table’, ‘cat’, ‘cat or eagle’, and ‘substance or event’ express categories. However, in a much narrower sense only categories of being or ontological categories qualify as ‘categories’. Aristotle was likely the first to explicitly acknowledge the centrality of categories in this sense to metaphysics. Examples of such categories are substance (and more specifically body and soul), event, time, place, absence, boundary, property, relation, proposition, set, and number. Categories of this kind are, or at least purport to be, highly general, or more basic, kinds of being.

1 One should distinguish cosmology in this sense from the (more specialized) astrophysical study of the history, structure, and basic dynamics of the universe. Nevertheless, cosmology as a branch of metaphysics may utilize the findings of this branch of astronomy.

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The metaphysical concerns with the general order in which entities are related to one another and with the organization of entities by their ontological categories reflect the systematic character of metaphysics. In particular, metaphysics seeks to develop a system of ontological categories which organizes everything that there is, or everything that there could be. One of the ultimate goals of metaphysical inquiry is to validate an ontological theory that specifies which categories these are. Insofar as metaphysics is concerned with the fundamental structure of reality, metaphysicians have sought to develop ontological taxonomies that organize or classify everything that there is, or everything that there could be. It should not be assumed that an ontological taxonomy must have a genus-species structure, or that it must classify actual or possible kinds of entities in terms of their ontological categories. Nevertheless, tree-like taxonomies which have a genus-species structure and which classify actual or possible kinds of entities in terms of the ontological categories to which they belong have historically had pride of place in the enterprise of ontological classification. Recent examples of such systems of ontological classification include Lowe’s (1998), Chisholm’s (1996) and Hoffman and Rosenkrantz’s (1994). Each of these systems involves a fundamental ontological divide. In Lowe’s system, it is the division between particular and universal; in Chisholm’s, it is the division between contingent being and necessary being; and in Hoffman and Rosenkrantz’s, it is the division between concrete entity and abstract entity. In each case, it is necessarily true that everything falls on one side of the divide or the other, and impossible that anything falls on both. In Lowe’s (2006) neo-Aristotelian four-category ontology, the species of particular are individual substance and trope, and the species of universal are insubstantial universal (whose divisions are sharable property and relation) and substantial universal (also known as a natural kind). In Chisholm’s system, the divisions of contingent being are contingent state (having event as a sub-category) and contingent individual (whose divisions are contingent substance and boundary) and the divisions of necessary being are necessary state and necessary non-state (whose divisions are attribute and necessary substance). Finally, in the system of Hoffman and Rosenkrantz, the species of concrete entity include substance (whose divisions are physical object and soul), event, time, place, trope, boundary, collection, and absence, and the species of abstract entities include property, relation, set, and proposition.

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Although philosophers have proposed various schemes of ontological classification, involving different fundamental ontological divides, and therefore, different ontological categories, a number of such schemes may be equivalent in the sense that each of them necessarily organizes the same entities as the others. As Lowe has observed, ‘there is often more than one way to organize what is in effect the same categorial scheme, just as there are different axiomatizations of the same system of geometry’ (1998: 204). An account of ontological categories should be compatible with this observation. On the other hand, different historical schools of metaphysical thought have developed taxonomic systems of ontological categories which, even if individually intelligible, are at variance with one another both with respect to their classificatory divisions and with respect to their implications about what there is or could be. More specifically, some of these taxonomic systems countenance the existence of instances of ontological categories that others do not countenance, e.g., numbers, and some of these taxonomic systems countenance the possibility of instances of ontological categories that others do not countenance, e.g., souls, bodies. It appears that such metaphysical disagreements can legitimately be understood against the backdrop of at least three different conceptions of an ontological category. According to the first conception, a category must have an actual instance at some time. This requirement appears natural given that the primary goal of ontology is to categorize what there is. The second conception has, instead, the weaker requirement that a category possibly has an instance. Among other things, this alternative seems to permit a greater degree of neutrality in the face of various ontological controversies and uncertainties. The third conception substitutes the even weaker requirement that a category is such that it is epistemically possible for it to have an instance, and hence, is such that there isn’t anybody who knows that the category does not have an instance. This weaker requirement seems to permit an even greater degree of ontological neutrality. A taxonomic system of ontological categories may fail to be intelligible in a variety of ways, e.g., one or more of its putative classificatory categories may be unintelligible, one or more of its putative species-categories may not actually be species of their putative genus-categories, or the taxonomic system in question may entail that there are infinitely many different ontological categories. For instance, a taxonomy which entails that relations have infinitely many ontological sub-categories, i.e., monadic relations, dyadic relations, triadic relations, and so on, appears to be unintelligible. (This is not to deny that there are infinitely many different kinds

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of relations of these sorts; rather it is to say that a taxonomy according to which all of these kinds are ontological categories appears to be unintelligible.) On the other hand, the foregoing observations are at least logically consistent with the possibility of there being infinitely many different intelligible taxonomic systems of ontological categories, each one of which contains only finitely many ontological sub-categories of relations of the aforementioned kinds. Finally, it should be noted that some intelligible taxonomic systems of ontological categories are superior to others. For example, all other things being equal, systems in which categories at the same level of generality cannot be co-instantiated are superior to systems in which categories at the same level of generality can be co-instantiated. There appears to be an overarching conception of an ontological category applicable to any classificatory kind that figures within any intelligible taxonomic system of such categories. In the next section, I will attempt to elucidate this overarching conception by clarifying logically necessary conditions of a predicate’s properly expressing such a category. Such an elucidation is compatible with the intelligible historical variances among taxonomic systems of ontological categories described earlier, and in that sense, such an elucidation of the overarching concept in question is ontologically neutral. The analytical task of providing a set of logically necessary and sufficient conditions for a meaningful well-formed predicate’s properly expressing an ontological category differs from the ontological task of ascertaining the category to which ontological categories belong. For example, in carrying out the ontological task it must be asked whether categories are properties, concepts, sets, or collections, but this question need not be asked in carrying out the analytical task.2 These analytical and ontological tasks appear to be independent of one another. 5.3  C on di t ions on a pr e dic at e’s prope r ly e x pr e s s i ng a n on t ol o g ic a l c at e g or y In the first chapter of The Possibility of Metaphysics, Lowe defends serious or traditional-style metaphysics against a legion of opponents, including Kantians and positivists of various sorts. One of the grounds upon which serious metaphysics may be attacked is that its central notion of an ontological category is unintelligible or, at least, not sufficiently well understood. A traditional-style ontologist may reply that the notion of an

  For an exploration of such questions see Westerhoff (2005).

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ontological category is presupposed by the sciences, even if it is primitive or unanalyzable. Still, I believe that a further reply which provides an elucidation or analysis of an appropriate conception of an ontological category in terms of logical, modal, semantic, and epistemic notions would be helpful to the cause of serious metaphysics. My attempt to elucidate the notion of an ontological category will make use of the notion of a predicate’s expressing or connoting a kind. For example, the predicate ‘event’ expresses the ontological category event, a kind to which all and only events belong. Moreover, this predicate may be said to express that category without redundancy or gratuitous logical complexity, something that clearly cannot be said of certain other predicates, e.g., ‘event and event’ or ‘event or non-cubical cube’. In this chapter I aim to elucidate this key notion of a predicate’s properly expressing or connoting an ontological category. Note that what a predicate expresses or connotes is its meaning or intension, as opposed to its denotation or extension. It appears that necessarily equivalent predicates with the same denotation may differ in their meaning or connotation. For example, necessarily equivalent predicates such as ‘the successor of 5’ and ‘the smallest perfect number’ have the same denotation, in this case, the number 6, but differ in connotation.3 Thus, my attempted elucidation of a predicate’s (properly) expressing a category will be consistent with the possibility of there being two predicates that are necessarily equivalent, but only one of which properly expresses some ontological category. For instance, the predicate ‘event’ properly expresses an ontological category, while the necessarily equivalent predicates ‘event and event’ and ‘event or non-cubical cube’ do not. I am now prepared to attempt to put forward ten logically necessary conditions of a predicate’s properly expressing an ontological category; linguistic and temporal indexes needed to accommodate the relativity of a predicate’s connotation to a language and a time will be left implicit for the sake of expository ease. Necessarily, a meaningful well-formed predicate ‘F’ properly expresses an ontological category only if ‘F’ satisfies conditions (1)–(10) below.4 (1) There exists an F.5 3 Two predicates ‘F1’ and ‘F2’ are necessarily equivalent if and only if they are mutually entailing. A predicate ‘F1’ entails a predicate ‘F2’ in the relevant sense if and only if in any possible world, W, in which ‘F1’ and ‘F2’ have the same meaning as they do in the actual world, something satisfies ‘F1’ only if it satisfies ‘F2’. 4 ‘F’ is a schematic letter which should be replaced by an appropriate predicate expression. 5 This condition should be read as equivalent to ‘At some time there exists something that is F.’

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According to what I have referred to as the first conception of ontological categories, predicates with empty extensions do not express such categories. For example, according to this conception, if every entity were concrete, then the predicate ‘abstract entity’ would not express an ontological category. Condition (1) entails that predicates of this kind do not express ontological categories. However, there is much serious disagreement about which categories have actual instances. For example, there have been, and continue to be, serious debates about whether ontological categories such as material substance, soul, property, number, and absence are instantiated. Moreover, given our epistemic limitations with respect to answering ontological questions, it is problematic whether any of us will ever be in a position to know whether there are entities such as material substances, souls, properties, numbers, and absences. Thus, if the categories comprising a proposed ontological taxonomy were conceived of in the first way, there would be two significant costs. The first is that the taxonomy in question would be highly controversial. The second is that it would be doubtful whether we would ever be in a position to settle decisively the relevant ontological controversies. However, there is another way to conceive of the categories comprising an ontological taxonomy. This second conception of ontological categories requires merely that the categories in question possibly have instances, in the sense of broadly logical or metaphysical possibility. Given such a conception of ontological categories, (1) should be replaced with: (1′) It is possible that there exists an F.

Moreover, because a universal law has implications about the character of all relevant possible cases, there is a philosophically significant sense in which a complete general characterization of reality as an ordered law-governed system requires an ontological taxonomy that organizes not just all categories that are actually instantiated, but organizes the conceivably broader class of all categories that are possibly instantiated. For instance, conceivably, the category of (Cartesian) souls is possibly, but not actually, instantiated.6 Alternatively, it might be argued that a complete characterization of reality as an ordered lawgoverned system requires an ontological taxonomy that organizes the class of all categories whose instantiation is nomically possible, or consistent with the laws of nature. Such a conception of the categories comprising an ontological taxonomy is equivalent to the second conception of such categories if metaphysical possibility is identifiable with nomic possibility. However, if there are metaphysically possible entities whose existence is not nomically possible, then no such equivalence 6

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Even though it is evidently a necessary truth that all actually instantiated categories are possibly instantiated, the converse claim that all possibly instantiated categories are actually instantiated is not at all evident.7 I conclude that, given the broad goals of metaphysical inquiry, the second conception of categories should be acknowledged as an appropriate one within the context of ontological taxonomy. Finally, given what I referred to as the third conception of ontological categories, (1) should be replaced with: (1′′) It is epistemically possible that there exists an F.

There are significant disagreements about which categories possibly have instances, for example, about whether the ostensible category of (Cartesian) souls possibly has an instance. Materialists have questioned the intelligibility or coherence of the notion of a soul of this kind. But Joshua Hoffman and I have argued that such souls are possible (Hoffman and Rosenkrantz 1991). Thus, I think it is fair to say that the question of whether such a soul is possible remains controversial within ontology. If a soul of this kind is impossible, then, given either the first or second conception of categories, there is no such thing as a category of such souls. In the light of examples of this sort, it is evident that if the categories comprising an ontological taxonomy were conceived of in the second way, then this would result in a lack of ontological neutrality similar to that which would result if those ontological categories were conceived of in the first way. The third conception of ontological categories requires merely that the categories in question are such that their instantiation is consistent with everything anybody knows to be the case. Arguably, the instantiation of the ostensible category of (Cartesian) souls is at least epistemically possible in some such sense.8 The advantage of this third conception of a category is that it allows one to construct an ontological taxonomy that classifies everything that exists (or could exist) while remaining neutral, to a considerable extent, on disagreements about what exists or could exist. holds and, in the philosophically significant sense referred to in the text, a complete characterization of reality as an ordered law-governed system cannot be given in terms of an ontological taxonomy comprised (wholly) of categories whose instantiation is nomically possible. 7 Nevertheless, this converse claim has had defenders. If they are right, then a category is possibly instantiated if and only if it is actually instantiated. If so, then the first and second conceptions of categories are necessarily equivalent. 8 If souls of this sort are epistemically possible, then nobody knows that souls of this sort do not exist, and a fortiori, nobody knows that the existence of such souls is impossible.

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Given (1′) or (1′′), it follows that a self-contradictory predicate, e.g., ‘animate inanimate object’, does not express a category. Likewise, for any predicate which is self-evidently incoherent or unintelligible. (2) It is impossible for something to be F contingently.

For example, since ‘property’ expresses a category, it is impossible for there to be a property that is a property accidentally or contingently. Unlike a red sock, which is such that it could fail to be a red sock (because, for example, it could be dyed and become a blue sock), a property is such that it could not fail to be a property. Accordingly, there is a sense in which a predicate that expresses a category expresses an essence. (3) ‘F’ is a non-relational predicate that is used substantivally, that is, as a noun.

Thus, relational predicates such as ‘self-identical’ and ‘not belonging to any of Smith’s favourite categories of abstracta’ do not express categories, and predicates such as ‘sweet’ and ‘square’, used as adjectives, do not express categories. (4) ‘F’ does not express a natural kind, a kind of artificial entity or artefact, or a kind of social entity.

Natural kinds, e.g., water, piece of gold, carbon-based living organism, DNA, electron, iron, are not basic or general enough to count as ontological categories.9 The same is true of kinds of artefact, e.g., ship, table, kinds of artificial purposeful activities such as push-up, and pull-up,10 and kinds of social entity, e.g., economic recovery, spontaneous market.11 In contrast with a natural kind (see note 9), the extent to which what it is for something to be an instance of an ontological kind can be explained is wholly a function of the extent to which it can be explained a priori.12 9 In the relevant sense of ‘natural kind’ the following entailment obtains. A kind, K, is natural ⇒ (i) K figures in one or more natural laws, and (ii) what it is for something to be an instance of K can be explained at least in part by means of a posteriori theoretical discoveries of natural science. For example, what it is for something to be an instance of the natural kind water can be explained at least in part in terms of the a posteriori theoretical discovery that water molecules are H2O molecules. 10 I propose the following account of the relevant sense of ‘artificial kind’. A kind, K, is artificial ⇔ necessarily, for any x, if x is an instance of K, then x has a function or purpose, f, such that: x’s having f causally depends upon there being at least one contingently existing person who intends that entities of kind K be used for f at some time. 11 I propose the following account of the relevant sense of ‘social kind’. A kind, K, is social ⇔ (i) K is not artificial, (ii) necessarily, for any x, if x is an instance of K, then x stands in some natural causal relation to one or more intentions, and (iii) K is not a kind of the most general sort that satisfies clauses (i) and (ii). 12 Representative partial or total explanations – knowable a priori – of what it is for something to be an instance of an ontological kind include examples such as the following. (a) An (individual)

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(5) If ‘F’ is a negative predicate, then ‘F’ is the negation of an atomic predicate which satisfies (4).

For instance, whereas the predicate ‘event’ properly expresses an ontological category, the equivalent negative predicate ‘non-non-event’ given its redundancy, does not. As the negation of a non-atomic predicate, ‘nonnon-event’ does not satisfy condition (5). (6) If ‘F’ is not a negative predicate, then there is not a more positive expression of what ‘F’ expresses than ‘F’.

For example, suppose that the two conjunctive predicates ‘non-thinking unextended substance’ and ‘located unextended substance’ are necessarily equivalent and that each of them expresses a condition that is logically necessary and sufficient for something’s being a point-particle. In that case, do both of these conjunctive predicates properly express the category of being such a particle? In my view, the second of these predicates is more positive, logically simpler, and more informative about the basic nature of such a particle than the first. I conclude that of the two substance is an instance of an ontological category such that: possibly, that category has just one instance over an interval of time. (b) A physical thing is a spatially located substance. (c) A (Cartesian) soul is a non-located substance that reflectively thinks. (d) An event is something that occurs at a time. (e) A time is an instance of an ontological category such that: necessarily, any instance of that category is earlier or later than another instance of that category. (f) A place is an instance of an ontological category such that: necessarily, any instance of that category lies in a positive or negative direction from another instance of that category. (g) A boundary is an insubstantial concretum whose existence entails the existence of something having more dimensions than it has. (h) An absence is an insubstantial concretum which consists of a lack of one or more concreta and which is wholly extended either between parts of a bounding concretum or between bounding concreta. (i) On some conceptions of tropes, tropes are concrete ways in which concreta are in and of themselves. (j) An (abstract) property is an instance of an ontological category such that: necessarily, any instance of that category exemplifies another instance of that category; on some moderate realist conceptions of properties, properties are abstract ways in which entities are in and of themselves; on some extreme realist conceptions of properties, properties are abstract ways in which entities could be in and of themselves. (k) A collective is an insubstantial concrete entity such that for any two concreta x and y, there is a collective having x and y as parts, and no other parts that are not parts of either x or y or both. (l) A set is an abstract entity that has one or more elements, or else is empty. (m) A proposition is an abstract entity that is either true or false. (n) A relation is an abstract entity which something bears to itself or to one or more other things. I maintain that explanations such as (a)–(n) could not be enhanced by means of a posteriori theoretical discoveries of natural science. But note although such enhancements are impossible, there may be species of the ontological categories referred to in (a)–(n) which are natural kinds and which are such that what it is to be an instance of these more specific kinds can at least in part be explained by means of a posteriori theoretical discoveries of natural science. For example, [individual] substance is an ontological category and, as I have argued in detail elsewhere, carbon-based living organism is a natural kind which is a species of that ontological category and which is such that what it is to be an instance of that more specific natural kind can at least in part be explained by means of a posteriori theoretical discoveries of natural science. See Rosenkrantz (2001).

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predicates in question it is only the second which is the proper expression of the category under discussion. In the light of my argument above it can be seen that of the two predicates in question, it is only the second which satisfies condition (6). (7) If ‘F’ is a conjunctive predicate which has another non-atomic predicate as a part, then such a part is either a negative predicate as in (5) or a conjunctive predicate; the number of such negative parts of ‘F’ does not exceed the number of non-negative predicates which are parts of ‘F’. (8) ‘F’ is either atomic (logically simple), negative, or conjunctive, and may be of any one of these three sorts.

For example, atomic, negative, and conjunctive predicates such as ‘substance’, ‘non-concretum’, and ‘reflectively thinking unlocated substance’, respectively, express ontological categories. In particular, arguably, the latter two predicates express definitions of the categories of abstract entity and (Cartesian) soul, respectively. Intuitively, however, a disjunctive predicate, e.g., ‘substance or attribute’, ‘body or soul’, does not express a category. An ontological category does not consist of a disjunction of categories whose instances would be by and large ontologically dissimilar, as in the first example. Moreover, because an ontological category is essentially general in character, such a category does consist merely of a list of other categories, even if the instances of such categories would ontologically resemble one another in some significant respect, as in the second example (where bodies and souls are both substances). For related reasons, a conjunctive predicate such as ‘abstract and not a property and not a relation and not a proposition’ does not express an ontological category (even if it is equivalent, say, to ‘set’). In other words, it is intuitively implausible to suppose that an ontological category consists predominately of a list of the categories to which a certain kind of entity does not belong. (9) Neither ‘F’ nor any of its parts is synonymous with a non-atomic predicate of the kinds excluded by (8), (7), and (6).

For instance, if it were stipulated that the atomic predicate ‘subprop’ abbreviates the disjunctive predicate ‘substance or property’, then ‘subprop’ would not express a category; it would be no more than a disjunctive predicate in disguise. (10) ‘F’ is not a conjunctive predicate such that one of its conjuncts entails another one of its conjuncts, unless ‘F’ is such that: (i) only one of its conjuncts expresses the notion of entity, and (ii) only one of its conjuncts entails another one of its conjuncts.

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Condition (10) has the consequence that, e.g., the predicates ‘substantial body’ and ‘substance and substance’ are not proper expressions of the categories of body and substance, respectively. This consequence of (10) is an intuitive one in the light of the fact that those predicates are gratuitously complex or redundant expressions of these categories. Another intuitive consequence of (10) is that, e.g., the predicates ‘substantial entity’ and ‘abstract entity’ are proper expressions of the categories of substance and abstractum, respectively. A further interesting and important question is whether conditions (1)–(10) are jointly logically sufficient for a meaningful well-formed predicate’s properly expressing an ontological category and thereby provide a philosophical analysis of what it is to be a meaningful well-formed predicate which properly expresses an ontological category.13 I am unaware of any good reason to reject the claim that conditions (1)–(10) provide such an analysis. It may be observed in this regard that the conjunction of these ten conditions seems to be consistent with the assertion that predicates such as ‘positive number’, ‘negative number’, ‘even number’, and ‘odd number’ – predicates that express kinds which figure in the a priori (abstract) science of arithmetic – properly express ontological categories (although not necessarily within the same ontological taxonomy). But it is not evident that this assertion is objectionable.14 13 As I understand the notion of a philosophical analysis, such an analysis consists of an analysans that provides an explanatory logically necessary and sufficient condition for an analysandum. 14 Earlier versions of this chapter were presented at The Great Conversations Lecture Series at the University of North Carolina at Greensboro on 23 March 2006, and at the conference on The Metaphysics of E. J. Lowe hosted by the Department of Philosophy of the State University of New York at Buffalo on 8–9 April 2006. I would like to express my appreciation for the very useful comments that I received at each of these gatherings. I would also like to express my appreciation to my colleague Joshua Hoffman for his many helpful and insightful comments.

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Are any kinds ontologically fundamental? Alexander Bird

6.1  I n t roduc t ion Are any natural kinds ontologically fundamental? This question may be put in a different way: do we need a category of kinds? We use kind terms in a name-like way, and we can count kinds (‘there are 92 naturally occurring chemical elements’). But if we look at the fundamental constituents of the states-of-affairs that involve kinds, do we find entities that are the natural kinds? Whereas David Armstrong takes a reductive attitude towards natural kinds, E. J. Lowe regards kinds as ontologically fundamental. His ontology requires four categories, one of which is reserved for the natural kinds – substantial universals as he calls them. In this chapter I shall examine Lowe’s claim that kinds are fundamental. I conclude that it is unwarranted. We can see that all that we require are universals. Kinds are complex universals, and their existence depends on the more basic universals, laws, and certain contingent facts. Among the basic universals, kinds are not required. 6.2  K i n d s i n L ow e’s f ou r- c at e g or y on t ol o g y Whereas some metaphysicians aim to produce an ontology with two categories (e.g. particulars and universals) and others have ontologies with just one category (e.g. tropes), E. J. Lowe (2006) has an ontology of four categories, in which we have individual substances (objects, particulars), modes (property/relation instances, tropes), and two species of universal: attributes (non-substantial universals, properties/relations) and substantial universals (kinds). These are related in a satisfying manner in what Lowe calls ‘the ontological square’ (see Figure 6.1). Consider a polar bear named Ursula. According to Lowe, the bear exemplifies the attribute of whiteness. This comes about in two ways. On 94

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substantial universals

characterized by

attributes

instantiated by

exemplified by

instantiated by

individual substances

characterized by

modes

Figure 6.1  Lowe’s Ontological Square with four categories.

the one hand there is a particular mode or trope of whiteness, the whiteness of this bear Ursula. Ursula’s whiteness mode is an instance of whiteness the attribute, and Ursula is characterized by her whiteness mode. So this manner of Ursula’s being white involves the bottom and right-hand connections in the ontological square. At the same time Ursula belongs to the kind Ursus maritimus. Since it is in the nature of the kind to be white, we can say that U. maritimus is characterized by the attribute whiteness. This is parallel to the fact that individual Ursula is characterized by her whiteness mode. The kind (substantial universal) U. maritimus is instantiated by the individual Ursula. This is parallel to the fact that the attribute of whiteness is instantiated by the mode that is Ursula’s whiteness. This account of Ursula’s whiteness involves the left and top sides of the square.1 In Lowe’s view, when an individual, such as Ursula, instantiates a kind, such as U. maritimus, and the kind is characterized by an attribute, such as whiteness, it is not entailed that the individual in fact exemplifies the attribute. Rather, the individual is disposed to exemplify the attribute. So if we knew only that the top and left-hand connections held, we would be able to conclude only that the individual was disposed to manifest the attribute, not that she actually manifests it (Lowe 2006: 16). Furthermore, the top connection, between kind and attribute provides the simplest version of the general form of a law of nature. Laws are the characterization of kinds by attributes. The ontology that has just the bottom left and top right nodes (see Figure 6.2): particulars/substances and non-substantial universals/attri­ butes, with the single connection (exemplification or instantiation) is a

  See Schneider (2009) for a careful articulation of the Ontological Square.

1

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instantiated by (exemplified by)

particulars (individual substances)

Figure 6.2  Armstrong’s two categories.

popular one; it is Armstrong’s for example. So an obvious question is: why do we need the additional two categories: modes and substantial universals/kinds, plus the two additional connections between them, instantiation and characterization? I shall not consider the need for modes. Here, rather, I shall question the need for the category of kinds. Armstrong (1997: 67) puts the case, for and against, thus: The electron is not at present thought of as having any structure and all electrons are thought of as identical in nature. Perhaps, then, we should recognize a kind: electronhood? It would appear, however, that a reductive account is available of electronhood. Unlike an ordinary macroscopic object, or even a molecule or atom, the electron is not credited with very many properties. And for properties to make it electron there are required only mass, charge, and the absolute value of the spin, properties that are identical in all electrons. When, then, should not electronhood be identified with the property that is the conjunction of these three properties?

6.3  D o l aw s r e qu i r e k i n d s ? As we have just seen, Lowe uses the left-hand side of his ontological square in the characterization of laws of nature. As I summarized the view, laws are the characterization of kinds by attributes. So is it the case that an adequate account of laws requires the existence of kinds?2 2 The argument from laws is not Lowe’s only argument for the category of substantial universals; he has further arguments from individuation and instantiation.

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The involvement of kinds in laws seems to be required by the example given, that U. maritimus is white – if that is a law at all. For that does not appear to allow for a simple reduction in the manner that Armstrong suggests for propositions concerning electrons. Lowe gives another example: Kepler’s first law, that planets travel in ellipses. Here again it looks as if we are predicating something (‘travels in ellipses’) of a kind (the kind planet) in a manner that does not allow for easy reduction of the latter. Is Lowe right, that this is what a law is, in its most basic form: the characterization of a kind by an attribute? Counterexamples spring easily to mind. Newton’s law of gravitation is one: F=G

m1m2 r2

Here it would appear that no kinds are mentioned, just the masses of two objects m1, and m2, their separation, r, and the force between them, F. Lowe (2006: 158) thinks that this law does conform to the approved pattern, since the law can be understood as characterizing the nature of massive bodies quite generally, just as ‘gold dissolves in aqua regia’ states a fact about gold: It is true that many very different kinds of things can be massive, that is, possess mass  – for instance, stars, trees, and fish. However, what all these things have in common is that they are composed of matter: each of them is a massive thing because each of them is constituted, at any given time at which it exists, by a certain mass of matter, albeit by different such masses at different times. Strictly speaking, then, Newton’s law of gravitation is a law concerning the nature of masses of matter. One might think that this is stretching the notion of kind or substantive universal, but perhaps this is such an (almost) all embracing kind, that although a kind, it does not attract our attention as such because it is not useful for distinguishing one class of things from another. A more significant problem is that not all laws can be dealt with in this way. Consider Coulomb’s law of electrostatic force: F = − ∈0

q1q2 r2

If Lowe were to treat this analogously to Newton’s law of gravitation, then he would have to say that charged bodies form a kind. But that suggestion is implausible. Note that this law governs neutrally charged objects just as much as charged ones. It tells us that the force on a neutrally

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charged object is zero, and this is not trivial, since it allows for predictions and explanations. For example, a cloud chamber photograph may show the tracks of particles in an electric field: the negatively charged particles curve in one direction, the positively charged objects curve in the opposite direction, and the neutral objects travel in a straight line. The law explains all these behaviours. So the kind governed by Coulomb’s laws includes every object. Is this kind then, the charged-or-neutral kind, the most inclusive kind of all? That seems odd – what is so special about charge? Indeed, returning to Newton’s law, in Einstein’s reformulation, that too encompasses bodies of zero (rest-)mass (photons are subject to the same law). Hence there is a charged-or-neutral all-encompassing kind and there is a massive-or-massless kind, and these are coextensive.3 This is straining the position. What seems to be clear is that such laws have nothing to do with kinds at all. Rather, these are universal laws (they cover everything, without exception) and concern not the kinds to which entities belong but the properties (mass, charge) that the entities possess. Thus it is not the case that all laws can be considered as the characterization of kinds by attributes. However, that conclusion does not show that laws form no basis for asserting the existence of kinds. For some laws might have this structure, and these might include the examples to which Lowe refers. The problem with saying this is that it leads to the conclusion that there is more than one sort of law of nature. In one the fundamental structure involves kinds, in the other it does not. It is then unclear what makes them both sorts of law. More plausible is the idea that there is just one sort of law and either (a) kinds are not involved in laws at all, or (b) if kinds are involved, then they do not form a fundamental category distinct from the category of universals/attributes. Option (b) ought to include the possibility that kinds form a category distinct from that of universals/attributes but not a fundamental category – facts about kinds, including laws, might supervene on laws involving just universals. Consider Lowe’s example, the law that planets travel in ellipses. In this case there is some doubt over whether ‘planet’ forms a genuine kind at all. 3 As E. J. Lowe has pointed out to me there are no known massless charged particles. Although there has been speculation about such a possibility, it might be that such particles are indeed impossible. And so the massive-or-massless kind might not be perfectly coextensive with the charged-or-neutral kind, if we exclude the massless items from the latter. See Lowe (2009a) for more details on the syntax and semantics of laws containing complex sortal terms such as ‘charged body’.

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Though, interestingly, it does not matter much where the dividing line for ‘planet’ falls as far as this law is concerned. For entities smaller than planets obey the ellipse law (comets, asteroids). This suggests that the law does not really concern any kind planet at all. And indeed it does not. For Kepler’s first law is derivable from Newton’s laws of gravitation and motion plus the assumptions: (i) the system has only two bodies, (ii) one body (the Sun) is much more massive than the other (the planet), (iii) the orbit is periodic.4 The reference to ‘planets’ in the law makes assumptions (ii) and (iii) true, but what explains the elliptical orbit is not the fact that the object is a planet, but that it is much less massive than the object it is orbiting. As far as this law is concerned, it seems that response (a) is correct, and Armstrong’s reductionism is vindicated. 6. 4  K i n d s a s c om bi n at ions of prope r t i e s Now let us consider the other law mentioned, that U. maritimus is white. While this looks less like a traditional law, it does look more promising as a proposition that involves a kind in a way that does not permit the easy elimination that was available for ‘planets travel in ellipses’. Nonetheless, the proposal that natural kinds are homeostatic property clusters at least suggests a possible reduction. According to the homeostatic property cluster view, under certain circumstances a combination of properties can constitute a natural kind (Boyd 1999, Millikan 1999). This occurs when the laws of nature ensure that certain combinations of properties are disposed to be more frequently instantiated than other, nearby combinations of properties. In some cases the laws make those other combinations of properties impossible. So while the property of having nuclear charge of three times the charge of a proton is instantiated in many entities (lithium atoms), and the property having nuclear charge of four times the charge of a proton is also instantiated in many entities (beryllium atoms), the property of having a nuclear charge of pi times the charge on a proton is not instantiated by any entities. The property of having nuclear charge of three times the charge of a proton can be combined with various properties of nuclear mass, ranging from 6.6 to 19.9 x 10-27 kg, but not with any nuclear mass properties greater or less than these limits. These other combinations are excluded by the laws of nuclear 4 We need assumption (iii) since parabolic and hyperbolic paths are also solutions to Newton’s equations in a two-body system.

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physics. In other cases the nearby combinations of properties are not uninstantiated, but are infrequently instantiated. This may be the consequence of homeostatic mechanisms that keep such combinations rare. Certain combinations of weight, length, fur colour, numbers of toes, etc. are commonly instantiated in wood mice. Mice that weigh 25 g, are 8 cm long, and have brown fur are common. However, a mouse that was 80 g, 12 cm, and had bright orange fur would be less evolutionarily fit (being less able to breed with other mice, and more vulnerable to predation) and so will be unlikely to have many offspring compared to the more normal mice; hence that combination of properties (along with other murine properties) is likely to be infrequently instantiated at best compared to standard combinations of mouse properties. Now consider ranges of properties in combination, e.g. weight of 20 g to 35 g and length of 7 cm to 12 cm and … (similarly for other murine properties). We could regard this collection of properties as the natural kind Apodemus sylvaticus. Of course, other combinations of ranges (weight 25–40 g and length 8–13 cm and …) might also claim to be the collection of properties that is the kind. This question is the same as that which we face when we consider which collection of particles is some particular person or object; the metaphysics of vagueness has various competing answers to that question. That problem does not itself require us to deny that the object is indeed the sum of its parts, even though there is vagueness surrounding which parts those are. Likewise we can regard the kind as the sum of its constituting properties, even though it is vague which properties those are. We could regard the combinations or sums of properties as constituting a new category of entities (as briefly suggested above). More plausibly they belong to the same category as the entities of which they are composed, just as complex particulars are particulars as well as the particulars of which they are composed. Since the properties in question are universals (Lowe’s attributes), we should therefore think of a natural kind as a certain sort of complex universal. But even if natural kinds were members of a sui generis category, their existence would not be fundamental but would be dependent  – dependent on the (non-substantial, i.e. nonkind) universals, the laws, and possibly certain contingent features of the world. Either way, we can see that what kinds there are in a world does not require the existence of natural kinds as fundamental entities. As it stands, this argument may not convince Lowe, since he holds that the laws themselves involve kinds. But as we have already seen, this is implausible for fundamental laws.

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6.5  T h e i n f e r e nc e probl e m Lowe claims that his ontology has an advantage over Armstrong’s when it comes to our understanding of the laws of nature. We have seen that there is no special reason to think that laws need to be understood in terms of substantial universals as opposed to attributes. Lowe’s view might nonetheless be favoured if it can avoid the metaphysical problems that beset Armstrong’s view. Armstrong holds that laws should be understood as second-order relations between first-order universals (attributes). The second-order relation is symbolized by ‘N’ (for ‘necessitation’). So ‘N(F,G)’ symbolizes the law that Fs are Gs. Armstrong tells us that: (I) N(F,G) entails ∀x(Fx → Gx) The inference problem (van Fraassen 1989: 38–9) for Armstrong is to explain how it is that N achieves this. There are other second-order relations among universals that do not have this property. So what is it about N that means that when two universals are related by N there is also a universal generalization holding between them? Lowe believes that his account avoids this problem, since it does not invoke the general second-order relation N or anything like it. Rather, as we have seen, laws involve the characterization of a substantial kind, S, by an attribute, A: (II) A(S) Unlike Armstrong, Lowe (2006: 131) does not think that laws entail universal generalizations; so it is not the case that A(S) entails ∀x(Sx→Ax), and so the inference problem does not arise for Lowe as it does for Armstrong (Lowe 2009b). Rather, as mentioned above, the law does entail that each member of the kind in question is disposed in a certain way. The law that polar bears are white entails that polar bears are disposed to be white; this law is not falsified by the fact that some polar bears can appear pale green (on account of algae growing in their fur). The law that planets travel in ellipses entails that planets are disposed to travel in ellipses; this law is not falsified by the anomalous orbit of Uranus, disturbed by the gravitational pull of Neptune. And so it is true that: (III) A(S) entails ∀x(Sx → x is disposed to be A) However, it is unclear that Lowe’s view really does avoid the problems associated with Armstrong’s view. First, it is not quite correct to say

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that Lowe’s view does do without second-order properties and relations. Consider the law given above. S is universal and so is A. Since A is a universal characterizing a universal, it must be a second-order universal. Lowe might claim that this is not right, since S is a substantial universal and A is an attribute, whereas in Armstrong’s law N and F and G are all universals of the same category. But that seems to me to be a terminological difference. Armstrong could claim, on the ground that it is second order, that N is of a different category from F and G, and so say the same as Lowe. The Lowean law above is only the simplest form of a law. Consider ‘water dissolves salt’. We might symbolize this: D(W,S). As just argued, D, the dissolving relation, should be considered a second-order universal; and in this case, it is a second-order relation. Lowe (2006: 143–4) denies this on the ground that D can also relate particular objects, in instances of the law. So when some particular volume of water is dissolving some particular lump of salt (or is disposed to) then that relation is also D. But that does not seem quite correct to me. For particulars are not characterized by attributes; they are characterized by modes, and D is not a mode. Lowe does say that particulars exemplify attributes. But since characterization and exemplification are different connections between entities, it is a fallacy of equivocation (regarding the expression ‘stand in’) to say that both universals and particulars can stand in the relation D. Lowe does emphasize another difference between his view and Armstrong’s, that Armstrong employs one general relation N, whereas Lowe thinks that there is no general law-making relation. Rather, each law involves a specific attribute that suffices for a law when it characterizes a substantial universal. While this is an important difference, and one where my own sympathies lie with Lowe, it is worth noting that something like Lowe’s view may be reconstructed using Armstrong’s materials. Consider the Armstrongian law N(F,G) and now abstract the property F, leaving N(_,G). The latter can be regarded as a second-order property which in combination with a first-order universal delivers a law. For example, consider Lowe’s ‘planets travel in elliptical orbits’. Armstrong would construe thus as N(planet, travels in elliptical orbits). Now think of this as the (second-order) attribute N(_, travels in elliptical orbits) characterizing the universal planet. This is just the form that Lowe ascribes to laws, except that in this case the attribute property is complex. So Lowe’s account of laws can be reconstructed in Armstrong’s terms, differing only in that where Lowe has a simple attribute, Armstrong has a complex universal which in every case involves N plus some particular

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first-order universal. Now let us ask the question, what is it about Lowe’s understanding of laws that avoids the inference problem for Armstrong? The comparison between the views shows that where Lowe has a simple attribute, Armstrong has a complex one. But that should make no difference to the issue of how each is able to entail facts about particulars. If there is a mystery about how N can make (I) true, there must be a corresponding mystery about how A makes (III) true. The fact that N is a general component of laws in Armstrong’s account, while A is a specific universal does not make any difference to this problem; indeed, as seen, Armstrong can create a specific universal that is the analogue of Lowe’s. Equally, responses on behalf of one view will be available to the other. For example, one might argue that it is part of the essence of A that (III) is true. If that is an adequate answer for Lowe, then Armstrong can say that it is part of the essence of N that (I) is true.5 The conclusion of this section is that Lowe’s account of laws does not provide a metaphysics that avoids the inference problem for Armstrong, and so does not give us an independent, metaphysical reason for adopting a category of kinds. 6.6   C onc l us ion E. J. Lowe’s four categories do provide a satisfying ontology. Yet I believe that it is over-inflated. It does not need the category of substantial universals (natural kinds). Lowe thinks that they are needed to account for the laws of nature. But that does not seem right because many laws of nature, including the fundamental ones, do not make any mention of kinds. And in other cases where laws do appear to concern kinds, we can see that what is really doing the work is a law that governs non-kind universals. In such cases it looks as if a simple reduction of kinds to combinations of universals is available along the lines proposed by Armstrong. Not all kinds can be dealt with so easily, for example those in biology. Nonetheless, the strategy can be extended, by considering kinds as homeostatic property clusters. Although Boyd does not see the latter in ontological terms, we can construe them as sums of properties, just as complex particulars are the sums of their component parts. This approach does not eliminate kinds, but shows that they are a special class of complex universal. Finally 5 Such a response might well be Armstrong’s best option. But it does undermine his quasi-Humean rejection of essences of this sort and denial of metaphysically necessary connections between distinct existences. See Bird (2005).

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I considered the thought that while a fundamental and distinct category of kinds might not be strictly necessary to account for the claims of science, it might be required in order to avoid the metaphysical problems facing a sparser ontology. I have argued that analogous metaphysical problems in accounting for the relationship of laws to particulars beset Lowe’s four-category ontology as much as Armstrong’s two category ontology.

ch apter 7

Are four categories two too many? John Heil

This chapter was originally written for an event honouring E. J. Lowe. I have not attempted to alter its tone. I consider Lowe a philosopher of the first rank, a philosopher who has resisted the idea that philosophical problems are to be addressed in ways that keep ontology at arm’s length. Nowadays, too much work in metaphysics amounts to little more than the rearrangement of elements in a familiar landscape or the addition of epicycles to going theories. Lowe’s work is a fine example of what the Australians call ontological seriousness. He recognizes that metaphysical issues are not to be addressed by picking and choosing metaphysical nuggets that happen to support favoured theses. When you get on the bus, you must ride it to the end of the line. I see Lowe as a throwback to my Enlightenment heroes: Locke, Descartes, Priestley, Leibniz, Spinoza, and, in their own ways, Berkeley, Hume, and Kant. The best of these were throwbacks to their medieval scholastic predecessors, to Aquinas, and to Plato and Aristotle. The linguisticization of philosophy, and, in particular, metaphysics, in the twentieth century has blinded us to ways of thinking that were once universal. One symptom of this is the contemporary slant on the doctrine of truthmaking, the idea that, when a judgement concerning the world is true, something makes it true. Who, it is asked, is responsible for the truthmaking concept? The very question betrays a lack of understanding of the history of philosophy. The truthmaking concept is present in Plato, in Aristotle, in the medievals, and in the Enlightenment. If it is not discussed by name, this is only because it was woven into the philosophical fabric, too obvious to discuss. If there is no spelled-out truthmaking doctrine, this is because there is no need to spell out what everyone accepts. Originally presented at a conference, ‘The Metaphysics of E. J. Lowe’, at the State University of New York at Buffalo, 8–9 April 2006. Parenthetical references are to Lowe (2006). I am grateful to E. J. Lowe, and to David Robb for discussion.

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The fact that nowadays we need to discuss truthmaking explicitly speaks volumes about the tenor of contemporary philosophy. In invoking truthmaking here, I am not concerned with the question whether every truth requires a truthmaker, but in the idea that we can have rational confidence that certain of our claims about the world are true without having a very clear idea what it is about the world in virtue of which they are true. Physicists express confidence that the quantum theory is true, but there is little agreement on the character of the truthmakers, how the world must be if quantum theory is true. The idea that we can ‘read off’ the nature of a truthmaker by a careful analysis of our expressions of various truths is a near cousin to the Berkeleyan idea that all there is to science is the discovery of equations that enable us to predict and manipulate the phenomena. You can see what I have in mind by considering relations. Beginning perhaps with Aristotle, philosophers have felt obliged to give an account of the ontology of relations. What are relations? Aristotle was only the first to note that relations seem not to be accidents, features of objects standing in the relations. But if relations are ‘outside’ or ‘between’ their relata, they would need to be substances, an even worse prospect. One possibility is that, while relations are not ‘reducible’ to ‘monadic’ features of their relata, they are ‘founded’ on those features. Consider Simmias’ being taller than Socrates. Suppose Simmias is six-feet tall and Socrates is five-feet tall. If you have Simmias and Socrates possessing these intrinsic features, you thereby have its being true that Simmias is taller than Socrates, you have Simmias being taller than Socrates. This works nicely for ‘internal’ relations, but what of ‘external’ relations: being a mile apart, being caused by? I am optimistic that relations quite generally can be shown to be ‘internal’, hence ‘no addition of being’. Relational truths are ‘founded on’ – made true by – non-relational features of the world. Suppose something like this were so. How should we describe the resulting view? Is it eliminativist or reductionist? Does it ‘eliminate’ relations, leaving only ‘monadic’ properties? Does it ‘reduce’ relations to monadic properties? Eliminativism seems hopeless (are we to say that Simmias isn’t taller than Socrates, Thebes isn’t northwest of Athens? And, in any case, didn’t Russell (1903a: chapter 26) show that reduction is equally hopeless? In fact, if the structural realists are right, scientific truths generally can be captured in a wholly relational vocabulary (Dipert 1997; Ladyman 2007). (From this they conclude that the world itself, the truthmaker for these theories, must be fundamentally

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relational: non-relational features of the world are constructed out of relations.) But you can reject both elimination and reduction without accepting the idea that truthmakers for relational truths are, in addition to the objects and their ‘monadic’ properties, a distinct category of relations. That is, truthmakers for relational claims might turn out to be non­relational features of the world (see Heil 2009; Parsons 2009). My aim here is not to drum up support for a quirky account of relations, but to illustrate a particular way of thinking that we seemed to lose sight of in the twentieth century. Most philosophers writing today accept Quine’s thesis that we are ‘committed to’ the existence of whatever we ineliminably quantify over. Our quantifying over relations indicates that we are committed to the existence of relations. This seemingly innocent thought, however, is at odds with the deeper idea that we are in no position to read off ontology from our theories. If we could, there would be no quantum mysteries. If we could, we would need to populate the world with relations – alongside the objects and their properties. Quine’s thesis of ontological commitment is meant to be of a piece with the thesis that philosophy is continuous with science. But what does this mean? In what sense is it true? Is it that fundamental metaphysical truths are implied by scientific theories? That seems unlikely. Rather metaphysics – ontology – is in the business of saying what the world must be like if we accept the truth of what the sciences tell us. We evaluate ontological theses by reflecting on their scope and power to illuminate our conception of the world given truths uncovered by the sciences, and, let us not forget, truths of ordinary experience. If we are to appreciate Lowe’s four-category ontology, we must see that ontology in this way. In so doing, we will see it as belonging to an important philosophical tradition, one twentieth-century philosophers who took the linguistic turn did their best to eradicate. 7.1  U n i v e r s a l s a s a n ac qu i r e d ta s t e The remarks that follow are meant less as objections to Lowe’s ‘four-category ontology’ than as requests for clarification. When it comes to ontology, I have the flat-footed belief that, if you can’t figure out how it works, if you can’t whistle it, as Charlie Martin liked to put it, you don’t get it. This is where I am with Lowe’s ontology. I think I have a grip on the modes and substances, but I’m stumped by universals.

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This apparently sets me at odds, not only with Lowe, but with those who regard ontology as a chalk-and-blackboard affair: ontological problems are tamed by providing intricate formal solutions to those problems. Not only am I too dense to get much out of such accounts, I find them unsatisfying in the way you might find ‘lite beer’ unsatisfying. Although few philosophers nowadays would agree, contemporary analytical metaphysics strikes me as insular and unproductive, metaphysics blended unobtrusively with the philosophy of language, nothing at all like the full-bodied metaphysics developed by our Enlightenment predecessors: Locke, Descartes, Spinoza, Leibniz, Kant. Let me call attention to two features of these philosophers’ views, features they share despite important differences elsewhere, features that today would be regarded with deepest suspicion. The first feature is a belief in properties coupled with a denial of universals. Locke et al. regarded properties as modes, what we nowadays (and for no very good reason, so far as I can tell) call tropes. Today universals have the upper hand, so much so that they constitute the default conception of properties. Universals are the reigning heavyweight champs: you can oust universals only if you have a decisive argument against them. I am content to throw myself in with Locke and the rest, however, and regard universals as the odd ducks. My suspicion is that belief in universals is part of what is involved in the indoctrination we all undergo en route to the Ph.D. We get used to the idea, and so learn to swallow our initial qualms. A second feature of what I think of as Enlightenment philosophy is one that would today be regarded by many philosophers as scarcely intelligible. This is the idea that there is no guarantee that things populating our world belong to the ontological categories we might take them to belong to when we engage in conceptual analysis. For Locke, Descartes, and Spinoza, material objects answering to sortals turn out to be modes, not substances: particular ways the particles are organized, or, alternatively, localized ‘thickenings’ of space or the One. A stunning, but ill-understood, instance of this is Locke’s assessment of persons. Locke takes issue with Descartes: persons are not thinking substances. Persons are not substances at all. Persons are modes – or perhaps gappy sequences of modes exhibiting the right sort of causal and psychological continuity. Although Locke is clear on the point, this feature of his view is rarely emphasized – perhaps because it doesn’t rise to the level of serious consideration.

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Today such views are interpreted as eliminativist. If trees, for instance, aren’t substances but ways the corpuscles are organized, then there are no trees. If the view is eliminativist, however, it is not obviously eliminativist about trees. What are eliminated are certain favoured philosophical theses and their posits. The move here is not to identify trees with collections of particles or thickenings in regions of space, but to suggest that truthmakers for claims about trees could turn out to be fleeting collections of particles or ripples in the fabric of space time. Such a conception is neither reductionist (talk of trees is not re-expressible as talk of particle-arrangements) nor eliminativist (‘there are trees’ is perfectly true). It merely acknowledges a chasm between ordinary conceptions of the world and ways the world is that serve as truthmakers for these conceptions. I do not expect much support from readers of this volume for these observations, but I would like at least to note that they were regarded as having merit by a diverse and much admired collection of philosophers. 7.2   W h at a r e u n i v e r s a l s ? I began with an admission: I don’t ‘get’ universals. In saying this, I am not being coy. I am admitting failure. I am admitting that, although I have learned to talk the talk, I really have no idea what I am talking about when the talk concerns universals. I have roughly the same feeling when I try to understand Kant. After many readings, I begin to relax into Kantian locutions. But, when I pause to think about it, I find that I am still in the dark as to what these boil down to. In my more cynical moments, I wonder whether commentators on Kant really understand better than I do, or whether they have just become adept at making readers comfortable with Kant’s prose. As someone who initiates Ph.D. students into the cult, I have been struck by the thought that philosophical education is most effective – and most pernicious – when it de-sensitizes us to questions of the kind smart firstyear undergraduates ask. How often do we adopt views not because we understand them, or because we have good reasons for holding them, but because we have grown comfortable with them?1 It helps when these views incorporate an element of the outrageous. This gives them an air of excitement, thereby defusing the perennial 1 Growing comfortable with the right views is a requirement for admission to what is now regarded as the profession of philosophy.

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philosophical worry that philosophy at its best merely tells us what we already know. It also insulates the views from one sort of criticism, the sort that begins with the observation that the views are in some way outrageous. I am probably alone among contributors to this volume in having such thoughts in so far as they concern universals. Universals have had, after all, a long and distinguished history. Astute philosophers have embraced universals. The idea that such philosophers might not have known what they were talking about sounds hollow coming from a light-hitting metaphysical middle infielder. I am not arguing against universals, however, merely expressing my own inability to come up with a clear idea of what they are, what they are meant to do, and why they are supposed to help us understand the world. 7.3  W h at u n i v e r s a l s a r e s a i d t o be David Armstrong thinks of universals as being wholly present in each of their instances. Sphericity is wholly present in every particular sphere. I don’t get it. Yes, I know, universals differ from particulars. A particular sphere cannot be wholly present in distinct places at once. But, Armstrong tells us, particulars are one kind of thing, universals another. Truths about particulars have no application to universals. It is unfair to try to think about universals using particulars as the model. But then I don’t know how to think about universals. D. C. Williams, famous for introducing a generation of philosophers to what he dubbed tropes, is on my side here (see Williams 1959). By Williams’s lights, philosophers who regard universals as identical across their instances aren’t thinking what they think they’re thinking. Once we consider an object’s being some particular way, we have a capacity to consider other objects as being the same way. But a way an object is, what Lowe calls a mode, Williams a trope, is as particular as can be. We can speak of the ‘same mode’ in the sense that we can speak of bankers wearing the same tie or driving the same car: distinct modes can be identical in the sense of being exactly similar. So, according to Williams, when philosophers think of universals as being identical across instances, when they ‘generize’, this is all they could be thinking. Lowe rejects Armstrong’s conception of universals. Universals have instances but are not identical with their instances. Lowe and Armstrong agree that universals depend on their instances; the instances are

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‘metaphysically prior’ to the universals. It is easy to see how this might be so for Armstrong. A universal is wholly present in its instances; if there are no instances, there is no place for the universal to be. Matters are less clear in Lowe’s case. Think of a situation in which some universal not previously instantiated comes to be instantiated. Arguably, this happens whenever we create a ‘new’ element in a collider. Now we have the instance and the universal. Do they come to be together? The universal wouldn’t have existed without the instance. This suggests an asymmetrical dependence of some kind. What kind? Once in place, the universal is supposed to be what it is in virtue of which the particular is what it is.2 Yes, I know, the idea that universals ‘come into existence’ is hopeless. But why? Imagine a world in which element E is created in a collider. The corresponding universal exists – presumably ‘timelessly’ – in this world. Now imagine a world, indiscernible from the first up to the moment E is about to be created, that ceases then to exist. In this world, there are no E-instances so no E-universals. Do the worlds differ universal-wise up to the E-creating event? I am sure there are straightforward answers to such questions, but, I am at a loss to imagine what those answers might be. My impoverished universal concept lacks easy projectability. Some will roll their eyes and note that, well, come on, universals are not concreta; universals are abstracta. Universals are not parts of the space time edifice. Let it be so. But now what exactly are we letting be so? What, for instance, constrains claims about abstracta? And how are abstracta related to concreta? We have the universal sphericity and we have the sphericity of this sphere. I like to think that, when the sphere rolls in a particular way, it rolls in that way because of its sphericity. What has the universal to do with this? How does appeal to the universal here help me understand why this sphere rolls? Sphericity is what Lowe sometimes calls an attribute. Let me note in passing that this use of ‘attribute’ differs from Descartes’s and Spinoza’s use of the term. For Descartes and Spinoza, extension is an attribute. This attribute is possessed by objects by virtue of those objects’ being extended in determinate ways: being one meter square, for instance, or being 2 Lowe tells us that universals ‘depend non-rigidly’ on their instances (a universal requires only some instance or other), but the instances ‘depend rigidly’ on the universals. Examples of rigid dependence are the dependence of a hole on its ‘host’, and the dependence of a heap of stones on the stones making it up (34). It takes more than I can muster to move from these examples to relations borne by instances to the universals of which they are instances.

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c­ rimson. By ‘attribute’ Lowe means ‘property or relation conceived of as a universal’. Instances of these attributes are modes. Here Lowe’s usage diverges from Locke’s, Descartes’s, and Spinoza’s in a different way. If sphericity is an attribute, the sphericity of this sphere is a mode. Lowe’s modes are instances of universals.3 Locke’s, Descartes’s, and Spinoza’s modes are not instances of universals, however, because, in their worlds, there are no universals. The difference here is momentous. It’s not that Descartes, Locke, and Lowe have modes, but Lowe adds universals. For Lowe a mode is of necessity an instance of a universal. But Descartes’s and Locke’s modes cannot be regarded as instances in this sense. In that regard, they differ from Lowe’s in a fundamental way. It is thus potentially misleading to use a single term, ‘mode,’ to designate what Descartes, Locke, and Lowe have in mind. In any case, for Lowe, some universals, the ‘characterizing universals’, are attributes. There is, however, another category of universal: the kinds. Every object, this sphere, for example, is an instance of a kind (and perhaps of many kinds, provided those kinds stand in the right relations). The kind is not just a complex attribute. Indeed the relation the kind bears to an attribute is the very same relation borne by a particular object to its modes. This sphere’s sphericity is a way this sphere is. Sphericity, the attribute, is a way the corresponding kind is. One traditional function of universals is a unifying function. Particular spheres share a single property: many spheres, one sphericity. I have already confessed that I do not understand how this works. It will be no surprise, then, when I say I understand even less well how it works in the realm of universals. Let me explain. The sphericity of this sphere, a mode, is distinct from the sphericity of any other sphere. Modes are ‘nontransferable’.4 Modes are dependent entities. A mode owes its identity to the object of which it is a mode. I think I have a grip on this. But now consider a spherical kind. Sphericity is a way this kind is. Here, however, the situation differs from the mode case. Presumably many different kinds are spherical. (Or if they aren’t, substitute some attribute shared among the kinds.) How does this work in the realm of universals? One and the same universal characterizes distinct kinds. In the realm of 3 Lowe describes both universals and modes as ‘ways’ (14); see also Levinson (1978). 4 Many self-described trope theorists follow Williams in regarding objects as congeries or bundles of tropes. Bundles can gain or lose tropes; a trope could migrate from one bundle to another. On such a picture, tropes become what A. J. Ayer, in describing sense data, called ‘junior substances’; see Armstrong 1989: 115.

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universals, however, there is only one of them, only one sphericity. What is it for that universal to characterize this kind and to characterize this other distinct kind? Some would regard this as a ridiculous question. It is of the essence of universals that they are shared. So what’s the problem? I am not saying that there is a problem here, I am saying only that I don’t know what to say. I don’t find it illuminating to appeal to relationships between particular modes and objects to which those modes belong to explicate relationships between property universals – attributes – and kinds. So I have a couple of nagging worries. First, we now seem to have a oneover-many problem in the realm of the one. At this point, I find myself completely at sea. Second, you might think that, if the relationship between attributes and the kinds they ‘characterize’ is the same as that between modes and particular objects of which they are modes, then attributes are ways kinds are. In that case, they would seem to owe their identity to the kinds they characterize. But, according to Lowe (chaps 7 and 10), the reverse is true: kinds depend both for their identity and for their existence on the attributes. The characterizing relation is an internal relation in which dependence goes one way in the case of particulars, and the other way in the case of universals. A mode is such that its existence necessitates, but is not necessitated by, the object it characterizes. So it would seem, turning this around, that kinds necessitate, but are not necessitated by, their attributes. I see how this works in a formal way: if you have a spherical kind, you have sphericity. But I wonder whether this sheds light on the characterization relation as it pertains to universals. You can’t have a red ball without having red and spherical modes. Yet these modes’ identities are wrapped up in the ball’s identity in a way the identities of attributes are not wrapped up in the kinds they characterize. Let me put this more plainly. I see how the relation between a mode and the object it characterizes could be an internal relation: if you have the object and you have the mode, you have the object’s being characterized by the mode.5 But the internal relation between a kind and its attributes is a different relation, not one that illuminates what it is for a kind to be characterized by an attribute. Undoubtedly there are tidy responses to each of these worries. I have the sneaking suspicion, however, that I will not be helped by those responses. I could be wrong. A part of me wants me to be wrong (at least about this). 5 In fact, as Lowe notes (167), if you have the mode, you have the object’s being characterized by the mode.

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But I feel like Charlie Brown and the football; in the back of my mind I know as I rush toward the target, it will elude me. 7. 4   U n i v e r s a l s a s e x pl a n at or y Suppose we set aside these pathetic autobiographical worries. Suppose we learn to love the universals, including the kinds. One benefit is that universals explain so much. At least we are assured that they explain much. I admit that I am not really very clear what they explain. Appeal to the kind electron is meant to explain why all electrons are alike, the kind horse explains why all horses, insofar as they are horses, are alike. I can see how this might be so if you thought of the kinds as patterns or moulds used by God or the Demiurge to stamp out objects that populate the world. But this is not what Lowe, Brian Ellis (2001, 2002), and others who regard kinds as universals – what once were called substantial forms – have in mind. Perhaps the kind explains the fact that the properties of electrons (and horses) cluster as they do. But what is the fact that we are explaining? The fact that there are electrons? No, that is something we turn to science to explain. The fact that the electrons are all alike and the horses are alike insofar as they are horses? Well, it is a fact that the electrons and horses are alike. But is this a fact that requires explaining? As a lover of modes, I think of similarity as an internal relation: if you have the relata you have the relation. But if that is so, then similarities we find among the electrons and among the horses seem not to require further explanation. In what way might kinds ‘explain uniformities amongst particulars’ (162–3). I will be told that the answer is obvious: the particulars are alike just in virtue of being instances of a single kind. But how is this explanatory? There is the kind and there are the particulars, its instances. In what sense does the presence of the kind explain anything? Suppose, following Locke, you thought that kinds were ‘nominal’. You would then have the idea, or the name, or the concept and its instances. It would be hard to see the idea, name, or concept as being explanatory, but why would a universal kind be any more explanatory? In each case we can say that individuals have the features they have because they are electrons. In the one case, they count as electrons because they are instances of a universal; in the other they count as electrons because they answer to the name or concept. In both cases we have a ‘because’; in neither case do we have an informative explanation.

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Perhaps kinds explain why we have electrons and not near-electrons. (A near-electron is very like an electron but differs in some small way: a near-electron might differ slightly from an electron in its mass.) Yes, but all it takes is one near-electron and we have the near-electron kind. Lowe worries that a ‘particularist,’ Locke, for instance, cannot explain why all electrons have similar powers and liabilities in terms of structural or ‘categorical’ similarities between them. Above all, [a particularist] cannot explain in these terms why all electrons have the same combination of powers and liabilities, and why certain other combinations of powers and liabilities are not to be found in any actually occurring species of fundamental particle. (161)

We explain why electrons are alike by noting that they are instances of a single kind, the electron kind, that possesses all the electron properties. But how does the presence of this kind explain the absence of particles with other combinations of ‘powers and liabilities’? The kind electron in no way excludes these other kinds, any more than particular electrons themselves exclude the possibility of particles with undreamt of combinations of properties. So here I am. I can’t see what exactly it is that the kinds are supposed to explain or make clear. I shall have more to say on this point presently. First, however, a look at dispositionality. 7.5  Di sp o s i t ion a l i t y Perhaps we can make progress by considering Lowe’s account of dispositionality. Here the idea is that an object, x, is disposed to F when (i) the kind of which x is an instance possesses F, but (ii) x is not F. This grain of salt is disposed to dissolve in water. Then the kind, salt, but not this grain of salt, possesses the property of dissolving in water. Consider this electron, e. Let us suppose that electrons annihilate when they encounter a positron. So e is disposed to annihilate on encountering a positron. This will be the case, even if e never encounters a positron. But now the electron kind is supposed to possess the property of annihilating in concert with a positron. It, the kind, doesn’t possess this property dispositionally; we are offering an explanation of dispositionality. So the electron kind is annihilating. Well and good, but it is also repelling other electrons and doing much else besides. The picture here is of the kind as being God-like: wholly ‘in act’. A kind is doing all its instances could do. As the electron example suggests,

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one reason this might be hard to swallow is that some of what an instance of a kind would do apparently exclude its doing other things. An electron would repel other electrons. Presumably, then, the electron kind is ‘characterized by’ repelling electrons. But an electron would annihilate were it to encounter a positron. So the kind electron, in addition to repelling other electrons is annihilating. I don’t want to say that this picture is impossible, but I admit I do not understand it. I do not see how a kind could be, timelessly perhaps, characterized by apparently incompatible properties. My puzzlement stems not from deep philosophical concerns, but from something far simpler: I just don’t get it. I don’t see how it’s supposed to work. Nor do I see how it is supposed to help us understand dispositionality. Concrete objects never, or only very rarely, do all they could do. This matchstick would ignite were it struck. What is the truthmaker for this dispositional assertion? Suppose that matchsticks are instances of some kind, K, and that K is characterized by igniting-when-struck. The matchstick would also taste metallic were you to touch it to your tongue. So the matchstick kind is also tasting-metallic-when-in-contact-with-a-tongue. The matchstick would puncture your eardrum were you to poke it into your ear. So the matchstick kind must possess the property of puncturingan-eardrum-on-insertion-into-an-ear. It’s hard to see how all this – and of course this is but the tip of a dispositional iceberg – could characterize a single object, no matter how protean. There is some hope here, because the object in question, the kind, is a universal, and it’s hard to know what constrains claims about universals. If such claims are constrained by consistency, however, I’m at a loss to see how one universal could encompass so much apparently incompatible diversity. Let me mention a more technical difficulty for Lowe’s position as I understand it. This grain of salt would dissolve in water. Thus the kind salt is dissolving in water. The kind enters into or is characterized by a relation to the kind water. Of course this grain of salt might never dissolve; it might never come into contact with water. Still, it is water-­soluble. Suppose this grain of salt exists outside the light cone of any water. In that case, although soluble, the grain could never dissolve. (I mean all this to be consistent with Lowe’s position.) But now suppose the world were such that no salt were within the light cone of any water. In such a world would salt be water soluble? I am strongly moved to think so. Yet in this world there are no instances of the relation salt dissolving in water. This would suggest that, in the

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imagined world, the salt kind is not characterized by water solubility (and, importantly, water is not characterized by the reciprocal universal). Lowe seems to deny this, but I don’t see how he is entitled to deny it, given the idea that universals require instances. In a world where no salt dissolves, what connects solubility to the salt kind? The salt is there, all there, and it is soluble. But how could this be in virtue of the kind salt’s dissolving? As long as we are imagining worlds, let’s imagine a world in which water, but not salt, is altogether absent. In such a world, would salt differ dispositionally from salt in our world, would it fail to be water soluble? Why should it? Yet here, surely, it won’t do to say that the salt kind includes solubility in water: the kind water is absent in a world lacking instances of water. Consider a universe consisting of a single, eternally ‘relaxed’ rubber band. It would seem that it could be true of this rubber band that it would stretch (or that it is flexible). But there are no instances of stretching, hence no universals to characterize the kind of which this rubber band is an instance. Now imagine the rubber band is stretched. Here we have the universals neatly in place. But it is hard to see anything like an order of explanation moving from the universal to the particular. It is hard to see that the rubber band is flexible because the kind stretches. When you consider the endless dispositionalities possessed by every object, and when you recognize that only a tiny fraction of these will ever be manifested, you will not find it difficult to suppose that there could be dispositions present in the world but never manifested. Here I am thinking not of particular dispositions – the solubility of this grain of salt – but of types of disposition. It would be near to miraculous if there were not genuine kinds of dispositionality never manifested in the actual world. Lowe would seem to be committed to the denial of this apparent possibility. In this regard Lowe’s conception of dispositionality resembles David Armstrong’s. Both are a species of conception that seeks to explicate dispositionality for some manifestation in terms of the actuality of the manifestation, both apparently hold that, if Fs are disposed to G, then some F, somewhere, somewhen, Gs. Perhaps, however, we should admit dispositionality as a fundamental feature of the ontological landscape, a feature that cannot be reduced to the non-dispositional. If you go this way, one important piece of the defence of universals falls away. We might not need – we might not want – to appeal to universals in accounting for dispositionality.

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Armstrong’s universals exist in, and only in, the spatio-temporal world. What of Lowe’s? Lowe is cagey on this point: universals ‘are not spatiotemporally located entities: they do not literally exist in the places or at the times in and at which their particular instances exist’ (158). On the one hand, universals are immanent. This suggests spatio-temporality and scientific respectability. But immanence turns out only to mean that universals require instances. On the other hand, universals are not identifiable with their instances. Universals are not in their instances, and not someplace else either. Perhaps we can obtain guidance on this point by considering what Lowe says about laws. Lowe follows Armstrong in distinguishing law statements from laws themselves. Laws are universal states of affairs, kinds characterized by various attributes. A law expressed by the sentence ‘Electrons have negative charge’ comprises a kind, electron, characterized by an attribute, being negatively charged. Laws on this view do not govern. Kinds do not influence or control their instances. Kinds are not cause-like.6 Indeed, any ontological dependence here goes in the other direction: kinds metaphysically depend on their instances.7 This is the doctrine of immanence. So what is the role of kinds? What exactly do kinds explain? Well, electrons exhibit negative charge because they are instances of the electron kind, a kind characterized by being negatively charged. But for all they contribute, kinds might be shadows or even terms or concepts; kinds might be abstracta in the traditional sense of abstracta. (I return to this possibility below.) Someone who doubted universals might nevertheless accept the contention that electrons are negatively charged as expressing something like a necessary truth, although one subject to revision. Why is this electron negatively charged? Because it wouldn’t be an electron otherwise. Both Lowe and someone who embraced a more deflationary view would say this. Is Lowe’s answer somehow meatier, more ontologically serious? Suppose you thought that law statements served a predictive function. Do the kinds have the upper hand here? Kinds don’t direct traffic. We can say that any of their instances will, in similar circumstances, behave More accurately, kinds are not efficient causes, they are Aristotelian formal causes. 7 Kinds depend ‘non-rigidly’ on instances; instances depend ‘rigidly’ on the kinds. As noted earlier, it is hard to see ‘rigid’ dependence as ontologically deep. At the risk of losing all credibility, I suggest that the dependence of instances on kinds resembles the dependence of dogs on the dog idea, concept, or term. If there were no dog idea, concept, or term, there would be nothing called a dog, although there might be plenty of dogs. 6

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similarly. But we could say the same, substituting terms or concepts for kinds-as-universals. Suppose the idea or concept of gold includes gold’s being soluble in aqua regia. Then we can say that whatever answers to this idea or concept is soluble in aqua regia. My aim is not to replace kinds with terms or concepts, nominal kinds, but to encourage Lowe (and the Aristotelians, generally) to explain more clearly what advantage kinds-as-universals have over ideas, terms, or concepts in this regard. Is it that an abandonment of kinds leads to rampant Humeanism? How so? Someone sympathetic to Locke who rejected universals might take modes to be powers. This gold dissolves in aqua regia because it has the power so to dissolve (and, significantly, aqua regia has the reciprocal power to dissolve gold). Notice that this gold’s power to dissolve is a power to dissolve in any portion of aqua regia; and this aqua regia’s reciprocal power is a power to dissolve any portion of gold. Individual bits of gold are indifferent as to instances of aqua regia: any would do. Similarly, volumes of aqua regia are indifferent as to portions of gold. Does any of this presuppose universals? If it does, I don’t see how. It assumes that different individuals can be alike in answering to our gold and aqua regia ideas, terms, or concepts. We might even think of the ideas, terms, and concepts as expressing kinds. The kinds in question would not be universals, however, only particulars similar enough to fall under the appropriate idea, term, or concept. Lest anyone imagine that appeal to ideas, terms, or concepts here is ontologically frivolous, let me remind you of two points. First, kinds conceived of as universals reside above the spatio-temporal fray. It is very hard to see them as anything more than pale reflections of goings-on in the world around us. Second, we do not come by ideas or invent terms and concepts ad lib. Scientific terminology reflects on-going hands-on involvement with the world.8 According to Lowe, we can truly say of any particular instance of aqua regia that it has the causal power to dissolve gold and of every instance of gold that it has the causal liability to be dissolved by aqua regia. Indeed, in my view, the fact that a particular instance of aqua regia has the power to dissolve gold is simply a consequence of two more fundamental facts: the fact that it is an instance of aqua regia and the fact – the law – that aqua regia dissolves gold. In short, particular objects derive their powers and liabilities from the laws governing the kinds which they instantiate. (160) 8 It is worth noting in passing that early modern and Enlightenment philosophers who had no use for universals were also major players in the scientific revolution.

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Lowe says that the power of aqua regia to dissolve gold is a consequence of facts about kinds, that objects derive their powers from the kinds. To the unwary reader this might suggest a picture of the kinds as somehow operative in the spatio-temporal world. But the sense in which it is true to say that the power of aqua regia to dissolve gold is a ‘consequence of’ or ‘derives from’ a universal is hard to distinguish from the sense in which it is true to say that this is a ‘consequence of’ ‘derives from’ instances of aqua regia being aqua regia by virtue of answering to the aqua regia idea, term, or concept. Going with Locke here is supposed to lead to Humean disconnectedness. Without the universals, it is all mere cosmic happenstance that distinct portions of gold are all soluble in aqua regia. Lowe again: For these philosophers, it would seem, laws must simply consist in regularities or uniformities concerning the powers and liabilities of particular objects. But how are such uniformities to be explained? Without the possibility of any appeal to universals, it might seem that such uniformities can amount to no more than cosmic coincidences. I can explain the uniform possession of a power to dissolve gold by all particular bodies of aqua regia by the facts that all of these particulars are instances of the same kind of stuff and that this kind of stuff is one in whose nature it is to dissolve gold – the latter fact constituting a natural law governing the kinds aqua regia and gold. But what can the opponent of universals say? (160)

Imagine Locke noting that anything lacking the gold-dissolving power would not count as aqua regia. In what sense is it a better ‘explanation’ to appeal to a universal here? What explanatory advantage is there to saying that instances of aqua regia have this power because they are instances of aqua regia? It is hard not to see a proponent of kinds-as-universals as positing an entity – the universal – where none is called for, then claiming an explanatory advance. You might worry that moving in Locke’s direction makes powers, laws, kinds, and the like ‘mind-dependent’. I don’t see it. The objects possess their properties mind-independently, and the properties empower their possessors. Our singling some of these out for special recognition reflects our interests, but what is singled out is as objective, mind-independent as can be. 7.7  T h r e e l i t t l e pu z z l e s Let me conclude this discussion by mentioning three aspects of Lowe’s view that you might find puzzling.

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First, according to Lowe kinds depend on attributes that characterize them. The dependence here is what Lowe calls ‘rigid existential dependence’. Examples of rigid existential dependence include the dependence of a hole on its ‘host’ and a heap of stones on the individual stones that make it up. Suppose kinds were bundles of attributes. In that case the rigid existential dependence of the kind on its attributes would resemble the dependence of a heap of stones on its constituent stones. But Lowe is not a bundle theorist. Kinds are not made up of attributes, attributes are ways kinds are. Kinds, in this regard, are substances. This picture is harder to square with the thesis that kinds depend rigidly and existentially on their attributes. Second, Lowe tells us that kinds are characterized by attributes, properties, and relations regarded as universals. The doctrine is reminiscent of the idea that the forms are self-exemplifying. What’s hard to understand, however, is how this could be so if universals are not (or ‘not literally’) in space and time. How could a kind be spherical, or dissolving, or rolling, or red if it is ‘not literally’ in the spatiotemporal world? Or are kinds ‘not literally’ spherical, or dissolving, or rolling, or red? If they are not literally these things in what sense are they characterized by these things? Third, consider this grain of salt. It is an instance of the salt kind. The salt kind is dissolving in water, tumbling down an inclined plane, and reflecting ultraviolet light in a particular way, but this crystal is doing none of these. Why not? Why do some of the properties of kinds find their way into instances of those kinds and some do not? What is the selection mechanism here? It’s hard to see how instances of kinds are in any way explained by those kinds when the kinds are one way, their instances another. 7.8  On e mor e s ho t at u n i v e r s a l s The line I have been taking here is doubtless flat-footed and uncharitable. It is as much an admission of a failure of imagination on my part as it is a criticism of Lowe on universals. I confess that I could be missing the mark badly. Indeed this is something that has occurred to me in the course of coming to terms with D. C. Williams’s (1959) discussion of universals.9 I shall briefly summarize Williams’s position, then suggest that there is some reason to think that Lowe’s considered view is, in important respects, similar to Williams’s. In that case, many of my reservations would be met.

  The discussion that follows is developed in more detail in Heil (In press).

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Some readers will be surprised to find Williams’s name associated with an account of universals. Williams is best known for defending a one category ‘trope’ ontology. But Williams did in fact advance an account of universals, an account that could have been embraced by Locke. Unsurprisingly, Williams’s begins with tropes, abstract particulars, Lowe’s modes: Socrates’ whiteness, for instance. Socrates’ whiteness is abstract, not by virtue of residing in Platonic realm outside of space and time. Its abstractness consists in the fact that its ‘separation’ from Socrates is something that could be accomplished only by means of a mental operation, abstraction, Locke’s ‘partial consideration’. You can consider Socrates, the man, but you can also consider Socrates’ colour, his mass, his height, his shape. These are ways Socrates is, modes, Williams’s tropes. Socrates is all these ways; these ways are all ways Socrates is. They are objective and as mind independent as you please. But in abstracting, in considering Socrates’ whiteness, you are considering, as it were, whiteness itself. In considering Socrates’ whiteness, a way Socrates is, you thereby consider a way other things might be: they might be this way, they might have this colour. Williams dubs this ‘generizing’, but the idea is implicit in Locke’s suggestion that wholly particular ideas can be used to express general thoughts (see Heil 2010). A philosopher who regards universals as ontologically fundamental will understand ‘the same’ in ‘Socrates and Simmias are the same colour’ as an expression of strict identity: there is some one entity shared by Socrates, Simmias, and every other white thing, everything with this colour, the same colour. Another possibility is that the ‘sameness’ in question is the sameness of exact resemblance. Williams’s suggestion is that in such cases we employ a notion of ‘“identity” which is just exact resemblance’ (1959: 8). This is the sense of identity in play when we think of electrons as being identical or a mother and daughter as having the same eyes. The electrons and eyes are identical in the sense of being exactly similar. Sameness is identity, but identity is not univocal. ‘Universals are not made nor discovered but are, as it were, “acknowledged” by a relaxation of the identity conditions of thought and language’ (8). That universals are determined by a ‘weaker’ identity condition than particulars does not even mean that they have an inferior or diluted reality. A tabulation of universals is just one way of counting … the same world which is counted, in a legitimately different and more discriminating way, in a tabulation of particulars. (1959: 9)

The upshot, what Williams calls ‘trope-kind’ theory, is straight out of Locke. The world is a world of particulars, but particulars are pregnant

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with generality. As soon as you have something being some particular way, you have the possibility that something else could be the same way. There is nothing in anything which is not either a trope or resolvable into tropes, so every trope, of whatever level of complexity, manifests its universal or kind. Generization, moreover, does not even stop short of concreteness, 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 attention or description, either the case or the kind of any given occasion, we can identify a universal once for all in a single instance, only conceiving ipso facto that it is capable of other instances. (1959: 10)

Williams regards trope-kind theory as a flat out, albeit ‘modest’, realism about universals (what Keith Campbell (1990: 44) calls ‘painless realism’), in as much as it holds that universals are real entities, and it is an immanent realism in as much as it holds them to exist in rebus – to be present in, and in fact components of, their instances. To make plain the sense in which it holds that an abstract universal is ‘in’ a concrete particular we need only make explicit the analysis of predication, characterization, or instantiation which has been barely implicit here all along. That Socrates is wise, i.e., that he is an instance of Wisdom, which is an ‘instantiation’ or ‘characterization’ in the full sense, is sufficiently expanded in the formula that the concrete particular Socrates ‘embraces’ [an] abstract particular (trope) which ‘manifests’ Wisdom. (1959: 10)

You might doubt that painless realism deserves to be called realism. If realism about the Fs requires that the world include, in addition to whatever else it includes, a class of entity, the Fs, then trope-kind theory is no realism. If, in contrast, realism about the Fs requires only that judgements about the Fs be, often enough, true, matters are different. Statements about universals can be true, but truthmakers for these statements are wholly particular. Whether previous immanent realists would recognize their view in this opinion that universals are immanent because they are, to speak crudely, the similarity roles (or ‘adjectival identities’) of abstract occurrents, I have some doubt. I am sure, from experience with myself, that an immanent realist begins by thinking he means more, but can bring himself to see, or think he sees, that he couldn’t mean more  – that every attempt to state an alternative results in something verbally but not significantly different from just redefining ‘identity’ by resemblance. (1959: 10)

What has this to do with Lowe’s conception of universals? Consider what Lowe has to say about abstracta: Abstract entities are not denizens of some ‘Platonic’ realm which is ‘separated’ from the world of things existing in space and time … To say that abstract

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entities do not exist ‘in’ space and time is not to say that they somehow exist ‘elsewhere,’ a notion which is doubtfully coherent in any case. It is merely to say that when we speak of abstract entities we must ‘abstract away’ from all spatiotemporal determinations and distinctions. (2002: 66)

This, according to Lowe, is how it is with sets. Although the planets are concrete objects, each one occupying some particular spatial location at every time during its existence, the set whose members are the planets cannot be assigned a spatial location and cannot be said to persist through, or undergo change in, time. A set of objects exists, timelessly and without spatial location, in any possible world just in case those objects exist in that world. Time and place simply do not enter into the existence- and identityconditions of sets and that is why they qualify as ‘abstract’ objects. (2002: 66)

Abstract objects, then, are not a special category of object, but concrete objects considered apart from, or independently of, their spatio-temporal trappings. In the case of sets or collections of objects, this is a matter of considering just those objects’ cardinality. The same holds for properties, conceived as universals, such as the property of being red or the property of being square. Even if the properties are, like these ones, properties exemplified by concrete things, such as flowers and books, the properties themselves are abstract entities because time and place do not enter into their existence- and identity-conditions. According to ‘Aristotelian’ realism concerning universals, it is a necessary condition of a property P’s existing in a world w that some object should exemplify P in w – and if that object is a concrete one, P will be exemplified by it at some time and in some place. But this does not imply that P itself exists at any time or in any place. By implication, then, I am rejecting here the doctrine, strangely popular just now, that universals exemplified by concrete objects are ‘wholly present’ in the space–time locations of those objects – a view which I have elsewhere argued to be incoherent. (Lowe 2002: 66; see also Lowe 1998: 155–6)

If you read such passages as expressing a version of Williams’s trope-kind theory, the result is a conception of universals according to which they are, as D. M. Armstrong (1997, 112–13) puts it, ‘no addition of being’. I like to think that this might be what Lowe has in mind. If that is so, however, universals and kinds would not, after all, constitute fundamental ontological categories. The situation would parallel accounts of relations according to which relational truths are grounded in non-relational features of the world. We are back to a two-category ontology. If, however, this is not what Lowe has in mind, I admit defeat. Nothing I have said here provides decisive reasons to doubt the existence of universals as ontologically fundamental. At most, my observations amount

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to a plea addressed to defenders of universals: consider providing those of us with tin ears better reasons for thinking that we couldn’t live without them. As a start, it would be good to have down-to-earth descriptions of the ontology universals, relations among universals, and relations of universals to particulars that do not fall back on metaphor. If anyone can do this, E. J. Lowe can.

ch apter 8

Four categories – and more Peter Simons

Philosophy will not regain its proper status until the gradual ­elaboration of categoreal schemes, definitely stated at each stage of progress, is recognized as its proper objective.

Alfred North Whitehead (1978: 8)

8.1  F ou r c at e g or i e s Jonathan Lowe has proposed that the four fundamental categories of things in the world are: substances, kinds, modes, and properties (Lowe 2006). Substances and modes are individual or particular; kinds and properties are universal. Substances are independent; modes are dependent on substances. Their respective species, namely kinds and properties, are themselves generically dependent on instances, but properties are also indirectly dependent on kinds in that there could not be properties unless there were instances thereof, i.e. modes, there could not be modes unless there were substances, and there cannot be substances that are not of a kind, so properties are indirectly dependent on kinds. This four-category ontology has a venerable pedigree, going back to Aristotle. In Book 2 of the Categories, Aristotle divides things ‘said without combination’ into those which are and those which are not said of a subject, and those which are and those which are not in a subject, where by ‘in’ Aristotle explains he means ‘in not as a part, but as unable to exist without’ what they are in, i.e. dependent. So the four categories arise from the crossing of two distinctions: the said of/not said of distinction, and the in/not in distinction. Aristotle calls those things which are not in something substance, whether first (individual) or second (universal, or kinds). Those things which are in something are accidents (symbebeka). In modern analytic philosophy, under the influence of predicate logic and its pioneers, this fourfold classification of things at the fundamental level was generally reduced to a twofold distinction between individual 126

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things and properties or attributes (allowing for relations as well as properties). Things were what attributes were predicated of, and a sentence was true if the thing in question had or exemplified the property in question. As Jonathan has shown, such a reduction is an impoverishment rather than a welcome simplification: it overlooks the difference between those kinds or universals which provide identity conditions for things that fall under them (sortal universals, kinds), and those which merely tell us what things are like (properties). Further, it ignores the grounds in the individuals themselves for the predicability of properties of them, namely their individual modes (or tropes, as they are now more widely known). As a long-time proponent of the importance of modes or tropes, I am happy to agree that the substance/mode distinction is a crucial one in ontology and that we neglect it at our peril. While unlike Jonathan I am a nominalist rather than a realist about universals, that is a relatively marginal difference of opinion in the present context so I propose to leave it on one side. Nothing in this chapter depends on taking one side rather than the other in that dispute. However, where I disagree with Jonathan over categories is not in the ones he proposes and the distinctions he makes, but in considering that we need more than he thinks, and that we need to dig more deeply into how the categories are distinguished one from another. 8.2  Di spu t e s ov e r c at e g or i e s Contemporary philosophy is at length beginning to rediscover the importance of categories. I mentioned in the previous section the impoverishing effect of predicate logic on the acceptance of two of the categories Jonathan Lowe upholds. The spectacular advantages of modern logic over traditional logic and the high prestige attached to its early proponents (Peirce, Frege, Russell) and their intellectual enterprises, combined with the standard way of providing semantics for such logic, conspired to make ontology, and consequently categories, appear to hang on the coat-tails of logic and especially semantics. Whether like Armstrong you accept a fourfold ontology of things, properties, relations, and states of affairs, or like Quine an ontology of things and sets, the underlying motivation appears to be that expressions come in different syntactic sorts: names, predicates (monadic and polyadic), and sentences, or that the semantics for predicate logic can be accomplished à la Tarski with just things and sets. Of course there are many variations of ontology among modern logicians. Church for instance, like Frege, has an ontology of things and an infinite

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hierarchy of functions, while more parsimonious logicians like Leśniewski try to get by with things alone. But the basic principle appeared to be that the ontology can be read off logic plus semantics. Like Jonathan, however, I consider ontology (and indeed all of metaphysics) to be the relatively prior discipline: until we have a general inventory of the items there are in the world we are not ready to give a definitive semantic account of what we are doing when we reason validly. Taking things this way round deprives the ontologist and in particular the ontologist interested in the most general kinds of things, the categories, of a methodological handrail to assist in determining which categories there are. And indeed the merest glance at the history of philosophy suffices to show a considerable variety of viewpoints exists. The most authoritative history remains the mammoth Geschichte der Kategorienlehre (1845) of Adolf Trendelenburg. It is striking how much diversity there was, even in ancient times, when the Stoic theory of categories is completely opposed to that of Aristotle. Most famously, Kant criticized Aristotle for rhapsodically ‘tossing out’ his categories, without system or principle; he replaced Aristotle’s eight or ten by his own very different twelve, derived from an analysis of judgement forms that is itself not beyond criticism. The question of how one arrives at and justifies a certain table of categories is a crucial one once we relinquish logico-linguistic clues. If ontology is prior to logic and language, there is no magic bullet or easy recipe. A system of categories has to prove itself as a framework for common sense and science, and in the to and fro of criticism, both empirical and conceptual. Any help is welcome, whether from the history of philosophy or elsewhere. It is in this spirit that Jonathan’s categories are proposed, and I thoroughly endorse the spirit, while disagreeing with some of the details. 8.3  T wo k i n d s of c at e g or i e s Aristotle’s categories are clearly intended to delimit the fundamentally different kinds of thing in the world: they are the supreme genera of being. As such they are ontic. Whether they actually succeed in ‘dividing reality at its joints’ is moot, but that is the intention. Kant’s categories on the other hand are not intended for any such thing. As a transcendental idealist, Kant does not think we are able to divide reality as it is in itself, but only as thought by us, or brought under concepts. His categories are therefore (merely) organizing principles of cognition, and this is why he

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looks to the forms of judgement to provide the ‘transcendental clue’ for the categories. It is not often I find myself in agreement with Kant, but in one respect I think he is right. We need certain concepts in order to make sense of experience, and some of these concepts fail to correspond to distinctions in reality. Since these concepts are there to help us in the knowledge enterprise, I call them auxiliary concepts and the most general ones auxiliary categories. Among the auxiliary categories are existence and the logical constants. Wittgenstein famously said of the latter that they ‘do not represent’ (sc. anything in reality), but serve the ‘logic of facts’.1 Put another way, we would not need the logical constants of negation, conjunction, disjunction, implication, quantification, etc. if we were omniscient. God does not need to know that something is not in a certain way, e.g. that the Earth is not a sphere, since she knows exactly in what way it is. Nor does she need to know it is this way or that, since she knows definitively it is this way. Negation, disjunction, existential quantification are all expedients for helping us over our partial ignorance. Existence is not a category dividing things because everything exists, and I think there are a host of other auxiliary categories including modality and abstraction. No matter, auxiliary categories are not my focus: ontic categories are. Like Aristotle and Lowe, I think some categories are ontic: they are concepts that (assuming things go well) divide reality at its joints, that is, reflect fundamental distinctions among the things themselves. 8. 4  Fac t or s: g rou n d s of c at e g or i a l di s t i nc t ions Leaving aside the question of how we come up with and defend a particular scheme of (ontic) categories, we may ask what is different about things that is the reason or ground in reality why they fall into these different categories. One answer might be that there is nothing: they simply do. I call this view surdism because it makes categorial distinctions surd or brute. Now at some level or other there may be surd distinctions, but not here, I think. The reason is that when we distinguish things in the different categories we have quite a lot to say about what it is that does so. For example substances differ from accidents in that substances are independent while accidents are dependent on substances. Admittedly there is a 1 ‘My fundamental thought is that the logical constants do not represent. That the logic of the facts cannot be represented’ (Wittgenstein 1922: 4.0312).

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little more to it than this when we come down to details, but the basic distinction remains, and it turns on the idea of dependence, about which Jonathan has written insightfully (Lowe 2010). Likewise the universal/ particular distinction turns on whether something is the kind of thing that can be predicated or said of another thing, or, as I would say (since predication is a logico-linguistic notion) whether something is such that other things can exemplify it or not. Universals are exemplifiables, indeed they are exemplifieds, particulars are only exemplifiers. Another distinction which is important in many ontological schemes is the distinction between things that are simple and those that are complex. Simple things are those which have no (proper) parts, while complex things have proper parts. Another distinction we find in many schemes such as that of Aristotle is that between the container or place of a thing and the thing in that place, location versus occupant. The last two distinctions turn on relations of part–whole and occupation. I suggest that all categorial distinctions among things can be given at least a partial descriptive–explanatory account along these lines, in which grounds of the distinction are given. To have a name for the grounds of categorial distinction, I borrow a term from mathematics and call them factors. An ontology which explicitly mentions and gives an account of the factors distinguishing the categories I call a factored ontology. It turns out there are more of them than one might expect. 8.5  S om e fac t or e d on t ol o g i e s We already saw that Aristotle’s and Lowe’s fourfold distinction between substances, kinds, properties, and modes is a factored ontology. It has a precedent. Empedocles divided stuffs into the four elements, which were earth, air, fire, and water, and mixtures of these in different proportions, giving the variety of stuffs we observe around us. Aristotle apparently approved of and used Empedocles’s theory. The four elements however do not simply sit there as four different basic stuffs: they are generated by two distinctions or factors: the temperature factor (hot vs cold) and the humidity factor (wet vs dry). Hot and wet gives air, hot and dry gives fire, cold and wet gives water, while cold and dry gives earth. The elements are the basic kinds of things that exist; wetness, hotness etc. are accidents or properties of the elements, and cannot exist separately. But the accidents are the factors that generate the elements. In the same way, the predicability or exemplifiability factor and the dependence factor generate the Aristotle–Lowe fourfold distinction.

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Table 8.1 Brentano’s ‘ family tree’ of Aristotle’s categories. Entity Independent Dependent not wrt another

inherent dynamic circumstantial

with respect to another

accident (symbebekos) affection (pathos)

Substance

wrt matter wrt form

Quantity Quality

source target

Doing Undergoing

where when

Place Time Relation

Notice that as Empedocles’ factors are not elements, so these factors are not among the categories: dependence or being dependent or an individual instance of one thing depending on another are not in any of the categories. This is a general feature of factors: they are behind the categories, not among them. So they do not exist in their own right, but only in so far as they occur in and differentiate the basic things that exist. Jonathan Lowe is one of the few ontologists to have realized this. It may be this peculiarly ethereal status that lends credence to the idea that the differences among the categories are surd. Once the idea of factoring is understood, it turns out that several prominent category schemes are factored. The eight categories of Aristotle’s mature category scheme appear to resist factoring, but if we follow the painstaking investigation of Franz Brentano’s doctoral dissertation On the Several Senses of Being in Aristotle (1862), written with Trendelenburg as supervisor, it turns out that they are also factored, according to the ‘family tree’ (Brentano 1862: 177) shown in Table 8.1. Kant’s categories, though auxiliary rather than ontic, are expressly factored: each object is characterized by four factors, from the four families of Quality, Quantity, Relation and Modality. Each of these families has (according to Kant) three members or values, so if all combinations are consistent there are 34 = 81 possibilities. From the Aristotelian point of

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view there are then not twelve but eighty-one categories of object, and what Kant calls the twelve categories are not the kinds of objects but the factors. The most sophisticated use of factoring in ontology is due to the Polish phenomenologist Roman Ingarden. In his largest work The Controversy over the Existence of the World he distinguishes between categories (which he calls modes of being) and the factors (moments of existence) that generate them. He distinguishes four different notions of dependence and independence, and other distinctions, eventually generating fifteen categories of object, including past and present things, events and properties, states of affairs, intentional objects like fictional characters, ideal objects, and the absolute. While Ingarden’s categories are fairly conservative, his method is explicit factoring and is not. It is not just in ontology that explicitly searching for factors helps to generate better classificatory schemes. The two most mature classificatory disciplines, namely biology and library science, have separately but convergently come up with factoring as a way to impart sound taxonomic system. In library science, following the conceptual revolution introduced by S. R. Ranganathan (1892–1972), factors are called facets; in biology, following another conceptual revolution introduced by Willi Hennig (1913–1976), they are called characters, and those which serve to identify past events of speciation and build the phylogenetic tree are called synapomorphic characters. Neither facets nor characters are in themselves revolutionary: they simply consist in looking for common properties behind the differences among things. What makes them (and factoring in ontology) special is that they take the construction of classifications beyond simply dividing and grouping, and they systematize it to a greater level than hitherto. Both aspects are welcome to ontology. 8.6   C at e g or i a l f l e x i bi l i t y Ranganathan expressly introduced facets in order to solve a problem facing document classification. In any but the most elementary division of objects they are divided in different respects, and this gives rise to the possibility of cross-classification. Should a book about the class system in eighteenth-century France be classified under the sociology of class or social history or French history or the history of the eighteenth century? All are possible and in principle none is inherently preferable to the others, whatever a librarian’s needs for shelving similar books together. Likewise, in Kant a judgement may be positive, apodictic, hypothetical,

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and singular, as in ‘If John saw the accident, he was in the front of the house.’ There is no point served in saying it is primarily positive, or primarily hypothetical. It is all four, equally. Likewise, in Aristotle’s fourfold classification, a mode is particular and dependent, but it is not one before it is the other. What this means is that when category systems become more ramified, as for example that of Ingarden, none of the factorial distinctions takes inherent priority over others except in the case where one distinction presupposes another, as some do. For example in Aristotle there is no sense in asking whether a substance is a substance in respect of something else, but there is sense in asking whether an accident is in respect of something else, for that distinguishes between non-relational accidents like being white and relational accidents like being taller than Socrates, whereas the idea of a relational substance appears nonsensical. 8.7   T h e n e e d f or mor e t h a n f ou r c at e g or i e s When does an ontologist know she is getting near to bedrock? When the concepts used to explain distinctions use the distinctions themselves. The use of auxiliary categories, such as logical concepts, may be accepted, for example it is acceptable to qualify a substance as not dependent, since auxiliary categories are topic-neutral go-anywhere concepts that cut no ontological ice. It is different if ontological concepts crop up in the explanation: then that ontology needs to be considered as part of the categorial machinery. Take again the concept of substance. At first sight this appears to be straightforward: something is a substance if it is not dependent on anything else. But while this is a fair concept, it may set the bar too high. By this standard, perhaps only Spinoza’s universe counts as a substance, and everything else, including you and me, as a mode. Or it may be that nothing composite can count as a substance, since a composite as such depends on its parts: without them, it would be no composite. That would suggest by contrast that Leibniz’s view on substances, that they are monads with no (proper) parts, is to be preferred. Of course an Aristotelian would think (I believe correctly) that there are many substances, and that some or many of them are complex. Therefore more effort needs to be put into deciding what kind of independence is at stake when something is to count as a substance. Some substances appear to have some of their parts essentially. An organism has some genetic material essentially, for example. Perhaps a person has her brain essentially, it being essential to her existence and continuation as a person. Assuming an oxygen atom is a substance, its

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individual nucleons are essential parts of it. Assuming a star is a substance, for it to be a star it must be massive enough to sustain nuclear fusion during its lifetime, so it absolutely must be complex rather than simple. But for anyone who like Jonathan Lowe subscribes to sortalism, the view that the kind of an individual dictates the kind of persistence and continuation it may sustain, the individual star is also, if in a different sense, dependent on the kind star. Further, an Aristotelian substance is an enduring individual or continuant, one which exists in time but persists in its existence from one time to another not by the accretion of ever new temporal parts, the way a process does, but by being the selfsame identical thing at different times. So for something to be a substance it has to be such that it is independent of any individuals which are not parts of it or are essential to its coming into existence (such as an organism’s parent or parents), while it may depend generically and perhaps physically on the presence of certain conditions or kinds of material (e.g. a human being is dependent on warmth and water, but not on any particular source of warmth or any particular batch of water). Putting all of this together we might hazard a definition of an Aristotelian substance as a single individual that exists at more than one time, exists at different times not by virtue of having successive temporal parts, and is such that it does not depend on any individuals except those if any which are essential to its coming into existence and those if any which are essential parts of it throughout its existence. Whether this is the final word or not, it is closer to the reality than the simple formula that a substance is an independent individual. Now collect together all the non-auxiliary concepts involved in this: we have existing at a time, parts, temporal and essential, and perhaps the idea of an essential generator. While existence as such may be an auxiliary concept, existing at a time is not, though for some kinds of thing to exist is to exist at some time or other. It is an ontic matter whether a given (temporal) object exists at a given time or not. Therefore we need the notions of time, part, dependence, and essence (along with some logic) to explicate what it means to be a substance. I suggest then that all of these go into the mix as potential factors. Or take the concept of exemplification (or instantiation, I am not here troubling to make a distinction), needed to distinguish universals from particulars. A universal is something that is essentially such that it exists only if something exemplifies it, whether it is a substantial or an accidental universal. Indeed for it to exist is perhaps indeed simply for something to exemplify it, to be a this of this kind, or a this like such

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and such. For a realist about universals, this makes exemplifying into a candidate factor. For a nominalist, the buck is passed back to the idea of similarity in a respect and the abstraction of this respect from the plurality of things thus alike. If both of these are auxiliary notions, so is that of a universal. Consider again the candidate factors we have so far rounded up: dependence, part, essence, time, perhaps exemplification. Dependence and essence seem to go closely together and may be part of a single family of factors. Certainly when we look at their modal features they look remarkably similar: x depends on y if x cannot exist unless y exists (with various riders); x is essentially F if x cannot exist unless it is F. One might suppose this means we can explicate dependence and essence via modal notions of necessity and so on, but Jonathan has argued convincingly that modality is too loose and sloppy a notion to fully characterize the idea of dependence. So let us leave modality aside, not deciding whether it is auxiliary or ontic, and accept dependence and essence as ontic factors, whether of one family or two. Part–whole is not one of the four categories, but the relationship is all around us, and ontology cannot get by without it. But it is no auxiliary: it is a matter of independent ontic fact whether this or that object is part of another. We simply aspire to recognize such facts, and an omniscient being would know them. Now consider time. Like space, time is a dimension in which things may be extended: processes have temporal as well as spatial parts. A football match is played in two halves, one of which is finished before the second begins. These are temporal halves, unlike the spatial halves consisting in the events occurring in the two spatial halves of the football field. The ontology of space and time is a minefield of difficulties, starting with the key question whether space and time exist as entities in their own right or are in some manner parasitic (dependent) on the events and things in them. The physical and metaphysical jury is still out on that dispute so there is no point in trying to adjudicate it here. Suffice it to say that if spaces and times exist they appear to be particulars, whether substantial or not; simply slotting them into the categories of particulars fails to do justice to their key roles in ontology. We should therefore consider the more neutral relation of occupation (of locations by their occupants) as a candidate factorial relation, and then seek to distinguish space from time in some other way. Occupation makes sense outside space and time as well: abstractly, the black queen occupies position d8 at the start of a chess game, while the number 43 occupies place 14 in the sequence of prime numbers.

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As to what distinguishes space from time, I am inclined towards the causal theory, according to which spatiotemporal location A is absolutely earlier than B if and only if there can be a causal influence of some event at A on an event at B (cf. van Fraassen 1970). That brings causation into the picture as a potential ontic factor, and I am happy for it to be there. Arguably, not everything that happens is caused to happen: standard interpretations of quantum theory accept that some events happen spontaneously, or uncaused. However even an uncaused event cannot be made not to have happened once it has happened: it and its existence are determinate from the time of its occurrence. A future event may be undetermined by present and past events, and when coming about, if not uncaused, then it will have been determined by prior events. So I consider the concept of determination, which may properly encompass causation, as another candidate factor. The present of an event is the cusp of its determination: before then it is not determined, afterwards it is. There are other candidate factor families I would include on the ontic side: number and plurality among them. Number seems like a purely logical concept, because we can define numbers logically, but it is an ontic fact whether an animal has two or four legs, for example, and not something we merely throw over the appearances as a conceptual aid. The reason we can define the numbers is that we can use the concept of numerical difference ≠, and this is an ontic concept for two reasons. Firstly, what makes it true that A ≠ B is an ontic matter: it is there being both A and B. Or to put it in the idiom of truthmaking: the truthmaker for A ≠ B is (just) A and B, those things. Secondly, for those who (like myself) consider that Leibniz’s Principle of Identity is a conceptual truth (here expressed contrapositively): A ≠ B if and only if A exists and B exists and for some F: F(A) and not F(B)

it would appear that the respect in which A differs from B must be ontic. So number is not purely logical at all, but has its roots in the ontic fact of difference. Taken together, these various factor families generate a much richer system of categories than just four, and to overlook the contributions of all of them is to engage with ontology at too abstract a level, or to impute more to the Kantian side of categories than a realist should. The exact number of categories that result from the crossing of factorial distinctions is not clear, and perhaps is not all that important. Rather the work for ontologists consists in investigating the factors in their families, separately and in combination. Well-developed theories of number and part–whole

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already exist in the form of arithmetic and mereology respectively, and the ontology of space and time has been attacked from the geometric as well as the physical side. Jonathan has contributed to the theory of dependence, as have others such as Kit Fine and Fabrice Correia. There is much work still to be done, but it is progressing in various quarters. 8.8  B a s ic r e l at ions Whereas the factored ontologies we discussed at the outset are all discrete or digital, in that each factor family consists of a finite number of values, often just two, the approach to factoring outlined in the previous section highlights formal relations such as difference, part–whole, determination, occupation, dependence. This in turn implies that rather than dividing objects according to whether they do or do not have parts, whether they are one or many, whether they are past or future, and so on, the ontological facts of note concern whether this object is part of that, earlier than that, partially determinative of that, and so on. This is another reason why it will be hard to nail down a finite list of categories. For example, is a collection of three things of a different category from a collection of five things? If the difference between one and more than one is a categorial distinction, it seems so, yet both three and five are many rather than one. Rather than allowing pseudo-disputes as to what is a categorial distinction and what is merely a taxonomic one, it seems more sensible simply to pursue the differences as they arise. An interesting common feature of the basic relations of difference, part–whole, determination, dependence, exemplification, and so on is that they are all, as relations, in a certain sense unusual or odd. Whereas with an honest-to-goodness relation like being a parent of or being older than we can happily consider what might be the truthmakers for the relational truths involved, in all of these cases we come across a puzzle. If we try to treat the relations (qua instances or relational tropes) as parts of the furniture of the universe, they readily generate vicious infinite regresses. If A’s exemplifying B is a relation, what about A’s standing in the exemplifying relation to B? We get the Plato–Aristotle Third Man regress. If A stands in R to B, is A related to the relation? We get one of Bradley’s regresses. If being a part of something is a relation, is it itself part of the whole in addition to the part that is part of it? If two things are different from each of the two, is the one different from the two in the same way that each one is different from another? If determination happens at a time, is determination itself determined to happen? Is it essential to A

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that it is essentially F, in addition to its being essentially F? And so on. While some of these regresses may arise from confusion, or are ultimately benign, enough of them survive as concerns for us to detect a pattern. The pattern is this. When we are close to metaphysical bedrock, the same questions keep arising about the basics as we use the basics to explain. In the case of relations, we have a name for it, namely that the relations in question are internal. A relation R is internal to A and B iff it is essential to A and B jointly that ARB, so that necessarily, if A and B both exist, then ARB. We might say the relation R is essential to the pair A,B in the way that an essential property is essential to its sole bearer. Internal relations are actually badly named in my view, because there are no such things (as particulars or universals) as internal relations. The reasons for thinking this are two. Firstly, when a relational predication ‘ARB’ is true for this sort of reason, we do not need a third thing alongside A and B to act as truthmaker for it, for by the nature of internal relatedness, A and B between them suffice to make it true that ARB. So on parsimony grounds we may dispense with the relation as a truthmaker or constituent of one. In addition to A and B, we don’t need a third thing called the difference between them to make it true that A ≠ B. In addition to A and B, where A is an essential part of B, we don’t need any additional part-of relation. Indeed the idea of a part-of relation as a constituent of reality is difficult to stomach even for non-essential parts, and we should perhaps look simply to common parts as truthmakers for statements of mereological overlapping. Secondly, if there is no relation as a third thing alongside the items related, there is nowhere for a regress to get started. If two modes are of the same kind, they are essentially alike, e.g. two modes of sphericity in two ball-bearings. That they (these two modes) are alike is an internal relatedness: they could not both exist and be unalike. So their likeness is not a third thing that gives rise to a regress of similarity such as Russell supposed characterizes any nominalistic attempt to eliminate universals. I suggest that the basic relations in factor families are one and all ‘internal’, not actual relations. It is another reason why factors are ‘ethereal’. For all that, the differences resulting, between one and many, between simple and complex, determined and undetermined, earlier and later, et cetera, are real differences. It is through these differences that the factors may be said to ‘exist’. They are not among the things of the world, among the things falling into the various categories, yet they structure these things in all their ontological aspects. They exist only insofar as things exist which are so structured. As Whitehead said with his own single ultimate of creativity in mind, ‘In all philosophic theory there is an

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ultimate which is actual in virtue of its accidents. It is only then capable of characterization through its accidental embodiments, and apart from these accidents is devoid of actuality’ (1978: 7). 8.9  A v i s ion of m e ta ph y s ic s The search for a good scheme of categories is a good place to start and pursue ontology. But it does not stop there. Once basic factors have been provisionally identified, they need to be specified or at least constrained axiomatically, both separately and in their combinations. This becomes the enterprise of formal ontology, as envisaged in his Logical Investigations by Edmund Husserl. It is slow and difficult work, and to date incomplete. Husserl’s more specific enterprises of regional ontologies for different (and in Husserl’s view, fixed) subdomains of being should in my view be replaced by a general commitment to follow the formal kinds of entity identified in formal ontology into the many varieties of thing identified in our experience, whether everyday or in science. I call this enterprise systematics, by analogy with the overall taxonomic–investigative branch of biology going by that name. In systematics one comes into contact with empirical knowledge and the taxa identified in classificatory schemes are material rather than formal, as for example the differences between archaea, bacteria, and eucaryota, between glucose and dextrose, between particles with mass and those without. While ontology is the business of philosophers, if need be relying on the assistance of logicians, linguists, historians, computer scientists, physicists, indeed anyone who can offer anything of interest, it is in systematics that ontology comes to application, and pays its way. An ontologist without an interest in the direct application of her theories and distinctions to the real world but prefers to slug it out a priori with other philosophers is shadow-boxing and deserves all the neglect with which real scientists often unfairly treat all philosophers. By the same token, an ontologist who is afraid of making errors, chancing speculative hypotheses, or getting empirical dirt under her philosophical fingernails, is playing a self-indulgent glass-bead game. We need metaphysicians who are committed to the real-world relevance of their theories, while neither minimizing the considerable difficulties involved nor supposing that the scientists can do their work for them. There are not too many such metaphysicians. Fortunately, Jonathan Lowe is one, and while we do not see eye to eye on theory, we do agree substantially on the importance of the right attitude to metaphysics: realist, ambitious, yet realistically fallibilist, and above all, serious. I salute him.

ch apter 9

Neo-Aristotelianism and substance Joshua Hoffman

In this chapter, I characterize Aristotle’s groundbreaking work on ontological categories, and his two analyses of what it is to be an individual substance. Based on this characterization, I then list a set of three conditions that a theory of substance must meet to qualify as a neo-Aristotelian theory of substance. Several other conditions that characterize Aristotle’s theory of substance are also listed, but I judge these to be inessential to a neo-Aristotelian theory of substance. I then turn to an examination of three contemporary or near-contemporary neo-Aristotelian theories of substance, with the aim of showing that they all satisfy the three essential conditions of being neo-Aristotelian theories, and I am able to show that all three also share at least some of the other features of Aristotle’s theory of substance. 9.1  A r i s t o t l e on s u b s ta nc e a n d on t ol o g ic a l c at e g or i e s Neo-Aristotelianism in metaphysics is an extension of and/or in imitation of Aristotle’s metaphysics. A neo-Aristotelian theory of substance, then, is one that is an extension of and/or is in imitation of Aristotle’s views about substance. I begin, therefore, with a brief account of what Aristotle had to say about substance.1 It is important from the start to avoid a confusion caused by the fact that many translators of Aristotle have used the English term ‘substance’ to translate the term ‘primary ousia’. This translation is apt to lead to confusion on the part of an English reader of Aristotle, because Aristotle identifies in the Metaphysics a very different sort of thing with ‘primary ousia’ than he does in the Categories. In the Metaphysics, Aristotle identifies 1 By a substance, I mean an individual thing or object, and not merely a quantity of stuff. Hence, I am using the term ‘substance’ as a count noun and a sortal term.

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forms with primary ousia, while in the Categories he identifies things like organisms with primary ousia. What is going on here – how can Aristotle have been so confused about which things are substances as to think that forms are substances (the very confusion that got Plato in so much trouble, and which leads to the Third Man problem)? The answer is that Aristotle was not naming substances when he used the term, ‘primary ousia’. Rather, he was naming ‘basic entities’ or ‘primary beings’ – which is the literal meaning of ‘primary ousia’. Once we realize that, we can see that he used that term consistently, and just changed his mind, from the (earlier) time when he wrote the Categories to the (later) time when he wrote the Metaphysics, about which kinds of things are basic entities or primary beings. At first, he thought that they are substances, for example, organisms, but later, he concluded (perhaps because of his hylomorphism, i.e., his view that substances are a combination of form and matter) that forms are the basic entities. It is a matter of some controversy exactly which kinds of substances Aristotle thought that there are. He definitely counted organisms among substances, but he definitely rejected atoms and he seems to have rejected artefacts as substances. His rejection of atoms was based on arguments that there cannot be atoms, and his seeming rejection of artefacts was made on the grounds that artefacts lack a nature qua artefact.2 That still leaves open the possibility of inanimate natural compounds being substances, examples being things such as rocks and pieces of bronze. Whether Aristotle included these things among substances is controversial, though it seems to me that he should have done so, since they have both the sort of unity and nature required to be a substance. In the Categories, Aristotle provided the first explicit theory of ontological categories. He lists eleven categories of being: substance, ‘secondary being’ or kind (i.e., species or genus), quality, number, place, time, relation, state, action, affect or being-acted-upon, and position or arrangement of parts. I find this list of categories to be unacceptable. First, because it leaves out important categories (or, at least, strong candidates to be categories) that are at the same level of generality as that of substance, time, place, quality, and relation, for example, event and proposition (among others). Second, because it includes some that I think are not at the same level of generality as those just listed, viz., action, affect, and arrangement of 2 I think that he was right about artefacts, and find his argument for their rejection to be cogent, though not the only cogent one.

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parts. Since Aristotle makes no distinctions between the levels of generality of the categories on his list, his theory of categories is at the very least in need of clarification along the lines suggested, and, in my view, also in need of supplementation.3 Another feature of Aristotle’s theory of categories that most contemporary metaphysicians would reject is his claim (in the Categories) that substances are in some sense more fundamental than other categories of being, i.e., that substances are the primary beings or the primary ousia. He thought that there is some kind of asymmetrical dependence of all of the other categories upon substance.4 On the other hand, the idea that there is some sort of independence that substances uniquely possess is an idea that has inspired a number of early modern and contemporary metaphysicians.5 Finally, Aristotle seems to have thought that ‘existence’ is not univocal, and that an instance of one category of being, say, a time, exists in a different sense than does an instance of another category of being, say, a substance. This, too, most contemporary metaphysicians would reject.6 9.2  A r i s t o t l e’s a n a ly s e s of s u b s ta nc e Aristotle offered two analyses of substance: (1) substance as that which can persist through intrinsic change; and (2) that which is neither said-of nor in a subject.7 In stating the former, Aristotle says the following: It seems most distinctive of substance that what is numerically one and the same is able to receive contraries. In no other case could one bring forward anything, numerically one, which is able to receive contraries. (Aristotle Categories 4a10–11)

Aristotle makes clear in his discussion of this idea that his analysis of substance in terms of being able to persist (remain ‘numerically one’) 3 It would have served Aristotle well to have employed the sort of hierarchy he introduced into biological science – the hierarchy of species and genera – in his theory of ontological categories. For an example of this sort of treatment of categories, see Hoffman and Rosenkrantz (1994: 14–22). 4 His later view, that forms are more fundamental than any other category of beings, is equally unacceptable. 5 Among the early moderns, Descartes, Leibniz, and Spinoza understand substance in terms of some sort of independence. As we shall see, the analyses of substance both of Jonathan Lowe and Joshua Hoffman/Gary Rosenkrantz among contemporary philosophers do so as well. 6 We do find an echo of Aristotle’s view about existence in Descartes, for example, in his argument for the existence of God in the Third Meditation. 7 Both are to be found in Aristotle, Categories.

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through the reception of contraries, that by contraries he means intrinsic, and not merely relational, contraries. In Aristotle’s terms, these are qualities. Given Aristotle’s categorical scheme, this is a not implausible analysis. It does indeed seem to be the case that regarding kinds, qualities, relations, times, places, numbers, states, affects, actions, and arrangements of parts, none of them can persist through intrinsic change. On the other hand, there are candidates for inclusion in a list of categories at the same level of generality as substance, quality, and so forth, some of whose instances do seem to be able to persist through intrinsic change, and yet are not substances. Two come to mind, privations (or absences) and boundaries (or limits).8 For example, the hole in the doughnut seems to be able to undergo a change in shape (e.g., when the doughnut is gently pressed), and the surface of the doughnut likewise (in the same case). Moreover, if there are atoms (or if atoms are even possible), then though atomic (indivisible) particles are certainly substances, i.e., bodies, they do not satisfy Aristotle’s change analysis, because atoms cannot undergo intrinsic change. Of course, Aristotle rejected the possibility of atoms, and he no doubt would deny the possible existence of privations and limits. But these are highly controversial claims, and in the case of the denial of the possibility of atoms, highly implausible. To that extent, Aristotle’s change analysis of substance is, as it stands, itself highly implausible.9 Did Aristotle think that his change analysis in some way expresses the fundamentality of substances vis-à-vis the other categories? It is difficult to know. There is no straightforward and obvious connection between the two ideas.10 Aristotle’s other analysis of substance states that a substance is something that is neither ‘said-of ’ nor ‘ in’ something (Categories 2a14). His idea is 8 Among absences are entities such as holes, shadows, and silences. Among limits are surfaces, edges (lines), and points. 9 It can be made much more plausible by revising it as follows: x is a substance =df. x belongs to a category at level C which is capable of being instantiated by something that can undergo intrinsic change (where level C is the level of generality of categories such as substance, time, place, property, relation, and so forth). This revised analysis remains incompatible with the possible existence of limits and absences, but this is much less of a problem than the incompatibility with the possibility of atoms that Aristotle’s version of the change analysis implies. 10 It is true that a substance can exist without any of its qualities (in Aristotle’s sense of inessential properties), but any given quality (understood as an Aristotelian universal) can exist without any given substance – by inhering in another substance. If Aristotle believed in tropes, or particularized properties, then, of course, no trope can exist without the substance to which it belongs, but no substance can exist without any of its essential tropes. Similar things can be said about the relations between substances and the other categories that Aristotle recognizes.

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that every other category of being is either said-of or in something. More specifically, he held that kinds (species and genera) are said-of substances, qualities are in substances, and so forth, where ‘said-of’ and ‘in’ are technical terms whose meanings have to be inferred from various things that Aristotle says about them.11 There are two sorts of criticisms of Aristotle’s second analysis of substance that come to mind. First, he neither provides nor implies any clear meaning of what it is for something to be ‘in’ something else. Second, to the extent that he does, it does not seem to be the case that either spaces or times (or spacetime) are ‘in’ anything else, while it does seem to be the case that substances (bodies) are ‘in’ time and space (or spacetime). Similar difficulties for this analysis arise regarding some of Aristotle’s other categories vis-à-vis substance. Nor is it altogether clear how this second analysis of substance is supposed to imply that substances are independent of every other kind of being, while every other kind of being is dependent on substance. In other words, it is not clear even if it were true that only substances are neither said-of nor in something else, that this implies that substances are asymmetrically independent of everything else. However, this does seem to be what Aristotle took his second analysis to imply.12 9.3   A r i s t o t e l i a n a n d n e o -A r i s t o t e l i a n t h e or i e s of s u b s ta nc e I am now in a position to summarize the features of Aristotle’s metaphysics of substance that provide the basis for saying that a later philosopher defends a ‘neo-Aristotelian’ theory of substance. (i) Aristotle holds that the category of substance is neither eliminable nor reducible to any other category of being. To eliminate substances is to assert that there aren’t any. I take it that this is what certain ‘event theorists’ such as Whitehead have held. To reduce substances to other kinds of beings is, in effect, to demote the category of substance to a lower level of generality than the level at which Aristotle places it. For example, to hold that substances are merely collections of tropes is to imply that the category of substance is a sub-category of the category of collection (or perhaps a sub-category of the category of trope). Analogously, those who 11 For a detailed discussion of just what they mean, see Hoffman and Rosenkrantz (1994, chapter 2, i). A very useful source for this interpretation of Aristotle is Ackrill (1964: 74–6). 12 For a more detailed argument along these lines, see Hoffman and Rosenkrantz (1994, chapter 2, i).

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hold the relational theory of space demote the category of space or place to a sub-category of the category of relation, while those who contend that space is absolute maintain that the category of space or place is at the same level of generality as that of substance, property, and so forth. Thus, a neo-Aristotelian theory of substance is essentially one that maintains that substances are neither reducible to any other category of being nor eliminable from our ontology. (ii) As I have indicated, Aristotle believed that substances are in some way ontologically fundamental, basic, or primary. Since I don’t think this a defensible doctrine, I would not judge it essential to a neo-Aristotelian theory of substance. (iii) Aristotle was anything but a sceptic, subjectivist, or relativist about metaphysics. Thus, a neo-Aristotelian theory of substance is, essentially not skeptical, subjectivist, or relativistic about the category of substance. This means that thinkers such as Hume and Kant, not to mention many contemporary or near-contemporary thinkers such as Quine, do not hold neo-Aristotelian theories of substance.13 (iv) Aristotle, as noted above, was the founder of category theory in metaphysics. His theory of substance is part and parcel of a more general theory of ontological categories. Thus, a neo-Aristotelian theory of substance is one that places the category of substance in a wider scheme of ontological categories. This may be more or less explicit, but the more explicit the more neo-Aristotelian the theory. There has been a notable revival of interest in category theory in recent decades. (v) In giving content to the concept of a substance, and as a general feature of his philosophical methodology, Aristotle insists that one begin with the commonsense concept of a substance, and strive to retain as much as possible of that concept – one’s theory of substance should hew as closely as possible to common sense. Aristotle’s views about substance reflect common sense in a number of ways: that there are a multiplicity of substances (contra Parmenides), that substances are material (contra Plato), that substances persist through intrinsic change (contra Parmenides and probably contra Democritus14), that substances have properties, that a given substance in some sense unifies the properties it possesses,15 that substances are (at the very least typically) contingent beings (again, contra 13 For a spirited defence of neo-Aristotelianism in metaphysics in general, see Lowe (1998). 14 It is probably the case that Democritus did not believe in compound, non-atomic substances, in which case he held that no substance could persist through intrinsic change. 15 Capturing this datum about substances has always been a serious challenge for so-called bundle theories of substance.

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Parmenides), that substances can be understood as a combination of form and matter,16 that substances have both essential and accidental properties, and so forth. (As mentioned earlier, Aristotle did conclude, contrary to common sense, that artefacts are not substances, but he had good reasons to make a revision to the commonsense view in this way.) It seems to me that this approach to metaphysics (and to philosophy in general) is the correct one, and essential to a neo-Aristotelian view of substance.17 For this reason, a thinker such as Spinoza, though a realist and objectivist about substance, is not a neo-Aristotelian  – he is actually a neo-­Parmenidean because of his wholesale rejection of the commonsense view of substance. On the other hand, it seems to me that an Idealist like Berkeley still qualifies as a neo-Aristotelian (to some significant) degree.18 The commonsense concept of a substance is complex enough that one could, like Berkeley, reject its materialism while retaining enough of its other features to qualify as a neo-Aristotelian. In this respect, neo-­A ristotelianism does seem to me to come in degrees. I take it that this critical commonsense approach to substance is essential to neo-Aristotelianism. (vi) Aristotle thought that the notion of a substance can be philosophically analysed.19 He accepted the Socratic idea of philosophical analysis and sought analyses as an important part of philosophical methodology. I don’t regard this as an essential feature of a neo-Aristotelian theory of substance, for something could qualify as one and also maintain that being a substance is primitive and unanalyzable. Nevertheless, many neoAristotelians have followed Aristotle’s lead regarding the analyzability of substance. (vii) As noted previously, Aristotle believed that substances uniquely possess some kind of ontological independence. Although he never made a cogent case for this by means of his own analyses of substance, many 16 The basic idea that particular substance (namely, a body of some kind) has both form and matter is just the commonsense claim that one can distinguish between the stuff of which it is composed from the way that that stuff is arranged. Aristotle’s distinction goes beyond this core idea. 17 Scott Soames (2003: vol. i) identifies the re-emergence of this (quite Aristotelian) methodology as one of the important achievements of the analytical movement in twentieth-century philosophy, with G. E. Moore being one of its most prominent defenders. For a fascinating and thorough exploration of Aristotle’s philosophical methodology, see Irwin (1988). 18 Note that Berkeley accepts all of the preceding views about substance that I judged to be essential to neo-Aristotelianism. Interestingly, he was quite concerned to claim for himself the title of defender of common sense, though this claim was only true of his views in some respects, while in others he notably deviated from common sense. 19 That is, he thought he could provide non-circular, logically necessary and sufficient conditions for something’s being a substance.

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Entia Contingent States Events

Necessary

Individuals Boundaries

Substances

States

Nonstates

Attributes

Substance

Figure 9.1  Chisholm’s table of categories.

neo-Aristotelians have attempted to improve the case for the independence of substances. Let me sum up. I take the essential features of a neo-Aristotelian theory of substance to be one that (a) neither eliminates substances nor reduces them to another category; (b) holds a realist, objectivist view of substances; and (c) presumes that any analysis of substance should be consistent with the features that commonsensically belong to substances, unless there is a cogent argument to reject some feature or features of that sort. Moreover, though the following attributes of a theory of substance are not essential to neo-Aristotelianism, to the extent that a theory possesses them, it is to that degree more Aristotelian: (d) taking substances to be in some sense primary ontological entities; (e) placing the category of substance in a wider categorial framework; (f) providing an analysis of the concept of substance; and (g) holding that substances uniquely possess some kind of ontological independence. 9. 4  C h i s hol m’s n e o -A r i s t o t e l i a n t h e or y of s u b s ta nc e Although his theory of categories changed over time, Chisholm’s final theory can be found in A Realistic Theory of Categories. It begins, appropriately, with a table of categories, arranged in tree form, from the most general category, and then with increasing specificity, down to the fourth level (Chisholm 1996: 3), see Figure 9.1. For Chisholm, entia is the universal category, while contingent being and necessary being are the contradictories under one or the other of which every entity falls.20 Under contingent being, Chisholm places states and 20 As we shall see, there are alternative ways of forming the first branching off of the universal category.

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individuals. As far as I can tell, what he means by an ‘individual’ is just a nonstate (1996: 71), and what he means by a ‘state’ is a concrete state of affairs, one kind of which is a concrete event. Chisholm recognizes two kinds of individuals, namely, contingent substances and boundaries (or limits). On the other side of the table of categories, under necessary being, Chisholm places necessary states, and two kinds of necessary nonstates, namely, (Platonic) attributes and necessary substance. Note that Chisholm’s table of categories is intended to be a list of all of those ontological kinds that actually exist; he does not provide us with a list of categories that are merely epistemically possible. Thus, not appearing on Chisholm’s table are categories many of which are postulated by other philosophers, such as tropes, privations or absences, contingently existing attributes (or Aristotelian attributes), collections or sums, sets, numbers, propositions, spaces, and times. However, Chisholm does claim that some of these can be reduced to or eliminated in favour of categories on his table. For example, he proposes to reduce propositions to attributes, sets to attributes, and spaces and times to (relational) attributes, or to eliminate some or all of them.21 Chisholm analyses a contingent individual as a contingent entity that is not a state of anything (call this D1). He then analyses x is a boundary of y as x’s being necessarily such that it is a constituent of y (let this be D2). He then uses these two analyses to analyse x is a contingent substance as x is a contingent individual that is not a boundary (D3) (1996: 88). Chisholm takes the notion of a constituent to be undefined, but he does claim that there are only two kinds of constituents of material substances, namely, boundaries and material parts (1996: 88). He also analyses the notions of being a spatial substance and being a nonspatial substance as follows: x is a spatial substance iff x is a spatial object that is not a boundary (call this D4), and x is a nonspatial substance iff x is a substance that is not a spatial substance (let this be D5) (1996: 93). Furthermore, Chisholm also claims that ‘no physical object [i.e., substance] x is necessarily such that it is a constituent of another physical object’, and that ‘every spatial boundary is necessarily such that there is some physical object [i.e., substance] that contains it as a constituent’ (1996: 96). As one can infer from his table of categories, Chisholm entertains the possibility of there being a necessary substance, though he does not 21 It isn’t clear to me in most of these instances whether Chisholm favours elimination or reduction.

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definitively endorse this possibility. Although he does not offer an analysis of something’s being a necessary substance, if he had followed the strategy he used to come up with (D3), he would have offered the following (D6): x is a necessary substance iff x is a necessary nonstate that is not an attribute. He could then have combined (D3) and (D6) to generate the following analysis of a substance (D7): x is a substance iff x is either a contingent individual that is not a boundary or a necessary nonstate that is not an attribute. How well does Chisholm’s analysis of substance match with my characterization of a neo-Aristotelian theory of substance? It certainly meets two of the three essential features of such a theory: it neither eliminates substances nor reduces them to another category, and affirms that substantiality is an objective kind. It also seems to satisfy the third requirement, that of matching up fairly closely with our commonsense concept of substance. For example, Chisholm seems to affirm that people, atoms, molecules, rocks, and so forth are substances, that there is a plurality of them, that they have essential and accidental features, that they can undergo change, and move. Chisholm also places the category of substance within a more general theory of categories, in much the same way that Aristotle did. Moreover, as we have seen, he thought that being a substance can be philosophically analysed (though I have doubts about the adequacy of his analysis).22 Finally, there is a sense in which Chisholm, like Aristotle, thought that contingent substances, at least, possess some kind of ontological independence: unlike other kinds of contingent entities, they are not essentially constituents of other entities. As he puts it at one point, ‘contingent individuals … are divided into those that are ontologically dependent on other individuals and those that are not dependent on other individuals. Those that are thus dependent are boundaries; those that are not are substances’ (1996: 71–2). To conclude, Chisholm’s theory of substance qualifies nicely as a neoAristotelian theory of substance. 22 I believe that (D3), Chisholm’s analysis of being a contingent substance is flawed. He states that necessarily, if x is F, then there is a state of x’s being F. Let F be an essential property of a contingent substance, x. Then for Chisholm this implies that there is a state of x’s being F, and since F is an essential property of x, x is necessarily such that it is a constituent of the state of x’s being F. This implies that x is a boundary, and not a substance, by (D2). But (D3) states that a contingent substance is something that is a nonstate (an individual) that is not a boundary. Chisholm takes the notion of a constituent to be undefined, but on any intuitive notion of what a constituent is, the state of x’s being F has x as a constituent.

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Universals

Properties and Relations

Kinds Non-natural

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Natural

Non-substantial

Abstracta

Substantial

Non-objects

Objects

Modes

Non-substances

Cavities

Surfaces

Events

Substances

Stuffs

Organisms

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Figure 9.2  Lowe’s framework of ontological categories. The figure is reproduced from Lowe (2006) with the permission of Oxford University Press.

9.5  L ow e’s n e o -A r i s t o t e l i a n t h e or y of s u b s ta nc e E. J. Lowe’s theory of substance is embedded in an evolving wider framework of ontological categories. The sources to which I shall refer are two of his monographs, The Possibility of Metaphysics (1998) and The FourCategory Ontology (2006). Lowe presents his theory of categories in the former work (181) as shown in Figure 9.2. As Figure 9.2 shows, with this scheme Lowe, in contrast to Chisholm, divides entities into universals and particulars, with substance falling under concreta and then object. On this scheme, substance is at a lower level of generality than kind and property, and at the same level of generality as mode (or trope). In his The Four-Category Ontology, Lowe emphasizes that there are only four basic ontological categories: the two kinds of concrete particulars, substance and trope, and the two types of abstract universals, kind and property. Thus, Figure 9.3 can represent the new scheme. Tropes are particularized attributes, and Lowe states that they are instances of properties, while substances (a species of ‘object’) are instances

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Entities Particulars

Objects

Substances

Universals

Tropes

Kinds

Properties

Non-substances

Figure 9.3  The scheme of ontological categories, according to Lowe.

of kinds. Kinds are essential to the substances that fall under them – they are what Aristotle called ‘secondary beings’. Lowe is a ‘moderate realist’ or an ‘Aristotelian realist’ about kinds and properties – he holds that while they are multiply exemplifiable, they exist in their instances and are contingent upon the existence of their instances. Of course, there are further, more specific, levels of categories that fall under the ones depicted in Figure 9.3.23 Lowe (2006: 111) represents these relations between his four basic categories24 as shown in Figure 9.4. Like both Aristotle and Chisholm, Lowe’s latest system of categories is intended to postulate what kinds of entities there are, and not just to represent what kinds of entities are epistemically possible. It would appear that Lowe intends to reduce many of the latter to the former and to eliminate others. For example, Lowe seems prepared to eliminate concrete states of affairs/events, and to reduce times and places to relations between substances. It isn’t always clear, however, whether Lowe proposes to reduce or eliminate other categories than the four he gives pride of place, or, whether, in some cases, he is making the weaker claim that a given nonbasic category is asymmetrically dependent upon the basic ones. It would appear that for Lowe among the nonbasic categories are ‘objects’ such as absences (e.g., holes) and collections. In The Possibility of Metaphysics, Lowe provides an analysis of being a substance, and develops several related definitions and principles. 23 Though how specific a kind can be to qualify as an ontological category is a very interesting and difficult question. 24 Although Figure 9.2 does, Figure 9.3 does not appear to place substance at the same level of basicness as trope, kind, and property. But Lowe says in various places that among ‘objects’, substances are basic. Apparently, he takes this to imply that they are, after all, at the same level of basicness as trope, kind, and property, and that other ‘objects’ are at a lower level of basicness.

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Characterized by

(4) Attributes

Instantiated by

Exemplified by

Instantiated by

(1) Substances

Characterized by

(2) Modes

Figure 9.4  Lowe’s representation of relations between his four basic categories. The figure is reproduced from Lowe (2006) with the permission of Oxford University Press.

The identity of x depends on the identity of y =df Necessarily, there is a function F such that it is part of the essence of x that x is the F of y. (Lowe 1998: 149) If the identity of x depends on the identity of y, then, necessarily, x exists only if y exists. (Lowe 1998: 150) If x is not identical with y and the identity of x depends on the identity of y, then the identity of y does not depend on the identity of x. (Lowe 1998: 150)

These lead to the following (equivalent) analyses of being a substance: x is a substance =df x is a particular and there is no particular y such that y is not identical with x and x depends for its existence upon y. (Lowe 1998: 151) x is a substance if and only if x is a particular and there is no particular y such that y is not identical with x and the identity of x depends on the identity of y. (Lowe 1998: 151)25

Lowe’s theories of categories and of substance are self-consciously neoAristotelian (Lowe 2006: 21). He believes that Aristotle postulated both 25 One of the most serious problems for this analysis, I think, is posed by the case of a material compound, say a hydrogen atom, which has its material proper parts essentially, e.g., its proton and its electron. I take it that a hydrogen atom is a material substance. But it certainly seems that the identity of that hydrogen atom depends on the identity of its proton, and the existence of the hydrogen atom depends on the existence of that proton. Lowe’s analyses of substance then imply that the hydrogen atom (and any other material compound that has its parts essentially) is not a substance. For a more detailed critical examination of Lowe’s analysis of substance, see my (In press).

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immanent universals (that is, moderate realism) and tropes (particularized attributes and relations), as well as substances. His theory of substance not only meets all of the essential requirements of neo-­A ristotelianism – it takes substance to be a basic ontological category, is a realist theory of substance, and identifies substances (to a large extent) with what we commonsensically take to be substances – but also meets most if not all of the other characteristics of neo-Aristotelianism listed above. For instance, as one can see from his two definitions of substance, they imply that substances uniquely possess some sort of ontological independence; Lowe seems sympathetic with the Aristotelian view that substance is the most fundamental ontological kind; his theory of substance is embedded in a wider categorial scheme; and he attempts to provide a philosophical analysis of substance. 9.6   T h e Hof f m a n/Ro s e n k r a n t z n e o -A r i s t o t e l i a n t h e or y of s u b s ta nc e The third example of a neo-Aristotelian (and contemporary) theory of substance is that of Hoffman and Rosenkrantz, in Substance Among Other Categories and Substance: Its Nature and Existence (1997). Like both Chisholm and Lowe, Hoffman and Rosenkrantz embed their theory of substance within a broader categorial scheme, which in their case is shown in Figure 9.5. An important difference between this scheme and those of Chisholm and Lowe, is that Hoffman and Rosenkrantz do not intend it to display a hierarchy of actually instantiated ontological categories, but rather a hierarchy of epistemically possible ontological categories (through a certain level of generality). To formulate such a hierarchy is not, of course, the only task of metaphysics, but it is a task that is a useful preparation for the more basic task of formulating the hierarchy of actually instantiated categories.26 A second difference is that Hoffman and Rosenkrantz divide the universal category of entity (at what they call Level A) into the two subcategories of abstract entity and concrete entity (at what they call Level B), as opposed to Chisholm’s necessary being and contingent being, and to 26 Nevertheless, the hierarchy of epistemically possible ontological categories, being more neutral with respect to many metaphysical controversies than is a narrower hierarchy of actually instantiated ontological categories, has certain important advantages that flow from that neutrality. For example, Hoffman and Rosenkrantz claim that their analysis of substance, unlike those of Chisholm and Lowe, is compatible with the possible instantiation of any of the ontological categories appearing on their much more inclusive scheme of categories. For more on ontological neutrality, see Hoffman (In press) and Hoffman and Rosenkrantz (1997, chapter 1, section ii).

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Level A B

C

Entity Abstract

Property

Event

Relation Proposition

D

Concrete

Place

Limit

Time

Privation

Collection

Trope

Substance

Material Object

Spirit

Figure 9.5  The Hoffman/Rosenkrantz scheme of ontological categories. The figure is reproduced from Hoffman and Rosenkrantz (1994: 18).

Lowe’s universal and particular. Under concrete entity (at Level C), they place substance, time, place, collection, trope, boundary, event, and privation or absence. Under abstract entity they place property, relation, and proposition. It is left open that other Level C categories might be added to those already cited. For example, number and set might be placed under abstract entity. The analysis of substance that Hoffman and Rosenkrantz develop is formulated in reference to the system of categories just described, and it is intended to be compatible with any consistent, epistemically possible system of categories. Like those of Chisholm and Lowe, it incorporates into the analysis of being a substance the idea that substances possess some sort of ontological independence, which Hoffman and Rosenkrantz call ‘independence within its own kind’.27 x is a substance =df x instantiates a Level C category, C1, such that: (i) C1 could have a single instance throughout an interval of time, and (ii) C1’s instantiation does not entail the instantiation of another Level C category that could have a single instance throughout an interval of time. (Hoffman and Rosenkrantz 1997: 63) 27 Actually, given clause (ii) of the analysis, a more accurate description of the sort of independence the analysis involves is ‘independence within its own kind plus’, where the ‘plus’ refers to the property that clause (ii) describes.

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The idea behind this analysis is that the ontological category of being a substance possesses a unique characteristic, namely, the one spelled out in the above analysis: possibly being instantiated by a single instance throughout an interval of time without entailing the instantiation of any other ontological category that is possibly instantiated by a single instance throughout an interval of time. Hoffman and Rosenkrantz argue that the only other Level C category that plausibly could be instantiated by only one instance throughout an interval of time is the category of being a privation (Hoffman and Rosenkrantz 1997: chapter 2).28 Thus, being a substance is analyzable in terms of instantiating a Level C category that, among all Level C categories, uniquely possesses the characteristic in question. The Hoffman/Rosenkrantz theory of substance has all three of the essential attributes of a neo-Aristotelian theory of substance: it is a realist theory of substance, it neither reduces nor eliminates substances, and it is compatible with most if not all of our commonsense intuitions about substances. Furthermore, it embeds its theory of substance within a broader theory of ontological categories, endorses Aristotle’s view that substances uniquely possess some kind of ontological independence, and offers a philosophical analysis of being a substance. 9.7  C onc lus ion In recent decades, there has been a revival of neo-Aristotelianism in metaphysics, and with respect to the most salient category of a commonsense ontology, individual substance. While neo-Aristotelian metaphysicians disagree amongst themselves over precisely how to analyse the concept of an individual substance, and over which broader system of categories in which to embed the category of substance, they share many convictions about the status of metaphysics and the proper methods for doing metaphysics. It is these convictions that distinguish contemporary neoAristotelian theories of substance both from those who would eliminate substances or reduce them to instances of some other ontological category or categories, and from metaphysical antirealists.29 28 For example, suppose that there was a single, doughnut-shaped material object. Then there would also be a single hole. However, later in this chapter, Hoffman and Rosenkrantz also offer a slightly more complicated version of their analysis to account for the rather implausible possibility of there being a privation without there being a substance. 29 Thanks to Gary Rosenkrantz for helpful comments on a draft of this chapter.

c h a p t e r 10

Developmental potential Louis M. Guenin

What, if anything, is developmental potential? The physical sciences deploy a well-defined concept of potential. Where F is a force field and there exists a scalar field ϕ such that F = −∇ϕ, it is said that F is conservative and that ϕ is a potential function for F. Thus do we speak of gravitational potential and electric potential. But biology has no concept equivalent to conservative force. Biology has no concept of potential as a scalar field. Metaphysics nurtures more general notions of potential. If we start from ontological fundamentals, what might we be able to say of developmental potential? To progress, we must first acquire an understanding of development. That poses a challenge unto itself. The etymology of ‘development’ suggests an unfolding or unwrapping. Development has sometimes been characterized as the sequential manifestation of things latent in a develope. Fresh voice was given to this notion in the eighteenth century when investigators reported that they had observed homunculi under the microscope. This led many subsequent thinkers to embrace preformationism and to reject the Aristotelian understanding of development as epigenesis.1 Then came the latter-day vitalists. Aristotle had given expression to ‘animation’ when he conceived a thing’s psuchē (ψυχή , L. anima) as a formal but not efficient cause. The vitalists held that a living thing contains a nonphysical agent, or entelechy, that animates the thing.2 Bergson imagined an élan vital. Other vitalists spoke of a vital fluid or animal heat. They surmised that an entelechy directs and promotes development toward a natural end. Absent an entelechy, embryonic development does 1 The Aristotelian understanding may be found in On the Generation of Animals 734 a17–734b2. The hold exerted by preformationism is remarked upon in Nagel 1979: 260–1. 2 In adopting Aristotle’s teleology, vitalism reversed his nomenclature. Aristotle associates entelecheia (εντελεχεια) not with origination or potentiality, but with actuality (Gill 1989: 184–5; Makin 2006: xxvii–xxx).

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not occur. Hans Driesch took totipotency of an early embryo’s blastomeres as proof of vitalism. Vitalists thought that because of entelechies, chemical and physical laws alone could not explain development. Thus did they infer the autonomy of biology. But for failure to yield laws or sustain predictions or retrodictions, vitalism succumbed to the criticism that it cannot explain biological phenomena. Claims about entelechies, it was cogently argued, are ‘inaccessible to empirical test and thus devoid of empirical meaning’ (Hempel 1965: 257, 304). In view of the ‘sterility of vitalism as a guide in biological research’, the view was pronounced ‘almost entirely a dead issue in the philosophy of biology’ (Nagel 1961: 427–9). Failure of biology to give a complete explanation of development, so it has been remarked, presents an accidental feature of the current state of science, not a reason to believe in occult agents (Sober 2000: 24). After preformationism and vitalism were sent by the board, the Aristotelian view again began to hold sway. Nowadays it is straightforwardly said that development is epigenetic. Development has been characterized as a progression from a more simple to a more complex organization, as a sequence whose prenatal terms for a given creature follow a stereotype for the species (Hamburger 1957). Even so, a rigorous definition of development is not ready at hand. Let us introduce, from an ontological point of view, this definition: development is a self-directed epigenetic process consisting of sequential phase changes, consequent on interaction of genome, epigenetic systems, and external environment, which transform a living thing into successive stages of an individual of its kind. This definition uses its first token of ‘epigenetic’ in the historic sense to signify that a developing life form produces new parts while maintaining itself; it uses ‘epigenetic systems’ (a relatively recent addition to the argot of molecular biology) to signify cellular mechanisms that effect heritable changes in phenotype without changing DNA coding sequences. We next observe that degenerate growths such as teratomas undergo development in the foregoing sense. Theirs is not organismic development, the concern of developmental biology. Let us therefore say the following. Organismic development is a self-directed epigenetic process in which the genome, epigenetic systems, and external environment of a product of oocyte activation or a product of a plant propagule interact so as to produce and transform an organism by means of capacity-conferring phase changes occurring in a morphological sequence usual for organisms of its kind over the course of a life.

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The import of ‘capacity-conferring’ will become clear in a moment. Hereafter all uses of ‘development’, except where the context otherwise indicates, will refer to organismic development. 10.1   T h e c onc e p t of p o t e n t i a l We return to potential. Aristotle says that [E]verything that comes to be moves towards a principle, i.e., an end. For that for the sake of which a thing is, is its principle, and the becoming is for the sake of the end; and the actuality is the end, and it is for the sake of this that the potentiality is acquired. (Metaphysics 1050a6–11)

What is this ‘potentiality’? Aristotle has started from the understanding that with respect to a given thing, there exists an origin of change – either change in another thing, or change ‘in the thing itself qua other’. An origin of change of either sort is potentiality ‘in the strictest sense’ (Met. 1019a15–1020a6, 1046a1–2, 10–16, 19–28), or what we shall here call a ‘capacity’.3 Gravitational potential, in consequence of a gravitational field created by a body, is a capacity to originate a change in kinetic energy of another body. An example of change in a thing itself qua other occurs when a physician treats himself, this because he thereby exercises an accidental property of a physician (Physics 192b20–33). There also occurs another sort of change, namely, change ‘in a thing itself qua itself’. This occurs when a physician dines, inasmuch as self-nourishment exercises a nonaccidental property of a diner. The origin of change in a thing itself qua itself is a ‘nature’ of the thing (Met. 1014b16–1015a19, 1049a13–18).4 Whenever change occurs in consequence of a potentiality, whether a capacity or a nature, the potentiality’s end becomes actuality.5 Commenting on all this, W. D. Ross recalls that ‘the conception of potentiality has often been used to cover mere barrenness of thought’. But, adds Ross, ‘there is a real point in Aristotle’s insistence on the conception. The point is that change is not catastrophic’ (Ross 2004: 182). Aristotle goes on to evoke other senses of ‘potentiality’ when he declares that actuality is to potentiality as 3 ‘Capacity’ translates dunamis (δυναμισ) in Met. ϴ, chapters 1–5. The appropriateness of this translation is explained in Makin 2006: xxiii. 4 A nature ‘is in the same genus as dunamis’ (1049b5–10). 5 An account of change as a continuous process toward a goal, and of potentiality as analogous to a set of operating rules for performing a complex task, is given in Gill 1989: 174, 184, 192–3, 200–2, 206–7.

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what is building is to what can build, what is awake to what is asleep, what is seeing to what has its eyes shut but has sight, what is shaped out of the matter to the matter, and what has been wrought to the unwrought. (Met. 1048a35–1048b9)6

The first three of these famous actuality–potentiality examples contrast an object exercising a capacity and an object possessing but not exercising a capacity. The fourth and fifth advert to the distinction between substance and matter. Matter, by virtue of form, composes substance. Substance is taken to be the actualization of matter’s potentiality (Met. 1045a23–25, 1045b16–23).7 A block of wood is potentially a statue of Hermes, and building materials are potentially a house insofar as they consist of just those materials that a builder may form into such (Met. 1048a32–33).8 Still another conception of potentiality remains  – a conception that avails for our present purposes. Aristotle says that a human is by nature capable of becoming capable of theorizing.9 This example adumbrates the notion that potential is a capacity to acquire, develop, or regain a capacity.10 The second capacity is the end of the first. For example, a fetus in utero possesses the capacity to develop the capacity to feel pleasure or pain. We express this succinctly by saying, ‘the fetus possesses the potential to become sentient’, or, because we expect the acquired capacity to be exercised, ‘the fetus possesses the potential to feel pleasure or pain’. This sense of potential comports with what seems to go on in development. Developmental potential cannot consist merely in a capacity to acquire a property; such a capacity is possessed by anything that can change. Development is not merely change or growth. Development exercises capacities to acquire capacities. We therefore adopt the following definition: An organism’s developmental potential in respect of Φ-ing in a situation of kind ψ is a capacity to develop a capacity to Φ by undergoing in a situation of kind ψ a nomologically possible process of organismic development.

6 As adapted from the translations of Ross 1924 and Gill 1989: 214. 7 See Makin 2006: xxxix, 139. 8 To avoid countenancing a ‘slum of possibles’ (in Quine’s phrase), we do not speak of ‘a potential statue’ or of ‘a potential house’ (on which see Makin 2006: 157). 9 De Anima 417a22–30 (sense [a]), 417b30–34; Physics 255a30– b4; Gill 1989: 178, 180–1. See also Met. 1048a33–34. 10 Such conception finds contemporary expression in Koslicki 2008: 146n.; Molnar 2003: 32–3; Lowe 1995; and Scheffler 1985: 46–7. Here and in the following, we revert to use of ‘potential’ rather than ‘potentiality’. The latter, traceable to the late scholastics’ rendering of dunamis as potentialitas (Frede 1994: 178), confers no obvious advantage other than, as Makin has suggested to me, its univocality as a noun, ‘potential’ being both noun and adjective. Use of ‘developmental potential’ hews to scientific parlance exemplified in ‘gravitational potential’ and ‘electric potential’.

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A developmental potential is a type of capacity-developing capacity.11 Notwithstanding the repudiation of Aristotelian teleology in postDarwinian thought, developmental potential as we have just rendered it inherits what Nagel called the ‘strong teleological flavor’ of the concept of development (Nagel 1979: 261). Capacities are capacities for their exercises or fulfillments.12 The capacity to Φ is the end of the potential to develop the capacity to Φ. In the embryo at about two weeks, gastrulation is said to orient cells according to a plan of organization; later development is often characterized as a progression through stages toward the end of maturity. Scientists studying populations of stem cells of developing organisms speak of the ‘fates’ and ‘trajectories’ of subpopulations, and of ‘pathways’ that end in specialized cells. But unlike Aristotle’s, our rendition of developmental potential does not suggest purposes or final causes. Nor does it posit fixed essences possessed by all and only creatures of a given species. Our conception does not suppose with Aristotle that every human is capable of theorizing. It does not imply the conclusion, lamented by Dewey, that ‘potentiality never means … the possibility of novelty, of invention, of radical deviation.…’13 Rather our conception allows for what we have learned from genetics and the theory of evolution. There is no set of properties held by all and only creatures of a given species. Variation is the norm.14 10.2   Di sp o s i t ion a l c h a r ac t e r i z at ion A capacity is a power to do or undergo something, to act or to be acted upon.15 Let us suppose, as do many philosophers, that a power is a disposition. Whence a developmental potential is a type of disposition­developing disposition. Among philosophers who recognize dispositions of a concrete object as properties, the question that has dominated discussion is whether a 11 Because potential is not a capacity of a capacity, we refrain from calling potential a ‘secondorder’ or ‘iterative’ capacity. In the lexicon of Aristotelian scholarship, developmental potential is a ‘first potentiality’ (on which see Gill 1989: 181). 12 Thus put by C. B. Martin in Armstrong, Martin, and Place 1996: 174, 187–8. 13 In the Aristotelian ‘tight and pent in universe’, Dewey goes on to say, ‘development is … only a name for the predetermined movement from the acorn to the oak tree’ (Dewey 1920: 58). I am indebted for this reference to Scheffler 1985: 131. 14 As discussed in Guenin 2008: 102–4, 113–23. 15 Ross translates dunamis as ‘potency’ in the sense of ‘power’ (Ross 1924). Of this, ‘pluripotency’ is a legacy. A capacity to act is sometimes called an ‘active power’, a capacity to be acted upon a ‘passive power’. Some writers reserve ‘power’ for the former (as in Ross 1924: 240–1; Ross 2004: 182) and call the latter a ‘susceptibility’.

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disposition is identical with the property or properties of the object constituting its causal basis for manifestation. Causal dualism, appealing to Hume’s precept that an effect is distinct from its cause, holds that a disposition and the object’s causal basis for manifestation are distinct. A microstructural basis causes a disposition and the disposition causes manifestation. It is further held that dispositions exhibit intentionality – that they are directed at manifestations, that they are ‘pregnant with’ possible outcomes.16 Epiphenomenalist functionalist dualism declares that a disposition is a property of possessing a causal basis sufficient for an object’s contribution to causing a manifestation, and that a disposition itself is causally impotent (Prior, Pargetter, and Jackson 1982: 255). This impotence claim clashes with the intuition that every property of a concretum possesses causal efficacy. Categorical monism holds, in its reductionist version, that all properties are categorical and that dispositions are identical with properties constituting their causal bases. ‘The brittleness of glass’, writes Armstrong, ‘is nothing but a microstructure of the glass’ (Armstrong, Martin, and Place 1996: 40). The claimed identity is typetype, that of a brittleness universal with a microstructure universal. It is then said that dispositions and enabling circumstances cause manifestations in accordance with laws of nature. Dispositional eliminativism takes a property ascription’s implication of a stronger-than-material conditional to be a criterion of the property being dispositional, declares that all real properties satisfy this criterion, and hence declares all properties to be dispositions.17 The objection arises that this view reduces causation by manifestation to an infinite regress of disposition-conferrals (to a ‘passing around of powers’). But this objection founders for supposing that manifestation is a property. Instead manifestation is a process.18 Dispositional eliminativism may yet be refuted. This may be accomplished by denying its conditional criterion of dispositionality, as we shall see anon. Opposed to the above claims concerning types of properties stand several versions of multipredicative monism. This is the position that ‘dispositional’ and ‘categorical’ are not types of properties but are among types of predicates ascribable to properties. Dispositional ascriptions relate what a thing does or can do. Categorical ascriptions relate how the thing is put together. To ascribe a disposition is merely to characterize a property dispositionally. The limit version holds that every property of a concretum 16 As argued by U. T. Place in Armstrong, Martin, and Place 1996; see also Molnar 2003. 17 The view that all properties are dispositions, traced to the Eleatic Stranger in The Sophist 247d–3, may be found in Popper 1934, Popper 1959, and Mellor 1974. 18 As argued in Lowe 2006: 139–140.

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is at once dispositional and categorical. Pure dispositionality and pure categoricality are extremes or ‘limits’ never ascribable.19 The instantiation version holds that dispositional predication signifies characterization of a substantial universal by a monadic property universal or by a relational property universal. An object instantiating a kind possesses a disposition to exemplify a universal characterizing the kind.20 Laws of nature are characterizations of kinds by property universals. Presuming that such a characterization does not guarantee exemplification by instances of a kind, it is reasoned that laws admit exceptions. The functionalist bipredicative version portrays dispositional and categorical modes of characterization as differing in sense while coinciding in reference. A dispositional property ascription implies ‘by conceptual necessity’ both a functional role for the ascribed property and a subjunctive conditional; a categorical property ascription describes what a thing is but does not convey any such necessary implications. Each instance of a property characterized dispositionally is identical with an instance of the property characterized categorically. The brittleness instance possessed by this vase is identical with a microstructural property instance possessed by this vase. The categorical instance is the causal basis. By virtue of this token-token identity, dispositions are causes.21 Although the foregoing reasoning presupposes property universals,22 a revised account could recognize a trope ascribed by a dispositional ascription as identical with the causal basis. Various of the foregoing accounts of dispositions travel with accounts of causation and of natural laws – this because an account’s plausibility as to the former may depend on its consequences for the latter. Accounts differ as to whether dispositions and capacities depend on laws, or the other way round,23 on whether dispositions determine kinds, and on how and whether laws involve universals. Discussants of all stripes suppose 19 Chapters by C. B. Martin in Armstrong, Martin, and Place 1996; Heil 2003: 111–25. This view replaces an earlier ‘dual aspects’ account that was not clearly an advance over dualism. 20 Lowe 2006; Lowe 2009a. For example, salt on the grocer’s shelf possesses the disposition to exemplify the saltkind-characterizing dyadic relational property of dissolving when in water, or, in the alternative, Lowe’s account has saltkind and waterkind standing in the asymmetric universal relation ‘dissolvable by’. Distinct from this is the ‘immersion in’ relation whose exemplification by instances of salt and water would constitute an enabling circumstance (as described hereafter) for manifestation of solubility. 21 This view is given in Mumford 1998. There it is argued that the epiphenomenalist view asserting dispositional impotence collapses into multipredicative monism (116). I am indebted to this work for insights concerning the taxonomy of views. 22 As even in Hempel’s covering law model of dispositional explanation, which includes in the explanatory schema a sentence affirming instantiation of a property (Hempel 1978: 139). 23 The latter as argued in Lowe 2006, Cartwright 1989 (as to capacities), and Mumford 1998.

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that if we wish to learn about specific dispositions, we should study physical structures of objects in quest of finding causal bases for manifestation. Bases may reside at levels of organization from the subatomic to the macroscopic. The burden of this chapter lies elsewhere, namely, in adducing another means by which understanding may be obtained of developmental potentials qua propensities. A propensity or ‘probabilistic disposition’ is a disposition whose probability of manifestation is less than 1. (A disposition is said to be deterministic or ‘surefire’ if its probability of manifestation is 1.) In presenting the probabilistic model that follows, we shall assume multipredicative monism in its general form. This will license convenient reference to a disposition – as if referencing a token of an ontologically significant type of property – on the understanding that ‘disposition’ is shorthand for ‘property dispositionally characterized’. We assume, contrary to epiphenomenalism, the causal efficacy of dispositions. We suppose that a disposition and its causal basis are one and the same causally potent property. We do not take on board any of the other commitments of multipredicative monism’s aforementioned versions. 10.3   Prob a bi l i s t ic mode l l i ng of m a n i f e s tat ion We undertake to model an illustrative case, prenatal manifestation of human developmental potentials. We seek a probabilistic model countenanceable not only within multipredicative monism, but when generalized, within rival ontological views on dispositions. We must first tend to some ontological bookkeeping. We characterize a disposition by an ordered pair of the form 〈ψ, φ〉 where ψ is a kind of situation, φ a predicate, and φ-ing is a kind of occurrence or process that we call a ‘manifestation’. We refer to a situation in this context as ‘enabling circumstances’. (Among the circumstances may be what many writers call a ‘stimulus’ or ‘triggering’ occurrence.) This characterization suits developmental potential, since developmental potential is affected by intrinsic properties but not determined by them. Aristotle sees this. He conceives organismic development to involve change to an organism qua self and qua other, and allows for externalities to effect change contributing to the actualization of potential.24 Developmental potential is a relational power. Developmental potential is situation-dependent. 24 Met. 1046a11–16, 1048a27–29, 1049a8–12; Frede 1994: 177–8; Makin 2006: xxxii–xxxiii; Gill 1989: 233.

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Let Dx be the set of all ordered pairs of the form 〈ψ, φ〉 characterizing dispositions of object x. We observe that Dx may contain pairs 〈ψ, φκ〉 and 〈ψ, φ λ〉 for κ ≠ λ (i.e., Dx is not a function), as well as pairs 〈ψκ, φ〉 and 〈ψλ, φ〉 for κ ≠ λ (i.e., Dx is not injective). Dx is a many-many relation. Some accounts would recognize a single ‘multiply-manifested disposition’ characterized by two or more elements of Dx differing only in their second components. We instead say that each element of Dx represents at least one disposition. We say ‘at least’ because for a given 〈ψ, φ〉, there may exist multiple causal bases each of which may, with enabling circumstances of kind ψ, contribute to causing an occurrence or process of kind φ-ing. Instead of supposing in such a case that a disposition is ‘multiply-realized’, we refine our accounting to say that for a given object x, a disposition is individuated by an ordered triple of the form 〈ψ, φ, β〉, where β consists of properties of x constituting a causal basis for manifestation. (There may also exist distinct potentials whose causal bases overlap mereologically. We should not confuse the distinct with the discrete.25) For a propensity, we assign some probability p that φ-ing occurs when x possesses β and enabling circumstances of kind ψ obtain. When dispositions are thus individuated, the argument from multiple realizability collapses. This is the argument that because a disposition may have multiple causal bases (properties by which it ‘is realized’), the disposition cannot be identical with whatever is its causal basis lest by transitivity of identity, the distinct bases be identical with each other (Prior et al. 1982: 253). Rather we should conclude that if there exist multiple causal bases that may contribute with enabling circumstances to φ-ing, this does not evidence a disposition with multiple causal bases. Instead it evidences a distinct disposition for each basis. But in respect of acquisition of a capacity, the penury of our biological knowledge leaves us presently unable to specify any β precisely. Hence in order to construct our model, we shall work from Dx. Where ψ is a kind of enabling circumstances, and φ-ing a kind of prenatal acquisition of the capacity to Φ, we take into account one and only one developmental potential qua propensity for 〈ψ, φ〉 ∈ Dx, regardless how many causal bases obtain. We may sometimes speak of an organism’s ‘developmental potential’ tout court, i.e., without mentioning any ψ or Φ. On such occasions we may be understood to refer to the set of all the organism’s developmental

25

  So remarked in Quine 1974: 15. See Simons 1987: 66, 68, 69, 147, 219.

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potentials in enabling circumstances of some assumed kind. We shall call that set total developmental potential. We observe that acquisition of a capacity may occur gradually and involve the sequential acquisition of properties. We assume that development is continuous such that some new capacitating property is acquired by virtue of some phase change at each prenatal instant of an organism’s life. Let A be the set of all the kinds of acquisitions of capacitating properties that are nomologically possible for an individual of the kind human prior to birth. For every developmental potential of a human conceptus characterized by 〈ψ, φ〉, A includes the kinds of occurrences that singly or together constitute φ-ing. Let τ be the longest plausible duration of prenatal development. We define an isomorphism g: (0, τ] → Ξ, where Ξ ⊂ ℘A, which maps each real number t ∈ (0, τ] to a subset of A that we call an instantaneous developmental stage and designate ‘ξt’. We define Ξ so that every element of A belongs to one and only one stage, and so that elements are assigned to time-indexed stages in the order in which capacitating properties are stereotypically acquired in development. Given g’s infinite domain and range, we distinguish multiple φs, and increase the number of potentials accordingly, rather than conceive of multiple ‘degrees’ of manifestation. We recognize the most advanced stage attained by a conceptus as an outcome of a random trial. We define the sample space Ω consisting of all stages ξt ∈ Ξ such that it is nomologically possible that ξt is the most advanced stage attained by a conceptus. Assuming that development may cease at any stage, Ω = Ξ. We undertake to model manifestation of developmental potentials whose manifestation is nomologically possible. Where κ is a kind of nutritive environment – e.g., the womb, the tissue culture dish, or a kind of artificial uterus – we construct a model for each ψκ. For a given ψκ, we define a random variable Κ: Ω → R given by Κ(ξt) = t. This assigns to each stage in Ω the real number representing the time by which the stage is indexed. We then obtain data concerning attainment of stages within the population of conceptuses. We use conventional methods of statistical inference to infer an absolutely continuous probability distribution PΚ induced by Κ on the Borel σ-algebra over R. By virtue of PΚ  ’s continuity, and in reliance on those inferential methods, we shall thereby be assigning probabilities to some events for which we do not have data. We then deduce PΚ  ’s associated cumulative distribution function FΚ. We conceive PΚ as the probabilistic projection of total developmental potential for individuals of the kind human in enabling circumstances of

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kind ψκ. This projection works by presenting probabilities of Borel sets of real numbers whose inverse images under the random variable are events whose member outcomes are stages whose members are kinds of capacitating property acquisitions.26 We proceed to differentiate FΚ so as to obtain the probability density function (‘PDF’) designated ‘ f Κ ’. We scrutinize f Κ  ’s support, i.e., the closure of the set of arguments at which the value of the function is nonzero. If there exists a finite supremum tK of f Κ  ’s support, we recognize tK’s inverse image under Κ, which we call ‘ξK ’, as the supremum of probable stages. Total developmental potential, so we then say, is bounded above. The supremum of total developmental potential consists of the potential whose manifestation concludes upon attainment of ξK . We then similarly model the probabilities of kinds of occurrences consisting of capacitating property acquisitions included in Ξ’s transitive closure for enabling circumstances of another kind ψλ. We may now compare PDFs for ψκ and ψλ in respect of support.27 A stage lying below the supremum of probable stages for enabling circumstances of kind ψλ may lie above the supremum of probable stages for enabling circumstances of kind ψκ. Comparison of the total developmental potentials will reveal potentials possessed in enabling circumstances of the first kind but not of the second. Understanding probabilities as to what a thing may become in various kinds of situations, and inferring boundedness of its total developmental potential, may contribute to understanding what the thing is. Observers constructing models of the sort just sketched may gain such insights even though they cannot yet infer the causal bases for manifestation of the included potentials. The mathematical structure evinces the generalizability of such a model to cases other than our illustration. The within account, including the conception of a probability distribution as a projection of total developmental potential, is consistent with the frequentist, subjectivist, intersubjectivist, and propensitist theories of probability (the last of which, in Popper’s version, declares that probabilities display propensities).28 The reasoning here does not comport with the classical or logical theories of probability.   The model’s mathematical details are given in Guenin 2011.   PDFs for enabling circumstances of various kinds are shown on the cover of Guenin 2008. 28   As argued in Guenin 2011. 26 27

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10. 4  A Qu i n e a n at tac k Let us test the foregoing account by posing the following Quinean attack. When philosophers suppose that ascription of a propensity is materially equivalent to, or at least implies, a stronger-than-material subjunctive conditional, they envision a conditional such as ‘if x is in a situation of kind ψ at t, necessarily x has a nonzero probability of beginning to φ at t’. A less formally expressed conditional might lack ‘necessarily’, but the subjunctive mood will still connote the modality.29 Expressed as ‘□∀t(ψt x → φt x)’ in quantified modal logic, the envisioned conditional ascribes de re necessity, this because the scope of ‘□’ includes the constant x.30 De re necessity is also ascribed by ‘□∀t∀x(x ∈ K ⊃ [ψt x → φt x])’, where K is a natural kind, hence a constant. But, the attack continues, ascribing necessary properties to things commits one to essentialism. Contrary to any deliverance of quantified modal logic, there are no de re modal properties. The dispositional idiom issues from a misconception. Because modal operators also render contexts in which they appear intensional and referentially opaque (i.e., such that a statement’s truth depends on the names used for the objects mentioned), a canonical scientific language will not include the dispositional idiom or intensional subjunctive conditionals. Such expressions serve in natural languages merely as placeholders awaiting eliminative paraphrase in terms of likenesses of submicroscopic structures and indicative conditionals. To speak of dispositions is also to imply that there are unactualized possibles. 10.5   De f e nc e ag a i ns t at tac k We may repel the foregoing attack as follows. The supposition that a conditional constitutes an analysans of a dispositional ascription has been exploded by the finkishness of dispositions (Martin 1994). A fink (or reverse fink) is an imaginable device that, in the case of a false (or true) dispositional ascription, renders the conditional associated with the disposition true (or false). The following also obtains about the antecedent of any true conditional associated with a disposition. Even if the context is enlarged by Gricean implicatures, the circumstances (including, but not 29 As asserted in Quine 1976: 73; see also Quine 1961: 158. The attack here, though inspired by arguments of Quine, is not intended as a representation of his view. 30 Here applying the criterion of de re modality given in Forbes 1985: 48. We use ‘→’ to denote a stronger-than-material conditional. The supposition of a de re modal property occurs, for example, in Place’s causal dualism (in Armstrong, Martin, and Place 1996: 26, 60, 65).

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limited to, absence of finks) whose failure would thwart manifestation,31 and whose attestations the antecedent therefore must conjoin, may be so numerous as to demand in the antecedent a ‘catch all’ denial of interference  – a statement that nothing prevents manifestation. (This is often called a ‘ceteris paribus clause’.) Some philosophers argue that in physics, law statements hold without such clauses, but the like claim for conditionals associated with biological dispositions seems implausible. A ‘catch all’ denial results in a conditional of the tautologous form ‘(ψt x ∧ ¬ ¬ φt x) → φt x’. Since a tautology is materially implied by any statement, implication of such a conditional does not serve to pick out a dispositional ascription. Reverse finks and the triviality of associating a disposition with a tautologous conditional also defeat Ryle’s view that dispositional ascriptions reduce to subjunctive conditionals, as well as Mumford’s premise that a dispositional ascription differs from a nondispositional in implying, by way of definition, a stronger-than-material conditional or a functional role implicating such a conditional. Lewis proposed that x is disposed to φ if and only if for some intrinsic property B, if a specified stimulus s were to occur while x retains B, s and x’s having of B would jointly be an x-complete cause of φ-ing (Lewis 1997). This analysis is immune to finks and other forms of dispositional mimicry. But the conditional that it proffers as analysans could be trivialized insofar as its antecedent’s specification of B requires a denial of interference to assure that its consequent’s declaration of an x-complete cause is true. For the foregoing reasons, conditionals have aptly been described as inexact gestures toward dispositions.32 Each ordered pair 〈ψ, φ〉 is loosely connected to a conditional whose antecedent references the first component and whose consequent references the second. The connection sustains only a rough-and-ready generalization (e.g., ‘fragile things usually do break when struck’). To evoke a disposition, one may also mention two-sidedness (a distinction obtains between possession and manifestation of a property such that the former may obtain while the latter does not occur) and interferability.33 Do any such gestures toward or indicia of a disposition implicate de re modality? Philosophers are wont to say that dispositions are modal. Yet in Cf. the reference to hindrances in Met. 1049a5–14.   Martin 1994: 8; Lewis 1997: 149; Heil 2003: 196. 33 As adduced in Cartwright 2007: 197–8, 200–5. 31

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so doing, they often have in mind attributes other than alethic modality. Some writers associate modality with implying or evoking a conditional.34 But a conditional without more does not assert necessity; if it did, every prediction would ascribe a de re modal property. Other philosophers associate modality with intensionality. On the contrary, contexts may be intensional without being modal. Still others advert to causal necessity (Place in Armstrong, Martin, and Place 1996: 58–9). As Quine observes, speakers sometimes use ‘necessarily’ to indicate subsumption under a Humean generalization about regularities in events, and Quine himself takes ‘necessarily’ to advert to a microstructural explanation (Quine 1976: 71–3). But even Quine leaves open whether quantifying across nonalethic necessity operators produces ontological trouble (Quine 1960: 196–7; Quine 1961: 158). In any case, multipredicative monism in its general form does not ascribe necessary properties to things – neither of the alethic nor of any other kind. General multipredicative monism characterizes properties de re, but not modally. Although Mumford’s version of multipredicative monism declares that a dispositional ascription implies a conditional ‘by conceptual necessity’, which claim we may express as ‘□∀x∀ψ∀φ ([〈ψ, φ〉 ∈ Dx ] ⊃ ∀t[ψt x → φt x])’, this affirms only de dicto modality, since the quantifiers, but no constants or free variables, lie within the scope of ‘□’. Mumford’s claim elicits the objection that the modality operator confers no advantage over declaring (as Mumford does) that the sentence that it precedes is analytic (Quine 1961: 156), as well as the objection that modal talk is a ‘confusing way of describing constraints built into concepts we deploy’ (Heil 2003: 186). Within any account, motivation for envisioning necessity operators in conditionals – the desire to distinguish conditionals associated with dispositions from other intensional conditionals of only casual significance35  – disappears after one abandons the notion that a dispositional ascription may be analysed by a conditional. As for possibilia, we have conceived dispositions to be real properties distinctively characterized. Whereupon, as Martin has said, ‘it is an elementary confusion to think of unmanifesting dispositions as unactualized possibilia, though that may characterize unmanifested manifestations’ (Martin 1994: 1). So far as manifestations are concerned, any conceptus attaining a stage more advanced than any ξt will have passed through ξt, 34 ‘There is only a stylistic difference between the “if-then” idiom and the modal idioms’ (Ryle 1949: 127–8). 35 Suggested in Quine 1974: 9; Quine 1976: 71.

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and therefore we may take as actualized all stages less advanced than ξK. Our model does not suppose existence of elements of Ω not actualized. Our references to dispositions do not imply existence of nonactual objects. We note an alternative construal of potential as a capacity-developing capacity that is not a disposition-developing disposition. One might come to this from Cartwright’s suggestion of capacities that are not dispositions inasmuch as exercise of the capacities does not require triggering, they are not susceptible to strengthening or weakening, or they are not causally intermittent. Against this construal, we observe firstly that developmental potential could be said to depend for its actualization on triggering, and that status of a component of ψ as a trigger may reveal only an arbitrary step in ontological bookkeeping (and a dubious one for implying that nonconditional powers such as radioactivity are not dispositions), secondly that it seems plausible that developmental potential changes through genetic and epigenetic changes in an organism, and thirdly that some dispositions, including developmental potential, may constantly be causally efficacious in virtue of the properties (e.g., microstructures) characterized by the dispositional idiom, regardless whether manifestation is intermittent. In any case, the capacities in point need not be dispositions for our probabilistic projection of total developmental potential to be useful. Our model will apply when actualization is either a manifestation or an exercise of an end that is either manifested or exercised. Probability distributions may help to support reliable inferences, some of which may avail in the exercise of practical reason, regardless whether one recognizes potentials in one’s ontology, or rather views references thereto as grammatical devices for conveying information about regularities in events. Ontological parsimony need not deter one from heeding probability measures any more than it deters one from reasoning according to calculations of gravitational and electric potentials. 10.6   I s de v e l opm e n ta l p o t e n t i a l i r r e duc i bly prob a bi l i s t ic ? We have introduced developmental potential as a capacity to develop a capacity, characterized such a capacity as a propensity, and related how a probability distribution may be said to project an organism’s bounded set of such propensities. We conclude by reflecting on how our successors might, with the benefit of future scientific knowledge, ultimately come to categorize developmental potential.

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For present purposes, let a model of a scientific theory be a sequence, conforming to the laws of the theory, of states of a system of the kind governed by the theory. A model is a nomologically possible trajectory of the system. A deterministic theory is a theory such that for any two models, if their time slices as of t are isomorphic, their time slices as of any later t′ are isomorphic.36 Given an initial state, there is only one nomologically possible future. A theory that is not deterministic is indeterministic. A process is random if there does not exist any scheme by which one could improve one’s chances when gambling on the outcome.37 To predict or retrodict is to assert that an event occurs or state of affairs obtains at some time other than the present. Theories issue in law statements. Law statements, either singly or in conjunction with factual statements, imply predictions. A law statement of universal form may, if written as a conditional, contain an antecedent consisting of multitudinous conjuncts, or, if written in subject–predicate form, contain a subject with multitudinous modifiers. We call any such conjunct or modifier a ‘qualification’. Some philosophers hold, while others deny, that any statement of a law of nature must include a ‘catch all’ expression asserting the satisfaction of all qualifications on which truth of the consequent, or satisfaction of the predicate, could depend. Meanwhile in respect of a given law statement ℒ of universal form, we may encounter situations in which ℒ’s antecedent or subject obtains but the consequent or predicate does not. Whereupon it may be remarked that ℒ does not hold for those situations, or it may be said that the law governs only with exceptions,38 and hence that the law, while establishing how things ‘tend’, yields no predictions for such situations. Rather we should say that ℒ is a simplification of some exceptionless law statement L containing one or more qualifications not expressed in ℒ – we often cling to a simplification as we study an idealization – so that while ℒ does not hold for the situations in point, L does hold and yield predictions. Simplifications of universal laws are not to be confused with probabilistic law statements, the latter of the form ‘in a situation of kind ψ, the probability of e is p’ for some p < 1. Here also the antecedent or subject specifying ψ may be laden with qualifications importuning a denial of 36 This conception follows Butterfield 1998. Another account defines a deterministic world as a world w such that if any other physically (nomologically) possible world w* ‘agrees with’ w as of t, w* agrees with w as of any other time t′ (Earman 1986: 13). 37 So stated in Popper 1957: 153, in the law of excluded gambling systems of Von Mises, and in the axiom of randomness posited by others. See Gillies 2000: 95–6, 105–8. 38 E.g., Lowe 2006: 16, 29, 94, 145 (considering statements such as ‘the planets move in elliptical orbits’).

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interference. A probabilistic law statement implies, with some probability, either by itself or in conjunction with factual statements, one or more predictions. A cognizable prediction, so we may say, is a prediction that we are able to infer and that, upon some substitution of observable values for its variables, predicts a detectable event or state of affairs. Not every nomologically-implied prediction is cognizable. We may learn of a law and prediction but lack enough data to supply values for the variables. Or we may be unable to solve the pertinent equations. States of dynamical systems exhibit such sensitivity to initial conditions specified by variables in the governing equations that minute variations in initial conditions result in significant variations in outcomes, and when we cannot detect such minute variations, the equations may yield nomologically-implied predictions but no cognizable prediction. In the following, we shall denote by ‘CP’ the sub-category of theories that do, and by ‘~CP’ the sub-category of theories that do not, issue in cognizable predictions. A disposition of a system component will be said to be deterministic or indeterministic according to some theory explaining the system. We may insightfully associate dispositions with categories of systems and theories explaining systems. We have the following categories and, mentioned parenthetically, exemplifying systems and theories39: (i) deterministic according to universal laws (CP: collision of two bodies explained by classical mechanics; ~CP: dynamical systems, a pencil standing on end explained by classical mechanics†), (ii) reducibly probabilistic and hence deterministic (CP: coin tossing explained by classical mechanics†; ~CP: evolution by natural selection†), (iii) deterministic and explained probabilistically (CP: Bohmian quantum mechanics†, statistical mechanics), and (iv) irreducibly probabilistic and hence indeterministic (CP: quantum mechanics according to the Copenhagen interpretation including state vector reduction†, radioisotope decay, particle decay, coin tossing explained by classical mechanics†; ~CP: classical thermodynamics [only as an approximation of reality], collisions among three or more particles, a pencil standing on end†, evolution†). Sometimes what we call by a single term may be separable phenomena explained by multiple theories of different categories. Within which of the foregoing categories should we expect ultimately to place developmental potential? Glymour has drawn attention to indications of stochastic behaviour of ion channels, synapses, neurons, and other cells. Glymour also argues that, on the supposition that there occur indeterministic physical

39

  The categorizations of entries marked ‘†’ remain topics of investigation and discussion.

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phenomena, at least some evolutionary change is indeterministic, whereupon evolutionary theory must be probabilistic (Glymour 2003: 83–8). It has also been argued that fitness of an organism is indeterministic. As one explanation of indeterministic change would have it, indeterminism in phenomena at the level of quantum mechanics ‘percolates up’ so as to affect phenomena at higher levels, this analogously to how decay of a nucleus registers in a Geiger counter. Mutation is commonly supposed to be random. Occurrence of a disposition’s enabling circumstances may be random. On the other hand, some philosophers hold that some biological phenomena, including organisms’ fitness, are deterministic. Future advances in scientific knowledge may give us much to learn about many categorial matters. Quantum mechanics according to the Copenhagen interpretation could yield to a theory accounting for a hidden variable. Dispositions of radioisotopes to decay might even be shown to be reducibly probabilistic. But embryological development is sometimes offered as a counterexample against reducibility of biology to chemistry and physics. Will development yield to deductive-nomological explanations in terms of nucleotide sequences and epigenetic systems? Or even deeper explanations? Even irreducibly probabilistic phenomena may be explained by laws of probabilistic form implying predictions of probabilistic form. The differential equation of radioisotope decay and its exponential solution imply probabilistic predictions. We may at least imagine that there arise law statements of probabilistic form explaining developmental potentials projected by probability distributions, and that someday predictions implied by such laws become cognizable.40 I am grateful for discussions and correspondence to Dagfinn Føllesdal, Mary Louise Gill, Donald Gillies, Peter Koellner, Kathrin Koslicki, M. William Lensch, E. J. Lowe, Stephen Makin, Israel Scheffler, Barry Smith, and Elliott Sober. 40

ch apter 11

The origin of life and the definition of life Storrs McCall

1 1.1   L i f e’s or ig i n, a n d t h e di v i s ion be t w e e n l i f e a n d non-l i f e The physicist Paul Davies gives an excellent, eloquent account of the origin of life in his book The 5th Miracle (1999). Davies’s principal thesis is that although nothing rules out the possibility of life having originated on some other planet (e.g. Mars), the oldest forms of life on Earth consist of bacteria and other micro-organisms which eat unappetizing substances like sulphur and hydrogen sulphide and live in scalding volcanic jets four kilometres down at the bottom of the sea. These jets are known as ‘black smokers’ (Davies 1999: 166–86). Such organisms have probably existed on Earth for the last 3 or 4 billion years, and modern life-forms, which live in environments containing oxygen and derive energy directly or indirectly from sunlight, have literally ‘ascended from the depths’. Such an account flies in the face of more traditional origin-of-life Edens located on the surface of the Earth, or in atmospheres containing methane, hydrogen, and ammonia (Davies 1999: 86–7). But for heat-loving organisms living in rock crevices at the bottom of the sea, the Hades of a sulphurous thermal jet was doubtless heaven enough. The problem Davies sets himself is to imagine conditions in the deep past which would have favoured, or at least permitted, the emergence of DNA and the manufacture of proteins by unicellular organisms. With DNA and protein-manufacture we have life: without them, merely physics and chemistry. Why is this? The reason is, according to Davies, that only with DNA and RNA do we arrive at the encoding of information, and the distinction between hardware and software, that separates living from non-living matter. DNA is built up out of long sequences composed of the four bases A (adenine), C (cytosine), G (guanine), and T (thymine). In the so-called genetic code a triplet composed of three bases, e.g. CGA or GTT, denotes a particular one of the twenty amino acids that go 174

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into the manufacture of proteins. Proteins consist of sequences of amino acids, and the information supplied by a DNA molecule enables cells to manufacture just the right proteins for the growth and development of the organism to which the DNA molecule belongs. Protein manufacture takes place in tiny mini-factories contained within the cell itself. Davies’s overall thesis is that the division between living and non-living beings coincides with the introduction of informational software in the form of the genetic code. The hardware is the DNA and RNA molecules; the software is the encoded message they convey to the protein-making factories, which assemble proteins out of amino acid components. No coded informational software, no life. For those who of us who have wondered about the precise definition of life, and sought a clear line dividing animate from inanimate beings, Davies’s distinction between DNA molecules and the coded information they carry seems exactly right. In postulating a discrete jump or discontinuity between life and non-life, he goes against Aristotle’s view when he says: Nature proceeds little by little from things lifeless to animal life in such a way that it is impossible to determine the exact line of demarcation, nor on which side thereof an intermediate form should lie. (Historia Animalium 88b4–6)

One additional factor, which Davies does not mention but which accords with his analysis, concerns the ‘Central Dogma’ of molecular biology, formulated by Francis Crick in 1958. The ‘Central Dogma’ adds to the hardware/software distinction the one-way, unidirectional character of the information flow from DNA to proteins, as follows: Once ‘information’ has passed into protein, it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. (Crick 1958: 153)

If the hardware/software distinction, plus the specific nature of the genetic code based on triplets of nucleotides, plus the one-way information flow of the Central Dogma, do not together constitute a definition of life for Davies, they at least form a set of necessary conditions for life. In a later piece, Davies adds the idea of software ‘controlling’ hardware in organisms: In biology, genes are regarded as repositories of information  – genetic databanks. In this case the information is semantic; it contains coded instructions for the implementation of an algorithm. So in molecular biology we have the

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informational level of description, full of language about constructing proteins according to a blueprint, and the hardware level in terms of molecules of specific atomic sequences and shapes. Biologists flip between these two modes of description without addressing the issue how information controls hardware (e.g. in ‘gene silencing’ or transcription-inhibition) – a classic case of downward causation. (Davies 2006: 45)

Davies’s appeal to the notion of ‘downward causation’ is noteworthy here. Downward causation is an idea that makes sense only within the context of a ‘layered’ conception of science, in which scientific disciplines are ranked according to which are more fundamental than others. The bottom level is occupied by elementary particle physics, and above that lies solid-state physics, chemistry, biology, etc. A classic statement of the layered conception is found in Oppenheim and Putnam’s ‘Unity of science as a working hypothesis’ (1958), which puts forward the idea of all science being reducible to particle physics: It is not absurd to suppose that psychological laws may eventually be explained in terms of the behavior of individual neurons in the brain; that the behavior of individual cells – including neurons – may eventually be explained in terms of their biochemical constitution; and that the behavior of molecules – including the macro-molecules that make up living cells – may eventually be explained in terms of atomic physics. (Oppenheim and Putnam 1958: 7)

Upward causation, according to which causal principles and laws at lower levels govern the occurrence of phenomena at higher levels, is part and parcel of Oppenheim and Putnam’s vision of the unity of science. But downward causation is not. If it can be shown that the higher-level informational content of the genetic code can bring about lower-level events such as protein manufacture within cells, instances of downward causation like this will show that biology is not reducible to physics, or to any science which lacks the idea of informational software. To answer the question, What is life?, the concept of biological information is crucial. Nevertheless, although all this is true, Davies’s information-based dividing line between the living and the non-living world still lacks, in my opinion, a necessary element. The manufacture of proteins is covered by the genetic code. But there is more to life than protein manufacture. Essential to an organism’s development is the manufacture of the right protein at the right place and at the right time. Davies paints a fascinating picture of cells as containing a wide variety of machines at the nanotechnology level: Each cell is packed with tiny structures that might have come straight from an engineer’s manual. Minuscule tweezers, scissors, pumps, motors, levers, valves,

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pipes, chains, and even vehicles abound. … The various components fit together to form a smoothly functioning whole, like an elaborate factory production line. The miracle of life is not that it is made of nanotools, but that these tiny diverse parts are integrated in a highly organized way. (Davies 1999: 97–8)

Moving from events at the micro level to larger-scale events in the growth and development of an organism like paramecium, or a chicken, or a human being, an obvious fact is that biological development is not haphazard, but follows a pattern or plan. Paramecia develop cilia, which they use for locomotion and to convey food into their mouth. Chickens grow a heart, lungs, and feathers. Human beings develop the ability to walk on two legs. Each species of animal and plant, and each individual within each species, appears to develop according to a plan or template which governs its growth, minute by minute, day by day, and year by year. Departures from the standard pattern may be caused by lack of food, or disease, or amputation of a limb, etc. But when this occurs the process of morphogenesis (development of form) reasserts itself for each individual within the limits that starvation, or disease, or amputation, permit. The question I wish to raise, for those who hold that an organism’s development is dictated by DNA-based genetic information, is whether a different kind of information, not encoded in DNA, may not also play an essential role in morphogenesis. If this were so then Davies’s definition of life, as based essentially on the genetic code, would have to be amended. A source of non-genetic biological information would be needed as an additional necessary condition for the existence of life as we know it. Information theory recognizes two distinct varieties of information: digital and analog. Digital information is discrete, consisting of a series of distinct bits such as 0’s and 1’s, or the dots and dashes of Morse code, or the sequence of nucleotides in DNA. Analog information on the other hand is continuous, and both the input and the output signals in a communication channel can assume values anywhere within a given range. A digital camera takes pictures consisting of discrete information ‘pixels’, the divisions between neighbouring pixels being too small for the eye to detect. But the pictures taken by a film camera change intensity or colour continuously from one region to another. The information inputs and outputs of computers are digital, while the communication channel between the steering wheel of a car and the direction followed by the wheels is analog. The question to be discussed in the remainder of the chapter is whether the digital information supplied by DNA for the development and growth of organisms needs to be supplemented by analog information. This analog information could not

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be based on the genetic code, but would have to come from an entirely different source. A further difference between DNA-based information, and the analog information suggested in this chapter to be underlying development, is that the former, based on nucleotide sequences, is one-dimensional, whereas the latter can be three-dimensional or four-dimensional. If fourdimensional, it can incorporate time as well as space. These matters are discussed below. 1 1.2   T h e pe r s i s t e nc e of pat t e r n i n s i ng l e - c e l l e d org a n i s m s In the last fifty years a number of publications have appeared that describe the emergence and persistence of pattern in the growth and development of Ciliates, a group of protozoans. Ciliates are characterized by the presence of rows of stiff hair-like cilia. These beat rhythmically, and serve both for locomotion and to convey food into the animal’s gullet. Stentor coeruleus, one of the largest ciliates, is shaped like a trumpet and can grow to a millimetre in length; most ciliates are measured in micrometres. Ciliates possess within their one-celled body two different kinds of nucleus containing DNA: small micronuclei and a chain of larger nuclei known as macronuclei. They reproduce by fission. Because of its large size, the anatomical structure of Stentor is easily visible under a low-power microscope, and simple surgical operations such as excisions and grafting can be performed using the sharp point of a glass needle (Tartar 1961: 220). A series of such operations results in an organism with thoroughly rearranged and relocated cortical parts. What is remarkable is the way in which such Stentors can rapidly regenerate their original bodily shape and structure. Tartar’s experiments include (i) re-growing a complete mini-Stentor from a bodily fragment, and (ii) regeneration of ‘minced’ Stentors. In each case the standard Stentor-pattern is step-by-step re-established, and an individual of more or less normal shape emerges. Under (i), Tartar found that body fragments as small as only 1/123rd the volume of a large Stentor could regenerate completely. Figure 29 of Tartar (1961: 122) shows a normal and a tiny regenerated Stentor drawn to the same scale: one is a perfect replica of the other. Under (ii), figure 10 of Tartar (1962: 17) is reproduced in Figure 11.1. Figure 11.1 shows a ‘minced’ Stentor, from which the head and tail have been excised. The cortex has been cut into pieces which ‘float’ freely

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b

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Figure 11.1  The regeneration of a minced Stentor. The figure is reproduced from Tartar (1962) with the permission of Elsevier.

on the endoplasm. These pieces move about, under Tartar’s probing, so that the normal striped pattern and rows of cilia are disrupted. The surface of the minced Stentor looks like a patchwork quilt, with up to 50 separate patches, oriented randomly. Within hours, however, spontaneous movement and rotation of the patches brings about re-alignment of the stripes, and within a day the overall striped pattern has re-emerged. A tail has grown, and a new oral primordium is created where wide stripes lie side-by-side with narrow stripes. It may be asked, what mechanism causes the cortical patches to move and rotate, so that the striped pattern is re-created? One has the impression that it is the pattern itself that is doing the work – that the pattern carries the pieces of minced Stentor along with it, and pushes them into place. This description may be dismissed as merely a metaphor, but it may also be more than a metaphor, and may contain a germ of literal truth, related to how the downward causal influence of biological information guides growth and development. In the next section I propose a ‘4D pattern hypothesis’ to account for minced Stentor regeneration, and I discuss the relation between ‘pattern information’ and ‘genetic information’ in Section 11.4.

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The 4D pattern hypothesis postulates that, in addition to the digital information stored within DNA, a four-dimensional pattern guides development. This pattern is species-specific, and within certain advanced species also individual-specific. DNA controls the overall structure and form of the pattern: in human beings, it establishes not only that we walk upright and possess a complex central nervous system, but also fixes the colour of our eyes, our personality-type, and the probability of being right- or left-handed. All this hangs on DNA. But in addition to this genetic information, the 4D pattern contains information that is analog, not digital. How it operates, and how it guides development and regeneration, may best be described by comparing it to the explanation given by the theory of General Relativity of how bits of matter move in space and time. Newton explained the motion of the planets by postulating gravitational force. Einstein replaced the theory. A freely falling body follows a geodesic, the shortest path a given body in motion can take between two points in curved spacetime. The curvature of spacetime thus determines how objects move when they are not knocked out of their paths by other bodies. Reciprocally, the degree of curvature of spacetime is determined by the masses of the bodies that move in it. In general relativity, ‘Spacetime tells matter how to move, and matter tells spacetime how to curve’ (Wheeler 1998: 235). The 4D pattern hypothesis extends this idea to the domain of life. The coming-into-being of an organism creates a pattern in spacetime, and that pattern tells the organism, at each moment, how to grow and develop. A ‘freely developing’ organism is like a freely falling body. It can be thrown out of its normal development path by disease, or starvation, or surgical intervention, or by a genetic mutation. But if so, the usual 4D development pattern reasserts itself to a degree that is consistent with the organism’s altered circumstances. What is distinctive about 4D patterns, in contrast to 3D patterns, is that they are dynamic. A 3D pattern is a model or plan for a threedimensional structure, such as an architect’s plan for a house. It is static. But a 4D pattern is not static. It is a moving plan for change, development, and growth along the time axis as well as in the three dimensions of space. Such a plan is exemplified by the curved 4D geodesics followed by planets around the Sun, which alter their shape if a wandering star gets too close. What the 4D pattern hypothesis does, in extending this dynamic pattern to living beings, is to suggest that there is far more

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structure to spacetime than Einsteinian curvature. Wherever life exists, spacetime is filled with smaller, more detailed dynamic patterns that govern growth and development. These patterns themselves change as the organisms interact with their environment. Like spacetime curvature, a 4D pattern is created by the very organism whose growth the pattern directs. This sounds like a paradox, but it is not. Just as matter both creates curvature and follows curvature when it moves in empty space, so the DNA of an organism creates a fourdimensional pattern which the organism follows when it develops, provided it is not impeded by external factors. An important difference exists between the 4D patterns created by living organisms, and other 4D patterns in the ‘block universe’, which extends from the Big Bang to the end of time (if there is an end). The block universe contains a 4D shape for every object that ever has existed or ever will exist, and every event that has taken place or will take place, in every region of spacetime. Our universe has an overall 4D structure, which in the present era features large-scale expansion and at some future time may change to contraction. The 4D patterns of living beings are tiny by comparison, occupying small regions of spacetime ranging from a thread measuring only microns in diameter for a bacterium to a column metres in diameter and extending through decades for an elephant. Moreover, the 4D pattern of an organism at birth is its normal pattern, the pattern it would follow in the absence of disease or injury. Unlike patterns in the block universe, which are simply extended along the time axis and never change (because future events are already built into them), biological 4D patterns have a normative character and do change with time. If an elephant is injured, or if a Stentor is minced, the normal, original elephant-pattern or Stentor-pattern is disrupted and in time reasserts itself, but only within the bounds of what is physically possible. The ‘final’ 4D pattern of the animal may still be recognizably elephantine or Stentor-like, but it will bear the scars of the individual’s vicissitudes until its death. In this sense, biological 4D patterns are dynamic while block universe patterns are not. The dynamism results from the power of normative biological patterns to ‘re-assert themselves’; a power that (with certain exceptions) ordinary block universe patterns lack. Let us apply these ideas to Tartar’s experiments with Stentor. Just as general relativity cannot predict what would happen if the Earth came in contact with a large comet or asteroid, i.e. what sized pieces if any would fly off into space, so a Stentor’s 4D pattern cannot predict into how many pieces Dr Tartar is going to cut its ectoplasm. But once cut, the Stentor’s

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pattern begins to reassert itself, and to realign the pieces along the customary stripes. In the same way, if bits of planet Earth were to be expelled following an encounter with a comet, those pieces would follow their own 4D geodesics. (It is conjectured that the Moon was wrenched out of the Earth by a close encounter with another body, and subsequently fell into its 28-day spiral spacetime path.) Could a 4D pattern explain how minced Stentors regenerate? The concept of a 4D pattern for biological development resembles that of a morphogenetic or gradient or development field, first proposed by Alexander Gurwitsch in 1922 and discussed at length by Hans Spemann (1938), Paul Weiss (1939), Julian Huxley and Gavin de Beer (1934), and Joseph Needham (1950). A significant difference between a 4D pattern and a field is that the latter is three dimensional and the former is four dimensional, providing a temporal as well as a spatial plan. Morphogenetic fields were conceived on the model of electric or magnetic fields, in which a physical force influences the development of organisms in the way that a magnet influences the behaviour of iron filings. The history of morphogenetic fields in biology is discussed in a fine analytic paper by Scott Gilbert et al., who remark: In one of the most astounding developments in Western scientific history, the gradient-field, or epimorphic field concept, as embodied in normal ontogeny and as studied by experimental embryologists, seems to have simply vanished from the intellectual patrimony of Western biologists. (Gilbert et al. 1996: 360)

What killed the morphogenetic field, according to Gilbert, was the rise of genetics with its alternative explanation of how development proceeds. ‘Since morphogenesis was subsumed in the larger category of gene expression, fields were not needed’ (1996: 360). The switching on and off of genes, resulting in the manufacture of the right proteins, at the right places and times, that were needed for an organism’s growth and development, supplied what seemed to be a full explanation. The morphogenetic field was not required, and discussion of it was dropped. Do the same considerations apply to the 4D pattern hypothesis? Does the switching on and off of genes explain how minced Stentors regenerate, making the idea of a 4D pattern unnecessary? Consider the movements executed by the 50-odd patches into which the cortex of a minced Stentor is cut (see Figure 11.1 above). Before the oral primordium is formed, the stripes on the patches must be aligned, which means that the patches must be rotated. But given a particular

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patch, should it rotate clockwise or counter-clockwise? And how much? If every patch rotated clockwise 30°, no improvement in stripe alignment would result. A major difficulty is, that the direction and amount that each patch needs to rotate depends upon the rotation of its neighbours, but their rotation depends on the rotation of their neighbours, and so on. Unless there is an overall rotation plan, this is an insoluble problem. What is required is an alignment-of-stripes HQ, which receives positional information about the orientation of each patch and issues orders accordingly. But even an alignment-of-stripes HQ needs to work with a plan, i.e. needs in some sense to know where it is going and what it is trying to achieve. In other words, it needs to be guided by a pattern. Years ago Lewis Wolpert proposed a theory, based on the concept of ‘positional information’, of how cells in many-celled organisms differentiated, and organized themselves into patterned structures. The problem he faced was how genetic information can be translated in a reliable manner to give specific and different spatial patterns of cellular differentiation. He suggested that there may be a universal mechanism whereby the cells in a developing system may have their position specified with respect to one or more points in the system. This specification of position is positional information. … Pattern regulation, which is the ability of the system to form the pattern even when parts are removed, or added, and to show size invariance as in the French Flag problem, is largely dependent on the ability of cells to change their positional information and interpret this change. (Wolpert 1969: 1)

Concerning positional information, one might ask whether the sum total of all ‘positional information’ in a system of cells would not in itself constitute a ‘pattern’. If so, and if positional information is genetically based, then a link might be established between DNA-based digital information and pattern formation. On this, see J. Frankel (1989). I return to this important point in Section 11.4 below. First we must deal with the question of whether ‘following a pattern’ implies the pre-existence of the pattern. As will be seen, it does not, provided the pattern is a fourdimensional rather than a three-dimensional one. Since the time of Aristotle, battles in biology have been waged between the preformationists and the supporters of epigenesis. Good discussions of epigenesis and preformation are found in Huxley and de Beer (1934: 1–8), and in Maienschein (2005). No doubt the preformationists felt that if development followed a plan, that plan in some sense had to exist before

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the development took place. Such an idea carries implications of vitalism and final causes, and would be rejected by all modern biologists. But, significantly, the 4D pattern hypothesis does not imply the existence of a pre-existing pattern, or of teleological causes, any more than general relativity implies teleology. Instead of pre-existing, the pattern of planetary movements followed by the solar system is built into curved spacetime structure. This structure, in turn, is determined by solar and planetary masses and motions. It is the same with biological 4D patterns. The 4D biological development pattern of Stentor exists in time as well as in space, and the typical standard three-dimensional form of Stentor emerges as time passes. It does not pre-exist, any more than the future shape of the universe pre-exists. Nevertheless, the 3D form that a freely developing Stentor assumes is determined by the spacetime Stentor-pattern, in the same way that the future motion of the planets is determined by spacetime curvature that in turn is caused by the planets themselves. Bearing this in mind, we are now able to give an analysis of how minced and scrambled Stentors are able to reconstitute themselves. Their patches move and rotate, guided by the 4D Stentor pattern, over a period of one or two days until the stripes are aligned and a new mouth and holdfast (tail) emerge. It is as if a lot of new bodies were suddenly thrown into the solar system from outer space. After a while, they would align themselves with the planets and revolve about the Sun. Solar system patterns, like Stentor patterns, persist throughout the universe, and reconstitute themselves when temporarily disrupted. Once the four-dimensional character of these patterns is recognized, together with the reciprocal phenomenon of ‘pattern-determining-movement-of-matter’ and ‘matter-determiningpattern’, no mystery concerning how pattern can influence the development of the very thing that causes it should remain. 1 1. 4  C onc lus ion: g e n e t ic i n f or m at ion a n d t h e rol e of DN A It is unlikely that biologists today would accept any but a biochemical explanation of Stentor regeneration, based upon genetic information encoded in Stentor’s DNA. Can we reconcile the roles of digital genetic information and analog pattern information in regeneration and development? Beginning with the normal creation of two individual Stentors through fission, a fairly clear relationship between genetic and pattern information, for each of the newly formed organisms, can be conceived. The

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genetic information determines the overall structure of each ‘freely developing’ 4D pattern, one for each new individual. At the end of the process of division the two individuals twist apart, as in figure 14 of Tartar (1961: 68). The anterior daughter cell inherits the oral apparatus of the parent, and the posterior cell generates new mouthparts guided by its own 4D pattern. In this process the role of genetic information is clear. Each of the two ‘daughter’ Stentors that result from fission possesses both micronuclei and a chain of macronuclei (Tartar 1961: 280–3). The structure of the 4D pattern of each organism is entirely genetically determined by the digital information in its own DNA. This implies that, at the time of fission, there can be no difference between two Stentor patterns without an underlying difference in DNA. Using a philosophical term, we could say that, at the moment of birth or creation of a new organism, 4D biological pattern supervenes upon DNA structure. There can be genetic mutations, certainly, but then the new 4D phenotype supervenes upon the mutant genotype.1 Once a new individual Stentor has come into being, however, the relationship between digital genetic and analog pattern information may change. The powers of these different kinds of information to influence bodily structure may be altered. If Tartar, for example, minces a Stentor into a disorganized lump of protoplasm, with patches of floating ectoplasm, then the role of the Stentor 4D pattern in regeneration becomes crucial, and the role of genetic and biochemical factors is diminished. It is highly unlikely that a purely biochemical explanation could ever be given of how a minced Stentor regenerates, as may be seen by the following considerations. As noted earlier, before a new oral primordium is formed in the dis­aggregated Stentor, the overall striped pattern has to be restored. This means that the cortical patches have to move and rotate in an orchestrated fashion. To think there might be a set of genetic or biochemical causes for each movement and each rotation of each cortical patch is far-fetched. The timing alone of such a set of motions, including the distance travelled and the precise angle through which each patch is rotated, is beyond the powers of any gene or any biochemical process to direct. What is needed is the guidance of an analog pattern, on the model of curved spacetime guiding the movement of the planets. Such detailed guidance cannot be provided by a collection of digital genes, no matter how large.

  For the concept of supervenience, see Kim (1993).

1

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An earlier publication of Tartar’s strengthens the case for making a sharp distinction between the roles of digital genetic information and analog pattern information in Stentor regeneration. Tartar found that partial realignment of the striped pattern and other regenerative changes could take place even if Stentor’s nuclei were removed. In that case, genetic control of the regenerative process would necessarily be lacking. In Tartar’s words: We are particularly interested in any morphogenetic capacities or pattern activities which may be expressed even in the absence of the nucleus. From recent experiments it can be stated that enucleate S. coeruleus can (1) regenerate the holdfast, (2) form a new contractile vacuole, (3) heal the ectoplasm after cutting or grafting, and (4) align minced pattern patches in parallel and rejoin severed pigment stripes. Harmonization of disordered striping is, however, not as certain as in nucleate stentors and some patchiness of the stripe pattern may long remain. Enucleates can do much with their cortical pattern short of the major structurization of the oral primordium. (Tartar 1956: 91–2)

What this evidence points to is the need to recognize analog pattern ­control as supplementing, and in some cases replacing, digital genetic control of regeneration. But in general, pattern control of development (as opposed to regeneration) can at most supplement, not replace, genetic control. Another significant discovery of Tartar’s was that enucleated Stentors died after about five days (Tartar 1956: 91). The conclusion we are led to therefore, is the one sketched at the beginning of the section, that the general, overall structure of an organism’s development is established at the beginning of its life by its genes, and that the absence of digital genetic information results in death. But the detailed realization of this overall structure, especially in regenerative processes, requires a 4D template. Above and beyond genetic factors, an analog 4D pattern is needed.

ch apter 12

Essence, necessity, and explanation Kathrin Koslicki

1 2 .1   I n t roduc t or y r e m a r k s It is perhaps still quite common among contemporary metaphysicians to think of essence along modal lines: an essential truth, on this conception, is just a modal truth of a certain kind (viz., one that is both necessary and de re, i.e., about a certain object); and an essential property is just a feature an object has necessarily, if it is to exist.1 The essential truths, according to this approach, are thus a subset of the necessary truths; and the essential properties of objects are included among its necessary properties. Quine for example has such a modal conception of essence in mind, when he argues that the view he calls ‘Aristotelian essentialism’ is incoherent, because it requires quantification into intensional contexts (cf. Quine 1953). But the view Quine calls ‘Aristotelian essentialism’ is for a variety of reasons not one Aristotle himself would have found congenial. One important respect, which will concern us here, in which Aristotle would have wanted to distance himself from what Quine calls ‘Aristotelian essentialism’ is that Aristotle does not subscribe to a modal conception of essence. For Aristotle, the essential truths are not even included among the necessary truths; and the essential features of an object are similarly not included among its necessary features. Rather, Aristotle conceives of the necessary truths as being distinct and derivative from the essential truths; and he conceives of the necessary features of objects, traditionally known as the ‘propria’ or ‘necessary accidents’, as being distinct and derivative from, the essential features of objects. Such a non-modal conception of essence also constitutes a central component of the neo-Aristotelian 1 This chapter should be read as a sequel to Koslicki (In press), in which I raise many of the issues discussed here from the point of view of contemporary metaphysics, but do not go into the details of Aristotle’s response to these questions as laid out in the Posterior Analytics and the biological treatises.

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approach to metaphysics defended over the last several decades by Kit Fine (see for example Fine 1994, 1995a, 1995b, 1995c). Like Aristotle, Fine holds that we should not try to reduce essence to modality; rather, the modal status of necessary truths, in Fine’s view, is grounded in, and hence derivative from, facts about essences. As Fine points out, a non-modal approach to essence enjoys potential advantages over a modal approach, in that the former can make room for distinctions which are simply glossed over by the latter. For example, consider Socrates and the singleton set containing Socrates. Intuitively, it is not part of the nature of Socrates that he is the sole member of the singleton set containing Socrates, since presumably no feature concerning sets is relevant to a characterization of what it is to be Socrates. In contrast, it does seem plausible to think that it is part of the nature of Socrates’ singleton set that it contains Socrates as its sole member. However, since necessarily each exists just in case the other does and Socrates is necessarily a member of the singleton set containing Socrates (if he exists), necessity coupled with existence alone does not suffice to capture the asymmetry in question. The modal approach to essence will thus generate the result that it is an essential feature of Socrates that he is the sole member of Socrates’ singleton set, just as it is an essential feature of Socrates’ singleton set that it has Socrates as its sole member. The same point applies when we express the ontological asymmetry in question using the vocabulary of ontological dependence: for while it seems plausible to think that Socrates’ singleton set ontologically depends on Socrates as its sole member, it is not equally plausible to think that Socrates is also ontologically dependent on the singleton set of which he is the sole member. Given that the modal approach to essence lacks the resources to recognize an asymmetry in the relation between Socrates and Socrates’ singleton set, a modal account of ontological dependence can be expected to suffer from a similar deficiency. Both Aristotle and Fine, in their conception of the relation between essence and modality, rely on a distinction between what belongs to the essence of an object and what merely follows from the essence of an object. On both Fine’s and Aristotle’s conception, the essential truths characterize the essence of an object and state what features are essential to it, while the necessary truths characterize what merely follows from the essence of an object and state what features are necessary (but nonessential) to it. In order for this type of approach to essence and modality to be successful, we must be able to identify an appropriate consequence

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relation which in fact generates the result that the necessary truths about objects follow from the essential truths. For example, if it is an essential feature of triangles that they have three angles and a merely necessary (but non-essential) feature of triangles that they have three sides, then we must be given some indication of how the second feature in some way derives from the first. In Section 12.2 of this chapter, I discuss Fine’s way of drawing the distinction between what is part of the essence of an object and what merely follows from the essence of an object. Fine’s approach to essence and modality has the advantage over the traditional approach to de re modality that it is set up to reflect the sensitivity of essentialist truths towards their grounds, viz., the identity of those objects in virtue of which these claims are true. But Fine’s approach, as far as I can see, does not settle all the questions we would like to have answered concerning the derivation of propositions stating necessary (but non-essential) features of objects (e.g., the triangle’s being three-sided) from propositions stating their essential features (e.g., the triangle’s being three-angled), since the relevant notion of consequence that is needed for this purpose cannot be merely that of logical entailment. In Section 12.3, I turn to Aristotle’s account of the distinction between what belongs to the essence proper of a thing and what merely follows from the essence proper of a thing. The relevant consequence relation which characterizes this contrast, according to Aristotle, is that supplied by his technical concept of demonstration (apodeixis), as developed in the Posterior Analytics (henceforth abbreviated ‘APo’). Demonstration encompasses more than deductive entailment, in that the explanatory order of priority represented in a successful demonstration must mirror precisely the causal order of priority present in the phenomena in question. In particular, as essences are the causal bedrock of Aristotle’s metaphysics, so definitions, the linguistic counterparts of essences, are the explanatory bedrock of Aristotle’s theory of demonstration. Aristotle’s central idea, to trace the explanatory power of definitions to the causal power of essences, has the potential to open the door to a philosophically satisfying response to the question of how the necessary features of an object are related to its essential features. 1 2 .2  F i n e’s non-moda l c onc e p t ion of e s s e nc e Fine (1994) urges us to resist the modern assimilation of essence to modality:

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My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (Fine 1994: 3)

In Fine’s view, a modal account of essence succeeds in providing a necessary criterion, but fails to provide a sufficient criterion, for essentialist claims. Thus, if an object has a certain property essentially, then it follows that the object has the property necessarily (or that it has the property necessarily, if it exists). But the converse, so Fine argues, does not always hold: it does not in general follow that if an object has a certain property necessarily, then it also has the property essentially. The relation between Socrates and Socrates’ singleton set provides an illustration of this contrast. For while it is necessary that Socrates is the sole member of Socrates’ singleton set, it is not plausible, in Fine’s view, to think that it is also an essential property of Socrates to be the sole member of Socrates’ singleton set, even though it is plausible to think that it is an essential property of Socrates’ singleton set that it has Socrates as its sole member. The example involving Socrates and Socrates’ singleton set serves to bring out one of the main shortcomings Fine sees with the modal account of essence: while de re modal truths, as they are traditionally construed, are insensitive towards the ground or source of their truth, essentialist truths, for Fine, precisely do manifest such a sensitivity towards their ground, viz., the identity of the object or objects in virtue of which the claim in question is true. To represent this sensitivity, Fine utilizes an indexed modal operator, ‘□x,’ to be read as ‘it is true in virtue of the identity of x that …, ’ which denotes an unanalysed relation between an object, x, and a proposition. Essentialist claims of the form, ‘□x A’, in this framework, are thus explicitly relativized to their source, viz., in this case, the object, x, in whose identity the truth of the proposition that A is said to be grounded. Essences themselves, for Fine, can be identified for the purposes at hand with collections of propositions that are true in virtue of the identity of an object or objects. Such a collection of propositions which is true in virtue of x’s identity can simultaneously be thought of as a real definition of x. (Real definitions contrast with nominal definitions and concern objects themselves, rather than the linguistic expressions we use to refer to objects or the concepts we use to conceive of them.)

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Using this apparatus, we can now represent the asymmetry in the relation between Socrates and Socrates’ singleton set as follows: (1)  a. □ (Socrates is the sole member of Socrates’ singleton set) b. □Socrates (Socrates is the sole member of Socrates’ singleton set) c. □Socrates’ singleton set (Socrates is the sole member of Socrates’ singleton set) In Fine’s view, all three statements make distinct claims: the de re modal claim in (1.a) is true, as far as it goes, but manages to state only a necessary condition that would be required to hold in order for either (1.b) or (1.c) to be true. The true essentialist claim in (1.c) correctly represents Socrates’ singleton set as being the object in whose identity the truth of the proposition in question is grounded. (1.b), on the other hand, misrepresents the ground for the truth of the proposition in question as being Socrates’ identity, rather than the identity of Socrates’ singleton set. The traditional modal account of essences cannot distinguish these three claims: as long as we take essentialist claims simply to be de re modal statements, as traditionally construed, we will remain blind, in Fine’s view, to such distinctions with respect to ground as those illustrated in (1.b) and (1.c). But we are required to draw precisely such distinctions, if we want to be able to recognize such ontological asymmetries as that illustrated by the relation between Socrates and Socrates’ singleton set. Given the sensitivity of essentialist claims to the object or objects in whose identity their truth is grounded, we can thus expect, on Fine’s conception, that each object, or type of object, will generate its own sphere of essential truths, namely those that are true in virtue of the identity of just the objects in question. The essentialist claims that are true in virtue of the identity of certain objects include, in Fine’s view, those that belong to the essence, narrowly construed, of the objects in question, or what Fine calls ‘constitutive essence’. But they also include the logical consequences of these claims: these latter propositions belong to the essence of an object, more widely construed, or what Fine calls ‘consequential essence’. Thus, if the proposition that Socrates’ singleton set has Socrates as its sole member belongs to the constitutive essence of Socrates’ singleton set, then the proposition that Socrates’ singleton set has some member or other belongs to the consequential essence of Socrates’ singleton set, since the latter logically follows from the former.2 2 I am here relying primarily on Fine 1995a: 276–80, for the way in which the constitutive/consequential distinction for essences is to be drawn; but similar thoughts (though presented in a more

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But this puts us before an immediate difficulty. For the logical truths are logically entailed by any proposition whatsoever. By the method just outlined, they therefore make it into the consequential essence of any object whatsoever. For example, following this reasoning, the proposition that 2 is self-identical will be included in the consequential essence of Socrates’ singleton set (just as it will be included in the consequential essence of every other object). At the same time, however, the essential truths are also supposed to be those claims which are true in virtue of the identity of some object or objects: we would therefore expect these truths to be immediately relevant to a characterization of the nature of, or what it is to be, these very objects in virtue of whose identity they are true. But it is not plausible to think for example that the truth of the proposition that 2 is self-identical is grounded in the identity of Socrates’ singleton set or that we would appeal to this proposition in a characterization of what it is to be Socrates’ singleton set. Since the logical truths are just those which remain true under any re-interpretation of the non-logical vocabulary, we cannot expect these truths to be grounded in the identity of any particular objects at all; rather, the logical truths are true regardless of which particular object is under consideration. If these truths are grounded in the identity of anything at all, the only plausible candidate would be the logical operations, not the objects to which these logical operations are applied. To address the quandary just raised, Fine proposes a procedure he calls ‘generalizing out’, which in effect allows us to remove the logical truths from the consequential essence of any object. The ‘generalizing out’ procedure takes advantage of the special feature of logical truths just noted, viz., that they remain true under all re-interpretations of the non-logical vocabulary. The central idea underlying this procedure is this: if an object enters as a constituent into a proposition belonging to the consequential essence of another object only through logical closure, then such an object can be ‘generalized away’. For example, the proposition that the number 2 is self-identical belongs to the consequential essence of Socrates’ singleton set; but so does, for every object whatsoever, the proposition that that object is self-identical. In this way, the number 2 can be ‘generalized out’ of the proposition that the number 2 is self-identical, which belongs to the consequential essence of Socrates’ singleton set.3 condensed fashion) are also found in Fine 1995b: Sections 3–4. See also Koslicki (In press, Section 4), for further discussion of Fine’s constitutive/consequential distinction for essences. 3 The following is a more precise characterization of the notion of ‘generalizing out’ (cf. Fine 1995a: 277–8). Consider a proposition P(y), which has an object, y, as a constituent. For example, P(y) might be the proposition that Socrates is identical to Socrates for y=Socrates. Fine’s first step is

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The ‘generalizing out’ procedure is certainly helpful with respect to the quandary just posed, since it allows us to carve out an intermediate restricted consequential essence for every object, namely that collection of propositions which includes all the logical consequences of those propositions that belong to the object’s constitutive essence, minus the logical truths. The restricted consequential essence of Socrates’ singleton set for example includes the proposition that Socrates’ singleton set contains some member or other, but not the logical truth that 2 is self-identical, since the latter is blocked from the restricted consequential essence of Socrates’ singleton set by means of the ‘generalizing out’ procedure. And this is just as it should be, since the proposition that Socrates’ singleton set has some member or other does pertain to the nature of Socrates’ singleton set, albeit only indirectly (by being logically entailed by a proposition that directly pertains to the nature of Socrates’ singleton set), while the proposition that 2 is self-identical does not even pertain indirectly to the nature of Socrates’ singleton set. We thus arrive at two types of claims which, on Fine’s account, can be regarded as properly essentialist claims pertaining to the nature of some object or objects. The first category consists of those propositions which directly pertain to the nature of an object; these propositions make up an object’s constitutive essence. The second category consists of those propositions which pertain to the nature of an object only indirectly, namely by being logically entailed by propositions of the first kind, minus the logical truths; these propositions make up an object’s restricted consequential essence. The logical truths can be discounted, since they only make it into an object’s unrestricted consequential essence by default, so to speak, i.e., by being logically entailed by any proposition whatsoever. In addition to these two types of propositions (i.e., the properly constitutive essential truths and the restrictedly consequential essential truths that are logically derived from them), an important further category of propositions must also be accommodated in some fashion. This third category consists of propositions which Aristotle would characterize as to define the notion of a ‘generalization’ for propositions, rather than objects (i.e., constituents of propositions): the generalization of a proposition, P(y), is the proposition that P(v) holds for all objects, v. Thus, the generalization of the proposition that Socrates is identical to Socrates is the proposition for all objects, v, that v is identical to v. (To obtain the generalization, P(v), of a proposition, P(y), all occurrences of the constituent, y, must be replaced by occurrences of v.) Given the notion of a generalization, defined for propositions, we can now make sense of the idea that an object can be ‘generalized out’ of a collection, C, of propositions in the following way: an object, y, can be generalized out of a collection, C, of propositions if C contains the generalization of a proposition P(y), whenever it contains the proposition P(y) itself.

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necessary (but non-essential) truths, i.e., propositions stating the necessary (but non-essential) features of objects, viz., their so-called ‘necessary accidents’ or ‘propria’. Propositions that belong to this third category resemble those of the second category above, in that they pertain to the nature of an object only indirectly, namely by following from propositions that directly pertain to the nature of an object. But the notion of ‘following from’ cannot be analysed as ‘is a direct logical consequence of the constitutively essential truths’. For, unlike the propositions that are included in an object’s restricted consequential essence, these necessary (but non-essential) truths do not logically follow solely from propositions that belong to an object’s constitutive essence. To account for this third category of propositions, a notion of ‘following from’ that goes beyond logical consequence, as it is conceived of in the relation between an object’s constitutive essence and its restricted consequential essence, is needed. To illustrate, for Aristotle, it is part of the essence proper of planets that they are heavenly bodies that are near; but it is not part of the essence proper of planets, in his view, that they do not twinkle. The latter proposition states merely a necessary (but non-essential) feature of planets which follows from, but is not itself part of, the essence proper of planets. But the proposition that planets do not twinkle, stated in (2.b), does not logically follow from the proposition that planets are heavenly bodies that are near, stated in (2.a), at least not without the help of additional premises: (2)  a. Planets are heavenly bodies which are near. b. Planets are heavenly bodies which do not twinkle. The inference from (2.a) to (2.b) becomes logically valid if we supply (2.c) for example as an auxiliary premise: (2)  c. Heavenly bodies which are near do not twinkle. But the appeal to (2.c) in deriving a necessary truth about planets from an essential truth about planets is problematic for several reasons. First, (2.c) is a statement about heavenly bodies in general, not about planets in particular. Secondly, if (2.b) states a derived necessary (but non-essential) feature of planets, then presumably, by the same reasoning, (2.c) ought to be regarded as stating a derived necessary (but non-essential) feature of heavenly bodies in general as well. These two considerations suggest that propositions stating necessary (but non-essential) features of planets cannot be logically derived from propositions stating essential features of planets alone.

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Moreover, as Aristotle notices as well in the Posterior Analytics, once we allow ourselves to appeal to auxiliary premises, we face a further difficulty. For the inference from the explanatorily less basic necessary truth in (2.b) to the explanatorily more basic essentialist claim in (2.a) can also be made logically valid with the addition of an auxiliary premise, such as (2.d): (2)  d. Heavenly bodies which do not twinkle are near. But we would be moving in the wrong explanatory direction if we were to try to derive the essence proper of planets from their merely necessary (but non-essential) features. Thus, the relevant entailment relation that is needed for the purpose of deriving the necessary truths from the essential truths also cannot be that of logical consequence supplemented by an appeal to auxiliary premises, since the relation in question will then lack the requisite asymmetry.4 It thus seems that a full account of the modal status of propositions stating necessary (but non-essential) features of objects, such as (2.b), requires additional apparatus beyond the notion of logical consequence, as it is employed in Fine’s constitutive/consequential distinction for essences. A proposition can be derived from the propositions that belong to the properly constitutive essence of an object if it is a direct logical consequence of these propositions. But propositions stating necessary (but non-essential) features of objects may not follow logically from the properly constitutive essential truths alone; and yet, these propositions should be asymmetrically derivable in some fashion from propositions stating essential features. What, then, is the appropriate sense of ‘following from’ that can be used to account for the modal status of propositions of this third category? As far as I can see, this question is, as it stands, left open by Fine’s account of essence and modality. 1 2 .3   T h e c aus a l rol e of e s s e nc e s i n A r i s t o t l e’s ph i l o s oph y of s c i e nc e As it turns out, Aristotle thought quite hard about many of the questions just raised in connection with Fine’s account of essence and modality. As 4 The dialectical situation here is reminiscent of Sylvain Bromberger’s famous ‘flagpole’ objection to Hempel’s Deductive-Nomological model of scientific explanation. For just as the length of the flagpole’s shadow can be logically deduced from the length of the flagpole with the help of auxiliary premises, so the length of the flagpole can also be logically deduced from the length of the flagpole’s shadow with the help of auxiliary premises. But it would be odd to explain the flagpole’s length by appeal to the length of its shadow. As we will observe below, Aristotle anticipated the

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I hope to show in what follows, Aristotle’s responses to these questions are philosophically extremely interesting and pertinent to current debates in contemporary metaphysics. 12.3.1  Deduction, demonstration, and definition Like Fine, Aristotle also recognizes the need for a distinction between what belongs to the essence proper of an object and what merely follows from the essence proper of an object.5 But, unlike Fine, Aristotle’s derived notion, as observed earlier, also extends to necessary truths which do not follow by logic alone directly from the propositions that belong to the essence proper of a thing.6 For Aristotle, the notion of ‘following from’ that is at issue in the distinction between the properly essential truths and the derived necessary truths is that given by his technical concept of ‘demonstration’ (apodeixis), as developed in the Posterior Analytics. In Aristotle’s view, the proposition that planets do not twinkle follows from a proposition that states the essence proper of planets, in the sense that it can be demonstrated from such a proposition (viz., the proposition that planets are heavenly bodies which are near), together with an auxiliary premise (viz., the proposition that heavenly bodies which are near do not twinkle). We are thus to regard the proposition that planets are heavenly bodies which do not twinkle as a derived proposition, or theorem, of modern reaction to Bromberger’s case and proposed to supplement logical entailment with causal priority, in order to arrive at an appropriately asymmetric conception of scientific explanation. 5 According to Fine, essences (for the purposes at hand) can be identified with collections of propositions that are true in virtue of the identity of some object or objects. Aristotle, as I read him, would not be happy with this characterization of essences as collections of propositions. For Aristotle, the essence of a kind of thing includes at least its form. (Whether the essence of a kind of thing also includes additional components besides the form, e.g., the matter, is a controversial question which I will leave open for present purposes.) For example, the essence of a living being encompasses at least its soul, i.e., the form of the living being. But, given Aristotle’s conception of the soul as associated with certain kinds of powers or capacities [dynameis] (e.g., the capacity for growth and nourishment, locomotion, perception, and thought), it would be strange to think of the soul of a living being as a collection of propositions. It is perhaps more natural to think of definitions, which Aristotle takes to be linguistic entities [logoi] of some sort (viz., formulae or statements of the essence), as collections of propositions (or perhaps as only a single proposition, if there is only a single canonical way of stating the essence of a kind of thing). I will now switch to a less propositional conception of essences, according to which definitions state, but are not to be identified with, essences. 6 A further difference between Fine’s and Aristotle’s account, which will become more salient below, is that Aristotle thinks of essences (at least in contexts that are relevant to our present concerns) as being associated with kinds of phenomena (e.g., the kind of thing, thunder), rather than with individuals belonging to these kinds (e.g., individual occurrences of thunder). Fine, on the other hand, seems quite happy to conceive of essences as individual essences, rather than (or perhaps in addition to) kind-essences.

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astronomy, since it appears as the conclusion of a demonstrative argument which belongs to the theory of astronomy. The premises of such a demonstrative argument can either be themselves first principles, or axioms, or they can be theorems which follow from (theorems which follow from …) first principles or axioms. The first principles in question may include (i) axioms that are special to astronomy; (ii) axioms that are common to all rigorous disciplines (e.g., the axioms of logic); or (iii) axioms that are imported into astronomy from related special disciplines (e.g., physics, optics, or applied mathematics). A demonstrative argument, in Aristotle’s view, must be at least deductively valid; that is, a demonstration is at least a deduction. But not all deductively valid arguments also amount to demonstrations.7 The question of which conditions must be fulfilled by an argument in order for it to be deductively valid belongs to the subject-matter of logic; but the question of what additional criteria must be met by a deductively valid argument in order for it to constitute a demonstration is a question that is of relevance to science and the philosophy of science.8 For the acquisition of demonstrative knowledge (epistēmē) (i.e., knowledge that is obtained by way of, or at least can be presented in the form of, demonstrative arguments) is the aim of science, as Aristotle conceives of it. As Aristotle specifies in APo A.2, a subject, S, demonstratively knows (epistasthai) a proposition, p, if and only if (i) p cannot be otherwise, i.e., p is necessary; and (ii) S grasps why p is the case, i.e., S is in possession of an explanation for p’s being the case.9 The elucidation of what Aristotle takes to be involved in condition (ii), being in possession of an explanation for why p is the case, will take up the remainder of this chapter. The first The question of how tightly connected Aristotle’s philosophy of science, as laid out in the Posterior Analytics, is to his syllogistic logic, as developed in the Prior Analytics, is a complicated one, which has received considerable attention in the literature. I shall loosely follow the reading advocated in Barnes (1981), according to which Aristotle’s theory of demonstration is couched in terms of his syllogistic logic, only because Aristotle had come to think that deductive entailment is best characterized in syllogistic terms. But, wherever possible, I will in what follows abstract away from the peculiarities and limitations of Aristotle’s syllogistic logic, in my characterization of his philosophy of science. 8 The term, ‘science’ (like its Latin relative, ‘scientia’), is here used to apply to any rigorous discipline which aims at the acquisition of the kind of knowledge to which Aristotle applies his technical term, ‘epistēmē’, as it is characterized in the Posterior Analytics. Any such rigorous discipline, in Aristotle’s view, must be capable of being presented as an axiomatized theory, which consists of first principles or axioms together with the theorems which can be demonstrated on the basis of these first principles. Geometry, for example, is a paradigmatic example of such a rigorous discipline. 9 Quite possibly, Aristotle also requires, in order for a subject, S, to have demonstrative knowledge of a proposition, p, not only (i) that p cannot be otherwise, but also that (i′) S grasps that p cannot be otherwise. 7

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condition, that demonstrative knowledge concerns only necessary propositions, might at first sight seem puzzling to the contemporary reader; but we should keep in mind that, for Aristotle, science is concerned only with lawful (i.e., necessary) connections among kinds of phenomena, i.e., universals, rather than with the accidental features of individual instances of these kinds. Thus, for Aristotle, questions such as the following would count as properly scientific: ‘what is thunder?’, ‘why does thunder occur?’, ‘why is thunder loud?’, or ‘why does thunder accompany lightning?’10 Individual instances of a kind of phenomenon, in Aristotle’s view, can only be perceived through sense-perception; but they are not the proper subject-matter for scientific demonstration and definition.11 One of Aristotle’s central goals in the Posterior Analytics is to spell out in detail what distinguishes demonstrative arguments from those that are merely deductively valid; the latter he takes himself to have already characterized in his treatise on syllogistic logic, the Prior Analytics. Consider for example the following two arguments: (2)  c. Heavenly bodies which are near do not twinkle.12 a. Planets are heavenly bodies which are near. b. Therefore, planets are heavenly bodies which do not twinkle. 10 Both the question, ‘what is thunder?’, and the question, ‘why does thunder occur?’, for Aristotle, are answered simultaneously, once it has been discovered what the essence of thunder is, i.e., what it is to be thunder. Aristotle thinks that the first question, ‘what is thunder?’, asks for a definition (i.e., a statement of the essence) and is answered, in this case, as follows: ‘thunder is a kind of noise in the clouds caused by the extinction of fire’. This (alleged) definition of thunder also immediately delivers an answer to the second question, ‘why does thunder occur?’: ‘because fire is extinguished in the clouds’. 11 Moreover, since demonstration is a species of deduction, any proposition which is suitable to occur in a demonstration must also at least be suitable to occur in a deduction. But such propositions, for Aristotle, are of the form, AxB, where A and B are terms (i.e., with A being the predicate-term and B being the subject-term) denoting universals (i.e., species and genera) and x corresponds to one of the four syllogistic relations that can obtain between terms (‘A belongs to all B’, ‘A belongs to no B’, ‘A belongs to some B’, or ‘A does not belong to some B’). Neither Aristotle’s theory of deduction nor his theory of demonstration makes room for singular propositions (e.g., that Socrates is wise). 12 It is an interesting question what the status is, in Fine’s or Aristotle’s system, of auxiliary general premises such as (2.c), that heavenly bodies which are near do not twinkle. Can this proposition itself be derived from essential truths of some kind? Consider the more general proposition that what is near does not twinkle. Neither the phrase, ‘what is near’, nor the phrase, ‘what does not twinkle’, picks out a genuine natural kind which (in Aristotle’s eyes at least) could be expected to be associated with an essence. If we want to maintain that in general all necessary propositions can be derived in some way from facts about essences, as both Fine and Aristotle seem to want to do, our best bet in this case might be to look for a ground for the necessity of the proposition in question in the essence of the phenomenon of light and its interaction with distance. The proposition that heavenly bodies which are near do not twinkle would then present us with a particular instance of a more general proposition concerning the interaction between light and distance. If this route towards grounding the necessity of the proposition in question in essential

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(2)  d. Heavenly bodies which do not twinkle are near. b. Planets are heavenly bodies which do not twinkle. a. Therefore, planets are heavenly bodies which are near. Aristotle would characterize both arguments as deductively valid; but only one of them, viz., the first, succeeds in meeting the additional criteria imposed on deductively valid arguments which are also demonstrative.13 If we abstract away, for a moment, from the syllogistic form of these arguments, both can be summarized in the form of ‘because’-statements as follows: the first argument in effect states that planets do not twinkle because they are near, while the second argument in effect states that planets are near because they do not twinkle. What follows the connective, ‘because’, in these statements is what Aristotle would call the ‘middle term’, i.e., the term which is common to both premises and therefore serves to connect the remaining two terms which occur in the premises and the conclusion.14 In a proper demonstrative argument, the middle term must be explanatory of the conclusion, in a very specific sense: the middle term must state what properly belongs to the definition of the kind of phenomenon in question (viz., in this case, planets). Successful definitions and explanations, for Aristotle, are the linguistic correlates of essences and causes.15 A definition (horos or horismos), truths of some kind proves to be feasible, we would also need to allow (not surprisingly) that the derivation of theorems of astronomy may rely on the importation of axioms and/or theorems from other related disciplines, such as physics and optics. In any case, as our excursion into Aristotle’s biology below will indicate, one cannot hope to succeed in grounding the necessary truths about one particular kind of phenomenon (e.g., camels) solely in facts about the essences of that kind of phenomenon; rather, the derivations in question only go through if we are permitted to appeal to facts about the essences of related phenomena as well. 13 Cf. Aristotle’s distinction in APo A.13 between arguments which merely state a fact or what is the case (to hoti), as in the second argument, and arguments which also explain why a given fact is the case (to dihoti), as in the first argument. The solution to the puzzle raised there, as to how exactly this distinction is to be drawn, is not completed until APo B.16, when much more machinery connecting definitions to demonstrations has been put in place. 14 According to Aristotle’s logic, both arguments exemplify the first figure syllogism known as Barbara and are hence of the following form: AaB, BaC; therefore, AaC. (‘A holds of all B’; ‘B holds of all C’; therefore, ‘A holds of all C’.) In the first argument, A stands for ‘not twinkling’, B for ‘being near’, and C for ‘planets’; in the second argument, A stands for ‘being near’, B for ‘not twinkling’, and C for ‘planets’. The syllogistic relation, a, which holds between the terms, A, B, and C, indicates that the propositions in question express universal affirmative judgements. The corresponding ‘because’-statement thus has the schematic form: ‘A belongs to all C because of B’. 15 By ‘explanation’, I mean here something that could serve as an answer to what Aristotle would regard as a properly scientific question (e.g., such questions as ‘what is thunder?’, ‘why does thunder occur?’, ‘why is thunder loud?’, or ‘why does thunder accompany lightning?’). An explanation, understood in this way, could be stated either by means of a ‘because’-statement or by means of an argument, as illustrated above. In what follows, when I use the term, ‘explanation’ (or grammatical correlates), I have in mind only causal explanation; but I understand ‘cause’

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according to Aristotle, is a formula or statement (logos) of the essence (to ti ēn einai), i.e., of what it is to be a certain kind of thing.16 And since essences, for Aristotle, themselves cause the other necessary (but non-essential) features of a thing, so definitions, as the linguistic correlates of essences, explain, together with other axioms, the propositions describing these necessary (but non-essential) features. On Aristotle’s way of thinking, then, the explanatory power inherent in definitions, in their role as the linguistic correlates of essences, is a direct reflection of the causal power of essences. This idea really constitutes the crucial step in Aristotle’s attempt in the Posterior Analytics to supplement the notion of demonstration with scientifically useful content beyond what is already provided by the purely logical consequence relation of deduction.17 Given their role as the linguistic correlates of essences, Aristotle takes definitions to figure among the first principles or axioms of a demonstrative science. As first principles or axioms, definitions are thus explanatorily basic, in the sense that no further demonstrative proof of them can be given. Like any other axiom, definitions cannot be demonstrated from other explanatorily more basic premises, since no other premises are explanatorily more basic than the axioms of a theory. Thus, once we have here in the Aristotelian, rather than the contemporary Humean, way. Thus, a causal explanation, according to the conception I will adopt, could in principle consist in citing any of the four Aristotelian causes (formal, final, material, or efficient cause), while a causal explanation, understood in the contemporary Humean way, typically consists in citing only what Aristotle would consider to be an efficient cause, i.e., the source of a particular motion or change. The Greek does not disambiguate between ‘cause’ and ‘explanation’, since the same terms (‘aitia’ and ‘aition’) can be translated in both ways. 16 For the sake of simplicity, I speak here as though Aristotle recognizes only a single kind of definition; this is in fact not so, as is attested for example by APo B.10, where Aristotle distinguishes between at least three or four different ways in which the term, ‘definition’, is employed (depending on how one reads the chapter). Among other things, Aristotle seems to recognize nominal definitions (‘an account of what a name signifies’) in addition to more or less partial or complete real definitions, viz., statements of the essence. A term like ‘centaur’ might for example have a nominal definition (viz., ‘the term ‘centaur’ signifies a mythical creature with the head, trunk, and arms of a human being and the body and legs of a horse’), even though no real definition in this case is possible, since the kind allegedly denoted by the term does not exist. My current use of the term, ‘definition’, is intended to correspond to what is typically accessible to a scientist only at the end of a successful investigation into the nature of a particular phenomenon. At the start of a scientific investigation, the inquirer may have only a very partial and indeterminate grasp of the phenomenon he is investigating: he might know for example only that thunder is some kind of noise in the clouds, but not yet know specifically what kind of noise in the clouds thunder is and what causes it. At the conclusion of his investigation (if indeed the investigation was successful), the scientist will have discovered the essence of thunder. It is the linguistic correlate of this mature scientific understanding of the essence underlying a natural phenomenon (i.e., a complete real definition) that I am here calling ‘definition’. 17 For a similar emphasis on the causal role of essences, as reflected in the explanatory role of definitions, see also Charles (2002: especially Part II); Charles (2010b); and Lennox (2010).

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explained for example why planets do not twinkle by citing their nearness, no further demonstrative proof of the premise that planets are heavenly bodies that are near is possible, in Aristotle’s view, since we have at that point reached the definition of planets. To ask why planets are heavenly bodies that are near (assuming that this proposition in fact gives at least a partial correct statement of the essence of planets) would be a silly question, in Aristotle’s mind: for to be a heavenly body that is near, after all, is just what it is to be a planet.18 These results also help us to see more clearly what has gone wrong in the case of the second argument above, as compared to the first argument. In the second argument, ‘not twinkling’ is invoked as a middle term allegedly to explain why being near belongs to all planets. In the first argument, on the other hand, ‘being near’ is used as a middle term to explain why not twinkling belongs to all planets. But the attempt to explain why planets are near on the basis of their not twinkling at best captures an evidential order of priority, not a causal order of priority. We might have learned that planets are near on the basis of observing that they do not twinkle; but it would be strange to suggest that the nearness of planets is actually caused by the fact that they do not twinkle. 12.3.2  Aristotle’s explanatory method in biology It is one thing to posit, in the abstract, that the explanatory order of priority represented in a successful demonstration must directly mirror the causal order of priority present among the phenomena in question, but quite another to apply and test this model of scientific theorizing as a practising scientist. If, as theorists about science, we are to assign to definitions the heavy explanatory lifting they are required to do in Aristotle’s 18 Since definitions, like all first principles, cannot be demonstrated, they also cannot be known demonstratively [epistasthai]. Aristotle uses a distinct term [‘nous’] for the epistemic state corresponding to one’s grasp of first principles. The term, ‘nous’, in this context, can be (and has been) translated into English in a variety of different ways, e.g., as intuition, understanding, or comprehension. In his very difficult and condensed discussion of nous in the very last chapter of the Posterior Analytics (APo B.19), Aristotle states that we reach the epistemic state of nous (i.e., grasp of the first principles) through a process of induction [epagōgē]. For Aristotle, induction begins with the perception of particulars and somehow leads through a series of steps involving memory, learning, and experience, to the ability to ‘give an account’, which itself amounts to or leads to the grasp of first principles. But how exactly this cognitive achievement comes about is not spelled out in any detail. Aristotle devotes considerable attention to perception (De Anima), deductive reasoning (Prior Analytics), demonstrative reasoning (Posterior Analytics), and dialectical reasoning (Topics); but, as far as we know, he never wrote a separate treatise on inductive reasoning and the grasp of first principles.

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theory of demonstration, a practising scientist would need to find that essences (the non-linguistic counterparts of definitions) actually do the requisite amount of heavy causal lifting to justify the placement of definitions among the explanatorily basic axioms of a theory. Does the natural world Aristotle encounters in fact conform to the model of scientific theorizing he sets out in the Posterior Analytics?19 In particular, given Aristotle’s background assumptions about the natural world, is his central thesis, that all necessary (but non-essential) features of a kind of thing can be causally traced back to facts about essences and hence explained by appeal to definitions, tenable from the point of view of a practising scientist?20 12.3.2.1  Case-study: the multiple stomachs of camels These questions are best addressed by turning to Aristotle’s biological t­reatises.21 In particular, I will focus my remarks in what follows on a single example from Parts of Animals (henceforth abbreviated ‘PA’): Aristotle’s 19 There are many interesting and worthwhile questions that arise concerning the relation between Aristotle’s theorizing about science, in the Posterior Analytics, and his behaviour as a practising scientist, as illustrated for example in the biological works. One interesting debate that has ensued among scholars for example concerns the question of how (if at all) the blatant absence of explicitly syllogistic reasoning in the biological treatises is compatible with Aristotle’s theory of demonstration, as developed in the Posterior Analytics. (For discussion, see for example Balme 1987a, 1987b; Barnes 1975 and Barnes 2002: ‘Introduction’; Bolton 1987; Charles 1990, 2002; Gotthelf 1987; Lennox 1987, 1990; et al.) Given my present concerns, we can bypass this question and view the information conveyed by a syllogistic argument, as illustrated above, as tantamount to what is conveyed by the corresponding ‘because’-statement. My interest currently is only with the specific question of whether, in the face of scientific evidence, Aristotle can maintain his central thesis that essences play the causal role required to justify the explanatory role assigned to definitions in his theory of demonstration. 20 Among Aristotle’s background assumptions, which shall become important in what follows, are these. (i) Species are eternal. (ii) Concrete particular substances are compounds of matter and form. (iii) The natural world is best understood along teleological lines. (iv) The natural world exhibits the following compositional hierarchy: concrete particular substances are composed of non-uniform parts (e.g., feathers, beaks, eyes, etc.); non-uniform parts are composed of uniform parts (e.g., blood, marrow, bone, etc.); uniform parts are composed of the four elements (viz., earth, air, fire, and water). (v) The composition and organization of the bodies of living organisms is constrained, on the material side, by the fact that only a limited amount of each element is available for each type of living organism. (vi) Hard materials (e.g., those composing horns, teeth, bones, nails, hair, and the like) contain a high proportion of earth. 21 For those who are not familiar with the life and work of Aristotle, it is worth emphasizing Aristotle’s excellent credentials not only as a theorist of science, but also as a practising scientist, especially in the field of biology. After his twenty-year-long stint as a student and associate at Plato’s Academy, Aristotle left Athens at the age of thirty-seven, after Plato’s death in 347 bc, and is thought to have spent the next ten years or so of his life, among other things, conducting extensive biological research along the coast of Asia Minor. The wealth of detailed observations Aristotle amassed during this period of his life is truly impressive and takes up approximately one quarter of his surviving texts (cf., History of Animals, Parts of Animals, Movement of Animals, Progression of Animals, and Generation of Animals).

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treatment of the question, ‘why do camels have multiple stomachs?’22 This specific case, while quite complex, allows us to illustrate the variety of explanatory factors on which Aristotle draws in the biological works; it also brings out some of the potential challenges Aristotle’s approach to scientific explanation faces, when put to the test against the vast array of observed correlations that need to be explained by a successful theory of biology. In PA iii.14, Aristotle discusses the question of why some animals have one stomach, while others have multiple stomachs.23 He notes that the number of stomachs an animal has seems to be correlated with several of its other features, e.g., with whether the animal is viviparous (i.e., gives birth to live young), sanguineous (i.e., blooded), or ambidentate (i.e., has front teeth in both of its jaws); with whether the animal is polydactylous (i.e., has many digits), has solid hoofs, or is cloven-hoofed; with whether the animals has horns; and with whether the animal eats very thorny and woody food. All animals that are viviparous and sanguineous, Aristotle notes, have only a single stomach, whether they are polydactylous (e.g., human beings, dogs, and lions), solid-hoofed (e.g., horses, mules, and donkeys), or cloven-hoofed (e.g., pigs), as long as they are ambidentate. Horned animals tend to be non-ambidentate and have multiple stomachs (e.g., sheep, cows, and goats). As Aristotle remarks in his discussion of horns (PA iii.2), animals that have horns, typically for the purposes of defending themselves, tend to be non-ambidentate, since (in his view) the earthy material that is needed for the construction of horns is then no longer available for the construction of front teeth in both jaws. To make up for the lack of front teeth in both jaws, horned animals tend to have multiple stomachs, to help them digest the food they eat properly. Camels are an interesting case for Aristotle: for even though they lack horns, camels are nevertheless similar to horned animals in that they are non-ambidentate and have multiple stomachs. As Aristotle notes in PA iii.2, very large animals (like the camel) do not need horns in order to defend themselves. But given the surplus earthy material that is freed up by their lack of horns, one might expect camels to have front teeth in 22 I am here drawing on Gotthelf (1987), who considers Aristotle’s discussion of the multiple stomachs of camels in PA iii.14 in detail. 23 That animals must have stomachs at all, in Aristotle’s view, follows from facts about essences in the following way. Like all ancient Greek philosophers, Aristotle takes it to be obvious that all living organisms, including plants, have a soul. The most basic capacity all living beings possess simply by virtue of being alive, i.e., simply by virtue of having a soul at all, is the capacity for growth and nourishment. Having this capacity requires that an organism have some method of ingesting food and extracting the nutrients found therein for its own use. Unlike plants, animals have internal organs for digesting the food they take in (viz., their stomachs) and internal organs for removing the residue that remains after the food is digested (viz., their intestines).

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both of their jaws, regardless of what their stomachs are like. So the question Aristotle wishes to answer concerning camels is this: why, given that camels lack horns, are they nevertheless non-ambidentate and have multiple stomachs? The answer he gives is as follows: The explanation of this is that it is more [necessary] for the camel to have multiple stomachs than to have front teeth. Its stomach, then, is constructed like that of non-ambidentates, and its teeth match its stomach – for the teeth in question would be of no service. Its food, moreover, being of a thorny character, and its tongue necessarily being made of a fleshy substance, nature uses the earthy matter which is saved from the teeth to give hardness to the palate. The camel ruminates like the horned animals, because its multiple stomachs resemble theirs. … For since the mouth, owing to its lack of teeth, only imperfectly performs its office as regards the food, the stomachs receive the food one from the other in succession, the first taking the unreduced substances, the second the same when somewhat reduced, the third when the reduction is complete, and the fourth when the whole has become a smooth pulp. (PA iii.14, 674a34–674b13)24

Aristotle thus reasons that, because their diet is so thorny and woody, camels benefit more from having multiple stomachs, in order for them to be able to digest the food they eat properly, than they would benefit from having front teeth in both jaws. But given the camel’s need for multiple stomachs, it is now no longer necessary for the camel to have front teeth in both of its jaws, since its multiple stomachs already take care of the task of dealing with the camel’s thorny and woody diet better than a second row of front teeth could. The surplus earthy material which is now freed up, due to the camel’s lack of the second row of front teeth, could of course go into the construction of horns. But since the camel does not need horns (due to its size), it would be better served by having the surplus earthy material used to make the roof of its mouth very durable, so that it can withstand the thorny and woody food it ingests without injury. 12.3.2.2  Telos, matter, and habitat Aristotle’s discussion above presents us with a number of lawful generalizations concerning camels, such as the following: (3)  a. Camels lack horns. b. Camels have multiple stomachs. c. Camels are non-ambidentate. 24 Translation by W. Ogle (see Barnes 1984). I have substituted ‘necessary’ for ‘essential’ in the first line of the cited passage, since the Greek has ‘ἀναγκαιότερον’ and the distinction is of course important for present purposes.

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d. Camels have hard and durable palates. e. Camels eat very thorny and woody food. In his explanation of why camels have the particular necessary (but non-essential) features they do, Aristotle finds himself appealing to a variety of explanatory factors originating roughly from the following three sources: (i) Telos: considerations concerning the proper functioning of an organism and the characteristic activities in which it engages; (ii) Matter: considerations concerning the types of materials that compose an entity; and (iii) Habitat: considerations concerning the environment in which an animal naturally resides. To illustrate: (4)  a. Living organisms are capable of growth and nourishment. b. Animals are capable of digesting food internally. c. Stomachs are internal organs capable of digesting food. d. Camels are very large animals residing in desertous regions. e. Deserts are geographical regions that are extremely hot and dry. f. Earthy material is hard and durable. Teleological considerations (e.g., (4.a)–(4.c)) for example dictate that camels, like all animals, must be able to ingest and internally digest food in some fashion, in order to manifest their capacity for growth and nourishment. Environmental considerations (e.g., (4.d)–(4.e)) dictate that, given their natural habitat, camels must be able to ingest and digest very thorny and woody food, since (so Aristotle presumably reasons) this is the only kind of food that is readily available to them in the desertous regions in which they naturally reside. Given these factors, together with other assumptions Aristotle makes, material considerations (e.g., (4.f)) dictate that the bodies of camels and the parts of their bodies exhibit certain physiological features, e.g., hard and durable palates made of predominantly earthy material. If Aristotle’s explanatory strategy in this particular case is to follow the outlines of his general approach to scientific explanation, his account of why camels have the necessary (but non-essential) features they do must indicate how these features can be traced back causally to facts about essences. But there is of course no reason to expect that the necessary (but non-essential) features of camels can be causally explained solely by reference to facts about the essence of camels: as illustrated above, facts about the essences of various other types of entities (e.g., animals and living organisms in general, stomachs, desertous regions or earthy material) also turn out to be relevant to a causal explanation of why camels have

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the particular necessary (but non-essential) features they do. For example, the fact that the palates of camels are hard and durable is at least in part causally explained by reference to the fact that the palates of camels are made of earthy material. But the fact that things made of predominantly earthy material are hard and durable, for Aristotle, is itself directly traceable to facts about the essence of earth. Thus, causal explanations of why camels have the particular necessary (but non-essential) features they do (viz., hard and durable palates) may also terminate in facts about the essences of other types of entities which are in some way implicated in the activities, physiology, or habitat of camels. 1 2 . 4   C onc l us ion Given a broadly non-modal conception of essence, the question arises of how propositions stating necessary (but non-essential) features of objects can be derived from propositions stating essential features. In the foregoing remarks, I singled out two crucial ways in which Aristotle’s construal of the relevant notion of ‘following from’, viz., demonstration, supplements that of deductive consequence. First, for Aristotle, the relevant notion of entailment that is found in a proper scientific explanation inherits its asymmetry from the actual causal order of priority that obtains among the phenomena being characterized. Secondly, we learn by examining Aristotle’s biology that a successful scientific explanation of the necessary (but non-essential) features of one type of phenomenon (e.g., camels) may require an appeal to facts about the essences of various other related types of phenomena (e.g., earth, stomachs, deserts, and the like). Both of these considerations strike me as important from the point of view of contemporary metaphysicians who are sympathetic to Fine’s project of grounding modality in essence.

c h a p t e r 13

No potency without actuality: the case of graph theory David S. Oderberg

13.1  I n t roduc t ion Dispositional essentialism is the thesis that at least some characteristics or properties1 of objects are dispositional in nature.2 What this means is that the essence of a dispositional property (disposition for short) is its relation to other properties, namely the stimulus and manifestation properties of the disposition. To take the stock example of fragility, and speaking loosely, the essence of this disposition is its relation to the stimulus of being (appropriately) stressed and the manifestation or response to the stimulus, which consists in breaking. A glass that possesses fragility will, if appropriately stressed, break. A more precise example is solubility: any solid, liquid, or gas that has the disposition of solubility in a liquid L will, when inserted into L, dissolve to form a homogeneous solution with L.3 Dispositional essentialists generally allow that not all properties are dispositional, though how to mark the distinction between the dispositional 1 I will henceforth use the term ‘property’ instead of ‘characteristic’ in deference to contemporary usage, whilst inserting the caveat that this is strictly a misuse of the term ‘property’, which has a more precise meaning in Aristotelian metaphysics: see Oderberg (2007: chapter 7). 2 It has been defended in various ways and to various extents by, apart from Bird (2007), Swoyer (1982), Ellis and Lierse (1994), Ellis (2001), and Molnar (2003). 3 Note that by ‘properties of the disposition’ I do not mean that the dispositional property itself has stimulus and manifestation properties. It is not as though fragility can be either stressed or break. Rather, ‘properties of the disposition’ should be read as elliptical for a more complex formulation: fragility has the (second-order) property of being such that objects that possess it will, if (appropriately) stressed, break, where being stressed and breaking are first-order properties. To put it even more precisely: the stimulus and manifestation properties of a disposition are those first-order properties that figure in the conditional whose antecedent is an open sentence consisting of a variable whose range is the objects possessing the disposition, combined with the predicate term denoting the first-order stimulus property of objects within the range, and whose consequent is an open sentence whose variable has the same range, combined with the predicate term denoting the first-order manifestation property of objects within the range. This is not to say that disposition ascriptions can be exhaustively analysed in terms of such conditionals, only that such conditionals are associated with disposition ascriptions and do at least partly explain what it is for such ascriptions to be true.

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and the non-dispositional, and what it means to be a non-dispositional property, are vexed issues. (See Molnar 2003: chapter 10 for an interesting discussion.) Alexander Bird (2007), however, argues for a stronger thesis, namely dispositional monism: this is the view that all properties have dispositional essences. More precisely, he argues that at the ‘fundamental level’, all properties are essentially dispositional. The fundamental level is that of properties with ‘non-redundant causal powers’ (13)4 which (together with the objects that possess them – presumably a subset of the objects of physics) generate all of the natural laws upon which supervene all other objects, properties, and laws found in nature. Dispositional monism is, on its face, a strong thesis. Is it plausible to think that all of the properties, at whatever level, could be pure potencies? (Again, I use terminology sometimes employed by Bird.) Whether there is a fundamental level is not my concern here, so we can leave that part of Bird’s dispositional monism to one side. On the assumption that the stimulus and manifestation properties of a given disposition are at the same level as the disposition itself, whether fundamental or not, it is still a strong claim to make that pure powers (again, Bird’s occasional usage) are all the properties there are at that level. Yet a strong thesis is not necessarily a false thesis. Most believers in dispositions take it for granted that some properties are non-dispositional. They usually assume that the stimulus and manifestation properties of a given disposition are themselves non-dispositional: a fragile object, when struck (non-dispositional), will break (non-dispositional). Yet dispositional monism requires that the stimulus and manifestation properties of a disposition be themselves dispositional. These properties too, then, will have to have their own relations to stimulus and manifestation properties, which also will be dispositional, and so on. Surely a vicious regress threatens, or else a vicious circularity? Bird (135–46) argues that this is not the case, building on ideas developed by Randall Dipert (1997). I will argue that Bird fails to save dispositional monism from just the objection that others have made against the very idea of a world of pure potency. 13.2  T h e r e g r e s s /c i rc u l a r i t y obj e c t ion Jonathan Lowe is perhaps the most prominent advocate of the regress/ circularity objection to a world of pure powers (Lowe 2006: 138).

  Page numbers on their own in brackets will henceforth refer to Bird (2007).

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Addressing Molnar’s claim that there is nothing incoherent in ‘pan­dispositionalism’ (though Molnar thinks it false a posteriori), Lowe points out that according to Molnar, ‘each power gets its identity from its manifestation’ (Molnar 2003: 195), and each power has only one kind of manifestation. Molnar should, I note, have added the stimulus property to the manifestation property as being the pair of properties from which each power gets its identity. (Let us leave aside whether each power has one and only one stimulus and manifestation; supposing that they do simplifies the discussion.) In any case, what Molnar’s claim amounts to is, with the inclusion of the stimulus, that the identity conditions of powers are given solely by their stimulus and manifestation properties. For instance, what solubility is as a disposition is just the property such that whatever has it will, if inserted into an appropriate liquid (stimulus), dissolve to form a homogeneous solution with that liquid (manifestation). Any property that is not so related to either of those stimulus and manifestation properties, or is so related only to one of them, will not be the property of solubility, whatever else it might be. And so Lowe argues as follows: ‘The problem … is that no property can get its identity fixed, because each property owes its identity to another, which in turn owes its identity to yet another – and so on and on, in a way that, very plausibly, generates either a vicious infinite regress or a vicious circle’ (Lowe 2006: 138). Howard Robinson (1982: 114–15) voices what amounts to the same objection but in terms of ‘determinate natures’: since ‘any real entity must possess a determinate nature’, a power must have a determinate nature, where this is given by its ‘actualisation’. (Again, the stimulus should also be included, as with Molnar.) But this actualization could only be a power itself if it had its own further actualization. This chain of relationships between powers and their actualizations could not go on forever, in the sense of powers’ only having other powers as their actualizations, because we would never reach a ‘determinate actualisation’ by which the determinate nature of the original power could be fixed. Its nature would remain indeterminate if the chain were infinite, therefore ‘[a] determinate power must issue at some point in its chain of consequences in an effect which is not itself a power’. Although Robinson only mentions infinite chains, his point can be extended to circular ones. If a power’s determinate nature is to be fixed by its relation to its actualization, then if that actualization were itself a power whose nature required further actualization, and if such a chain of powers and actualizations terminated in the original power under consideration which was putatively to function as

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the actualization of a prior power in the chain, then the nature of the original power would be determined, at least in part,5 by its own nature. Yet the determinacy of its own nature is what was originally in question, hence the viciousness of the circle. Although it seems that Robinson’s objection amounts to the same as Lowe’s, given the conceptual connection between identity and determinacy of nature, the latter’s formulation is to be preferred since talk of determinate natures might cause one to forget that the nature of powers is in an important sense indeterminate: there is a range of ways, all contingently unactualized, in which a power can manifest itself, whether those ways are all instances of a single kind of manifestation for every power (as I am assuming here) or are possibly instances of different kinds of manifestation. Talk of identity conditions avoids this potential confusion. Lowe’s point is that a chain of pure powers will not provide fixed identity conditions since such a chain would either be infinite or circular. Bird himself agrees (137–8) that if the existence of a world (or level) of pure powers issued in an infinite or circular chain, and hence in an infinite or circular chain of identity conditions, there would indeed be a problem. He denies, however, that either infinity or circularity is a consequence of postulating such a world. 13.3  G r a ph t h e or y a n d Di pe r t ’s di s c on t e n t s Bird, building on Dipert, argues that the mathematical discipline of graph theory successfully answers the regress/circularity objection. The background, in brief, is as follows. In the Categories (8a14; Loeb 1962: 59), Aristotle argues that no primary substance, such as a particular man or ox, is essentially relational (prós ti),6 since neither are so-called or defined with reference to something beyond them (ho gár tis anthropos où legetai tinós tis ánthropos, etc.). He ventures the possibility that some secondary substances such as the natural kinds head and hand are relational, but in the end concludes (8b17; Loeb 1962: 63), via arguments that need not be expounded here, that no substance, primary or secondary, is essentially relational. Now Dipert (1997: 348–9) takes Aristotle to be arguing that relations are ‘just ways of speaking that are ultimately reducible to monadic aspects of substance’. The argument for this is supposed to 5 ‘In part’ because, if we include the stimulus as well as the actualization, then if either of them, let alone both, figured in a chain whose final stimulus or actualization (respectively) was the original power itself, then the original power’s nature would, at least in part, be determined by itself. 6 All translations are my own unless specified otherwise.

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be (though the interpretation of Aristotle is highly contentious) that an infinite regress of relations would be incoherent: not all relata can themselves be relational, because then no relations could be defined. (In Lowe’s words, no relata would have fixed identity conditions; in Robinson’s, no relata would have a determinate nature.) Now it is not clear how the conclusion Dipert attributes to Aristotle is supposed to follow from the premises. It is one thing to say that all relations must eventually terminate in substances as relata, and another to say that relations are reducible to monadic properties of substances. That point aside, however, all we need to extract from the relevant, admittedly difficult, passages where Aristotle discusses relations is his fairly clear adherence to the proposition that not everything that exists is essentially relational because substances are not relational. Dipert, on the other hand, asserts confidently that he can prove, ‘for the first time in the history of philosophy’ (1997: 349), that the distinctness of relata can be established ‘through relations alone’, i.e. that, in a nutshell, it is coherent to suppose that everything that exists is relational in nature. (Dipert also thinks it is true, but let us focus on coherence; his arguments for truth are somewhat elusive.) The technique for demonstrating this is via appeal to graph theory. It is easier if we now skip to Bird’s account, bringing in Dipert soon after. Importantly, for the sakes both of brevity and of ease of exposition and discussion I will, somewhat unusually, weave my comments and criticisms into the account of how the graph-theoretic approach is supposed to solve the regress/circularity problem. According to Bird (139), the identity and distinctness of the members of a set of entities can supervene on some relation or set of relations on those entities. This is, as Bird and Dipert claim to have shown, ‘just a simple question in graph theory’. A graph, as the term is used in graph theory, is a way of representing a structure consisting of nodes (vertices, points) joined by lines to form edges, where the nodes are distinct relata (at the most abstract level, entities) and the edges are instances of a single dyadic relation R, be it symmetric or asymmetric. The structure of the graph is the ‘pattern’ of the edges, as Bird puts it.7 Graph theory studies the structures represented by graphs, in particular whether graphs are isomorphic, that is, whether they represent the same structure. With this very brief description (and at this stage deficient, as we will see) in place, 7 The terminology of graph theory is not uniform. Bird uses the ‘vertex/edge’ terminology, but I will use the ‘node/edges’ terminology, including the harmless replacement of ‘vertex’/‘vertices’ by ‘node’/‘nodes’ in quotations from his and Dipert’s texts.

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Figure 13.1 

we can now see what Bird means by translating his supervenience claim into a more specific one concerning graphs (139): (S*) The identity and distinctness of the nodes of a graph can supervene on the structure of that graph.

Take the graph in Figure 13.1 (140). According to Bird, a rotation of this graph through 180° takes all the nodes onto different nodes while leaving the structure unchanged. ‘Consequently’, he concludes, ‘the structure of this graph fails to determine the identity of its nodes’ (140). Graph theorists use the term ‘automorphism’ for any mapping of a graph onto itself. The identity mapping of each node onto itself is called the trivial automorphism of the graph. A mapping of at least some nodes onto different nodes while preserving structure is a non-trivial automorphism. Hence the 180o rotation of Figure 13.1 is a non-trivial automorphism, and since, according to Bird, the structure of this graph fails to determine the identity of its nodes, we need, if graph theory is to rescue pure powers from the regress/circularity objection, to find graphs that have no non-trivial automorphisms; such graphs are called asymmetric. Bird explains (140): ‘Such a graph would have no way of swapping nodes while leaving structure unchanged. Which is to say that the structure determines the identity of the nodes – the structure itself distinguishes each node from every other node; i.e. the identity of nodes supervenes on the set of instantiations of the edge relation.’ Sure enough, there are in fact infinitely many asymmetric graphs, which Dipert, as Bird notes, takes to refute the Aristotelian claim that the world could not be a world of relationally defined entities and nothing else.

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C

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Figure 13.2  C

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Figure 13.3 

Before considering asymmetric graphs, however, we need to pause and refer back to Dipert, Bird’s inspiration for the supposed graph-theoretic solution to the regress/circularity objection. It is standard for graphs to be defined set-theoretically: a graph consists of two sets, a set of nodes N and a set of edges E, with each edge having one or two nodes as its endpoints. If a node is an endpoint of an edge, it is incident on that edge, and the edge is also incident on the node. A node joined to another node by a line is a neighbour of the latter, the neighbour relation being of course symmetric.8 Now although the set-theoretic definition of graphs is standard, Dipert believes it is flawed: ‘set-theoretic entities are distinguished even when we can see they have the same graph-theoretical structure’. Take his example (1997: 343) shown in Figures 13.2 and 13.3. Now Dipert is aware that mathematicians are familiar with the fact that the same structure can be labelled in different ways, which is why graph theory employs the key concept of isomorphism: two graphs are isomorphic just in case there is a mapping (one-one correspondence) from the node set of one graph to the node set of the other such that for any two nodes of the first, they form an edge (are joined by a line) if and only

  See, for example: Gross and Yellen (2004); Wilson (1996); Trudeau (1976); Harary (1969).

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if the corresponding nodes of the second are. More formally, there is a bijection f from the node set N of graph G1 to the node set M of graph G2 such that for any nodes {u,v} in N, {u,v} are joined if and only if {f(u), f(v)} in M are joined. Now Figure 13.2 and Figure 13.3 are clearly the same structure, but the labelling is different. The mapping from the first to the second is: A → B, B → C, C → A. But what, exactly, is mapped? This is where the confusion over labelling begins to rear its head, because if all that is mapped are labels then there is still set-theoretical identity between Figure 13.2 and Figure 13.3. In graph theory, the official set-theoretic definition of a graph is in terms of sets of nodes, not sets of labels of nodes. For mathematical purposes this is a distinction without a difference, since the pure study of graphs is without ontological import. True, it can be applied to various ontological purposes, such as in the study of different kinds of network, but in its pure form nothing of ontological consequence lies behind the structures themselves. In which case, to talk of a node as opposed to a node label is inconsequential. But remember that both Dipert and Bird are interested in the ontology behind graphs: for Bird, they are a tool for defending a world of pure powers; Dipert goes further and proposes that the entire world, that is, the entirety of what exists, can be characterized as a graph or complex of graphs. So we are entitled, with ontology in mind, to distinguish between labels and what those labels are labels of. So to return to Figures 13.2 and 13.3, if we think of them as representing ontological structures, with the nodes as objects – let us suppose the nodes represent particles and the lines represent the single relation of repulsion  – then if the only difference between the diagrams is one of labelling, that is, each node in Figure 13.2 represents numerically the same particle as it does in Figure 13.3, the diagrams will still be set-theoretically identical. We do not say that the sets {Bob Dylan, Marilyn Monroe} and {Robert Zimmerman, Norma Jean Baker} are distinct just because their numerically identical members are differently labelled. Dipert remarks that Figure 13.2 and Figure 13.3 are set-theoretically different if graphs are defined set-theoretically, but that ‘[i]n a sense, however, the two have the same graph structure: they are just looked at, or labelled, in different ways’ (1997: 343). This is misleading on several fronts. First, as just noted, if the only difference between Figures 13.2 and 13.3 is the labelling and we pay no attention to what the labels might be labels of, the diagrams are set-theoretically identical. Secondly, although Dipert speaks correctly of Figures 13.2 and 13.3 having the same graph structure, only a few lines earlier he speaks of ‘graph 1’ and ‘graph 2’, which leads one to think that

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the figures are two graphs with the same graph structure. But they are not two graphs, they are two graph diagrams which instantiate a single graph structure. There is, at bottom, no such thing as two graphs with the same structure: if the putative two graphs have the same structure they are not two, but one; if they really are two graphs, they must have different structures. A graph is often defined by graph theorists as an isomorphism group, that is, an equivalence class of isomorphic graphs. While this may be operationally useful, the ontological truth is that a graph is no more identical to a group or to a class than it is to a diagram, a representation, or any concrete entity or plurality of such entities. A graph is a universal, an abstract structure that can be instantiated (as well as depicted/represented) by a diagram or some other representation, or by a concrete entity or plurality of such entities (or by other abstract objects). An isomorphism group can most easily be thought of as the equivalence class of all the actual (and perhaps possible) instantiations of a given graph structure, but not as identical with the structure. Thirdly, the expression ‘looked at, or labelled, in different ways’ is vague. If pure rearrangement of labels is all that Dipert wants us to read into the two diagrams, then set-theoretical identity is maintained. If something of ontological substance is behind the remark, however, then set-theoretical identity is lost and isomorphism comes into play. Returning to our particle/repulsion interpretation of the diagrams, suppose the particles in Figure 13.2 are named Alpha, Bravo, and Charlie. Then suppose Alpha switches places with Bravo, which switches places with Charlie, which switches places with Alpha. Then we have a new particle arrangement that is not set-theoretically identical with the first but is isomorphic to it. But now look how Dipert defines isomorphism (1997: 344): ‘Two graphs are structurally identical just when their labels can be rearranged so that they are set-theoretically identical.’ Three points must again be made. (1) Isomorphism has nothing to do with mere labelling. If Alpha, Bravo, and Charlie are renamed Bill, Bob, and Ben, or if Alpha, Bravo, and Charlie simply swap names, the resultant arrangement would be exactly the same in the sense that the three particles would instantiate exactly the same token structure, not merely the same type structure. A swapping of names would, in fact, be a trivial automorphism, not a non-trivial one, because a mere swapping of names is just a mapping of each particle onto itself (the same for a mere replacement of names, though spelling out how this would constitute a trivial automorphism is slightly more complex). So mere label rearrangement has nothing to do with isomorphism in general and everything to do with automorphism (which is a specific kind of

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isomorphism, where the nodes of a graph diagram are mapped onto the nodes of the same diagram). (2) To expand on the earlier point, there is no such thing as structurally identical graphs, only graph diagrams/representations or instantiations. In other words, despite the way some mathematicians talk, isomorphism is not a relation between graphs, only between representations or tokens of graphs (where the ‘or’ is inclusive: a graph diagram is also a token instantiation of a graph). A graph can only be trivially isomorphic to itself, not to another graph. Two graph diagrams can be isomorphic, in that they instantiate the same graph structure. Figures 13.2 and 13.3 are isomorphic. Within isomorphisms, there are automorphisms that consist of a graph representation’s being mapped onto itself in such a way that the resultant representation is set-theoretically identical to the original. The place-switching of Alpha, Bravo, and Charlie imagined above is not an automorphism because the resultant representation is not set-theoretically identical to the original: where Bravo originally repelled both Alpha and Charlie, after the switch it only repels Charlie (and so on). But now suppose only Alpha and Charlie swap places, while Bravo remains put. This mapping constitutes a non-trivial automorphism, with the resultant particle arrangement/graph representation set-theoretically identical to the original: Bravo still repels Alpha and Charlie who do not repel each other. Spatial location is in one sense relevant and in another not. We must imagine the particles as having some kind of spatial orientation to each other so that we can imagine place-swapping. But that Alpha and Charlie swap places is irrelevant to structure: the place-swap enables (indeed constitutes) an automorphism, resulting in an arrangement set-theoretically identical to the original. But the identity of arrangement is possible only because we abstract from spatial considerations and focus on the repulsion relations between the particles. (3) In the quotation from Dipert just given, set-theoretical identity makes its reappearance, after he has already disparaged it as a way of understanding structural identity. Indeed it must reappear, because there simply is no other way of comprehending isomorphism in terms of mappings. Forgetting talk of labels and continuing to do the two things I have been at pains to insist on  – concentrating on the underlying ontology and distinguishing between graphs and their representations or instantiations – we can see that two graph representations are isomorphic just in case the entities (or entities represented by nodes) in one can be rearranged so as to produce a representation set-theoretically identical to the other and vice versa. Figure 13.2 is isomorphic to Figure 13.3 just because

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the nodes of the former can be mapped onto the nodes of the latter in the way mentioned earlier, and the converse mapping of the nodes of the latter onto those of the former produces the original Figure 13.2. This is just another way of saying that the nodes of Figure 13.2 can be rearranged to produce a representation set-theoretically identical to Figure 13.3 and vice versa. Set-theoretical identity is, then, indispensable when it comes to understanding structural identity, and Dipert is wrong to disparage it as a mere matter of labelling. Hence what he should have said, when giving his definition of structural identity, is something like the following: two graph representations are structurally identical when the nodes of one can be mapped onto the nodes of the other so that the resultant representation is set-theoretically identical to the first. In other words, structural identity means that one representation can be turned into the other by mapping nodes (and vice versa). Dipert goes on to complain that we need, ideally, to give an account of graphs such that ‘every difference between two graphs’ descriptions entails a difference in structure, and vice versa’. Set-theoretical notations, he tells us, ‘do not do so because differences in node labels result in distinct (that is, non-set-theoretically equivalent) expressions, or in diagrams that look different but are not structurally distinct. This obscurity arises because of the presumed “individual” node labels’ (1997: 344). What could the words ‘presumed “individual” node labels’ mean? After all, the nodes in a graph representation or instantiation are individual, so how are we supposed to grasp their individuality except by means of some form of labelling? As long as we remember what the labels are – mere names for some underlying entities – and that differently labelled graph representations can be of or instantiate the same graph structure, we will not go astray. We have to remember that we cannot get at graphs directly via some intellectual intuition: we can only get at them, i.e. grasp their essences, via their token representations and instantiations. We have to abstract the universal structure from the instances, and those instances have to use labels. We need not call the nodes ‘A’, ‘B’, ‘C’, or ‘Alpha’, ‘Bravo’, ‘Charlie’, and so on; we need only think of the nodes as ‘this one’, ‘that one’, ‘the other one …’ but these are still labels, albeit mental ones. There just is no other way to understand the essence of a graph or of graphs in general. Dipert’s argument with labels is not, I submit, innocent, any more than his dispute with set theory as used in graph theory. His ‘ideal’ is not to be found; rather, it is a treacherous objective, since there is no way in which to give a label-free description of differences in graph representations/instantiations that entails a difference in structure. On the contrary, as long as we

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understand how graphs work, we will know that we must employ differences of labelling before we can ascend to identity of structure. Similarly for the use of set theory, which Dipert believes ‘pollutes’ the mathematical theory of graphs (1997: 345). Of course isomorphism does not entail set-theoretical identity. Figures 13.2 and 13.3 demonstrate that, where the isomorphism is understood as more than mere label-shifting, that is, when it involves entity-shifting. Nevertheless, graphs can, and arguably can only, be understood set-theoretically in terms of what might be called a set-theoretical schema. A graph can be understood as a set N of nodes and a set E of edges, the latter consisting of unordered pairs of members of N. When graph theorists spell this out, they use variables that range over nodes and sets of pairs of variables for edges. These sets are themselves variables, which means that in the general definition of a graph what they provide is a set-theoretical schema which anything must satisfy if it is to count as a graph. Particular graphs, such as those diagrammed earlier, will satisfy specific instances of the schema. The graph diagrammed in Figure 13.2 satisfies the schema instance: N={A, B, C}, E={{A,B}, {B,C}}. In between the highest-level schematic definition of a graph and the particular schema instance lie the mid-level schematic definitions of kinds of graph. The graph diagrammed in both Figure 13.2 and Figure 14.3 satisfies the mid-level schema: N={x,y,z}, E={{x,y}, {y,z}}. The variables are, of course, proxies for individual names. How else could graphs be understood? Dipert goes on to say that if we identify ‘the concrete world’ with a graph, as he wishes to do, then ‘[w]e should not import assumed individuation of entities … when a key component of metaphysics is precisely the individuation of entities … we shall not assert, or assume, metaphysical distinctness unless we can show … structural distinctness’, which ‘[t]raditional logical metaphysics’ has failed to do (1997: 346). Now if these remarks make any sense at all, it has to be set-theoretical sense, and the distinctness of nodes has to be presupposed even though the ground of their individuation must then be explicated in terms of structural relations. To see what I mean, consider what Dipert says about Figure 13.2 (1997: 345). He points out, correctly, that node B has degree 2 (that is, has two neighbours), whereas A and C both have degree 1. He adds: ‘In fact, on close examination, once we ignore their different labels, nodes A and C begin to fade into one another’, since they have ‘the same structural features’. What could this mean – that if we look at A and C long enough, we will begin to think we are suffering from double vision? We have to presuppose their distinctness even to begin to be able to assess the graph

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Figure 13.4 

diagram correctly and conclude that nodes A and C – or Alpha and Charlie or whatever we choose to call them – are relationally indistinguishable. Now what Dipert (and Bird) must mean is that the structure of symmetric graphs does not fix the identity of the nodes, as Bird explicitly claims. My claim, though, is that because of regress or circularity no graph structure, symmetric or asymmetric, fixes the identity of its nodes. First, let us be more precise about Bird’s supervenience claim: structure can fix identity. Bird’s example, Figure 13.1, is of a symmetric graph which, he points out, preserves structure through a 180o rotation. If the nodes are defined purely relationally, then Bird’s idea must be that we cannot know, in principle, which of the degree 2 nodes is which, and which of the degree 3 nodes is which. In other words: (S**): The structure of a graph fixes the identity of its nodes if and only if it is in principle possible to determine, of any pair of nodes, which is which.

Rotation, and other permutations of the structure that non-trivial automorphisms can consist in (such as flipping across an axis), simply makes concrete why (S**) could be true. So suppose we label the four nodes of Figure 13.1 as in Figure 13.4, remembering that the issue is not one concerning labels per se. The nodes represent particles in mutual relations of repulsion. A rotation of 180o is equivalent to a swapping of places by Alpha and Delta, and Bravo and Charlie, respectively. Suppose we know that Alpha, Bravo, Charlie, and Delta are in their initial positions. We leave the laboratory in which they are located, return, and are asked which particle is which.

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Given our assumption that the particles are defined purely relationally, it seems in principle impossible to tell, since just such a rotation may have taken place. Are Alpha or Delta where we last saw them? Are Bravo and Charlie where we last saw them? We cannot know. The same goes for Figure 13.2, where the following is a non-trivial automorphism: A→C, C→A, B→B. Again, we cannot know even in principle which is Alpha and which is Charlie, given that such a permutation may have taken place. This does not mean the particles, any more than the nodes, ‘fade into one another’; there are still two particles, but we cannot know their identities, and if they are defined purely relationally there is no fact of the matter as to which is which. Now maybe Dipert could respond that it is incoherent even to suppose that Alpha was here and Charlie was there in the first place, and hence that the very idea of a physical realization of such a structure makes no sense. Perhaps we can accept this explanation, given Dipert’s assumption that structure determines identity. One might rejoin, however, that the identity problem for symmetric graphs gives as much reason to posit either primitive identities or identities defined non-relationally as it does to posit asymmetric graphs as possible structures for physical reality (though Bird objects to primitive identities for properties, which he calls quidditism: 2007: chapter 4). Leaving this issue to one side, however, the point on which I wish to focus is the regress/circularity objection. All of the three graph diagrams shown so far involve ineliminably circular definitions of their relata, a phenomenon that is independent of the symmetrical nature of the graphs they represent. In Figure 13.2, the individual called A, however we might choose to label it, is defined by its relation to B, which is defined by its relations to A and to C, which latter is defined by its relation to B. Mutatis mutandis for Figure 13.3. In Figure 13.4, again irrespective of how we choose to label the individuals represented by the diagram, Alpha is defined by its relations to Bravo and Charlie, which are both defined by their relations to Alpha, Delta, and each other, and mutatis mutandis for Delta. Each individual is defined by relations to others that are themselves, directly or indirectly, defined by their relations to that individual. This has nothing to do with symmetry, I suggest, and everything to do with circular definition pure and simple. 13. 4  A s y m m e t r ic g r a ph s t o t h e r e s c u e ? Part of the point of the above discussion has been to highlight some of the philosophical confusions underlying graph theory, which for all its

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mathematical neatness is by no means susceptible of easy metaphysical interpretation. Hence we do well to tread carefully, especially before claiming, as Dipert does, that the entire world is a graph, and as Bird slightly more modestly does, that the ‘fundamental level’ of reality is a graph. Another aspect of the discussion has been to highlight the fact that graph theory, when applied to physical reality, is supposed to be about individuals and about representations of physical structures. One cannot do away with all problems of interpretation simply by doing away with labelling and pretending there is an ideal of ‘pure graph structure’ in which individuals are a mere projection of ‘presumed “individual” node labels’ (Dipert 1997: 344). This matters because if individuals in graphs are thought of as mere projections of relations, the circularity problem might not seem so pressing. Non-trivial automorphisms will remain an issue because there will be little coherence in projecting two individuals onto symmetrical relational arrangements when it will be in principle impossible to say which individual is which. But this projectivist view of individuals might seek to evade the circularity problem by denying that projection requires any definition. The projectivist can simply posit, say, Alpha and Charlie in Figure 13.2, and refuse to admit that by so doing he is committed to defining one in terms of the other. They will be no more than projections of their symmetrical relational arrangements. True, because of symmetry he will not be able to say which individual is Alpha and which is Charlie, but he can decline to give a definition of either, resting with the mere positing of these individuals at the endpoints of relations to Bravo, just as Bravo is posited as the common endpoint of relations to Alpha and Charlie. All individuals are posited simultaneously, and there’s an end to it. If, however, we take seriously the idea that the nodes of graph diagrams, when interpreted physically, do represent real individuals, then circularity becomes a serious issue. Real individuals must have real identity conditions, and as Lowe remarks, if the identity conditions of a thing are circular, it has no fixed identity. And, we can add, if it has no fixed identity, there is little coherence in supposing it exists at all. Hence we should take the ‘presumed “individual” node labels’, as Dipert describes them, to denote real individuals, with no scare quotes needed. So they could, for instance, be thought of as intrinsically qualitatively identical real individuals, differentiated only by their relations to one another. Think of our particles as all intrinsically alike, so that their intrinsic qualities do not serve to identify them. Now ask whether a graph could do the job that the particles’ intrinsic qualities cannot. Both Bird and Dipert answer that

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Figure 13.5 

it could, but it must be an asymmetric graph, that is, one with no nontrivial automorphisms. Bird’s example of a simple, asymmetric graph has six nodes as in Figure 13.5. There are no non-trivial automorphisms for such a graph, which, according to Bird and Dipert, means that one can give ‘a unique, purely structural description for each vertex’ (Dipert 1997: 348). In Dipert’s case, however, he proceeds to give a description of his (slightly different) 6-node graph using labels (Dipert 1997: 348). Bird does not, but then he does not describe his graph. We could do so purely generally, as follows (reading the diagram left to right): there is a node of degree 1 adjacent to a node of degree 3 that is also adjacent to a node of degree 2 and to another node of degree 3, the former also being adjacent to the latter, and the latter also adjacent to another node of degree 2 which is adjacent to another node of degree 1. Now, the use of terms such as ‘the former’, ‘the latter’, ‘another’, and ‘also’ is just a proxy for labels. The existentially general description of the graph obviously allows substitution of names for each node, which again shows that a set-theoretical characterization is the only way of giving an accurate description of the graph’s structure. Asymmetric graphs do not take us away from the world of individuals and their names, and so identity conditions again are crucial to coherence. So how are identity conditions fixed by asymmetric graphs? Since there is no way of mapping the nodes onto each other that preserves their edge relationships, each node has a unique position in the graph. One and only one structural description applies to each, and each description differs from the rest. Problem solved? Not quite. Let us label the nodes as in Figure 13.6. Call the relation of ‘… being defined partly in term of its relation to …’ relation P. Then we notice, for example: P(A,B); P(B,A); P(C,B); P(B,C); P(E,F); P(F,E). But this is only part of the definitions, of course. For example, A’s complete definition is: A is a neighbour of B which is also a neighbour of C, which is a neighbour of D, and of D, which is also a neighbour of E which is a neighbour of F. And the

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C

A

B

D

E

F

Figure 13.6 

complete definition of F must also mention all the other nodes. The same for every node, whose definition must mention all the others. Circularity is rampant throughout such definitions, just as Lowe and others have suspected  – though they do not talk about asymmetric graphs. Bird and Dipert reply that, nevertheless, each node has a unique position and hence a unique structural definition. But this will not do, since unique definitions can still be circular, and every definition of every node in Figure 13.6 is just that. Nor will the fact that each definition is only partly circular suffice to deflect the objection, since if identity conditions are to be determinate they must be wholly so. We would not be satisfied if the essence of a hand were partly defined in terms of its relation to a body, whose essence was itself partly defined in terms of its relation to a hand. Nor would we rest content with a definition of knowledge partly in terms of belief and of belief partly in terms of knowledge. Identity conditions, if they obtain, are in this sense an all-or-nothing affair. One would expect Bird at this point to demonstrate how circularity is avoided, or is harmless. Pointing out that we ‘should now check that we have answered the original regress problem’ (142), by which he means the regress/circularity objection, he notes the following (143): ‘As is implicit in the statement of the regress problem, a finite solution [in terms of asymmetric graphs] is one that has circularity – or cycles, in the terminology of graph theory.’ His illustration is now Figure 13.7, where the arrows represent the direction of the relationship between a power and its manifestation. A power points to its manifestation, and this is represented by an arc, or directed line, going from the former to the latter. Graphs with directional lines representing asymmetric relations are called directed graphs or digraphs. Note that Figure 13.7 has an underlying undirected graph, namely Figure 13.1. But though Figure 13.1 is symmetrical, the addition of directedness makes Figure 13.7 asymmetrical. Again, labelling the

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Figure 13.7  A

B

C

D

Figure 13.8 

nodes as in Figure 13.8 it can be shown that the graph diagram has no nontrivial automorphism, and so is asymmetric. The addition of directedness can turn a symmetric graph into an asymmetric one but this does not eliminate circularity, it merely emphasizes it. And all that Bird says in response to the regress/circularity objection at this point is to note that any finite solution has circularity in it; in other words, he merely accepts the point but does nothing whatsoever to repel the charge that the circularity is objectionable, which in fact he admitted earlier (see above). The cyclicality he mentions applies both to directed and undirected graphs: for either kind of graph, there is, for at least one node, a path  – directed in digraphs, undirected in undirected graphs – that begins with that node and ends with that node. The graphs themselves manifest the circularity on their face. To acknowledge it is quite evidently not to answer the objection based on it. To make matters worse, the cyclicality he refers to is an additional circularity to the general one I remarked on earlier. For example, there is a cycle in the triangular subgraph of Figure 13.6. More precisely, there are three cycles, one for each node on the triangle. But all the other nodes have circular identity conditions as well even though they do not lie on cycles. A cycle is a further circularity, which means that every asymmetric graph with at least one cycle has a double circularity built into it, at least for the nodes on the cycle.

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Figure 13.9 

As for the infinite case, Bird goes on to say (143): ‘However, it is worth noting that infinite graphs can lack non-trivial automorphisms and so represent the determinate identity of the properties represented by its [sic] nodes.’ Again, nothing more is added to explain how an infinite graph can provide determinate identity conditions. Moreover, the infinity involved, given that both Bird and Dipert are concerned with physical realizations of the asymmetric graph structure, must be an actual infinity, a concept that is itself fraught with metaphysical difficulty (Smith and Craig 1993: 9–24). To say that each property has unique identity conditions within an infinite asymmetric graph does nothing to repulse the problem of fixed identity conditions posed by the infinity itself. Two final points are worth making about Bird’s discussion of asymmetric graphs. First, he remarks that if we restrict the identity of dispositions to their essential manifestations (not their stimuli as well), then to avoid isomorphic subgraphs of the asymmetric graph in which the dispositions are located, we have to regard the dispositions as multi-track, that is, as having more than one essential manifestation. The reason for avoiding isomorphic subgraphs is that the dispositional monist may want to identify dispositions with parts of asymmetric graphs, namely, for each disposition, the path beginning with it, then traversing its manifestation and any other manifestations that lead back to it. Leaving aside the circularity involved in such a path, as noted previously, there is also the problem, as Bird observes, that there might be isomorphic subgraphs of an asymmetric graph, and so two dispositions might share the same structure of manifestation relations. This needs to be avoided, and can be, according to Bird, by postulating multi-track dispositions with more than one essential manifestation. For then we can posit a directed walk from any node through every other node, which means the subgraph of each disposition is just the whole, asymmetric graph, as per Figure 13.9 (144).

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Figure 13.10 

One might think that there is no directed walk from each vertex through every other, because at some point you have to go against the direction of the arrows and/or go through the same node more than once and/or miss out some edges altogether. That is, the directed walk Bird seems to have in mind is one that traverses each node and each edge only once, and always in the direction of the edge. However, Bird has confirmed (in correspondence) that his conception of a directed walk is more liberal: it is enough if you can identify a given disposition by its position in the graph via following its edges in their correct directions, even if it means traversing the same node more than once. But given this more liberal conception, a third kind of circularity is introduced: it means saying, for some nodes A and B, that A is partly defined by its manifestation B which is partly defined by A. So there is the overall circularity present in all finite asymmetric graphs, the circularity of the specific cycles in finite graphs, and the circularity of traversing the same node more than once in graphs representing multi-track dispositions.9 The second point concerns loops, that is to say a line connecting a node to itself, as in Figure 13.10 from Bird (144). Bird introduces it to show how even graphs with only single-track dispositions can be strongly asymmetric, that is, have no isomorphic subgraphs. Note that Figure 13.10 has a loop, that is, a line joining a node to itself. On Bird’s interpretation, this means that a disposition has itself as its essential manifestation. One might suspect whether this can ever be the case, though Bird has (in correspondence) cited the disposition of a magnet to make magnetic a piece of unmagnetized iron placed within its magnetic field. It is not clear that this verifies the supposition, however: the disposition is the state of being magnetic; the manifestation is not the state of being magnetic, but the behaviour of becoming magnetic. True, the previously In fact, Bird’s liberal conception of a downstream walk for Figure 13.9 no longer differentiates it from his Figure 6.6 (143) which contains isomorphic subgraphs, and which I do not reproduce here. For in that graph, you can also traverse all the nodes and edges, as long as you can traverse some of them more than once. Which means that Bird’s ‘sufficient condition for strong asymmetry’ (144) is false: from each node in his Figure 6.6 you can have a directed walk that includes every other vertex, yet still not have strong asymmetry because of the isomorphic subgraphs. 9

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unmagnetized iron ends up in the state of being magnetic as well, that is, it ends up with the same disposition as the first magnet, but having this state is not the precise manifestation of the first magnet’s disposition. Getting into that state is. In any case, if we allow loops then we give entry to yet a fourth circularity in our putative world of pure powers – the partial definition of a disposition in terms of itself with no mediation whatsoever. Only the whole definition of a thing in terms of itself with no mediation could be a more vicious kind of circularity. 13.5  C onc l us ion The upshot of this discussion is that the very idea of a world or even a level of pure potencies is incoherent. Hence there must be some actualities as well. This is just an example of the general Aristotelian truth that there is no potency without actuality. The general truth, however, is strong, since it is that wherever there is potency in the world, so there is actuality as well. In other words, everything in the material universe is a mixture of act and potency. But the conclusion I have drawn from my analysis of Bird and Dipert might seem a deal weaker, namely that if potency exists, so must actuality, but not necessarily wherever the potency is. In fact, however, the very nature of the circularity problem suggests that, because circularity enters very quickly into a finite graph, so must actuality to break it. Hence there must be actuality throughout the world of potency in order to break all of these quickly appearing circularities. And this thesis looks about as strong as the general truth that wherever there is potency, so there is actuality. In the infinite case, with a fairly narrow class of linear chains of directed edges, it might be possible for one to avoid any circularity at all and simply require a terminal actuality to preserve identity conditions all the way up the chain. To this I make the dialectical reply that the thesis of no potency without actuality has far more to be said in its favour than that the world is anything like the kind of restrictive, linear, directed infinite graph just supposed. And I add the ad hominem point that I doubt either Bird or Dipert have such a kind of infinite graph in mind. There is at least one philosopher who, at the time of writing, considers Bird’s graph-theoretic response to the regress/circularity objection of Lowe and others case closed. He writes, with little accompanying explanation: ‘I think Bird … successfully responds to this objection’ (Barker 2009: 243). This is a cause of some dismay, because whenever mathematical

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techniques, especially highly specialized ones, are wheeled in to solve a metaphysical problem, the prudent philosopher is obliged to step back and reflect very carefully. I doubt that mathematics on its own can ever solve a metaphysical problem. Even if I am wrong, however, it behoves metaphysicians to step very slowly through the minefield of mathematical machinery before pronouncing its successful application to a field where, as Aristotle would have said, there is little mathematical precision to be had.10 10 I am grateful to the mathematicians at Graphnet for answering my many questions about graph theory, and to Alexander Bird for helpful clarification of some of the passages in his discussion of this topic in Nature’s Metaphysics.

ch apter 14

A neo-Aristotelian substance ontology: neither relational nor constituent E. J. Lowe

Following the lead of Gustav Bergmann (1967), if not his precise termin­ ology, ontologies are sometimes divided into those that are ‘relational’ and those that are ‘constituent’ (Wolterstorff 1970). Substance ontologies in the Aristotelian tradition are commonly thought of as being constituent ontologies, because they typically espouse the hylemorphic dualism of Aristotle’s Metaphysics – a doctrine according to which an individual substance is always a combination of matter and form. But an alternative approach drawing more on the fourfold ontological scheme of Aristotle’s Categories is not committed to this doctrine and may regard individ­ ual (or ‘primary’) substances as having no constituent structure, their only possible complexity residing in their possession, in some cases, of a multiplicity of substantial parts. However, as we shall see, this does not imply that such an ontology falls instead into the relational camp: for although it invokes, in addition to the category of individual sub­ stance, also those of substantial kind (‘secondary’ substance), attribute, and mode (or ‘individual accident’), it need not and arguably should not take there to be external relations between entities in the different cat­ egories. On this view, truths of exemplification and instantiation, such as ‘Dobbin is white’ and ‘Dobbin is a horse’, do not need relational truth­ makers. Hence, it can be maintained that there are no such relations as ‘exemplification’ and ‘instantiation’, at most only certain relational truths of exemplification and instantiation – truths whose logical form is rela­ tional. This being so, I shall argue, such an ontology cannot fairly be classified as a ‘relational’ one. 1 4 .1   C ons t i t u e n t v e r s us r e l at ion a l on t ol o g i e s There is a common presumption that ontologies inspired by Aristotle are ‘constituent’ ontologies, whereas ones inspired by Plato are ‘relational’ – a presumption founded on the notion that Aristotle’s metaphysics is 229

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distinctively ‘immanent’ whereas Plato’s is distinctively ‘transcendent’. This way of putting matters is obviously rather crude and simplistic, but may still seem to capture an important difference. The immanent/tran­ scendent distinction appears to come down to this: that the immanentist sees the properties of concrete objects as being ingredients of those very objects, whereas the transcendentist sees them as being separate entities to which the objects stand in some special relation of exemplification. By ‘properties’ in this context I mean to speak very broadly, to include not only features, such as redness or squareness, but also forms, such as humanity or equinity. Of course, some may hold that forms are merely combinations of features but others, including myself, certainly deny this. I am also assuming that, at this point at least, both features and forms are to be understood as being universals, rather than particulars, and in this respect unlike the concrete objects – or ‘individual substances’ – which ‘possess’ them. However, it is certainly open to a metaphysician to hold that features and forms are themselves particulars, or indeed to hold that features and forms come in two different varieties – the universal and the particular – so that, for example, as well as redness the universal feature we have a plurality of particular rednesses, a different one belonging to each individual substance that is red. In Aristotle’s mature ontological system, as presented in the Metaphysics, individual substances are taken to be combinations of matter and form, with each such substance being constituted by a particular parcel of mat­ ter embodying, or organized by, a certain form. For example, on this view an individual house has as its immediate matter some bricks, mortar, and timber, which are organized in a certain distinctive way fit to serve the functions of a human dwelling. Similarly, an individual horse has as its immediate matter some flesh, blood, and bones, which are organized in a certain distinctive way fit to sustain a certain kind of life, that of a herbivorous quadruped. In each case, the ‘matter’ in question is not, or not purely, ‘prime’ matter, but is already ‘informed’ in certain distinct­ ive ways which make it suitable to receive the form of a house or a horse. Thus, bricks, mortar, and timber would not be matter suitable to receive the form of a horse, but at best that of something like a statue of a horse. According to this view, the matter and form of an individual substance are each ‘incomplete’ entities, completed by each other in their union in that substance. But its form is essential to the substance, unlike its matter, in the following sense: an individual house, say, cannot lose the form of house without thereby ceasing to be, whereas – while it must always have matter of an appropriate kind so long as it continues to be – it need not

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always have the same matter of that kind. Individual bricks and timbers in a house may be replaced without destroying the house – indeed, this may be the only way to preserve a certain house – but once its bricks and timbers cease to be organized in the form of a house, the house necessarily ceases to be. Clearly, according to this ‘hylemorphist’ Aristotelian picture, an indi­ vidual substance is a ‘combination’ of matter and form in a sense which rules out our thinking of its matter and form as being parts of the sub­ stance, at least in the normal sense of ‘part’. Here it might be objected that, for example, a brick in a house is a part of it in this familiar sense, and yet belongs to the ‘matter’ of the house: so can’t we at least say that the matter of a house is a ‘part’ of it in this sense? Not easily: for even if we were to concede that a brick is literally a part of the house, all the mat­ ter of the house, considered collectively, can hardly be so regarded. For the house coincides with its matter as a whole and hence, it appears, that matter could not qualify as a proper part of house, as the brick might. Nor, however, can the matter qualify as an improper part of the house, in the standard sense, since that would make it identical with the house: and yet the house is clearly not identical with its matter, not least because its matter can change while it persists. Equally, on the hylemorphist view, the house’s form cannot be regarded as a part, either proper or improper, of the house, in the standard sense of ‘part’. Nothing forbids the hyle­ morphist from saying that, in some other sense of the term, the matter and form of an individual substance are ‘parts’ of it, but saying this would at least not be very helpful, since it would invite confusion. It is better just to say that the matter and form are constituents, but not parts, of the substance. The key point is that, on this view, individual substances exhibit ‘internal’ ontological complexity, being combinations of ‘incom­ plete’ entities that are completed by each other in the substance. Another remark worth making here, however, is that, on this view, it is in fact questionable whether it is even strictly correct to say that, for example, a brick in a house is a ‘part’ of it – at least if, by this, one wants to imply that the brick so conceived qualifies as an individual sub­ stance in its own right. For, according to one influential interpretation of this Aristotelian view, the ‘brick’ that existed prior to the building of the house or that would exist in the event of the house being destroyed is not identifiable with the ‘brick’ that functions as a brick in the existent house. For the ‘brick’ in the latter sense is, supposedly, something that is properly understood only via its functional relationship to the rest of the matter of the house, as determined by the form which organizes that

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matter into a house. When the house is destroyed by disorganizing it – by removing its form  – various individual bricks and timbers may be left lying around where the house once stood, but these individual substances were not strictly parts of the functioning house and have really only come into existence upon its destruction. On this account, then, a true indi­ vidual substance never has other individual substances as parts. The only concrete things that can literally have such parts are mere aggregates, such as heaps and bundles, which are not substances because they lack substantial forms. It thus turns out that, on this view, we should not really describe individual substances as having material parts, in the shape of such items as bricks and bones, and thus should utilize another term for such items. In the case of living things, a good term for this purpose might be ‘organ’, understood in a suitably broad sense, to encompass not just items such as hearts, livers, and stomachs, but also blood and bones. In any case, one important point that emerges from all this is that precise terminology really does matter in these cases, and that indiscriminate use of the word ‘part’ is extremely unhelpful. So far, I have spoken a lot about forms, but not much about features, and how they might be accommodated by the approach now under dis­ cussion. Very roughly, I think that the answer should run somewhat as follows. The form of a substance constitutes its essence  – what it is, its ‘quiddity’ – whereas its features, or ‘qualities’, are how it is. A horse is what Dobbin is, for example. If Dobbin is white, however, that is partly how he is – a way that he is. I say ‘partly’ only to acknowledge that there are many other ways Dobbin is besides being white – such as being heavy – and by no means intend to imply that Dobbin’s whiteness is a part of Dobbin. However, Dobbin’s whiteness might nonetheless be thought to be a constituent of Dobbin, on this view, distinct from his form, which is equinity. And this might be maintained whether one thought of Dobbin’s whiteness as being a particular whiteness peculiar to him, or just the uni­ versal whiteness that he shares with other white substances. But how, then, are a substance’s features related to its form? Some of its features, it seems, are necessitated by its form – such as warm-bloodedness in the case of Dobbin – and these may be called, in the strictest sense of the term, the substance’s properties. Other of its features, however, are ‘accidental’, such as Dobbin’s whiteness, which may therefore be denominated one of his accidents. Even so, although Dobbin’s whiteness is accidental, that Dobbin has some colour is necessitated by his form and is thus essential to him. So we arrive at the following picture: an individual substance pos­ sesses a certain form, which constitutes its essence, from which ‘flow’ by

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necessity certain features of the substance, which are its properties in the strictest sense of the term. Some of these properties are ‘determinables’ rather than ‘determinates’, such as colour in the case of Dobbin, and then it is necessary that the substance should possess some determinate feature falling under the relevant determinable, but contingent which feature this is. Such contingent determinate features are the substance’s accidents, which can obviously change over time compatibly with the continued existence of the substance. The overall picture, even in this relatively simplified version of it, is quite complex, with an individual substance portrayed as having a rich and in some respects temporally inconstant constituent structure of form, matter, properties, and accidents, with form and properties remaining constant while matter and accidents are subject to change. So much, for the time being, for this sort of Aristotelian ontology, which is clearly of the ‘constituent’ kind. It is commonly contrasted with a kind of ‘relational’ ontology inspired, however loosely, by a Platonic ‘tran­ scendent’ metaphysics. According to this approach, at least as I shall be interpreting it here, features and forms do not reside within the concrete objects that are said to ‘possess’ them, as constituents of those objects, but instead exist ‘separately’ from the concrete world, serving as immutable and eternal patterns for concrete objects to exemplify or imitate, usually – or perhaps even always  – only imperfectly.1 On this view, the concrete objects themselves, such as Dobbin, are not ontologically complex, except inasmuch as they contain other such objects as parts, and there is noth­ ing ‘in’ them corresponding to the features and forms that they are said to exemplify. Those features and forms are one and all universals, each being exemplifiable, at least in principle, by a plurality of different con­ crete objects. In saying that there is nothing ‘in’ the objects correspond­ ing to those features and forms, I mean to exclude the idea that those objects possess particular features and forms, answering to or ‘resembling’ the universal features and forms that they exemplify. Exemplification, on this view, is an ‘external’ relation between a concrete object and a univer­ sal feature or form, consisting in some sort of imitation or resemblance relation. It is an ‘external’ relation at least in the sense that it does not hold of necessity between the items that it relates. A concrete object may 1 This interpretation of Plato’s view, although commonplace, is not incontrovertible and may well be historically inaccurate. However, I am presently concerned only with the view as I have characterized it, whether or not it is really Plato’s own view. For another interpretation of Plato, according to which he acknowledged the existence of immanent forms as well as transcendent ones, see Demos (1948). I am grateful to John Heil for drawing my attention to this.

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exemplify one feature or form at one time and a different one at another, and any given feature or form exists eternally and immutably, whether or not any concrete object exemplifies it at some time or indeed at any time. Moreover, as was just remarked, there is no particular feature or form that resides within a concrete object at any given time in virtue of which the object exemplifies, at that time, a certain universal feature or form  – a particular feature or form which necessarily resembles that universal and thereby explains why the concrete object does so at that time. Rather, the concrete object, holus bolus, either resembles or fails to resemble a given universal at a certain time, and thereby either exemplifies or fails to exem­ plify it at that time. Concrete objects, on this view, are in themselves fea­ tureless and formless ‘blobs’, which can be described as ‘having’ certain features and forms only in a derivative or relative sense, to the extent that they primitively resemble to some degree some universal feature or form. Because of this, moreover, concrete objects do not have essences or natures in any serious sense. Only the universal features and forms can be said to have, or rather be, essences. Consequently, there is something irredeem­ ably indeterminate about the very identity of concrete objects: they are many rather than one, to be sure, but they have no absolutely determinate principle of individuation. It is little wonder, then, that this view should encourage us to think that the domain of universals is somehow more fully real and intelligible than that of concrete objects, with the latter being mere shifting shadows of the former. 1 4 .2  T rou bl e s w i t h t r a ns c e n de n t i s m a n d h y l e mor ph i s m Having characterized (some may say caricatured) the two foregoing approaches – the hylemorphic and the transcendent, as we may call them – I now want to say why I reject them both, and what I would propose to put in their place. The troubles with the transcendent approach are many, both metaphysical and epistemological, and I shall only scratch the sur­ face of these. First, it simply isn’t clear how an inherently featureless and formless ‘blob’ – which is what a concrete object is, on the present view – could ‘resemble’ some universal feature or form. For, in the nature of the case, there could be nothing in virtue of which it could resemble one. The resemblance would have to be primitive or ‘brute’ and ungrounded, and hence inexplicable. To put the point in other words, the only way in which we can really understand resemblance is as an internal relation, whose obtaining in any given case is necessitated by the natures of its relata.

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Conceived as an external relation, it is simply mystifying. Of course, it may be that all external relations are ultimately mystifying, which would be a good reason for supposing that they don’t really exist. But, certainly, some candidates for the status of being an external relation do seem prima facie to be good ones, and moreover intelligible ones – for example, distance relations and causal relations. But resemblance is not such a candi­ date. Notice, moreover, that the transcendent view must hold that while resemblance between a concrete object and some feature or form is exter­ nal and primitive, resemblance between features and forms themselves is not. By any account, there is a resemblance, albeit a partial or imperfect one, between the colour features red and orange: but this resemblance is plainly grounded in the natures of those features and holds of necessity, whence it is an internal relation. But the idea that some resemblances can be external and others internal seems incoherent: we cannot really be talking about ‘resemblance’ in a single sense if we say this. And in that case, the advocate of the transcendent view may justly be accused of using the word ‘resemblance’ without any clear meaning, when he or she speaks of it as obtaining between concrete objects and universals. Hence, he or she is left without any substantive account of exemplification at all, that is, no account of what it means to say that a concrete object is, say, red. Why not simply abandon the domain of concrete objects altogether and say that reality is confined to the eternal domain of immutable univer­ sals, reconstructing ‘particulars’ as ‘bundles of universals’? And then in addition there are obvious epistemic difficulties inherent in the transcend­ ent view, at least if we take ourselves to be concrete beings who can have knowledge of universals. So I shall say no more about the transcendent view, and move on to criticisms of hylemorphism. Hylemorphism certainly has many attractive features, and many advan­ tages over the transcendent view. But its core difficulty lies in its central doctrine  – that every concrete object, or more precisely every concrete individual substance, is a ‘combination’ of matter and form. For what, really, are we to understand by ‘combination’ in this sense? Clearly, we are not supposed to think that combination in this sense just is, or is the result of, a ‘putting together’ of two mutually independent things, since matter and form are supposed to be ‘incomplete’ items which complete each other in the substance that combines them. Now, certainly, when some concrete things  – such as some bricks, timbers, and quantities of mortar – are put together to make a new concrete object, such as a house, those things have to be put together in the right sort of way, not just hap­ hazardly. But does this entitle us to suppose that the completed house

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is some sort of ‘combination’ of the things that have been put together  – or, more accurately, the ‘house-matter’ that those things have supposedly been turned into by their incorporation into the house – and the way in which they have been put together? The challenge that the hylemorphist presents us with is to explain why, if we don’t say something like this, we are entitled to suppose that a new individual substance is brought into being. One presumption behind that challenge would seem to be that a substance can’t simply be a so-called mereological sum of other sub­ stances – and with this I can agree, at least if by a ‘mereological sum’ we mean an entity whose identity is determined solely by the identities of its ‘summands’, rather as the identity of a set is determined solely by the identities of its members. I agree that only when other substances have been put together in the right sort of way does a new substance of a cer­ tain kind come into being, the way in question depending on the kind in question. Moreover, I have no objection to the ‘reification’ of ‘ways’, understood as features or forms, provided that we don’t treat ways as substances – so here too I am in agreement with the hylemorphist. Reification is not the same as hypostatization, but is merely the acknowledgement of some putative entity’s real existence. What I don’t understand is what it means to say that the completed house’s form – the way in which its ‘matter’ is organized – is an ‘incomplete’ constituent of the house which ‘combines’ together with that equally ‘incomplete’ matter to constitute the house, a complete substance. The words that particularly mystify me in this sort of account are ‘incomplete’, ‘combine’, and ‘constitute’. It’s not that I don’t understand these words perfectly well as they are commonly used in other contexts, just that I don’t understand their technical use in the hylemorphic theory and, equally importantly, why a need should be felt for this use of such terms. If I could understand the supposed need to say something like this, then I would make every possible effort to grasp the technical terminology. So let us remind ourselves why, allegedly, there is indeed such a need. As was just mentioned, the need supposedly arises in order to meet the challenge of explaining how a new substance is brought into existence. The sugges­ tion seems to be that, unless we can see the new substance as being a com­ bination of items neither of which can exist independently of the other in just such a combination, rather than as merely being composed of other independently existing things each possessing their own features, we shall be unable to justify the judgement that a new concrete object – an ‘add­ ition of being’ – really has been brought into existence, rather than some previously existing things merely being rearranged. Put in this way, the

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supposed problem is one that is familiar from recent debates in metaphys­ ics. Here, though, I would urge that some types of ‘rearrangement’ are ontologically more weighty than others. When a free proton and a free electron are ‘rearranged’ by increasing the distance between them from one mile to two miles, there is no reason at all to suppose that a new con­ crete object is brought into existence. But when they are ‘rearranged’ so that the electron is captured by the proton and occupies an orbital around it, then indeed we have a new concrete object of a very different kind: a hydrogen atom. This object has certain features, notably certain powers, which are quite different from those of protons and electrons and quite different, too, from those of a mereological sum of a free proton and a free electron. In the newly created hydrogen atom, the proton remains exactly what it was before, just a proton, and the electron remains just an electron. A new form is instantiated – one that is possessed neither by the proton nor by the electron – namely, the form of a hydrogen atom. This form is the form of the newly created object, the atom, not that of the proton or the electron, nor even of the pair of them. The form does not, in any sense that I can understand, ‘combine’ with the proton and the electron so as to constitute, together with them, the atom. The only things that do any ‘combining’ are the proton and the electron, when the former captures the latter and the latter occupies an orbital around the former. And the only things that constitute the atom are, again, the proton and the electron, which are its parts, in the perfectly familiar sense of ‘part’. So, as can be seen, I am perfectly happy to describe the case of the newly created hydrogen atom in terms of ‘combination’ and ‘constitution’, and indeed in terms of ‘form’. It’s just that I don’t need, and don’t understand, the ‘logical grammar’ of the hylemorphist who uses these terms in his own distinctively technical fashion. Furthermore, I have no serious need for the hylemorphist’s category of matter. I might be prepared to say that the ‘matter’ of the hydrogen atom is or consists of its proton and electron, but just in the sense that these are its parts and serve to compose it. However, the atom’s ‘matter’ in this sense is not, as the hylemorphist takes it to be, some ‘incomplete’ constituent of the atom that is completed by the atom’s ‘form’. In fact, I would prefer to abandon the term ‘matter’ altogether, as modern physics has done, at least as a fundamental theoretical term. Thus, although modern scientists talk, for instance, of ‘condensed matter physics’, fundamental particle physicists don’t nowadays speak of protons and electrons as having, or being composed of, matter  – although they might happily speak of them as being ‘packets of energy’ and certainly as possessing mass.

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e . j. l ow e 1 4 .3  T h e f ou r- c at e g or y on t ol o g y

The hylemorphist ontology described above is inspired by Aristotle, as modified perhaps by later thinkers such as Aquinas. But the basis of another kind of ontology can also be traced to Aristotle, this time to the Aristotle of his presumed early work, the Categories. The kind of ontology that I now have in mind is one whose key notions are briefly sketched in the opening passages of that work, before the classificatory divisions com­ monly known as the Aristotelian ‘categories’ are set out later in the trea­ tise. In those opening passages, Aristotle articulates a fourfold ontological scheme in terms of the two technical notions of ‘being said of a subject’ and ‘being in a subject’. Primary substances – what we have hitherto been calling ‘individual’ substances – are described as being neither said of a subject nor in a subject. Secondary substances – the species and genera to which primary substances belong – are described as being said of a sub­ ject but not in a subject. That leaves two other classes of items: those that are both said of a subject and in a subject, and those that are not said of a subject but are in a subject. Since these two classes receive no official names and have been variously denominated over the centuries, I propose to call them, respectively, attributes and modes. It seems that secondary substances and attributes are conceived to be different types of universal, while primary substances and modes are conceived to be different types of particular. Since the Aristotelian terminology of ‘being said of’ and ‘being in’ is perhaps less than fully perspicuous, with the former suggest­ ing a linguistic relation and the latter seemingly having only a metaphor­ ical sense, I prefer to use a different terminology: that of instantiation and characterization. Thus, I say that attributes and modes are characterizing entities, whereas primary and secondary substances are characterizable entities. And I say that secondary substances and attributes are instantiable entities, whereas primary substances and modes are instantiating entities. These terminological niceties, which though necessary are apt to prove confusing, are most conveniently laid out in diagrammatic form, using the familiar device known as the Ontological Square. I present it in Figure 14.1, first deploying Aristotle’s terminology. In my own version of the Ontological Square (Lowe 2006), I prefer to use the terms ‘object’ and ‘kind’ in place of the more cumbersome ‘primary substance’ and ‘sec­ ondary substance’. I also include a ‘diagonal’ relationship between objects and attributes, which is distinct from both instantiation and character­ ization, calling this, as seems appropriate, exemplification. My version is shown in Figure 14.2.

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Attributes Said of but not in a subject

Neither said of nor in a subject

Both said of and in a subject

Not said of but in a subject

Primary substances

Modes

Figure 14.1  Ontological square using Aristotle’s terminology. Kinds

characterized by

Attributes

instantiated by

exemplified by

instantiated by

Objects

characterized by

Modes

Figure 14.2  Ontological square with Lowe’s terminology.

I call the four classes of entities depicted here ontological categories, albeit with a cautionary note that these are not to be confused with, even though they are not unrelated to, Aristotle’s own list of ‘categories’ later in his treatise. More precisely, I regard these four as the fundamental onto­ logical categories, allowing that within each there may be various subcategories, sub-sub-categories, and so on. How, exactly, are the two ‘Aristotelian’ systems of ontology related to one another? Unsurprisingly, they overlap in many respects, but one key respect in which they obviously differ is that the four-category ontology, as

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I call it, unlike the hylemorphic ontology, does not include the category of matter. It might be thought that it also lacks the category of form, but that is not in fact so. For I believe that form, conceived as a type of uni­ versal, and more perspicuously termed substantial form, is really nothing other than secondary substance or substantial kind. We may refer to such universal forms either by using certain abstract nouns, such as ‘humanity’ and ‘equinity’, or else by using certain substantival nouns – what Locke called ‘sortal’ terms  – such as ‘man’ and ‘horse’. I believe that this is a grammatical distinction which fails to reflect any real ontological diffe­ rence. However, if that is so, then there is a very important ontological consequence. This is that primary substances, or individual concrete objects, ‘have’ forms only and precisely in the sense that they are particu­ lar instances of forms. Thus Dobbin is a particular instance of the substan­ tial kind or form horse, whereas Dobbin’s whiteness is a particular instance of the colour universal or attribute whiteness. By this account, it makes no sense at all to say that Dobbin is a ‘combination’ of the form horse and some ‘matter’. He is, to repeat, just a particular instance of that form, other such instances being the various other particular horses that exist or have existed. Being an instance of this form, Dobbin must certainly have material parts, such as a head and limbs, but in no sense is he a ‘combin­ ation’ of anything material and the universal form in question. What I am saying, then, is that individual objects or primary substances are nothing other than particular forms, or form-particulars – particular instances of universal forms, in precisely the same sense in which modes (or ‘tropes,’ as they are now often called) are particular instances of attributes. 1 4 . 4  T h e f ou r- c at e g or y on t ol o g y i s no t a r e l at ion a l on t ol o g y The crucial question that now arises is whether the four-category ontol­ ogy is, like the hylemorphic ontology, a constituent ontology or whether, rather, it is a relational ontology, like the transcendent ontology. The answer that I want to defend is that it is neither – and that this is very much to its credit. At first sight, it might seem that the four-category ontology must be a relational ontology, since the Ontological Square apparently depicts three relations supposedly holding between entities in different categories of the system: the instantiation relation between objects and kinds and between modes and attributes, the characterization relation between attributes and kinds and between modes and objects, and the exemplification relation between objects and attributes. However,

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if the system includes such relations amongst the entities whose existence it acknowledges, those entities must find a place in one or other of the system’s four fundamental categories. There seem to be only two that could possibly house them: the category of attributes and the category of modes. That is to say, the relations in question would have to be catego­ rized as being either relational attributes or relational modes. In fact, they would have to be classified in both of these ways, in the following sense: since the theory maintains that every attribute is instantiated by modes and that every mode instantiates an attribute  – because to this extent, at least, the theory is ‘immanentist’ where universals are concerned – it would have to maintain that there are relational instantiation, charac­ terization, and exemplification modes which instantiate corresponding relational attributes. But this really makes no sense on the system’s own terms. Consider, for instance, the case of the characterization of an object by a mode: for example, Dobbin’s particular whiteness’s being a charac­ teristic of Dobbin. As this example illustrates, characterization is sup­ posed to ‘obtain’ between entities in the category of modes and entities in the category of objects. This is so even if there are relational modes, such as, perhaps, a loving mode that characterizes John and Mary. What there cannot be is a relational mode that characterizes an object and a mode. Moreover, if we supposed that there could be, we would immediately be faced with the threat of an infinite regress, of the sort that F. H. Bradley famously described. For if it were the case that, in order for mode M to characterize object O, a relational characterization mode, M′, had to char­ acterize M and O, then by the same token another relational characteriza­ tion mode, M″, would have to characterize M′, M, and O – and so on ad infinitum. Here it may be responded that this is just so much the worse for the four-category ontology and simply demonstrates its inadequacy or even its incoherence. But that would be far too rash a conclusion, for the system certainly has the resources with which to dissolve the apparent difficulty, as we shall now see. Earlier I drew upon a distinction that is commonly made between internal and external relations, the idea being that an internal relation holds of necessity between its terms or relata, in virtue of their intrinsic features or natures, whereas an external relation may hold or fail to hold between its relata irrespective of their intrinsic features or natures. For instance, spatial relations between objects are commonly supposed to be external, because it seems that the distance between two objects could be altered without affecting in any way the intrinsic features or natures of those objects. By contrast, resemblance seems intelligible only when

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conceived as being an internal relation. For example, that red resembles orange, and indeed that it resembles orange more closely than it resem­ bles yellow, seem to be necessary truths that depend solely on the intrin­ sic natures of the colours in question. But to talk of there being  – that is, of there existing – internal relations in cases like these is to indulge in unnecessary reification. We can put the point in this way: while there may be relational truths to be recognized in such cases (truths whose logical form is relational) – such as the truth that red resembles orange – there need not be relational truthmakers of those truths. Understanding a truthmaker of a given proposition to be, at the very least, an entity (or plurality of entities) whose existence necessitates the truth of that prop­ osition (Lowe and Rami 2009), we can see that the truthmaker of the proposition that red resembles orange is quite simply the colours red and orange themselves. For, in the language of possible worlds, in every world in which those colours exist, the proposition that red resembles orange is true. We do not need to invoke, as a putative truthmaker of this proposition, or even as part of any such truthmaker, a relation of partial or imperfect resemblance between red and orange, conceived as an entity additional to red and orange themselves. The lesson is that, while it might be conveni­ ent to talk of ‘internal relations’, we should not suppose that in so talk­ ing we are talking of really existing entities of a relational nature, such as relational attributes or modes. Consequently, if the four-category ontology can fairly represent instantiation, characterization, and exemplification as being internal relations, it can avoid serious ontological commitment to them as entities to be included in one or other of its ontological categor­ ies and thereby avoid the threatened Bradleian regress, while at the same time escaping classification as a relational ontology. Now, the three ‘relations’ in question most plausibly are internal, or at least explicable in internalist terms. I make this latter qualification to accommodate the ‘relation’ of exemplification. That instantiation and characterization are internal relations is relatively easy to argue for. In the case of instantiation, all that we need to maintain is that an object necessarily instantiates its kind and that a mode necessarily instantiates its attribute, both of which claims are prima facie highly plausible. It is surely part of the essence of a whiteness mode, for instance, that it is an instance of the universal whiteness. Similarly, it is very plausibly part of the essence of a particular horse, Dobbin, that he is an instance of the kind horse. Analogous points can be made regarding characterization. It is surely part of the essence of Dobbin’s whiteness mode that it char­ acterizes Dobbin: for that mode depends for its very identity on its being

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Dobbin’s, and could not possibly ‘migrate’ to another object, much less continue to exist in Dobbin’s absence (any more than the Cheshire Cat’s grin could continue to exist without the cat). This leaves us only with characterization as a ‘relation’ between attributes and kinds. But what I have in mind in speaking in these terms are precisely certain essential connections between attributes and kinds, which are normally expressed in the language of natural law. We say, for instance, that electrons are negatively charged particles, thus expressing an essential connection between the kind electron and the attribute negative charge. Electrons, as a natural kind, have certain essential characteristics, of which negative charge – or, more exactly, unit negative charge  – is one. To put it another way, in no possible world are there electrons which lack negative charge. A world which contained particles exactly similar to electrons in every respect save that they were neutral, say, would not be a world containing neutral electrons. Kinds depend for their very identity on their essential characteristics, just as modes depend for their very identity on their objects or ‘bearers’. Consequently, the characterization ‘relation’ between attributes and kinds is an internal one and so ‘no addition of being’. I concede that in saying all this I am glossing over certain complications which would need to be accommodated by a more detailed account, but I think that these com­ plications raise no real difficulties for the sort of approach that I am now recommending. For instance, one difficulty might be thought to be that the exact numerical value of the negative charge on the electron is argu­ ably not a necessary feature of the electron, even if it necessarily possesses unit negative charge: for the ‘size’ of this unit might conceivably differ in different possible worlds. But then the proper response to this might just be to say that this value is not an essential characteristic of electrons and universally characterizes all particular electrons in the actual world for some reason that is extrinsic to their nature as electrons – a reason to do, say, with some global property of space in this world. I now pass on to the slightly more complicated case of exemplification. It seems clear that we can’t simply say that exemplification, like instantiation and characterization, is an ‘internal’ relation, because which attributes an object exemplifies can be a contingent matter. Dobbin, for example, is white, but could perhaps instead have been black. This is unlike the truth that Dobbin is warm-blooded, which is plausibly necessary, at least in a qualified sense that will be explained below. However, what we can say is the following. Dobbin is white in virtue of being characterized by a certain whiteness mode, call it W. Now, it is part of the essence of W that it characterizes Dobbin, since W depends for its identity on Dobbin.

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Equally, it is part of the essence of W that it instantiates the attribute whiteness. Hence, in any possible world in which W exists, W instantiates whiteness and characterizes Dobbin, whence it follows that in any such world it is true that Dobbin is white, since he is characterized by a white­ ness mode in that world. Thus W is a truthmaker of the proposition that Dobbin is white, as indeed would be any whiteness mode of Dobbin. But the proposition that Dobbin is white simply affirms that Dobbin exemplifies whiteness. Hence, we can explain truths of exemplification like this without invoking the existence of an exemplification relation. As for the contingency of the truth that Dobbin is white, this simply arises from two facts: first, that any whiteness mode of Dobbin’s, such as W, is itself a contingent being, and second that the ontological dependence between any such mode and Dobbin is asymmetrical. Such a mode does not exist in every possible world, and there are possible worlds in which Dobbin exists but no such mode exists. By contrast, the reason why Dobbin is necessarily warm-blooded is that Dobbin instantiates the kind horse, and warm-bloodedness is an essential characteristic of that kind. Here the truthmaker for the truth that Dobbin is warm-blooded is just Dobbin himself: for in any possible world in which Dobbin exists, he instantiates the kind horse and that kind is characterized by the attribute warm-bloodedness. This truth of exemplification is, then, a necessary truth: not in the unqualified sense that it obtains in every possible world whatsoever, but in the qualified sense that it obtains in every possible world in which Dobbin exists. It is an essential truth about Dobbin, whereas the truth that Dobbin is white is not. In short, we can explain all truths of exempli­ fication, and explain too their modal status, whether they be contingent or necessary, without invoking the existence of any relation of exemplifi­ cation, but simply by appealing to the ‘internal’ relations of instantiation and characterization, together with the truthmaking roles of objects and modes. For this reason, I maintain that the four-category ontology can­ not fairly be classified as being a relational ontology. 1 4 .5   T h e f ou r- c at e g or y on t ol o g y i s no t a c ons t i t u e n t on t ol o g y I turn now to the question of whether the four-category ontology can instead fairly be classified as a constituent ontology. I take it to be a neces­ sary feature of any such ontology that objects are regarded by it as pos­ sessing significant ontological structure, where this doesn’t involve their mere composition by other objects in at least some cases. That is to say, the

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mere fact that an ontology takes at least some objects not to be simple, in the sense of allowing that they possess other objects as parts, is not suffi­ cient for it to be classified as being a constituent ontology – not even if the ontology allows that one object may be constituted by another, distinct object (for instance, a bronze statue by a lump of bronze), both of which are composed of the same parts at the time of constitution. Rather, what is crucial for an ontology to qualify as ‘constituent’ is that it should main­ tain that objects have an ontological structure involving ‘constituents’ which belong to ontological categories other than the category of object itself. The hylemorphic ontology is clearly a constituent ontology in this sense, since it maintains that objects, or individual substances, are ‘com­ binations’ of matter and form, where neither matter nor form is conceived to be an entity belonging to the category of individual substance. Now, if the four-category ontology were fairly to be classified as a constituent ontology, what could it be taken to regard as being the ‘constituents’ of objects, in the sense now relevant? Clearly, there are only three candidates, since there are only three other ontological categories for these putative constituents to be drawn from. Let us examine them in turn. First, then, could we take an object’s kind to be a ‘constituent’ of the object? I have already acknowledged that ‘kind’ in this sense is equivalent to substantial form. But I have also insisted that objects, or individual substances, are just form-particulars or, if another wording is preferred, particularized forms. It is hard to see – or, at least, hard for me to see – how a particularized form could somehow contain within it, as a ‘constituent’, the universal form of which it is an instance. We would then seem to have two forms coinciding with one another, one the universal form and the other a particularized form instantiating that universal. Furthermore, it is part of the overall picture offered by the four-category ontology that uni­ versals are ontologically posterior to particulars – which is why it takes uni­ versals to be incapable of existing uninstantiated. On this view, although universals are perfectly real, they are perhaps best seen as being abstractions from, or invariants across, particulars. That being so, the particulars from which they are ‘abstractions’ should not be seen as containing those universals as ‘ingredients’ in their ontological make-up. For that would imply that the universals are more than mere abstractions  – that they are multiply located entities somehow inhabiting all the particulars that instantiate them. This, however, would certainly not make them onto­ logically posterior to those particulars, but on the contrary ontologically prior. Indeed, it would now be hard to see why we would really be entitled to speak of there being distinct particulars instantiating any given kind or

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substantial form, rather than just multiply located universal forms. And this would be to abandon the four-category ontology. Next let us consider whether the attributes exemplified by an object could be taken to be ‘constituents’ of the object. Again I think the answer must be ‘No’. For remember that Dobbin exemplifies the attribute whiteness, for example, solely in virtue of being characterized by a certain whiteness mode, W. Even if W could be thought to be a constituent of Dobbin – a question to which we shall turn in a moment – it is hard to see how whiteness the attribute could be, any more than Dobbin’s sub­ stantial kind, horse, can be. Against me here might be brought the testi­ mony of Aristotle himself, who describes (what we are calling) attributes as being both said of and in a subject, which suggests that whiteness the attribute can not only be said of – that is, be predicated of – Dobbin, but is also ‘in’ Dobbin. At the same time, Aristotle would deny that Dobbin’s kind, or ‘secondary substance’, horse, is ‘in’ Dobbin, allowing only that it may be said of Dobbin: which implies that he, at least, did not consider that, in this matter, what goes for substantial universals goes equally for attributive ones. However, while my version of the four-category ontol­ ogy has its historical roots in Aristotle’s, this by no means implies that I should agree with every aspect of his version. Indeed, I have already made it plain that I rather dislike the ‘said of’ versus ‘in’ distinction, and much prefer the terminology of instantiation, characterization, and exemplifi­ cation. To say that the attributes exemplified by Dobbin are ‘in’ Dobbin suggests that they have precisely the status of multiply located entities which I have just opposed in the case of kinds or ‘secondary substances’, on the grounds that it apparently gives these universals an unwarranted ontological priority over the particulars ‘in’ which they are said to res­ ide, and even threatens to make such particulars ontologically redundant. If whiteness the attribute were ‘in’ Dobbin, and equally ‘in’ all other white objects, why not say that ‘objects’ are really no more than bundles of attributes (or, perhaps, bundles of universals each of which includes some attributes together with a kind, or substantial form)? If the answer is returned that this would not accommodate the possibility of there being numerically distinct but qualitatively indistinguishable ‘objects’, either of two things could be said in response. One would be to propose that each object includes, in addition to a bundle of universals, a so-called ‘bare particular’, which renders it numerically distinct from any other quali­ tatively indistinguishable object. The other would be to point out that if universals are multiply locatable anyway, then the appearance of there being two or more qualitatively indistinguishable objects would be no

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more than a mere appearance, for in reality we would just have a sin­ gle but multiply located bundle of universals. This second response seems to me better than the first, but it clearly does not lead us to a constituent ontology in the required sense. The first response does perhaps do so, since each object is supposed to include entities belonging to two differ­ ent ontological categories: some universals together with a ‘bare particu­ lar’. However, this would be a radical departure from the four-category ontology, since that does not recognize such entities as bare particulars. The only particulars that it recognizes are objects and modes and neither of these are ‘bare’, precisely because they necessarily instantiate corre­ sponding universals – that is, are instances of universals. Altogether, then, we can see that the idea that the attributes exemplified by an object are constituents of the object inevitably takes us away from the four-category ontology, and consequently that this ontology cannot properly be seen as embodying such an idea. We are left now with modes as being the only entities which might be thought capable of qualifying as ‘constituents’ of objects according to the four-category ontology. But, once more, reflection on this possibility calls it seriously into question. Metaphysicians who conceive of objects as being bundles of modes or ‘tropes’, tied together somehow by a bare par­ ticular or a bare ‘substratum’, are certainly proposing a constituent ontol­ ogy. But that is certainly not how I conceive of objects, in accordance with the four-category ontology. First of all, I conceive of modes as being identity-dependent on their objects, and it is hard to see how the tropebundle-plus-substratum theorist could agree with me on this point. They, I think, would have to say that an object’s tropes are either not identi­ ty-dependent on anything, or that they are somehow mutually identitydependent, or else, finally, that they are all identity-dependent on their substratum  – and most probably the latter. But, again, this last cannot be the position of the four-category ontology, since it does not recognize the existence of ‘bare substrata’ at all. As for the other two suggestions, they only serve to undermine the idea that substrata are needed at all, in which case we are led to a pure trope theory which cannot therefore qual­ ify as a constituent ontology and certainly not as an interpretation of the four-category ontology. So our question is this: how could a four-category ontologist be supposed to endorse the idea the modes are ‘constituents’ of objects without sliding into one or other of the varieties of trope-bundle theory just described? The proper thing for a four-category ontologist to say about modes, I believe, is that they are ‘abstractions’ from objects, not constituents of them, for this explains their identity-dependence on their

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objects. Identity-dependence is not only an asymmetric relation of onto­ logical dependence: it also implies ontological priority on the part of the entity depended upon, with respect to the dependent entity. And this is precisely in accordance with the Aristotelian spirit of the four-category ontology, according to which individual substances  – objects, as we are calling them – have ultimate ontological priority over entities in any of the other three categories. I suggest, then, that within the four-category ontology we need to regard modes as being ‘aspects’ of objects, to which we can attend selectively in thought or perception, by means of what Locke called a ‘partial consideration’. These aspects explain the differ­ ential behaviour of different objects: for instance, why some objects roll down an inclined plane while others do not – the former being spherical or cylindrical, the latter not. But it is, after all, the whole object that rolls, not its sphericity or cylindricality. Nor does it make much sense to sup­ pose that its sphericity or cylindricality ‘drags along’ the object’s other modes with it, and thereby makes the object as whole move. To think in such terms is illicitly to hypostatize modes, treating them as simple sub­ stances within an object, rather than just as particular ‘ways’ an object is. I conclude that the four-category ontology, properly understood, has to be excluded both from the class of relational ontologies and from that of constituent ontologies. Attempts to force it into either of these camps simply turn it into some other kind of ontology altogether. Moreover, to the extent that both relational and constituent ontologies clearly run into certain difficulties which the four-category ontology escapes in virtue of belonging to neither camp, some credit must surely accrue to it.2 2 I am grateful for comments received when an earlier draft of this paper was presented at a Conference on Relational versus Constituent Ontology, held at the University of Notre Dame in March 2010.

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Index

abstract, 17, 52, 53, 60, 84, 88, 90, 92, 93, 111, 118, 122, 123, 124, 150, 153, 154; see also concrete actuality/act, 117, 139, 158, 159, 227 Aquinas, T., 105, 238 Aristotle, 2, 5, 7, 33, 37, 105, 106, 137, 142, 143, 144, 146, 183, 187, 195–206 Aristotelian, 35, 41, 133, 143, 146, 147, 148, 151, 153, 155, 156, 157, 160, 200, 231 categories, 42, 131, 238 causes, 118, 200 essentialism, 6, 187 hylemorphism, 229, 231 metaphysicians, 2 metaphysics, 1, 2, 3, 8, 26–7, 32–8, 42–3, 207, 230–3 ontology, 233, 239 realism, 124 spirit, 248 substance, 134 theories of substance, 140 tradition, 37, 229 on ‘being in’ vs ‘being said of ’, 143, 238, 246 on being, 33 on biology, 6, 175, 202–4 on categories, 4, 5, 83, 126, 128, 129, 130, 131, 133, 140–2, 239 on definition, 199, 200 on demonstrative knowledge, 197, 198, 201 on essence, 6, 39, 188, 189, 194, 195, 196 on law of non-contradiction, 42 on logic, 199 on mathematics, 228 on metaphysics, 1, 83 on methodology, 26 on necessary truths, 193 on ontology, 229, 238 on philosophical methodology, 145 on physics, 33 on potentiality/potency, 158–60

on pure relationalism, 210–12 on substance, 5, 130, 146, 149, 230 on teleology, 156 on telos, matter, and habitat, 204 Armstrong, D., 4, 60, 94, 96, 97, 99, 101–4, 110, 111, 112, 117, 118, 124, 127, 160, 161, 162, 167, 169, 250 Ayer, A. J., 112 Barnes, J., 197, 202 Bealer, G., 8, 24 being, 1, 44, 62, 64, 128, 139 and existence, 48–54, 64 and substance, 142 categories of, 4, 5, 83, 141, 142, 144 contingent vs necessary, 84, 147, 153 kinds of, 144 modes of, 52, 53, 132 no addition of, 124 qua being, 1, 33, 35, 38 Bergmann, G., 229 Berkeley, G., 59, 105, 106, 146 Bird, A., 4, 7, 103, 207, 208, 210–14, 219–28 Boyd, R., 99, 103 Bradley, F. H., 137, 241 Brentano, F., 131 bundle theory, 121, 235, 246, 247 Campbell, K., 123 Carnap, R., 29 Cartwright, N., 162, 168, 170 categories, 4, 16, 88, 89, 91, 94, 96, 103, 108, 126–39, 140–155, 229, 238, 240, 248; see also being, categories of auxiliary, 129, 133 basic, 150, 151 fundamental, 4, 5, 98, 104, 124, 126, 239, 241 ontological, 4, 5, 83–93, 124, 129, 140, 141, 145, 150, 153, 155, 239, 242, 245, 247 sub-categories, 85 Central Dogma of molecular biology, 174–6

259

260

Index

Chalmers, D., 2, 24, 26, 256 Chisholm, R., 5, 84, 147–50, 151, 153, 154 Church, A., 127 composition, 11, 25, 72, 73, 75, 82, 97, 100, 133, 159, 174, 202, 205, 236, 237, 244, 245 concrete, 53, 82, 84, 88, 116, 123, 124, 148, 150, 151, 153, 154, 160, 215, 218, 219, 230, 232, 233, 234, 235, 236, 237, 240; see also abstract constituent ontology, 244–8; see also relational ontology, constituent vs relational ontologies constituent vs relational ontologies, 229–34 Correia, F., 31, 137 countability, 67–9, 70, 72, 73, 74, 75, 77–82 Crane, T., 3, 28, 57 Crick, F., 175 Davies, P. C. W., 174–7 Definition, see real definition Democritus, 145 dependence, 111, 113, 118, 121, 130, 131, 132, 134, 135, 137, 142 existential, 121 identity-dependence, 152, 242, 243, 247 ontological, 31, 118, 188, 244, 248 Descartes, R., 105, 108, 111, 112, 142 development, biological, 6, 157, 158–66, 173, 175–86 developmental potential, see development, biological; see potentiality/potency Dewey, J., 160 Dipert, R. R., 106, 208, 210–23, 225, 227 dispositions, 95, 99, 101, 102, 115–17, 160–4, 167, 168, 172, 173, 207–8 downward causation, 176 Dummett, M., 49, 68, 70, 71, 81 eidicity, 2, 8, 10–13, 19–22, 25 eidos, see eidicity Einstein, A., 41, 98, 180 Ellis, B., 114, 207 Empedocles, 130, 131 epigenesis, 156, 157, 170, 173, 183 essence, 6, 26, 39, 40, 41, 49, 50, 51, 103, 134, 135, 138, 152, 187, 188, 189, 190, 194, 195, 196, 198, 200, 201, 205, 207, 223, 242, 243 and categories, 90 consequential, 191, 192, 193, 194 constitutive, 191, 193, 195 modal conception of, 187, 190 non-modal approach, 188, 189, 206 of concrete objects, 234 of graphs, 217 of substance, 232

essentialism, essentialist, 8, 10, 167, 189, 190, 191, 193, 195; see also Aristotelian essentialism dispositional, 6, 207 Evans, G., 50, 55 Fine, K., 2, 3, 6, 10, 27, 30, 31, 32, 39, 137, 188–93, 195, 196, 198, 206 finks, 167, 168 form, 114, 141, 159, 230, 232, 233, 234, 236, 237, 240, 245 and matter, 141, 146, 230, 231, 235, 236, 245 four-dimensional patterns in biology, 180–4 Frege, G., 14, 54, 55, 56, 58, 71, 127 fundamental, 39, 40, 42, 61, 84, 85, 94, 100, 106, 112, 117, 122, 124, 128, 129, 142, 143, 145, 156, 176, 208, 237; see also categories, fundamental entities, 100 facts, 9, 10, 11, 119 kind, 4, 79, 94, 153 laws, 100, 103 level, 7, 126, 208, 221 particle, 115, 237 principle, 42 structure, xi, 1, 35, 83, 84, 98 truth, 107 Geach, P. T., 68, 71, 81 Gilbert, S., 182 Glymour, C., 172, 173 God, 61, 63, 77, 114, 115, 129, 142 graph theory, 7, 210, 211, 212, 213, 217, 220, 223, 228 graphs, asymmetric, 212, 213, 219, 220–7 graphs, symmetric, 219, 220, 221, 224 ground, grounded, 1, 10, 11, 27, 31, 32, 39, 124, 127, 129, 130, 188, 189, 190, 191, 192, 206, 218, 234, 235 Guenin, L. M., 5, 156, 160, 166 gunk, 4, 73–81, 82 Gurwitsch, A., 182 Heil, J., 4, 5, 107, 121, 122, 162, 168, 169, 233 Hempel, C., 157, 162, 195 Higgs boson, 28 Hoffman, J., 5, 84, 89, 93, 142, 144, 153, 154, 155 Hofweber, T., 3, 28–30, 31, 32 Hume, D., 105, 145, 161 Husserl, E., 58, 139 hylemorphism, 141, 234–7 identity, 15, 16, 20, 21, 31, 68, 73, 81, 113, 123, 189, 190, 191, 210, 211, 220, 236 and essence, 190

Index and number, 66–71 as a ground, 191, 192, 196 concept of, 9, 23 criteria of, 82, 122, 124, 221, 222, 223, 224, 227 determinate, 225 law of, 20 Leibniz’s Principle of, 136 of concrete objects, 234 of dispositions, 225 of kinds, 113 of modes, 112 of nodes, 212, 219 of powers, 209 of relata, 211 personal, 40, 41, 133 relation of, 9, 14, 17, 21 relative, 69 self-identity, 67 set-theoretical, 214, 215, 216, 218 strict, 122 token-token, 162 transitivity of, 164 type-type, 161 vague, 70 individuation, 75, 76, 77, 82, 96, 164, 218 principle of, 234 information, 174, 175 biological, 176 digital and analog, 177, 185 Ingarden, R., 132, 133 intentionality, 45, 46, 48, 63, 161 Jackson, F., 24, 38, 41, 60, 161 Kant, I., 1, 5, 35, 36, 105, 108, 109, 128, 129, 131, 132, 136, 145 Kepler, J., 97, 99 Kinds, see natural kinds Koslicki, K., 6, 39, 159, 173, 187, 192 Kripke, S., 23 Ladyman, J. and Ross, D., 2, 26–7, 33–9 laws of nature, 4, 88, 95, 96, 97, 98, 99, 101, 102, 103, 118, 161, 162, 171, 208 ceteris paribus laws, 168 Laycock, H., 68, 71, 72, 74 Leibniz, G. W., 105, 108, 133, 136, 142 Leśniewski, S., 128 Lewis, D., 60, 73, 168, 183 Locke, J., 5, 105, 108, 112, 114, 115, 119, 120, 122, 240, 248 Loux, M., 7 Lowe, E. J., 4, 5, 6, 7, 26, 27, 33, 35, 38, 39, 44, 68, 69, 72, 75, 76, 77, 79, 80, 81, 82, 83, 84, 93, 96, 98, 100, 103, 104, 105, 107,

261 108, 110, 111, 112, 113, 118, 124, 125, 126, 130, 131, 134, 139, 142, 145, 150–3, 154, 155, 159, 161, 162, 171, 173, 209, 210, 211, 221, 223, 227, 238, 242 on categories, 84, 85, 86, 128, 129, 150, 151 on countability, 70, 75 on dependence, 121, 130 on dispositions, 115–17 on kinds, 94–6, 120, 121 on laws, 96–9, 103, 118–20 on powers, 208, 209, 210 on substance, 130, 153, 154 on universals, 110–15, 121, 122, 123, 124 vs Armstong, 101–3

Mackie, J. L., 49, 50 Martin, C. B., 107, 160, 161, 162, 167, 168, 169 mathematics, mathematical, 1, 7, 9, 13, 15, 16, 19, 20, 21, 22, 28, 29, 33, 35, 36, 37, 41, 42, 69, 130, 166, 197, 210, 214, 218, 221, 227, 228 McCall, S., 6, 174 McNally, L., 61, 62, 63 Meinong, A., 51, 52, 53 mereology, mereological, 17, 137, 138, 236, 237 metametaphysics, 2, 31 methodology, 2, 26, 27, 35, 37, 38, 39, 146 Millikan, R., 99 modality, 23, 24, 38, 61, 129, 135, 167, 169; see also necessity, possibility alethic, 169 and essence, 6, 188, 189, 195, 206 de dicto, 169 de re, 6, 167, 168, 189, 190, 191 modes, 4, 52, 53, 94, 96, 102, 107, 108, 110, 112, 113, 114, 119, 122, 126, 127, 130, 132, 138, 150, 176, 240, 242, 243, 244, 247 and attributes, 238, 240 of being, see being, modes of Molnar, G., 159, 161, 207, 208, 209 Moore, G. E., 146 morphogenetic field, 182 multiple realizability, 164 Mumford, S., 162, 168, 169 Nagel, E., 156, 157, 160 natural kinds, 4, 84, 90, 91, 94, 99, 100, 103, 119, 167, 198, 210, 243 and attributes, 95 and dispositions, 115 and powers, 120 as nominal, 114 category of, 94 natural laws, see laws of nature necessity, 16; see also modality, possibility

262

Index

conceptual, 162, 169 de re, 167, 187 logical, 20 metaphysical, 20, 39 neo-Aristotelian, 1, 5, 7, 26, 32, 38, 39, 84, 140, 144, 145, 146, 147, 149, 152, 153, 155, 187 Newton, I., 34, 97, 98, 99, 180 Nominalism, see realism numbers, 14, 27, 28, 29, 30, 31, 51, 68, 69, 70, 85, 100, 136, 143, 148, 166 Oderberg, D., 6, 7, 207 Olson, E., xi, 3, 4 ontological commitment, 3, 27, 53, 64, 65, 107, 242 Oppenheim, P. and Putnam, H., 176 Parmenides, 145 particulars, see universals pattern formation in organisms, 178–84 Pegasus, 53, 57, 63 Peirce, C., 127 phlogiston, 57 Plato, 7, 30, 105, 137, 141, 145, 202, 229, 233 Popper, K., 161, 166, 171 portions, 71–81, 82, 119, 120 possibility, see also modality, necessity epistemic, 40, 85, 89, 151, 153 metaphysical, 27, 35, 36, 38, 39, 88 nomic, 88 nomological, 165, 166, 171 potentiality/potency, 156, 158–60, 161, 163, 164, 165, 166, 170, 172, 173, 208, 227 powers, 115, 119, 120, 160, 170, 196, 210, 237 causal, 7, 208 pure, 7, 207–10, 212, 214, 227 circularity objection, 208–10, 220, 223 regress objection, 208–10, 220, 223 preformation, 156, 157, 183 Priest, G., 44, 51 Priestley, J., 105 propria, 187, 194 Putnam, H., 39, 176 quantification, 3, 29, 47, 68, 73, 75 and number, 66–71 domain of, 13, 14, 48, 55, 56–61 existential, 14, 20, 21, 27–9, 44, 48, 54, 55, 61, 64, 129 into intensional contexts, 187 over non-existents, 48, 65 over possible worlds, 60, 64 over relations, 107 restricted, 56 universal, 20, 31, 54

quantum mechanics, 42, 172, 173 Quine, W. V. O., 3, 14, 27, 30, 45, 46, 50, 51, 64, 107, 127, 145, 159, 164, 167, 169, 187 Quinean, 1, 2, 3, 6, 26, 27, 28, 32, 51, 52, 53, 64, 167 real definition, 190, 200 realism, 31, 123, 124, 153 about substance, 155 about universals, 123 anti-realism, 31 Aristotelian, 151 structural, 106 vs nominalism, 127, 135, 138 relational ontology, 240–4; see also constituent ontology, constituent vs relational ontologies Rescher, N., 55 Robinson, H., 209, 210, 211 Rosenkrantz, G., i, 4, 5, 84, 89, 91, 142, 144, 153, 154, 155 Ross, W. D., 158, 159, 160 Russell, B., 51, 52, 59, 106, 127, 138 Ryle, G., 168, 169 Schaffer, J., 31, 32 Schneider, L., 95 Sider, T., 37 Simons, P., 5, 74, 164 singleton Socrates, 188, 190, 191, 192 Soames, S., 146 Sober, E., 157, 173 sortals, 69, 82, 98, 108, 127, 134, 140, 240 spacetime curvature, 180 Spinoza, B., 105, 108, 111, 112, 133, 142, 146 stuff, 71, 72, 73, 74, 76, 79, 140, 146 portions of, 73, 79 substance, 1, 4, 9, 11, 25, 83, 84, 88, 91, 92, 94, 95, 106, 107, 108, 109, 112, 121, 126, 129, 130, 133, 134, 140, 142, 143, 145, 146, 149, 151, 152, 153, 155, 174, 202, 204, 211, 236 and artefacts, 146 and persons, 108 and relata, 211 category of, 5, 92, 93 contingent vs necessary, 84 form of, 232 individual, 94, 140, 229, 230, 231, 232, 235, 238, 245, 248 ontological, 215 primary, 210, 229, 238, 240 secondary, 210, 238, 240, 246 simple, 248 vs accident, 129 vs matter, 159 vs mode, 127

Index Tahko, T. E., 39, 42, 82 Tarski, A., 127 Tartar, V., 178, 179, 181, 185, 186 Thales, 32 tropes, 4, 5, 71, 84, 91, 94, 108, 110, 112, 122, 123, 124, 127, 137, 143, 144, 148, 150, 151, 153, 154, 162, 240, 247 truthmaking, 105, 106, 107, 109, 123, 136, 137, 138, 242, 244 Twin Earth, 39 universals, 4, 17, 66, 94, 95, 96, 100, 101–3, 107, 108, 109–25, 127, 150, 162, 198, 233, 235 and attributes, 111 and laws, 162 Armstrong’s conception of, 110 as abstract objects, 111 category of, 98 immanent, 118, 123, 153, 241 substantial, 101, 246

263 substantial vs insubstantial, 84 vs particulars, 84, 94, 100, 102, 113, 114, 130, 134, 138, 150, 230, 245

vagueness, 70, 72, 77, 80, 81, 82, 100 van Fraassen, B., 101, 136 van Inwagen, P., 46, 51, 53, 69 vitalism, 156, 157, 184 water, 9, 10, 11, 12, 23, 25, 32, 68, 71, 72, 73, 74, 75, 90, 102, 115, 116, 117, 121, 130 H2O, 9, 10, 11, 12, 23, 24, 25, 90 XYZ, 23 Whitehead, A. N., 126, 138, 144 Williams, D. C., 5, 110, 112, 121, 122, 123, 124 Williamson, T., 2 Wittgenstein, L., 129 Wolpert, L., 183 Wolterstoff, N., 7