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The series discourages the submission of manuscripts that contain reprints of previous published material and/or manuscripts that are below 160 pages/88,000 words. For inquiries and submission of proposals authors can contact the editor-in-chief Mariarosaria Taddeo via: mariarosaria.taddeo@oii.ox.ac.uk More information about this series at http://www.springer.com/series/6459 Bo R. Meinertsen Metaphysics of States of Affairs Truthmaking, Universals, and a Farewell to Bradley's Regress 123 Bo R. Meinertsen Department of Philosophy Tongji University Shanghai, China ISSN 0921-8599 ISSN 2542-8349 (electronic) Philosophical Studies Series ISBN 978-981-13-3067-4 ISBN 978-981-13-3068-1 (eBook) https://doi.org/10.1007/978-981-13-3068-1 Library of Congress Control Number: 2018960353 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore To my mother, Kirsten, and to the memory of my father, Jørgen Preface In Denmark, in the late 1990s, I first became interested in metaphysics of states of affairs, or state of affairs ontology, when as a student at the University of Copenhagen I read Armstrong's Universals and Scientific Realism. The focus of his work is the problem of universals; yet, in Armstrong's positive theory, the metaphysics of states of affairs is the (underdeveloped) linchpin. It is also the most fascinating part, I found. How excited I was when I then discovered that his A World of States of Affairs was forthcoming! But I felt that Armstrong was focusing too much on states of affairs' relation to other topics, such as causation, modality and numbers, whereas I wanted to delve into them directly, as it were. In England, where I had soon afterwards gone to pursue my interest, I learned that I could not just dive straight into states of affairs. The principal access to them is as truthmakers, which is their main ontological role. Though I am no longer so certain about this view, there is no doubt in my mind that a state of affairs ontology worth its salt needs to offer a plausible story about the role of truthmaking and how states of affairs play that role. What is more, truthmaking has two major bonuses. It can be used to define a notion of reducibility which is at the heart of the state of affairs ontology to be developed in this book. This notion is, roughly speaking, equivalent to Armstrong's notion of supervenience. And it can be used to defend a state of affairs ontology that, in the spirit of logical atomism, postulates no non-atomic states of affairs. I shall defend the position that states of affairs are complexes that are instantiations of properties or relations by particulars. In order for this view to be plausible, four things, among others, need to be secured. First, something like logical atomism (probably) needs to be true. As we shall see, it is (if a solution for negative truths can be found, an issue I cannot address in the present book). Second, and more importantly, the particulars in states of affairs should be bare particulars. Third, and more importantly still, states of affairs, the complexes, should be unified without giving rise to Bradley's regress. Fourth, state of affairs ontology should work better than its competitors. I argue for the first and fourth points in Part I of the book, and for the second and third in Parts II and III, respectively. vii Since this is my first book, I should like to provide a few wide-ranging acknowledgements in addition to those I give in the text when citing other philosophers. Over the years, I have discussed my work with many people, both students and professionals, both in person and by email. They have provided comments on my work, along with suggestions and encouragement. I am very grateful to all of them. There are far too many to mention here, but I would like to single out two groups. The first includes distinguished philosophers whom I have often only had brief contact with, or maybe never even met, but who nonetheless took time out of their busy schedules and kindly commented on my work. They are: Panayot Butchvarov, Ross Cameron, Chris Daly, Reinhardt Grossmann, Ingvar Johansson, E. J. Lowe, Fraser MacBride, Donald Mertz, Andrew Newman, Howard Peacock and Ernest Tegtmeier. Second, and more importantly, I would like to mention the colleagues and friends without whose comments this book probably would never have come into existence. Apologies to anyone inadvertently left out. The ones I have in mind range from junior colleagues to preeminent philosophers. They are: Mikel Burley, George Darby, John Divers, Jan Faye, Andrew McGonigal, Joseph Melia, Hugh Mellor, Katarina Perovic, Benjamin Schnieder, Scott Shalkowski, Peter Simons, William Vallicella and Jan Wieland. Hugh, as my amazing supervisor at the University of Cambridge, deserves special thanks for all that he taught me. So does Peter, as my supervisor, at the University of Leeds, of the thesis from which this long-overdue book originates. His impressive knowledge of metaphysics and ontology, and his equally impressive analytical skills, were priceless to my research. As to help and support of a more personal nature relating to my work, I am deeply grateful to Ole Andersen, Pernille Andersen and Hao Chen. Actually, John Divers should be mentioned here too. Many years ago when as a graduate student at Leeds I became seriously ill, his support was crucial for my return. I should also like to thank the publishers of dialectica and Grazer Philosophische Studien for permission to reuse material from my (2008) and (2011), respectively. Many thanks to the anonymous referees of both journals for their comments on my drafts. Many thanks also to my Editors at Springer, Leana Li, Ties Nijssen and Marirosaria Taddeo, and to their anonymous reviewer who provided detailed and helpful comments on an earlier draft of the manuscript. Finally, I wish to mention some of the many local colleagues, students and friends at Tongji University who encouraged or inspired me during the completion of this book. Many thanks to Jiang Bo, and to Sun Zhouxing, Yu Mingfeng, Zhao Qianfan, Zhao Xudong and, in particular, Joe Guo. Shanghai, China Bo R. Meinertsen March 2018 viii Preface Précis The book includes an introductory chapter followed by nine chapters divided into three parts: Part I on the main role for state of affairs ontology, and its two rivals; Part II on the constituents of states of affairs; and Part III on the unity of states of affairs. Here, I shall summarize a number of main points from each chapter. Chapter 1: Introduction I introduce the book as a whole, the nature of my project and its context. In particular, I introduce the main thesis of the book, the thesis of my state of affairs ontology, viz. that states of affairs are unified complexes that are instantiations of properties or relations by particulars. The book continues the important tradition of the metaphysics of states of affairs in analytic philosophy, as found in influential philosophers such as Russell, Wittgenstein, Bergmann, Grossmann, Armstrong and, more recently, William Vallicella. The chapter outlines the book's general approach, assumptions and restrictions. First, the general approach can to a large extent be described as Armstrongian: Armstrong, in his middle-period, is the philosopher who has been the single greatest inspiration for the state of affairs ontology I advocate. Second, I formulate assumptions which I shall appeal to throughout the book, including 'Lewis's Razor', what I call the Principle of Spatiotemporally Homogeneous Composition, and my view that properties and relations in states of affairs are universals (if trope theory and moderate realism fail, which I argue in Chaps. 3 and 4 that they do). Third, I restrict myself to contingent states of affairs about concreta, and I remain neutral with regard to endurantism versus perdurantism in the philosophy of time. I next introduce in some detail the main problem for state of affairs ontology, the problem of unity, a topic that occupies centre stage in much of Part III of the book, i.e. in Chaps. 9 and 10. This is the problem of how states of affairs are unified. I further introduce the main role for states of affairs, namely, truthmaking. Although the next chapter is devoted to exploring this notion, I distance myself from Armstrong's well-known truthmaker argument for states of affairs, since I am not professing to be 'arguing for the ix existence of states of affairs'. Another position on which states of affairs are also closely linked to truthmaking is Arianna Betti's. I consider and reject her criticism of states of affairs at the end of the chapter. Part I-The Main Role for State of Affairs Ontology, and Its two Rivals Chapter 2: Truthmaking I first argue that truthmaking is the principal role for state of affairs ontology. I also compare truthmaking with the Principle of Sufficient Reason, since this can illuminate it considerably. I next compare three competing approaches to truthmaking and defend the one which goes most naturally with state of affairs ontology, what is usually called 'truthmaker maximalism'. I further argue that, in the spirit of logical atomism, we need no non-atomic truthmakers for (fully) positive truths (fromwhich it follows that we need no corresponding non-atomic states of affairs). I also provide a brief quasi-definition of truthmaking it-'quasi', as it is arguably too fundamental to be defined properly-and characterize it implicitly. It is easy to show that truthmaking on this view leads to problems when applied to necessary truths. I explain why and how I am nonetheless going to do this at a later point, in Sect. 7.1.1, for the case of truths about internal relations. I finally use truthmaking for defining a highly important notion of reducibility, 'truthmaking-reducibility' or 'TM-reducibility', which I shall apply frequently at central points throughout the book. It is, roughly, the equivalent of Armstrong's 'supervenience'. Candidates for a certain kind of entity are included in (constituents of) states of affairs if and only if they are not TM-reducible. For example, I shall argue in Chap. 6 that negative and disjunctive properties are TM-reducible; and in Chap. 7 that the same goes for non-external relations. Thus, states of affairs which include these entities, which Armstrong calls 'secondor third-class states of affairs', are in my view merely apparent states of affairs. Chapter 3: A Partial Look at Trope Theory The first part of this chapter deals with I call 'basic trope theory'. This theory comes in two main versions: a 'bundle version' and a 'substance-attribute version'. Keith Campbell, the main proponent of basic trope theory in the bundle version, holds that a trope has both a 'particularity' and a 'nature', but that it is nonetheless simple. This feature may help trope theory solve (its counterpart of) the problem of unity, but it seems enigmatic: how can something simple 'ground' entirely distinct things. If this problem cannot be solved, trope theory seems incoherent. Besides, when we consider how basic trope theory in the bundle version handles truthmaking, it can be seen to fail. I argue that this version of trope theory needs a relation of 'compresence', and hence that it requires states of affairs in order to provide truthmakers. x Précis (I additionally argue tentatively that although the substance-attribute version of trope theory does not require states of affairs to account for truthmaking, it fails for other reasons.) In the second part of the chapter, I briefly consider more advanced versions of trope theory, but argue that they face fatal problems in accounting for either 'non-substantial change' or predication. Chapter 4: A Partial Look at Moderate Realism This chapter is on Donald Mertz's 'moderate realism'. Since Mertz's metaphysics is unfamiliar to most philosophers, a fair amount of the chapter is expository and aims to reflect his distinctive terminology and notation, but the main overall purpose is nonetheless to evaluate this ontology. Moderate realism attempts to build unity into complexes, as it were; at its heart are 'relation instances' which are also known as 'unit attributes'. Relation instances are simple, yet 'internally diverse'; they are 'non-composite wholes' analogously to how a circle is 'simple in its continuity', according to Mertz. I call Mertz's relation instances 'MR-facts' and show both how they can constitute ordinary objects and be truthmakers. Mertz claims they can solve his counterpart of the problem of unity. However, MR-facts are essentially relational, which creates insurmountable problems for the monadic case. What is more, as I argue in the final part of the chapter, the fact that relation instances are 'non-composite wholes' is Mertz's counterpart of Campbell's thesis that tropes are simple and as such highly implausible. Part II-The Constituents of States of Affairs Chapter 5: Bare Particulars I argue that the particulars in states of affairs are bare particulars. That indeed is why the chapter is entitled 'Bare Particulars': it is about particulars qua constituents of states of affairs, not about particulars as such. Ironically, however, on the view of bare particulars I defend, conjunctions of states of affairs are identical to ordinary particulars ('thick particulars'). Despite its being a common view that the particulars in states of affairs are bare-and an almost equally common view that bare particulars are absurd entities-it is far from clear what bare particulars are; specifically, what their bareness is. The main purpose of the chapter is twofold: (i) to give a viable account for what the bareness of bare particulars is, and (ii) examine some of their roles in states of affairs or related entities. As to (i), I look at some proposals from the literature, and argue that they fail. Instead, I defend the view that the bareness of bare particulars is that they instantiate, as opposed to include, their properties. As to (ii), I argue that bare particulars individuate thick particulars; and that they are the reason for the particularity of states of affairs ('the victory of particularity'). In the last section of the chapter, I put forward an in my view very important argument that particulars in states of affairs are always bare, what I call the generalization argument. Précis xi Chapter 6: Properties The chief purpose of this chapter is to find out which properties, among certain kinds of candidate, are (i) constituents of states of affairs, (ii) which of these are not constituents of states of affairs, and (iii) to discern how the former behave when hosted by states of affairs. A natural starting point when embarking on an examination of properties is the relationship between properties and predicates. I argue with Armstrong that this relationship is non-trivial, and I endorse his division of properties into three 'classes'. However, this classification does not by itself tell us whether a certain property is, or is not, TM-irreducible. We need to know this to find out which properties are constituents of states of affairs. I therefore discuss four kinds of property that are, I shall argue, not TM-irreducible: negative, disjunctive, unique qualitative properties (such as 'being the last dodo') and conjunctive properties. Armstrong agrees with my assessment of first three kinds, but not the last one. I argue, following Mellor's argument from 'Ramsey's test', that conjunctive properties, contrary to what Armstrong holds, are TM-reducible. Additional issues discussed in this chapter are the individuation of properties (universals) and Mertz's argument against states of affairs with universals. Chapter 7: Relations The subject of relations is vast and is receiving increasing attention, and this chapter can only touch on a few aspects of the topic. The chapter's aim is fourfold. First, as demonstrated in the previous chapter, some properties are TM-reducible and hence not constituents of monadic states of affairs. Similarly, some relations are TM-reducible and hence not constituents of polyadic states of affairs. Accordingly, I draw what I consider the most important distinction for this issue, namely, the distinction between internal, external and 'grounded' relations and argue that only external relations are not TM-reducible. Second, I defend relations, whether TM-reducible or not, against a neglected but potentially devastating objection to them by Panayot Butchvarov. Third, relying on Grossmann and, in particular, on Armstrong, I sketch a 'directionalist' account of the direction ('order') of non-symmetrical relations. This account enables me to provide 'identity conditions' for states of affairs. A state of affairs ontology worth its salt should be able to supply these goods, although as we shall see, there is relatively little that needs to be said about the issue. Fourth, I examine the phenomenon of reflexivity and argue that reflexive relations are TM-reducible. This matter is not only interesting in itself, but it is also important for later contrasting reflexivity with self-relating, a notion which is at the heart of my solution to the problem of unity and which I shall introduce in Chap. 9. Chapter 8: Concrete Universals This is a relatively brief chapter concerned with a requirement of both naturalism and the Principle of Spatiotemporally Homogeneous Composition, namely, that universals in states of affairs be concrete. The view that universals are concrete is xii Précis not exactly a popular view; it is often assumed as a matter of course that they are abstract, and there is no shortage of arguments against it. I briefly discuss some of them, including arguments by Douglas Ehring, Herbert Hochberg, James Moreland and Ernani Magalhães. However, my aim is not to establish a 'hard' conclusion that these arguments all fail; rather, it is just to characterize some features of the locatedness (location) of such universals, including their notorious 'multiple location'. In the final section of the chapter, I consider concrete polyadic universals, whose locatedness clearly is especially problematic: for example, they obviously cannot be in their instances, since they hold between them. I briefly sketch Armstrong's three suggestions for a way out of this predicament. I tentatively endorse his suggestion that spatial and temporal relations constitute spacetime, such that it is a category-mistake to ask for their location. Part III-The Unity of States of Affairs Chapter 9: The Problem of Unity and Relational Internalism In this chapter, I explain and motivate the problem of unity in non-metaphorical terms further than in Chap. 1, and I provide a solution to it. My general approach to the problem is what I call relational internalism (the unifier of a state of affairs is a relation of some sort in it). I identify a species of this approach, common internalism, and consider it in some detail. Unfortunately, it inevitably leads to Bradley's regress, which, as I argue in detail in the following chapter, is vicious. In the course of analysing common internalism, I explicate two important metaphysical principles underlying it, two principles which jointly are critical in generating the regress. It turns out that extant versions of relational internalism face the dilemma of either not solving the problem of unity at all or succeeding in this halfway and then leading to Bradley's regress. However, I propose a novel version of relational internalism, which I call self-relating internalism, on which a unique, formal constituent relation, the U*-relation, unifies a state of affairs by relating itself to the other constituents of the state of affairs. It thereby solves the problem of unity without giving rise to Bradley's regress. Chapter 10: The Unity of States of Affairs and Bradley's Regress This chapter is intimately related to the previous one, but it can to a large extent be read independently of it. In it, I discuss a number of issues raised in Chap. 9 in more detail. This includes the basic version of relational internalism, common internalism and the 'infinitary reading' of it, on which it is co-extensional with Bradley's regress. It further includes an attempt to apply Francesco Orilia's 'internalist' versus 'externalist' versions of Bradley's regress to common internalism. However, my preferred analysis of Bradley's regress involves a novel tack construing it as an argument. One advantage of this approach is that it will demonstrate precisely how the two crucial metaphysical principles from the analysis of common internalism in Précis xiii Chap. 9 are at work in the regress. Furthermore, it will enable me to show in detail that it indeed is a vicious regress. And finally, it enables me to show exactly how and why self-relating internalism solves the problem of unity without leading to Bradley's regress. I defend this approach to Bradley's regress (and the associated problem of unity) against recent criticism by Howard Peacock. In the two remaining sections of the chapter, following a review of self-relating internalism, I explore the nature of the U*-relation, including how the phenomenon of self-relating differs from reflexivity, whether or not U* is multigrade, and finally how U* compares and contrasts with material relations. xiv Précis Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Précis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 A State of Affairs Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Approach, Assumptions and Restrictions . . . . . . . . . . . . . . . . . 2 1.2.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.3 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 The Main Problem of State of Affairs Ontology: Initial Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 The Main Role for State of Affairs Ontology, and Its Two Rivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Betti's Criticism of States of Affairs . . . . . . . . . . . . . . . . . . . . . 13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Part I The Main Role for State of Affairs Ontology, and Its Two Rivals 2 Truthmaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 Truthmaking, Two Other Roles, and the Principle of Sufficient Reason . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Three Approaches to Truthmaking . . . . . . . . . . . . . . . . . . . . . . 23 2.3 The Relation of Truthmaking . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.1 Which Kind of Entity Are Truth-Bearers? . . . . . . . . . . . 26 2.3.2 Truthmaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 Truthmaking at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 TM-Reducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 xv 3 A Partial Look at Trope Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1 Basic Trope Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1.1 Selective Introduction of Tropes . . . . . . . . . . . . . . . . . . 39 3.1.2 The Simpleness of Tropes: Is It Enigmatic or Does It Lead to Absurdity? . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.3 'Free-Floating' Is Irrelevant to Relational Tropes . . . . . . 44 3.1.4 Mertz's Argument that Nominalism Requires the Elimination of Relations . . . . . . . . . . . . . . . . . . . . . 45 3.1.5 Trope Theory and Truthmaking: From Bundles to Substances and Attributes? . . . . . . . . . . . . . . . . . . . . 46 3.2 The Nuclear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.1 The Problem of Non-substantial Change . . . . . . . . . . . . 49 3.2.2 The Nuclear Theory as a Solution to the Problem of Non-substantial Change . . . . . . . . . . . . . . . . . . . . . . 49 3.2.3 The Nuclear Theory and Contingent Predication . . . . . . 51 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4 A Partial Look at Moderate Realism . . . . . . . . . . . . . . . . . . . . . . . 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Principles of Moderate Realism . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.1 Moderate Realism 'for the Sake of Argument' . . . . . . . . 56 4.2.2 Exclusivity and Uniqueness of Relation Instances . . . . . 57 4.2.3 The Universals of Moderate Realism . . . . . . . . . . . . . . . 59 4.2.4 Ontic Predication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2.5 Thick Particulars as Networks . . . . . . . . . . . . . . . . . . . . 63 4.3 The Simpleness of Relation Instances . . . . . . . . . . . . . . . . . . . 64 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Part II The Constituents of States of Affairs 5 Bare Particulars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1 Bare Particulars and Thick Particulars . . . . . . . . . . . . . . . . . . . 69 5.2 The Bareness of Bare Particulars Is That They Instantiate Their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.3 Interlude: Bare Particulars as Individuators . . . . . . . . . . . . . . . . 75 5.4 Bare Particulars Are the Reason for the Particularity of States of Affairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.5 The Generalization Argument: The Particulars in States of Affairs Are Always Bare . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 xvi Contents 6 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.1 Properties and States of Affairs . . . . . . . . . . . . . . . . . . . . . . . . 83 6.1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.1.2 Predicates and Armstrong's Tripartite Division of Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.1.3 Some TM-Reducible Kinds of Property . . . . . . . . . . . . . 86 6.1.4 Universals in States of Affairs . . . . . . . . . . . . . . . . . . . 91 6.2 Are There Conjunctive Universals? . . . . . . . . . . . . . . . . . . . . . 94 6.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.2.2 Mellor's Argument from Ramsey's Test . . . . . . . . . . . . 95 6.2.3 Conjunctive Universals in Armstrong . . . . . . . . . . . . . . 96 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.1 The Three Basic Kinds of Relation . . . . . . . . . . . . . . . . . . . . . 101 7.1.1 Internal and External Relations . . . . . . . . . . . . . . . . . . . 101 7.1.2 Grounded Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.2 Butchvarov's Phenomenological Argument Against Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.3 Direction: Some Armstrongian Remarks . . . . . . . . . . . . . . . . . . 107 7.3.1 Direction as a Feature of Non-symmetrical Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.3.2 Direction and the Identity Conditions of States of Affairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.4 Reflexive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8 Concrete Universals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.2 Three Basic Features of the Locatedness of Universals . . . . . . . 120 8.3 Objections to Concrete Universals . . . . . . . . . . . . . . . . . . . . . . 121 8.3.1 Ehring's Argument from Local External Relations . . . . . 121 8.3.2 Three Further Objections and the Question of Onus of Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 8.4 On Armstrong's Three Suggestions for the Location of Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Contents xvii Part III The Unity of States of Affairs 9 The Problem of Unity and Relational Internalism . . . . . . . . . . . . . 133 9.1 The Main Problem of State of Affairs Ontology: Further Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 9.2 Naive Internalism and Bradley's Regress . . . . . . . . . . . . . . . . . 137 9.3 Classic Internalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 9.4 Self-Relating Internalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10 The Unity of States of Affairs and Bradley's Regress . . . . . . . . . . . 147 10.1 The Problem of Unity and Relational Internalism . . . . . . . . . . . 147 10.2 Common Internalism and Bradley's Regress . . . . . . . . . . . . . . . 148 10.3 Classic Internalism's Attempt at Escaping the Regress . . . . . . . 150 10.4 The Argument Analysis of Bradley's Regress . . . . . . . . . . . . . . 151 10.5 Is It Vicious? The Explanation View . . . . . . . . . . . . . . . . . . . . 152 10.6 Self-Relating: Relational Internalism Without Bradley's Regress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 10.7 A Final Note on U* and Other Relations . . . . . . . . . . . . . . . . . 159 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 xviii Contents