The Mind of God and the Works of Nature: Laws and Powers in Naturalism, Platonism, and Classical Theism [1 ed.] 9042937629, 9789042937628

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STUDIES IN PHILOSOPHICAL THEOLOGY

THE MIND OF GOD AND THE WORKS OF NATURE LAWS AND POWERS IN NATURALISM, PLATONISM, AND CLASSICAL THEISM

BY

JAMES ORR

PEETERS

THE MIND OF GOD AND THE WORKS OF NATURE

STUDIES IN PHILOSOPHICAL THEOLOGY 65

SERIES EDITORS Willem B. Drees (Tilburg), Stephan van Erp (Leuven), Douglas Hedley (Cambridge)

ADVISORY BOARD L. Boeve (Leuven), V. Brümmer (Utrecht), I.U. Dalferth (Zürich & Claremont, CA), J. Greisch (Paris), M.T. Mjaaland (Oslo), C. Richter (Bonn), C. Schwöbel (Tübingen), S. Sorrentino (Salerno), J. Soskice (Cambridge), M. Stenmark (Uppsala), C. Taliaferro (Northfield, MN).

EDITORIAL PROFILE Philosophical theology is the study of philosophical problems which arise in reflection upon religion, religious beliefs and theological doctrines.

THE MIND OF GOD AND THE WORKS OF NATURE LAWS AND POWERS IN NATURALISM, PLATONISM, AND CLASSICAL THEISM

by

JAMES ORR

PEETERS LEUVEN – PARIS – BRISTOL, CT 2019

A catalogue record for this book is available from the Library of Congress.

© 2019 – Peeters, Bondgenotenlaan 153, 3000 Leuven, Belgium. ISBN 978-90-429-3762-8 eISBN 978-90-429-3763-5 D/2019/0602/5 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.

For Helen luxmea,quavivaviveredulcemihiest

CONTENTS INTRODUCTION. THE PUZZLE OF LAWMAKING . . . . . . . . . . . . . . . . . . .

1

CHAPTER 1. HUMEAN LAWLESSNESS AND NATURE’S KINDNESS . . . . .

11

CHAPTER 2. LAWS

AS RELATIONS: THE PRESSURE OF PLATONISM

...

35

CHAPTER 3. LAWS

AS POWERS: THE FRESCO PROBLEMS

..........

63

CHAPTER 4. THE TURN FROM NATURALISM: TWO PLATONIC STRATEGIES

91

CHAPTER 5. DIVINE

LAWMAKING AND CAUSAL POWERS

CHAPTER 6. DIVINE

CONCEPTS AND NATURAL ORDER

. . . . . . . . . . 123

. . . . . . . . . . . . 159

CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

ACKNOWLEDGMENTS It is a pleasure to record the uncountably many instances of kindness and generosity without which this project would have been considerably harder to undertake. I must in the first place express my deepest gratitude to the Master and Fellows of St. John’s College, Cambridge, the Faculty of Divinity at the University of Cambridge, and the Dean, Chapter, and Students of Christ Church, Oxford, for providing me with three idyllic intellectual environments in which to reflect on the philosophical questions discussed in this book. I am particularly grateful to the Arts and Humanities Research Council for its generous financial support, as well as to Alonzo, Susie, and Peter McDonald of the McDonald Agape Foundation for their unstinting support (financial and otherwise) over the period in which this book was completed. For comments and suggestions on various aspects of the book at different stages of its gestation my deepest thanks to Kenny Boyce, Jeremy Butterfield, Sarah Coakley, John Cottingham, Fiona Ellis, Douglas Hedley, Tim Lewens, Tim Mawson, Martin Pickup, Joseph Shaw, Roger Trigg, and Matthew Tugby. I am especially grateful to Brian Leftow for comments on a version of Chapter 3; to Alvin Plantinga for correspondence on a central issue in Chapter 6; and to Richard Swinburne for comments on earlier incarnations of Chapter 2, Chapter 3, and Chapter 5. Special thanks are owed to Jon Thompson who, in addition to providing me with a set of characteristically incisive comments, helped me to assemble the index. I would also like to thank Ingemar Spelmans and the editorial team at Peeters in Leuven for their enthusiasm, efficiency, and diligence in steering the manuscript to press. Any outstanding errors, egregious or otherwise, remain my own. For their many and various forms of encouragement at different stages of this project, my deepest thanks to Jonathan Aitken, Nigel Biggar, Joshua Hordern, Mark Mills-Powell, James Mumford, Catherine Pickstock, Lisbet Rausing, Sigrid Rausing, Tom Simpson, Eric Tippin, and Russell Winfield. I would also like to express heartfelt gratitude to my parents Anthony and Cate, limitless sources of strength and encouragement to me over many years; to my bewildered children, Godfrey and Honor; and, finally, to my wife Helen, to whom I owe far more than can adequately be expressed in words.

INTRODUCTION THE PUZZLE OF LAWMAKING

Secular philosophers have long worried that the very idea of physical law is a fossilized survival from a bygone age dominated by belief in the existence of a divine lawmaker. For all of its suspect theological freightage, though, lawhood continues to be an apparently indispensable conceptual tool for the natural scientist. One obvious explanation for its persistence is that the notion of law preserves some of our core intuitions about the physical world. For nature surrounds us on all sides with egularities that few of us could dismiss as accidental without concealing a smile. That a fragile glass hurled hard from an upper-floor window shatters on impact with the ground, that every electron has the same rest mass, that there are no spheres of uranium wider than a mile in diameter – all these are facts that strike us as ineliminably law-governed features of the world. Conversely, nature confronts us with countless instances of what seem inescapably to be brute coincidences: that wombats are born in Australia rather than Asia, that no human being has run 100 metres in less than 9.57 seconds, that there are no spheres of gold wider than a mile in diameter – these are regularities that do not strike us as lawful even though they are no less uniform than the ones that do. Before considered reflection gets underway, at least, our intuitions press us not only to draw a principled distinction between these two kinds of regularity, but also to infer that this distinction is based on objective facts about reality.1 More simply put: at an intuitive level, it is not up to us where the line between law and accident is to be drawn. It is not even up to our best scientists. For the task of scientific inquiry is not to stipulate the distinction between law and accident; it is to discover it. Intuitions such as these are so firmly entrenched that many are surprised to learn that the prevailing orthodoxy in Anglophone philosophy is that lawhood is a theologically inflected illusion that should hold us 1 References throughout this book to ‘regularities’ or ‘lawlike regularities’ are intended to capture whatever regularities feature in the content of law-statements formulated in our best scientific theories – that is to say, these terms are intended throughout to denote putatively lawful regularities, leaving open the key question of what (if anything) distinguishes them from accidental generalisations.

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captive no longer. In the halcyon days of logical empiricism, few philosophers would have denied that every regularity is an accidental regularity or that theories of natural necessity that claimed otherwise were at one with a belief in fairies and unicorns. On this sort of view, all that could distinguish ‘lawful’ from ‘lawless’ regularities are the various classificatory schemes we adopt to render the physical world transparent to scientific inquiry.2 More recently, however, the trenchant hostility towards realism has begun to wane. Dissatisfied with what they perceive to be the explanatory inadequacies of the alternatives, many philosophers now argue for a metaphysical basis for lawlike regularities that is independent of the conceptual frameworks within which they are situated – that is, for nomic realism. Representatives of this view can be divided, crudely but plausibly, into two camps. The division is nicely captured in the distinction drawn between the ‘School of Immanence’ and the ‘School of Imposition’ by Alfred North Whitehead, perhaps the first philosopher of the modern era to trace and classify the ways in which background metaphysical commitments – most notably with respect to objects, relations, and properties – account for the differences between competing schools of thought on the nature of lawhood. Whitehead begins his taxonomy by identifying an approach he labels the ‘School of Immanence,’ an approach that assigns the lawmaking role to the intrinsic properties of objects. Natural order is grounded in ‘the characters of real things which jointly compose the existences to be found in nature.’3 Translated into a more contemporary philosophical idiom, laws of nature are causal powers or dispositions, properties that dispose their bearers towards specific forms of causal interaction. Nomological possibility is fixed by the natures of the objects that contribute to any kind of law-governed behaviour: it is, we might say, the ‘bottom-up’ realist theory of lawmaking. On this model, laws of nature – to borrow 2 Paradoxically, there is an intriguing theological hinterland to this ostensibly naturalistic conception of lawhood. Several historical figures in the intellectual traditions of AbraKDPLF PRQRWKHLVP LQFOXGLQJ WKH $VKµDUƯWH RFFDVLRQDOLVWV HVSHFLDOO\ $O*KD]ƗOƯ  DQG Cartesian occasionalists (notably Malebranche and La Forge), advanced a similarly reductionist view that eliminated metaphysical constraints on God’s free and direct engagement with the created order. For a condensed account of this background, see Schmaltz 2013. The best historical treatment of the influence of Islamic occasionalism on European thought remains Perler & Rudolph 2000. For the influence of Malebranche on Hume’s (alleged) scepticism about ‘necessary connexions,’ see Nadler 1996. The compatibility between contemporary versions of Hume’s ‘regularity theory’ and a theistic metaphysical framework is explored in §1.4 below. 3 Whitehead 1933: 111.

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a judicious phrase from David Oderberg – are laws of natures.4 I shall refer throughout this book to this strand of nomic realism as the Powers Model.5 The School of Immanence is chiefly to be contrasted with the School of Imposition. The latter approach offers a ‘top-down’ theory that takes lawhood to be grounded not in the intrinsic features of things themselves, but rather in the connections between them.6 Since it is relations rather than properties that do the explanatory work, one corollary assumption of the Relations Model is that properties are only contingently tied to the forms of behaviour that law-statements describe. If lawmakers are relations between things rather than the properties of things, it follows that in one possible world a liquid might be acidic, while in another a liquid characterized by exactly same properties might be alkaline. The causal profile of the properties of the liquid is, as it were, a metaphysical blank to be filled in by the ways in which their extrinsic connections configure its nomic behaviour to be acidic or alkaline.7 Such a property is, to wield two technical terms, a quidditisic or categorical property. At one level, both strands of this realist renaissance signal a return to what has been the historically dominant commitment to the existence of objective forms of natural necessity. The ancestor of the Powers Model is Aristotle’s natural philosophy, which was fruitfully developed within the creationist metaphysical framework of Abrahamic monotheism.8 As this metaphysical picture came to be supplanted by the geometric and mechanistic ontologies of the sixteenth and seventeenth centuries,9 forerunners of the Relations Model began to emerge. The most influential of 4

Oderberg 2007: 144. The literature on causal powers – a designation that is often (though not always – see §1.2) taken to be equivalent to ‘dispositional properties’ – has grown considerably since the publication of Mellor 1974 and Harré & Madden 1975. Leading contributions to the debate on dispositions include: Mumford 1998; Molnar 2003; Bird 2007; Martin 2008; Heil 2012; and Vetter 2015. 6 Whitehead 1933: 112: ‘The doctrine of Imposed Law adopts the alternative metaphysical doctrines of External Relations between the existences which are the ultimate constituents of nature.’ 7 Ibid.: ‘The character of each of these ultimate things is thus conceived as its own private qualification. Such an existent is understandable in complete disconnection from any other such existent: the ultimate truth is that it requires nothing but itself in order to exist …’ 8 It is worth underlining that there are important differences between historical and contemporary versions of the Powers Model that should not be overlooked; but it remains the case that the two approaches share the same basic explanatory structure. For discussion of this point, see Clark 2015. 9 For a lucid overview of this crucial transition, see Lamont 2009 and Adams 2013. 5

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these was the natural philosophy of Descartes, which was later assumed to derive considerable support from the discoveries of the Newtonian revolution.10 However significant the shift in metaphysical outlooks inaugurate by the Cartesian and Newtonian revolutions, the elimination of powers or ‘occult qualities’ in favour of extrinsic geometric and mechanical relations did little to diminish the theological pedigree of the new framework. The ‘top-down’ approach to lawmaking was in fact to a large degree conceptually complicit with the voluntarist theologies that began to proliferate in late scholastic thought.11 Here the contrast with contemporary versions of the Relations Model could not be sharper: few contemporary philosophers consider the difference that theism’s theoretical resources might make to advancing a convincing realist case for lawmaking. This has led some historians and philosophers to note that the effect of naturalizing the Relations Model has led its contemporary supporters to commit to the existence of metaphysical puppet-strings that, in the absence of a divine puppet-master, mysteriously animate the natural world as brute causal principles. On this view, the Relations Model is an ersatz theological analysis of lawlike phenomena, the grafting of an ineliminably theistic Cartesian-Newtonian model of lawhood onto a naturalistic vine that had long been growing without it.12 Similarly, the resurgence of neo-Aristotelian accounts of lawhood in contemporary metaphysics has prompted remarkably few attempts to elaborate such an account within the theological terms that characterized the most sophisticated philosophies of nature to emerge in high-scholastic thought. Today, the overwhelming majority of realists would share the naturalistic 10 Osler 1985 sets out the theological roots of the concept of ‘laws of nature’ in Descartes’ thought as a solution to the problem of natural necessity. She notes (at 349) that ‘the doctrine of eternal truths and the epistemological and ontological status of the laws of nature … lie at the heart of his entire scientific enterprise.’ See also Henry 2004: 95-114, esp. 114: ‘Descartes was effectively responsible for single-handedly introducing the notion of laws of nature into natural philosophy.’ 11 For historical discussion of this complicity, see Foster 1934; Oakley 1961; and Osler 1994: 55-7. Harrison 2002 offers a dissenting view. 12 See, for instance, Whitehead 1933: 112: ‘Newton was certainly right … that the whole doctrine of Imposition [i.e. the Relations Model] is without interest apart from the correlative doctrine of a transcendant [sic] imposing Deity.’ Schaffer 2008: 95 notes that such realist attempts are ‘remnants of a dubious theology.’ The approach is also criticized by Swartz: 1985: 205: ‘Having abandoned God, the next best thing [for nomic realists] to do is to invoke a depersonalised necessity.’ More positively, Ott 2008: 249 remarks that ‘I do think the inability of those moderns who buy into the top-down position to detach their views from theology is indicative not of a weakness of mind but of just the opposite: if an intelligible notion of laws in this sense requires a divine agent, then so be it.’

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presumptions of their antirealist rivals regardless of their preference for the Powers Model or the Relations Model. One of this study’s central contentions is that the uneasy alignment between realism and naturalism has injected fresh energy into the ancient problem of universals. That universals should feature prominently in most contemporary realist theories of lawhood should hardly surprise us: they are obvious candidates to invoke for the purposes of securing the uniformity and systematicity of scientific laws. Yet preserving consistency with naturalism presses those seeking to combine realism about laws with realism about universals to posit ‘immanent’ or ‘Aristotelian’ universals – that is, entities that exist in space and time but that are nevertheless capable of being exemplified in multiple places at the same time, and that do not exist for as long as they are not exemplified. As we examine naturalistic versions of the two realist models, we shall see again and again that these features of construing universals in this way generate some intractable puzzles for realists. I shall argue that the cumulative effect of these worries is to generate an unpalatable choice for the naturalistic nomic realist between a cogent realist account of natural necessity and a commitment to his background ontology. Which of these two options should realists of this stripe be willing to abandon? The second part of this book invites the reader to persist with the quest for a viable realist theory with a contentious suggestion: relaxing an a priori commitment to metaphysical naturalism is a price worth paying for such a theory and our best hope of resolving the realist quest is to scrutinize the two most plausible alternatives to naturalism: platonism and theism. Since many philosophers regard any explanatory appeal to theism as scandalous or even unintelligible, Chapter 4 undertakes a critical analysis of platonic approaches to the problem of lawhood. It argues that in breaking with naturalistic orthodoxy the platonist can accommodate many of the explanatory inadequacies that undermine his naturalistic rivals. Platonic versions of the Powers Model and the Relations Model can explain the intuition that there might be laws that are never instantiated. They can explain what governed the emergence of the very first instances of nomic behaviour. They can also account for the vast mathematical ontology that scientific statements of law appear increasingly to presuppose. Theoretical achievements such as these are not insignificant. But the virtues of platonic nomic realism must be weighed against its vices. For once lawmaking is transferred to an abstract ontological domain, it begins to be very difficult to see how any metaphysical traffic is possible between concrete instances of natural regularities and the spaceless,

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timeless, and causally inert denizens of the platonic heaven that supporters of this account purport to be their ultimate ontological ground. Furthermore, the metatheoretical price to be paid for any platonic proposal is high, since it leaves the nomic realist with a revised ontology that not only strikes many as implausibly ad hoc, but also breaches important principles of qualitative and quantitative ontological parsimony by introducing a distinct ontological domain populated with vast numbers of abstract entities. It may by now be clear that it is the cumulative difficulties of formulating a case for nomic realism in either naturalistic or platonic terms that animate this book’s constructive case for a theistic solution, one that can deliver the explanatory goods that elude naturalistic accounts while avoiding the theoretical puzzles and ungainly ontology of platonic alternatives. Theistic solutions in philosophy tend to invite the objection that God is at least as mysterious than any problem he is introduced to explain. Many Humeans may view this move as a reductio ad theologiam on the part of realists: if locating lawmakers in the mental life and causal agency of God is the price to be paid for nomic realism, we would do better to abandon the realist quest altogether. Nonetheless, theists may be forgiven for thinking that such incredulity is more justifiably directed at those accounts that sever lawhood from its theological context from which the metaphor derived its intelligibility. The claim that lawhood is an irreducibly theological metaphor is neither novel nor radical: whatever else might be said for the small handful of attempts to retrieve and revise a theistic version of realism, they can hardly be dismissed as arbitrary explanatory enterprises. Few, after all, would defend the claim that monotheistic traditions introduce God as a legislator ex machina specifically to meet the challenges of explaining law-governed behaviour. Quite the reverse, in fact: many philosophers take the very idea of lawhood to be ineliminably theological. In much the same way as Elizabeth Anscombe once called for the abandonment of law-based conceptions of ethics on the basis that they could not discharge their theological freightage,13 similar disquiet has been expressed more recently in relation to law-based conceptions of physical reality.14 13

Anscombe 1958, esp. 4: ‘To have a law conception of ethics is to hold that what is needed for conformity with the virtues … is required by divine law … It is as if the notion “criminal” were to remain when criminal law and criminal courts had been abolished and forgotten.’ For a sophisticated recent attempt to transpose the three metaphysical conceptions of physical regularities into a theistic metaethical context, see Murphy 2011. 14 A.J. Ayer’s observations are broadly representative: ‘[O]ur present use of the expression “laws of nature” carries traces of the conception of Nature as subject to command …

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The animating assumption of this book is that these suspicions are well-grounded: metaphysical theism and nomic realism are indeed historically and conceptually conjoined philosophical positions. As the difficulties of combining naturalism and realism are thrown into increasingly sharper relief by the failure of recent attempts to do so, it is my hope that the task of reviving and revising this theological synthesis will not appear to be quite as contentious as it would once have been. Patristic and highscholastic metaphysics grounded natural order in the creative agency and mental life of a maximally rational and powerful divine being: God’s causal powers and intellective activity supplied a comprehensive and parsimonious explanatory account of the natural world. It is true enough, of course, that the rise of positivist and empiricist orthodoxies in twentiethcentury analytic philosophy pushed this view to the outermost margins of philosophical respectability; yet the striking renewal of confidence theistic solutions to philosophical problems in the last four decades has begun to drawn it back further towards the centre. For all that, it remains the case that remarkably few theologians or philosophers of religion have attempted a realist theory of lawmaking that draws on this tradition.15 Considerable attention has been devoted to the place of natural laws in discussions of teleological and cosmological arguments, but the question with which this book is chiefly concerned is neither the life-permitting content of lawlike phenomena nor their ultimate origination, but rather the question of what might motivate realists to ground the distinction between law-governed and accidental regularities in a theistic framework and what advantages might accrue to an explanatory scheme developed along these lines. Briefly put, the strategy at the heart of this scheme involves replacing the lawmaking universals commonly invoked by naturalists and platonists with divine ideas – that is, those ingredients in God’s mental life informing the creative decisions that provide the ultimate explanatory ground for the lawful regularities that order physical reality. However rebarbative this proposal might seem to secular philosophers, it is one that not only boasts a long historical pedigree in the intellectual traditions of Abrahamic monotheism but also offers a philosophically attractive alternative to standard realist appeals to lawmaking universals on which [T]he sovereign is thought to be so powerful that its dictates are bound to be obeyed … [T]he commands which are issued to Nature are delivered with such authority that it is impossible that she should disobey them’ (Ayer 1956: 146). 15 So far as I am aware, there have been only three theistic attempts to develop a realist theory of lawmaking: Ratzsch 1987; Swinburne 2004a: 30-5; 160-4 (see also Swinburne 2004b); and Foster 2004: 149-166.

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naturalistic and platonic realist theories invariably rely. Once universals have been substituted for appropriate items in God’s mental life (be these ‘concepts’ or ‘mental events’), items that structure the regularities that God’s causal powers ultimately originate and that scientific statements of law describe, a solution emerges to the puzzle of lawmaking that steers a careful and plausible course between naturalism and platonism. The most well-known attempts at formulating a strategy along the lines proposed in this book are historical ones. The most notable of these can be found scattered across the writings of Augustine,16 Aquinas,17 and Leibniz.18 Yet there has been enthusiasm for this approach among contemporary philosophers of religion for some time now.19 One generally overlooked attraction is that it promises to accommodate many of the intuitions that motivate realists and nominalists on the question of universals that are typically thought to be in conflict. On the theistic conceptualist alternative to universals, it is decisions in the mind of God, together with the creative actions that perfectly correspond to them, that provide the objective basis for the resemblances between particulars that immanent and platonic realists invoke universals to explain. This is achieved, moreover, in a way that avoids any metaphysically awkward commitment to multiply localized entities or to the existence of an abstract ontological domain. It will be clear from this map of the road ahead that every case for a theologically substantive realist theory of lawhood depends not only on the inadequacies of naturalistic and platonic theories, but also on the specific advantages of the constructive account it offers. It will need to explain how God’s agency as ‘primary’ cause does not overdetermine the ‘secondary’ causal behaviour of mundane objects in a way that makes it vulnerable to the difficulties that occasionalism presents. It will also need to show how universals can plausibly be substituted for mental 16 E.g. Augustine, de Libero Arbitrio II (a conceptualist argument for the existence of God from the atemporal character nature of propositional truth); and de Diversis Quaestionibus LXXXIII, 46. 17 The principal sources for the role of divine ideas in Aquinas’ thought are: In I Sent. 36; De Veritate q.3; Summa Theologiae Ia q.15. Comprehensive discussions of these and other relevant texts can be found in Wippel 1993; Boland 1996: 195-273; and Doolan 2008. 18 Leibniz’s theistic conceptualism is contained in Monadology §43-§46 (discussed by Rescher 1991 ad loc.). Cf. Rutherford 1995: 119: ‘As Leibniz sees it, the assertion of the reality of divine ideas is in fact the only way to uphold a nominalist ontology, while at the same time preserving an objective ground for possibility and truth.’ 19 Leading examples include Loux 1986 and Leftow 2006. For recent critical overviews of the issues to which divine conceptualism gives rise, see Welty 2006 and Craig 2016: 72-95.

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particulars without undermining the explanatory benefits of positing universals. And it will need to explain how any theory that places such primacy on the mental can account for patterns in physical reality without succumbing to a form of panpsychism. Before addressing these questions in the final part of the book, however, we must first examine how more metaphysically modest naturalistic theories attempt to offer convincing solutions to the puzzles of lawmaking.

CHAPTER 1 HUMEAN LAWLESSNESS AND NATURE’S KINDNESS

It would be foolish to undertake an exhaustive evaluation of the arguments for and against the view that there are objective forms of necessity in nature within the confines of a single study. Quite apart from the variety and complexity of the forms these arguments now take, the attempt would force us to delve deeply into a host of other contentious issues in contemporary metaphysics. The present inquiry will therefore confine itself almost exclusively to the two most plausible strategies in support of nomic realism discovered in the Introduction. If it should turn out that these fail, then clearly this result will attest indirectly to the strength of the case against realism. Nevertheless, the influence of nomic antirealism in the current analytic debate is so widespread that it would be equally foolish to leave it entirely to one side, and not only for the obvious reason that a philosophical case for a thesis is all the weaker for omitting to consider the case against it. It is also important not to ignore nomic antirealism altogether because, as we shall see, marshalling some of the objections to the neo-Humean analysis of laws will serve to sharpen the focus of this study on the underlying motivation for nomic realism, illuminating by contrast the substantive theoretical advantages that the latter confers. Scrutinizing nomic antirealism will also anticipate objections from non-theists to the effect that restricting the inquiry’s scope to nomic realism would load the dialectical dice in favour of their theistic opponents. The aims of this opening chapter are to set out the basic metaphysical starting points and motivating factors for rejecting realism, to uncover some of the theoretical failings of two historically influential varieties of antirealism, and to scrutinize the most promising and sophisticated antirealist analysis of regularities to date. It is organised as follows. §1.1 sets out nomic antirealism’s historic roots in Hume and the metaphysical vision of his contemporary champions, before explicating in more detail the categoricalist theory of property-identity that differentiates the two realist approaches discussed in the following chapters. §1.2 describes two positivist accounts of laws as ‘mere’ regularities, and briefly explains why these do not succeed. §1.3 outlines a theoretically powerful analysis of

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regularities that comes closest to securing the characteristics of laws, before arguing that, notwithstanding the internal coherence of this position, it remains a descriptivist account, and therefore fails to provide an account of laws as objective forms of natural necessity. §1.4 concludes the chapter by examining the rarely questioned assumption that nomic antirealism is fundamentally incompatible with theism. Here I suggest that, once situated within a theistic framework, the so-called ‘best-system’ analysis of antirealism discussed in §1.3 begins to appear more plausible, even if it proves ultimately incompatible with orthodox conceptions of divine agency.

1.1. The Empiricist Background It is an unfortunate feature of the current debate that nomic antirealism tends to reserve the rights to the label ‘empiricist.’ After all, every attempt to make sense of regularities does so with the aim of finding the most plausible philosophical account of the deliverances of sense-experience. It is true, of course, that nomic realists are willing to posit entities – universals, essences, kinds, and so on – that would not satisfy criteria for empirical verifiability advanced in the post-war heyday of logical empiricism. But these criteria are so stringent that they would exclude – if universally applied – vast stretches of the content of current scientific theories. It would be more appropriate, then, to characterize the basic position discussed in this chapter as a form of positivism. The aim of this section is to set out the radical implications of the positivist case for antirealist theories of lawmaking. 1.1.1. Hume’s Principle It is difficult to see the attractions of antirealist stances towards laws without grasping the metaphysical vision that underpins it. That vision has been elaborated with considerable sophistication in recent decades. Its basic structure, of course, reaches back to Hume, and in particular to his famous rejection of philosophical positions that introduce metaphysically substantive modal connections between ontologically discrete entities.1 Let us refer to this as Hume’s Principle. The principle can be described, simply but accurately, as a prohibition against connections in 1 Treatise of Human Nature I.3 §VI: ‘There is no object, which implies the existence of any other if we consider these objects in themselves.’

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virtue of which one object ‘implies’ another, on the basis that these connections are simply not available to sense-experience. Given its formative influence in analytic metaphysics, the contemporary motivation for adopting Hume’s Principle is not as clear as it might be.2 Its explicit target – then and now – is any thesis that posits causal connections between distinct entities. But it is easy to see that it also extends to denying that there are any nomic connections as well. All that a theory can justifiably include is what can directly be observed. This thesis animates Hume’s insistence that we are not warranted to infer anything about putatively causal relations between cause C and effect E other than that: C and E are spatiotemporally contiguous; C is temporally prior to E; and the conjunction of C and E can be subsumed under a larger generalisation or pattern of similar conjunctions. Needless to say, all three of these theses have been challenged, frequently by those sympathetic to Hume’s general outlook. And, of course, recent decades have witnessed a series of so-called ‘Hume Wars’ over whether to characterise his version of empiricism as a metaphysical, epistemological, or even projectivist thesis.3 For present purposes, however, these hermeneutical debates need not concern us. The crucial point to note is that however much they may disagree on the finer points, analytic metaphysicians who purport – rightly or wrongly – to take their cue from Hume do so by addressing a vast array of metaphysical topics in light of that single, simple rejection of modal connections in the mind-independent world. 1.1.2. The Neo-Humean Mosaic A strict application of Hume’s Principle leaves a remarkably barren metaphysical landscape in its wake. All that reality consists in, on this view, is a vast array of uncountably many ontologically disconnected entities. Few have expressed this vision more influentially than David Lewis:4 Humean supervenience is named in honor of the great denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another … [There are] perfectly natural intrinsic properties which need nothing bigger 2 See, for instance, the critical remarks in Wilson 2010, who notes (at 596) that ‘arguments for [the principle] are in short supply.’ For the difficulties of interpreting Hume on ‘distinctness,’ see Kail 2007: 133-6. 3 The main contributions to the debate are collected in Read & Richman 2000. 4 Lewis 1986a: ix.

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than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that.

The implications of this underlying ontology are considerable: the mosaic is all that there is at the fundamental level. Since everything else supervenes upon it, this includes the laws of nature. For once one grants the mosaic, it follows that laws could only turn out to be statements describing general and wholly contingent patterns in the collective behaviour of the ‘tiles’ that make up the mosaic. 1.1.3. The Role of Categoricalism We have already considered the distinction between categorical and dispositional properties in the Introduction. Categoricalism is, in effect, a central assumption of the neo-Humean landscape that Lewis describes. He specifies that these properties – that is, the mosaic-tiles – are ‘natural’ properties.5 Natural properties together exhaust the neo-Humean’s bedrock ontology. As we shall see throughout this study, the theoretical analysis of what it is to be a property – of those items that characterise and, on this view, exhaust reality – plays a crucial role in determining one’s position on regularities. If we take the stance of the Humean inheritance, Hume’s Principle requires us to treat properties as completely discrete ‘points’ that together make up the world. Now this does not in itself commit one to nomic antirealism, but nomic realists will need to find some another metaphysical ingredient to do the explanatory work. Indeed one striking feature of the realist theory examined in the next chapter is that it shares with neo-Humeanism the claim of property-identity. Properties, on this view, are completely self-contained, modally inert, intrinsic, and monadic. So analysed, properties cannot constrain reality in any way and, in particular, they cannot explain the source of whatever imposes regular patterns on the physical world (if, indeed, it is held that these patterns are imposed in the first place). A categorical property is a suchness or – to borrow the scholastic term – a quidditas. Quidditism or categoricalism has come in for much criticism of late,6 but it is difficult to see how to avoid it if one starts from Humean 5 By way of terminological clarification, in this context the term ‘properties’ is not intended to be ontologically commissive: most of those who endorse the approach I have been describing reject ‘properties’ in the sense this term is sometime used to mean universals. 6 See, for instance, Black 2000 and Hawthorne 2001.

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premises. Broadly speaking, the distinction between categorical and dispositional properties maps onto Locke’s distinction between primary and secondary ‘qualities.’ An increasing number of philosophers today would accept that some properties are categorical and others are dispositional. The question that concerns us in this study, however, is how best to construe fundamental properties – spin, charge, mass, and so on – since these are the ones that would feature most plausibly in laws. Those who take fundamental properties to be categorical are often referred to as ‘categorical monists’ (or, simply, ‘categoricalists’), while those who take them to be wholly dispositional ungrounded properties are usually referred to as ‘dispositional essentialists’ or ‘dispositional monists.’ But it is important to note that these positions represent two ends of a broad spectrum. It is perfectly possible – indeed relatively common – for metaphysicians to be committed to the view that both categorical and dispositional properties exist at the fundamental level.7 And, in recent years, some have even claimed that one and the same property can be treated in both categorical and dispositional terms, a position we will scrutinise more closely later on.8 But, to repeat, where one stands on this spectrum ultimately determines whether one is a supporter of nomic antirealism or the Relations Model (on the one hand) or a supporter of the Powers Model (on the other hand). There are several objections to categoricalism, but one especially vexing question for those who endorse it is that it raises the question of how it is possible to have epistemic access to properties whose nature is only contingently connected to their causal profile.9 It seems, in fact, that categoricalism may trigger a variation of Paul Benacerraf’s dilemma for mathematical realists.10 The dilemma begins with what Benacerraf terms a ‘reasonable’ epistemology, by which he means one that posits a causal connection between knowers and objects of knowledge. Notwithstanding the complexities that arise when it comes to establishing the nature and extent of the role of causality more generally, many would agree that our

7 E.g. Ellis 2001: 127: ‘We do not claim, as some philosophers have, that … fundamental dispositional properties are the ontological basis of all properties. On the contrary, we believe that there are equally fundamental categorical properties – for example, spatiotemporal relations and structures.’ 8 E.g. Heil 2003; Martin 2008; Jacobs 2011; Heil 2012; this view will be discussed in more detail in Chapter 3. 9 Lewis 2009. 10 Benacerraf 1973. The dilemma presents an important objection to platonic formulations of nomic realism, which will be examined more closely in Chapter 4.

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epistemic access to reality does involve some causal component.11 But in that case, it seems as if the only way we could gain epistemic or perceptual access to categorical properties must be via causal or nomic connections that are extrinsic to these properties. Yet since the link between these connections and the entities they connect is supposed to be contingent, what we know and what we perceive of properties will vary from world to world. In other words, categoricalism gives us little more than a recipe for scepticism about the nature of natural properties and, given the central role most would assign to properties of ‘constructing’ the world, for global scepticism about reality itself.

1.2. Two Deflationary Accounts Categorical properties collectively exhaust the neo-Humean ontology. It is therefore impossible for there to be ‘laws of nature’ in the prescriptive sense in which they are understood at the pre-theoretical level. All that laws amount to on the neo-Humean view are purely contingent arrangements of natural properties across the spacetime manifold; and these laws in turn ground counterfactual and causal facts. This basic stance triggers not only a wide range of profoundly counter-intuitive consequences for common-sense notions about the structure of physical reality,12 but also undermines assumptions widely perceived to be central to scientific practice. Most practising scientists, at any rate, would find it odd to be informed that it was their task to stipulate rather than discover what lawful regularities there are.13 The aim of this section is to show how the difficulties of finding a non-arbitrary basis for scientific theory to distinguish laws from regularities are thrown into sharp relief by two theories that, until relatively

11

A view persuasively advocated by Goldman 1967, on whom Benacerraf relies. In fact, reducing laws to ‘mere’ regularities as the Humean tradition proposes cuts so deeply against the grain of common-sense notions that nomic realists might be tempted to effect a Moorean shift against it. I am not aware of any attempt to do so in the literature, although Armstrong 1983: 53-4 does claim that inductive rationality is a Moorean fact; and, since he also insists that nomic realism is required to underwrite inductive rationality, it might be the case that nomic facts play a theoretical role akin to Moorean facts (on this point, see §2.2.1 below). See also Jacobs 2007: §2.3.1 for a good discussion of the methodological role of Moorean facts more generally. 13 I should note, however, that this claim is heavily contested by Giere 1999, who argues that laws are irrelevant to science as it is actually practised. Similar arguments are advanced by Cartwright 1983 and van Fraassen 1989. 12

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recently, commanded broad support within the tradition. Let us consider each of these in turn. 1.2.1. Naïve Regularity Theories A theory of laws that presupposes Hume’s Principle is, in the final analysis, committed to the view that each natural regularity is as contingent as every other. From this it follows that it is only possible to make epistemic modal distinctions between regularities. If strictly applied, Hume’s Principle only permits analyses of laws that cannot mark off lawful regularities from accidental ones in an objective sense. Thus the law-statement that water evaporates when heated amounts to nothing more than the claim that it is a contingent, universal generalisation that samples of water have evaporated when heated. Hume’s Principle prohibits positing any modal basis for linking together water, heat, and evaporation in a metaphysical explanation. So the truthmaker for this law-statement is just that every hitherto observed instance of water being heated is succeeded – other things being equal – by an instance of water evaporating. It is difficult to see how this kind of theory – often dubbed the naïve regularity theory of laws – can be characterised as a theory of laws, since it is, in effect, a statement of nomic antirealism, a brute elevation of any regularity whatever to the status of a law. One of this position’s most obvious shortcomings flows from this move, since it leaves the naïve regularity theorist with no apparent principle to distinguish laws from accidents. As we shall see in §1.3 below, there seems to be at least one possibility of making this distinction in a manner consistent with Hume’s Principle. But as far as this approach is concerned, it seems obvious that some ingredient is needed to distinguish the lawlike regularity that water evaporates when heated from the selfevidently accidental regularity that all the books on my lower book-shelf are paperbacks. Yet this ingredient is lacking on the naïve regularity theory. On this view, both statements exhibit exactly the same logical form: they are both true, universally quantified generalisations. Both count as regularities; and both count, therefore, as laws. In a recent exposition of naïve regularity theory, Stathis Psillos has suggested that although its supporters cannot invoke formal criteria to distinguish lawful from trivial regularities, it might still be possible for them to appeal to informal criteria. The idea here is that the first statement (‘water evaporates when heated’) can be distinguished as a lawful statement on the basis that it involves predicates that pick out a natural

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kind (water), whereas the second statement (‘all the books on my lower book-shelf are paperbacks’) does not; or perhaps the idea is that the former qualifies as a law because the scope of its application is unlimited (i.e. it applies to all water everywhere), whereas the latter does not because it is restricted (i.e. it does not apply to all bookshelves everywhere or all paperbacks everywhere). It is not at all clear, though, that these sophistications do a great deal to enhance the intelligibility of this approach. Indeed they represent a tacit admission of defeat. The modifications acknowledge that brute equivalences between laws and regularities are inadequate to play the role assigned to laws in scientific theories. In doing so, they give rise to a distinct deflationary approach, one that explicitly concedes that the only lawhood to which neo-Humeans can appeal is that which is conferred on certain regularities by our own attitudinal or cognitive practices. 1.2.2. Projectivist Regularity Theories One notable attempt to project lawhood onto certain regularities was undertaken by Nelson Goodman. He suggested that lawhood is a function of the extent to which certain predicates ‘entrench’ themselves in the wake of repeated past success. Predicates that become entrenched in this way becomes projectible predicates, which is to say that there is now a non-arbitrary – or, at least, less arbitrary – basis on which to characterise some law-statements as ‘lawful,’ namely the heuristic benefits they confer (relative to other statements of regularities) in predicting hitherto unobserved regularities. Projectibility, claimed Goodman, conferred the requisite degree of counterfactual stability on any law-statement that invoked suitably entrenched predicates. His crucial claim was that lawstatements are not employed for predicting future regularities because they state laws, but rather that they are treated as law-statements in the first place on the basis that they can be used for predictions.14 Put simply, the lawfulness of a statement is proportionate to the degree of its past predictive power. Goodman’s projectivist approach represents a clear advance on naïve regularity theories. For, as we have just seen, the neo-Humean can distinguish lawful regularities from accidental ones with a little more credibility than before: the former will include projectible predicates (specifically involving natural kinds) whereas the latter will not. Regularities 14

Goodman 1983: 21.

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in the behaviour of electric currents are summarised by Kirchoff’s Laws on the basis that those laws employ predicates that have been used in predictions with repeated success (i.e. confirmed by the observation of past instances).15 The trouble is that projectivism still does not overcome the fact that it remains an epistemic account of lawhood that depends entirely on the contingencies in the cognitive, attitudinal, or semantic practices of human beings. Projectibility is simply a feature of those generalisation that fulfil a particular role internal to our inductive practices. The degree to which predicates can be projected ultimately involves our psychological willingness to treat them as entrenched.16 So despite the ingenuity of Goodman’s proposal, it is ultimately unsuccessful. For it triggers a vicious explanatory circle in grounding the counterfactual stability of projectible predicates on prior assumptions about the counterfactual stability of certain regularities. Given the inherent subjectivism of the approach, it is no clearer how the projectivist variety of regularity theories can draw even the most intuitively obvious distinctions between law and accident. A generalised statement to the effect that there are no spheres of solid gold with a radius of more than a mile employs, after all, perfectly respectable, well-entrenched predicates: the use of the predicate ‘gold’ in this context makes it projectible on the basis of its confirmation by past instances. Such a statement should therefore qualify as a law on Goodman’s analysis; and yet we clearly do not want to endorse an analysis that treats a statement such as this as a law.17

1.3. The Best-System Analysis The explanatory difficulties of analysing laws in a manner consistent with the Humean vision was noted early on by John Stuart Mill. He proposed the innovative solution of treating the minimal set of propositions from which all natural uniformities could be inferred as laws.18 The basic idea is, once again, that law-statement are heuristic devices; but this approach differs from other versions of the regularity theory in more carefully circumscribing the basis on which a law-statement should 15 For Goodman, entrenchment is crucial for ruling out awkward or artificial predicates. 16 Psillos 2002: 142. 17 For a bold recent attempt to rehabilitate the projectivist view in the wake of criticisms of this sort, however, see Ward 2002. 18 Mill 1843: §3.4.1

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qualify as heuristic. In particular, Mill specified that only statements of regularity that made it possible to organise scientific knowledge as systematically and efficiently as possible could qualify as candidates for law-statements. This approach takes it for granted that the minimal propositions from which law-statements can be derived are purely epistemic features of the way we conceptualise sense-experience, and not features of the way the world is. Frank Ramsey introduced a little more nuance to Mill’s original insight by noting that, given Hume’s Principle, we are simply not in a position to know with any degree of confidence what hitherto unobserved regularities there might be. But since this is the case, we are unable to judge the propositions from which the totality of uniformities could be inferred. Given Hume’s empiricist constraints, observed regularities are the only regularities admissible into our systematic description. Ramsey noted that even if we possessed total knowledge of the entire natural history of the world, we would still want to integrate this knowledge into a single deductive system. It is the general axioms of this system, he claimed, that we should identify as the laws of nature.19 1.3.1. The Best-System Analysis In a series of influential papers, David Lewis elaborated Ramsey’s ingenious but fragmentary insights still further.20 That elaboration – typically referred to as the ‘best-system’ analysis of laws (hereafter, BSA) – now represents, together with various developments of it,21 the most widely accepted account of laws within the neo-Humean tradition. Lewis begins by noting that if neo-Humeans are to frame law-statements effectively, they need a language in which to do so. That language would require a set of primitive terms that could prevent trivial regularities from qualifying as laws. The candidates for those primitive terms should be what Lewis labels ‘perfectly natural’ properties. That is to say, the core vocabulary of the language of law-statements should only consist in predicates that apply to tiles of the neo-Humean mosaic – Lewis’ ‘local matters of particular fact.’ Lewis noted that BSA not only needed a language, but also a set of criteria with which to make the distinction between trivial and non-trivial 19 20 21

Ramsey 1928: §A. Lewis 1973: 73; Lewis 1983: 366-8; Lewis 1994: §3-§4. E.g. Loewer 1996; Cohen & Callender 2009.

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regularities more robust. The reason these criteria are needed, he saw, is that the number of regularities capable of being expressed using the appropriate kind of predicates would still be inconceivably large. For a proposition to be included in the system, he decided, it needed first of all to be true. It also needed to be maximally informative. As Mill had noted, the propositions that qualify as laws must make it possible to infer the maximum number of ‘nature’s uniformities.’ The difficulty here, as Ramsey saw, is that a system containing every maximally informative proposition would still vastly exceed anyone’s ability to comprehend it. So Lewis saw that the challenge for BSA was not just to express total scientific knowledge in a maximally informative way, but to do so in a way that was epistemically accessible. Once the system that achieves an optimal trade-off between informative strength and explanatory simplicity has been established, the fundamental axioms of that system would qualify as the laws of nature. If one is prepared to grant the Humean vision that motivates it,22 BSA delivers a coherent and powerful rationale for distinguishing ‘lawful’ from ‘accidental’ regularities. It can also account for different kinds of laws: derivative laws, for instance, are regularities that follow quickly from the best-system’s axioms, but do not themselves qualify for admission on the basis of the agreed criteria. Moreover, BSA captures the spirit of successful scientific theorising, which looks to formulate, in the most economical way, principles that have the broadest possible empirical application. And, of course, BSA shows how it is possible to construe regularities as laws on the basis of an admirably economical ontology of empirically available concrete particulars. For these and other reasons, BSA is generally agreed to be by some distance the most convincing deflationary analysis of the problem of laws. Those who are convinced by the merits of Hume’s Principle and accept the basic metaphysic that attends it are no longer likely to prefer the projectivist or naïve regularity theories.

22 Pace Lewis 1994: 480, I should stress that Hume’s Principle is logically independent of BSA. Realist analyses do also aim for optimal systematization – one can endorse BSA without Hume’s Principle. For instance, although he takes a staunchly antireductionist stance towards laws, Carroll 1994: 54-5 argues that where a proposition might qualify in an optimal deductive system, it is epistemologically relevant to assessing its lawfulness. But since we are examining it against the backdrop of a contingentist account, we can treat BSA as a Humean stance for the purposes of subsequent discussion. On this point, see also Cohen & Callender 2009: 3 n.1.

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1.3.2. Intuitive Costs Nevertheless, BSA faces a number of serious difficulties. These have been developed many times and in many different forms,23 and there have been many increasingly sophisticated responses and counter-responses since then.24 When debates in any discipline generate epicycles of this complexity, it is not usually a sign that we should expect an unambiguous resolution anytime soon. Still, the sheer ingenuity of BSA might tempt us into thinking that the axioms it characterises as laws do deliver at some level the objective distinction between law and accident that every theory of laws strives to achieve. We must concede, at least, that as an attempt to build an account of laws on such a modally barren metaphysical landscape that coheres to some degree with our pre-theoretical intuitions about laws, BSA is an undeniably impressive achievement. Nevertheless, I suggest that, for all that, it is a highly sophisticated illusion. For an optimally systematised description of natural history could no more explain why there are putatively lawful regularities than the description of a single regularity could. The indefinitely long shopping list of true, universally quantified contingent generalisations that BSA purports to axiomatise carries none of the prescriptive import associated with the notion of lawhood. All that BSA’s distilled description delivers in explanatory terms are psychological facts to do with how human beings happen to organise the content of their sense-experience in a way that is maximally conducive to their contingent cognitive capacities for theorising about the world. An optimised description might capture interesting and suggestive features of our epistemological negotiations with the world, but it would not and could not capture facts about its underlying ontological structure. 1.3.3. Whose System? Which Criteria? Let us suppose, however, that BSA can pick out ontologically fundamental regularities. We would still need to recognise that the foregoing complaints about BSA’s explanatory inadequacies assume that it is even possible to come up with an optimally systematised analysis in the first place. But what is the basis for accepting this assumption? For the standards of simplicity and strength to which BSA appeals may vary wildly 23 24

E.g. van Fraassen 1989: 41-55; Carroll 1994: 48-55; Mumford 2004: §3.5. E.g. Bird 2008; Cohen & Callender 2009; Schrenk 2014.

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across different scientific communities. Moreover, even if consensus could be reached with respect to these standards, establishing the correct trade-off between the two criteria would be almost impossible. This is because the theoretical balance that needs to be struck between informativeness and brevity will depend on the intuitions of the person making the judgment. Metaphysicians with empiricist leanings will be more likely to maximise the degree to which the system describes the world, whereas those with more rationalist inclinations may prize theoretical elegance and streamlining informative content in order to simplify the system. But suppose we assume not only that both canonical criteria of strength and simplicity and a non-arbitrary balance between them can be established. Advocates of BSA must still face up to the possibility – or even likelihood – that they would be forced to find a way of adjudicating between several best-systems. It may be that there are empirical theories that are simply incommensurable with respect to the balance they strike between explanatory power and theoretical simplicity. And it may be the case that tied systems are wholly or partly incompatible with one another.25 It is very difficult to see what independent grounds there might be for judging between rival systems, since simplicity and strength are optimality criteria that are determined relative to the system under consideration. They cannot be transferred across for the purposes of assessing a system that employs a complete distinct set of basic predicates and natural kinds. For example, the simplicity of a theory is partly a function of the language in which it is expressed. It is the predicates that are contingently selected as basic in a theory that will determine whether or not a statement is simple. Let us suppose that a theory took the notorious Goodmanian predicate ‘grue’ as basic. Relative to that theory, the generalisation would turn out to be less simple than the generalisation .26 By the same token, given that the strength of a theory is measured by how much information can be deduced from a system’s axioms, then it too is a criterion that depends on the resources of the language in which the theory in question is expressed.27 This strongly suggests that deductive strength is a system-relative criterion, and therefore that it would be useless for the purposes of 25 26 27

Kistler 2006: 172. Loewer 1996: 109. Cohen & Callender 2009: 6.

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adjudicating between competing best-systems. Things are even worse than this for BSA, because if both simplicity and strength are systemrelative, it follows that the correct balance between them will also be system-relative:28 Balance may seem transcendent, for a particular balance metric … need not mention any particular set of basic kinds … However, to actually obtain a balance score for any particular system, balance requires particular understandings of simplicity and strength and hence inherits the immanence of simplicity and strength.

The upshot is that BSA does not have the resources to generate intertheoretic commensurability criteria, and therefore no independent basis on which to compare the relative simplicity and strength of rival theories. We are forced to conclude that there is no way for BSA to accommodate the possibility of rival best-systems. 1.3.4. The Implications of Inductive Scepticism Still, let us grant for the sake of argument that it is possible to adjudicate correctly between rival best-systems. BSA must still explain how it is possible to arrive at so much as an approximately complete description of the world. For instance, given neo-Humeanism’s inductive scepticism, there is just no way of judging whether regularities currently judged to be candidates for axioms in a best-system are spatially and/or temporally localised regularities. It is perfectly possible – indeed plausible, given BSA’s background metaphysical assumptions – that putatively lawful regularities would not even feature in a complete omnitemporal description of physical reality. All that an optimally systematised description would achieve is a description of the extent to which human beings are capable of organising information about regularities that have occurred until now. The charge that BSA is an inherently relativistic exercise can be applied not only to the issues of criteria-selection and system-selection, but also to its tacit assumption that the nature of natural properties remains stable over time. And yet, once again, inductive scepticism destabilises any confidence in the idea that natural properties can be reliably determined in the first place. For once Hume’s Principle is accepted, one must deny that physical reality is constrained by any form of necessity and abandon the hope of establishing any objective basis on which to 28

Ibid.

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predict that future events will resemble past events. So for every natural property or kind that is identified as a tile in the mosaic, neo-Humeans must also concede that he cannot rule out the possibility that it is not a natural property or kind. To borrow Goodman’s example once more, he cannot consistently declare that the claim that ‘green’ is a natural property or predicate. For all that he is entitled to warrant, what is declared to be ‘green’ may just as well be ‘grue.’ BSA must assume, to the extent that it takes inductive scepticism as a methodological starting point, that natural history cannot be expected to continue to unfold as it has done until now. Even a being with knowledge of every past event in natural history would not be in a position to judge that the most extensive regularities among those observed were omnitemporal regularities. The second form that the relativism charge can take involves the issue of temporal asymmetry. Richard Swinburne has argued that it is incoherent to suppose that regularities could be condensed into a single omnitemporal description on the basis that this would imply present regularities could be determined by events that have not yet occurred:29 [S]ince whether some regularity constitutes a law depends, on [BSA], not merely on what has happened but on what will happen in the whole future history of the universe, it follows that whether A causes B now depends on that future history. Yet, how can what is yet to happen (in maybe two billion years’ time) make it the case that A now causes B, and thus explain why B happens? Whether A causes B is surely a matter of what happens now, and whether the world ends in two billion years’ time cannot make any difference to whether A now causes B.

Humeans may respond that Swinburne’s objection assumes an A-Theory of time, but that they follow (as many do) the B-Theory in rejecting objective distinctions between past, present, and future, treating all three as equally real. Nevertheless, to the extent that there is a direction of causation such that effects asymmetrically depend on their causes, the critic can still claim that it should not be up to vast future networks of effects that flow from the very causes under scrutiny. The upshot of these objections is straightforward. By assuming that it is possible to formulate anything approaching an optimal omnitemporal description of natural history, BSA is quietly drawing on metaphysical funds that its ontology cannot underwrite. All that Humeans can do when establishing the best system is to factor into it future regularities that they infer from psychological habit and/or scientific convention. But nothing 29

Swinburne 2004a: 31.

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can supply a warrant for this inference. In fact, it is far more probable, given a strict application of inductive scepticism, that the correct systematisation fails completely to resemble our current guesses. What BSA needs, then, is an account of why it is reasonable to expect a ‘total’ or ‘idealised’ science to feature any regularities that currently qualify as laws. It also needs to be able to provide an assurance that the criteria for establishing a best-system are grounded in objective features of reality – or, even better, an explanation of how purely contingent psychological criteria for theory-selection can be applied with such successful results to the omnitemporal set of regularities. By way of summary, advocates of BSA who begin with Hume’s Principle cannot introduce explanatory power into their analysis at a later stage. To adapt Schopenhauer’s objection to the cosmological argument, Hume’s Principle is not a cab one can dismiss before it reaches its final destination. Once one accepts it, one must also accept that there is no objective basis – beyond psychological habit or scientific convention – for supposing that constant conjunctions between entities in the past will continue to be constant in the future. Applying this to BSA, once one accepts Hume’s Principle there is no longer any objective basis for supposing that the complete description of natural history will resemble the one that science currently proposes. Hume’s Principle is tied indissolubly to inductive scepticism.

1.4. Optimality and Theism Detailed discussion of the different options available for making sense of regularities within a theistic framework will largely be confined to Chapter 5 and Chapter 6. But before we move on to consider the varieties of nomic realism, it is worth pausing to examine the widespread assumption that the deflationist views we have been assessing in this chapter are straightforwardly inconsistent with metaphysical theism. Although it is true, of course, that naturalism is the animating force behind the deflationist stance, the incompatibility thesis is, I suggest, a contestable one. For it is difficult to find anything in the theist’s fundamental metaphysical commitments – at least with respect to an ontology of physical reality30 – that 30 On this point, much depends on the degree to which theists resist occasionalist accounts of God’s causal contributions to reality. To the extent that occasionalism undermines libertarian and compatibilist doctrines of creaturely freewill, it is true that it is a difficult position to

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is strictly incompatible with the modal inertness of a neo-Humean ontology.31 The aim of the present section is to probe the claim and to suggest that BSA turns out to be much more convincing if certain theistic assumptions are granted. 1.4.1. General Considerations It is difficult to think of many theistic claims that could be reconciled to the austere ontology that neo-Humeanism presupposes. Most obviously, metaphysical theism could not accept that divine properties supervene on natural properties. Few theistic claims could meet any of the canonical criteria of logical tautology or empirical verifiability. But for all the plain incompatibility between theism and neo-Humeanism, it is worth noting that theism offends far fewer naturalistic scruples than one might think: God is not a spatial being, but many orthodox theists hold that he is temporal. Moreover, if causal inertia is the litmus test for abstractness, God is indisputably a concrete being. Finally, he is a particular if he exists at all – universals need not feature in the theist’s metaphysic, at least insofar as its account of God is concerned. Theism begins, then, with a far leaner ontology than one might suppose.32 There is another reason why a theistic transposition of BSA is worth considering. One striking dialectical feature of the way the case for BSA is articulated is that it often involves thought-experiments that invariably rely on invoking God – or, at least, an omnipotent being apprised of a complete knowledge of natural history – in order to elucidate the notions of totality and optimality needed to form discriminating judgments about reconcile to credal orthodoxy. But I cannot see that a theistic account of natural regularities requires one to take a view one way or the other on the question of creaturely freewill. Any theistic explanation will presuppose that God is free in the libertarian sense – indeed, as we shall see, it is a feature that confers an important theoretical advantage on the theistic account. But occasionalism does not deny that God is free in this sense. Occasionalism may undermine scientific realism, but nothing in the creeds or scriptures of the monotheistic traditions makes the rejection of that position anathema; indeed much of the perennial appeal of occasionalism is attributable to its consistency with the dominant conception of God as the supremely sovereign and self-sufficient creator and sustainer of everything distinct from Himself. 31 Quinn 1988: 55-61, for example, argues persuasively that an antirealist approach to causation and regularities is compatible with theistic commitment (provided occasionalism is acceptable). As Leftow 2012: 80 n. 24 notes, if nomic antirealism is correct, all the theist needs to claim is that ‘God settles what the regularities are to be in scripting His providential plan.’ 32 Chapter 5 and Chapter 6 will argue that for these and other reasons, theism is a better non-naturalistic explanatory option for the nomic realism than platonism.

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which regularities count as axiomatic. This is not, perhaps, especially surprising, since in effect BSA is attempting to arrive at a systematised description of the entire propositional content of everything that an omniscient and omnitemporal being could know about regularities in the physical world. It is not an exaggeration to claim that, from the perspective of BSA, the foundations of science are built on our current speculation of what such a being’s total apprehension of the entire natural history of the world might be. It is striking, in fact, how often expositions of BSA require thought-experiments involving God as a means of grasping its animating idea.33 If one distinguishes the basic idea of BSA from the regularity theory of laws with which it is most often associated, it is difficult to see why anyone with an antecedent commitment to theism – or, indeed, anyone undecided on the question of theism34 – would want to quarrel with the approach that it proposes. In fact, any theistic account of natural regularities is presumably committed to something like BSA as an ontological thesis. For once one grants the existence of maximally perfect being who is the sole ultimate causal origin of physical reality, then there may be good grounds to suppose that regularities observed hitherto are relatively close approximations of the principles of uniformity and systematicity with which God causally determines the nomological structure of the world. 1.4.2. A Theistic Transposition But let us turn to a more interesting question. Suppose for a moment that in addition to endorsing BSA as a basic idea, the theist sought to elaborate his position consistently with Hume’s Principle. As a historical matter, the metaphysical account of the natural world that underpinned occasionalism closely resembles the one that regularity theories presuppose. For, as we have already noted, occasionalism also denies that there are any genuine modal connections in nature.35 To frame this in terms of 33 E.g. Lewis 1973: 74; Beebee 2000: 574-5; Schrenk 2014. For a discussion of the theistic stamp of the thought-experiments that BSA invokes, see Schneider 2010. 34 Perhaps along the lines of an audience of ‘ideal agnostics’ invoked by van Inwagen 2006: 41-51. 35 The extent of Hume’s indebtedness to Malebranche is the subject of much debate, but there seems little doubt that the rejection of necessary connections is attributable at least in part to Malebranche’s influence. For helpful discussion of the historical context, see e.g. Nadler 1996 and Schmaltz 2013.

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the metaphor Lewis invokes, on the occasionalist view God places each tile of the mosaic and directly fixes whatever regularities there are in the mosaic. Theists who support an occasionalist conception of divine agency would therefore endorse Hume’s Principle, at least to the extent that it is a thesis about the physical world. But there is at least one central difference on a theistic version of BSA, namely that the theist does have a logically independent basis for applying the relevant optimality criteria. Since this is so, the theist claims that it will indeed be possible to organise the content of sense-experience in the way that BSA presumes is possible. It is important to stress once again that given standard empiricist constraints, non-theistic advocates of BSA have no basis whatsoever for supposing that future natural history will exhibit a single regularity that qualifies as a fundamental law in virtue of the fact that it features as an axiom in the best closed deductive systematisation of past natural history. Advocates of BSA tempted to speculate that past natural history is a reliable indicator of future natural history are, as I have already argued, guilty of forgetting the primary reason why it was necessary to formulate BSA in the first place. One recent defence of BSA implicitly notes this weakness:36 The extent to which we can axiomatise the particular matters of fact depend on how regular our world is. In nice deterministic worlds, we can in principle axiomatise to such an extent that we only need a list of initial conditions under the “facts” heading. At nasty, irregular worlds, only some very small proportion of the particular matters of fact might axiomatizable, so there won’t be very much under the “facts” heading.

The problem here is that there is just no way for the Humean to be confident in the judgment that the actual world is a ‘nice deterministic’ world. Indeed it would be vanishingly improbable, given inductive scepticism, that the regularities that have hitherto characterised the world would continue. To accommodate determinism in the actual world, the Humean is forced to posit some sort of mechanism that explains how the actual world is even putatively describable in the required way. 1.4.3. ‘Nature’s Kindness’ In the course of defending and updating BSA, Lewis dismisses many of the charges raised in §1.4 as begging questions in favour of the nomic realist view. But the central thrust of his counter-response does little to 36

Beebee 2000: 575.

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move the debate forward; it simply acknowledges what seems to be the trivially obvious truth that if one accepts the axioms that BSA characterises as laws, then one will also accept that they meet the explanatory objectives of laws:37 If you’re prepared to agree that theorems of the best system are rightly called laws, presumably you’ll also want to say that they underlie causal explanations; that they support counterfactuals; that they are not mere coincidences; that they and their consequences are in some good sense necessary; and that they may be confirmed by their instances. If not, not.

Now clearly this is unlikely to satisfy critics who reject BSA’s axioms as plausible candidates for laws precisely because they do not secure the theoretical goals that nomic realism sets for itself. A much more serious worry for BSA, claims Lewis, is a charge we have already noted, namely that any optimality criteria we select for judging between rival systems will be purely contingent. Simplicity, strength, and the correct balance between them are ultimately grounded in psychological factors. And this is, of course, a result that we would expect given the ineliminably Humean backdrop to this account: whatever modal facts there are supervene on the epistemic connections we make as a result of cognitive powers of association. But even if our habits are formally codified in a system of scientific conventions in a way that meets with indisputably widespread agreement, it seems to me that this is simply an elegant disguise for what remains at its core a contingent, psychologistic construal of regularities as laws. Neo-Humeans must concede the fact that given the ineliminably subjectivist cast of their proposal, it is possible that there would be rival best-systems from which to choose, and that some of these would be simply incommensurable. They would also need to concede, of course, that even if there was no dispute when it came to deciding BSA’s criteria and establishing the correct system, there is no reason to suppose that the proverbial community of extra-terrestrials would not decide on a systematic description of the same regularities that delivered radically different axioms from the ones that we had agreed upon. This latter consideration undercuts the kind of proposal to resolve possible tensions between comparably optimal systems that treats only the axioms that are common to the rival systems as laws.38 For there is no reason to expect any overlap at all between human best-systems and alien best-systems, or at least no reason to expect that overlap to yield axioms 37 38

Lewis 1994: 479. E.g. Beebee 2000: 575 n.7.

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ordinarily characterised as laws in our current scientific theories. Moreover, if laws are confined to those axioms upon which rival optimal systems converge, then we are likely to be left with very few fundamental laws indeed. Lewis advances an alternative solution:39 The real answer lies elsewhere: if nature is kind to us, the problem needn’t arise … Maybe some of the exchange rates between aspects of simplicity, etc., are a psychological matter, but not just anything goes. If nature is kind, the best system will be robustly best – so far ahead of its rivals that it will come out first under any standards of simplicity and strength and balance. We have no guarantee that nature is kind in this way, but no evidence that it isn’t. It’s a reasonable hope. Perhaps we presuppose it in our thinking about law.

The trouble with this counter-response is that it displays a remarkable degree of indifference towards Hume’s Principle and the inductive scepticism that attends it. For there is no non-psychological basis on which the neo-Humean is warranted to claim that nature is kind. Now Lewis partly concedes this (‘We have no guarantee that nature is kind in this way’); but he also states that it is reasonable for us to expect that there is one indisputably optimal way of systematising an omnitemporal description of the mosaic and its patterns. Why, though, should we expect this given the wholesale scepticism Hume’s Principle enforces? We cannot infer that future regularities will conform to past regularities, since we are forbidden from positing the kind of lawmaking modal connection that would ground that inference. Since this is so, the hope that a clear winner of the inter-system comparison will emerge when all the empirical data is in (i.e. when spacetime ceases to exist) seems hopelessly speculative. I have already suggested that if the issue of creaturely freedom is left to one side, nothing in credal orthodoxy requires theists to reject Hume’s Principle and to endorse nomic realism. After all, any theistic account of lawlike regularities will hold that they are sustained in an objective sense just because God ultimately settles which regularities obtain. If we follow the theistic transposition suggested in §1.4.1, God fixes the regularities in the behaviour of discrete properties across the spacetime manifold. That is to say, God is the causal origin of each mosaic-tile – each ‘local matter of particular fact’ – and this would explain what the non-theistic account cannot, namely the extremely improbable fact that the resulting mosaic depicts a pervasively intelligible and intricate picture of physical reality. 39

Lewis 1994: 479.

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This theistic picture might provide a basis for judging that there is a single optimal systematisation of the omnitemporal set of regularities. ‘Nature’s kindness’ is an abductive inference for nomic realists. That is to say, many nomic realists hold that the best explanation of the predictive success that certain regularities yield is that they are sustained by objective forms of natural necessity.40 But it is also illicitly introduced into Lewis’ antirealist analysis. Yet it is, of course, central to a theist’s metaphysic as well, and not for any reasons that involve providing an empirically adequate account of laws. In other words, the thesis that nature is potentially open to being systematised in an optimal way would not count as an ad hoc innovation in the theist’s approach to BSA. This contrasts sharply with the antirealist’s ‘reasonable hope’ that nature will turn out to be susceptible to systematisation. It is worth noting that theists do not need to subscribe here to Leibniz’s claim that the actual world is the best world. They can restrict themselves to the more modest contention that an omnibenevolent being would have reasons to create a world that exhibited stable, harmonious, and proportionate regularities. More importantly, the theistic hypothesis explains what the antirealist story cannot explain without it, namely how it is possible for cognitive beings to adopt what is, to all intents and purposes, a set of a priori principles – simplicity, strength, and the tradeoff between them – that are self-evidently contingent features of their psychology, and apply these with consistent and far-reaching success to establish spatiotemporally uniform lawful regularities. It is, at least, somewhat more probable on the theistic hypothesis that regularities can be systematised by cognitive beings in a law-yielding way. Theism explains the otherwise puzzling isomorphism that BSA takes for granted between (i) the a priori standards of theoretical elegance that we happen to apply as a species and (ii) the fact that nature can be described consistently with those standards in a heuristically powerful way. Since they posit a universe that is (omnitemporally) ordered, regular, and systematic, theists have rational grounds for treating the system that describes it more simply and powerfully than any other as the true system, from which it follows that the axioms it yields can be identified as laws in the objective sense. * * *

40

Foster 1983 offers a classic statement of this position.

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This chapter has evaluated the antirealist stance towards laws, concentrating on BSA as the most sophisticated version of that stance. We have seen that accounts of natural regularities consistent with the Humean vision described in §1.2 are profoundly counter-intuitive. It is true, of course, that counter-intuitive positions abound in philosophy and – increasingly – in the natural sciences as well; so this hardly amounts to an argument against deflationism. But we have seen that at various crucial points, the most convincing account to which nomic antirealists can appeal – that is, BSA – smuggles in some assumptions that appear flatly to contradict the neo-Humean’s theoretical framework. For there is no reason to expect nature to be ‘kind’ enough to us that there will be one self-evidently optimal system from which to derive the relevant axioms. On the neo-Humean vision, we have no reason whatever to expect that the fundamental axioms of the optimal systematization of regularities that have obtained to this point in natural history will feature anywhere in an omnitemporal optimal systematization of regularities throughout natural history. A subsidiary aim of this chapter has been to set out for the first time the BSA’s implications for theists who may be tempted by the metaphysical modesty of Hume’s Principle. I suggested that to the extent theists are motivated to endorse BSA on this basis, the resulting account would be indistinguishable from occasionalism. This may be an unwelcome result for credally orthodox theists. But, as unlikely as it may be that naturalists would switch their allegiance to it, occasionalism offers a much more convincing alternative to chance when it comes to combining Hume’s Principle with BSA. The crucial point, however, is this: the logical consistency of the occasionalist position destabilises the common platitude that all theists must reject regularity theories altogether. Finally, by throwing BSA’s theoretical vices into relief, this chapter has underscored three of the theoretical virtues to which realist alternatives must now aspire: explanatory power, inductive strength, and counterfactual resilience. The burden of the next two chapters is to scrutinize versions of nomic realism that purport to achieve these ambitions without breaching the constraints of metaphysical naturalism.

CHAPTER 2 LAWS AS RELATIONS: THE PRESSURE OF PLATONISM

A central component of the neo-Humean metaphysical vision examined in the previous chapter was categoricalist monism, the view that properties in themselves do not possess any intrinsic causal or nomic profile. Since categorical properties of this kind exhaust its ontology, nothing else animates neo-Humeanism’s barren modal landscape beyond psychological habit or scientific convention. One of the most striking features of the realist analysis we will be considering in the present chapter is that for all the powerful criticisms it raises against nomic antirealism, it shares exactly the same categoricalist stance towards property-identity. It follows that the version of nomic realism we are about to consider can no more treat properties as lawmakers in the robust, realist sense than the deflationary alternatives we have just examined. In order to attain its realist objectives, then, this species of the Relations Model is forced to look elsewhere for the source of lawmaking. As we shall see, the ingredient invoked to play the lawmaking role on this theory is relations between properties. Since both relations and properties are almost always characterised as universals on this view, it is usually labelled the ‘relations-between-universals’ account. In the Introduction, I defined this basic approach as the Relations Model; but this departure from standard terminological practice is warranted, I suggest, on the basis that it draws into much sharper focus what I take to be the central factor distinguishing the two basic approaches to nomic realism, namely that the one denies, while the other accepts, that natural properties are constituted by the causal contributions they make to reality. Nevertheless, I shall affix the acronym RBUIR to this version of the Relations Model on the basis that it characterizes laws as relations between universals and takes immanent realism to be the correct analysis of universals. Since the Relations Model assigns the lawmaking role to relations rather than properties, one question arises immediately: if properties are not suitable candidates for grounding laws, why think that relations are? We shall return to this central issue in due course, but it is possible to see at this early stage that the success of the Relations Model depends

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on a cogent analysis of the modal character of relations as lawmakers. And here, I suggest, we come up against what is perhaps the most intractable dilemma facing any realist analysis of laws. The dilemma is this: if the modal character of lawmaking relations consists neither in strict logical necessity nor in brute contingency, in what does it consist? The problem can be characterized more simply as the conflict between two plausible and powerful intuitions regarding the nature of natural laws. On the one hand, nomic realists wish to preserve the intuition that lawlike regularities have prescriptive force: the ball must drop from my hand when I release it in mid-air; the sugar must dissolve in this cup of hot tea as I stir it; electrons must attract protons; and so on. We can refer to this as the Governance Intuition. It is especially important for the Governance Intuition to be upheld if the nomic realist is to satisfy the three main explanatory desiderata to which every realist conception of laws should aspire, namely finding an objective basis with which to distinguish law-statements from accidental generalisations, underwriting inductive reasoning, and grounding counterfactual statements. On the other hand, the nomic realist must also accommodate the Contingency Intuition, the plausible thought that the nomological structure of the actual world might have been different. For it is easy to imagine a possible world in which the ball does not drop to the ground when released from my hand, or in which sugar never dissolves in a cup of tea, or in which electrons attract protons with an electrostatic force inversely proportional to the cube of the distance between them. The conflict between the Governance Intuition and the Contingency Intuition gives rise to what we can refer to as the Modal Hybridity Problem. This chapter sets out and evaluates David Armstrong’s formulation of the Relations Model, a version that attempts to preserve a balance between the Governance Intuition and the Contingency Intuition by grounding the modal character of laws in ‘non-logical’ or ‘quasi-causal’ relations of ‘necessitation’ between categorical properties. §2.1 sets out the broad metaphysical framework that supports Armstrong’s position, focusing in particular on his adoption of an immanent realist theory of universals, the impact of categoricalism on RBUIR, and the role played by his causal criterion of existence. §2.2 sets out some of the details of RBUIR, while §2.3 enumerates what I take to be the most potent objections against it. §2.4 outlines a number of other objections that arise as a result of certain classes of laws that one would expect to be explained on a realist analysis of laws but are not in fact explained by RBUIR.

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For all its undoubted attractions, it emerges that RBUIR occupies an unstable point midway between the antirealist accounts explored in Chapter 1 and the non-naturalistic realist accounts to be explored in the second half of this book. This inherent instability forces a dilemma on naturalistic supporters of RBUIR who wish to maintain, for a range of familiar and plausible reasons, that the referents of law-statements are mind-independent modal facts. For they must either pursue the Powers Model in Chapter 3 or abandon naturalism altogether in favour of nonnaturalistic options.

2.1. The Metaphysical Framework Despite the undoubted attractions of BSA’s metaphysical modesty, an increasing number of analytic philosophers have claimed that neoHumeanism is inadequate to the task of developing a convincing analysis of lawlike regularities. David Armstrong advanced one of the earliest and most extensive attacks against nomic antirealism.1 His criticisms provided the kind of motivation that nomic realism had previously lacked. The bare bones of his constructive case is that laws can be analysed in the robust, realist sense as logically contingent, dyadic necessitation relations between categorical properties. We will examine RBUIR more closely in §2.2 below. For present purposes, however, let us focus on some of the crucial assumptions that RBUIR makes. Perhaps its most distinctive commitments is the view that the central constitutive ingredients of laws – relations and properties – are universals. As we have already noted, since Armstrong begins with categoricalism, the inference to laws is an inference not to lawmaking properties (as the Powers Model will claim), but rather to lawmaking relations between properties. Michael Tooley2 and Fred Dretske,3 each of whom arrived independently at the Relations Model at around the same time,4 join Armstrong in arguing for the existence of prescriptive nomic facts

1

Armstrong 1983: chs. 2-5. Tooley 1977. 3 Dretske 1977. 4 Although each member of the triumvirate formulates the Relations Model in significantly different ways, Armstrong 1983: 85 claims that the sudden appearance of the three approaches is suggestive: ‘[The Relations Model] seems to be one of those not uncommon cases of an idea for which the time is ripe which is then hit upon independently by different people.’ 2

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or, to use Armstrong’s term, states-of-affairs, each of which is constituted by a necessitation relation and its relata. 2.1.1. Immanent Realism Realism about laws tends to be, as David Lewis noted, a ‘package-deal’ with realism about universals. This is primarily because universals provide the ‘generalising’ or ‘universalising’ metaphysical basis on which to secure many of the characteristics typically associated with laws.5 Realists about universals, it is claimed, have a firm basis for ascribing spatial and diachronic uniformity to regularities, and so avoid the difficulties that affect regularity theories. Traditionally conceived, universals are not subject to spatial or temporal restrictions. So given a plausible selection mechanism by which universals can be instantiated in their particulars, there should be no difficulty in grasping how universals might be instantiated at different times and in different places in a manner consistent with the axiom of multiple localisability.6 Prima facie, then, a theory of laws built around properties and relations construed as universals is in a position to satisfy the criteria of uniformity and universality more easily than one built around mere regularities. Let us look more carefully now at the details of RBUIR’s commitment to universals. It is, in brief, an ‘Aristotelian’ or immanent realist analysis. The position is easy enough to summarise: properties and relations are universals that exist only when instantiated in concrete particulars. Each instantiated universal is usually taken to be an atomic fact or state-ofaffairs. Immanent realism is immanent because the instantiated universal is deemed to be wholly present in every particular that exemplifies it. It is realist because it claims every property-instance exemplifies a universal. A notorious consequence of immanent realism is that it commits its supporters to the counterintuitive principle of ‘multiple localisability’: this white cup wholly instantiates whiteness, but so too does this white saucer. If that is the case, the same metaphysical entity exists in two 5 As Lewis 1983: 368 notes, integrating these two is a crucial explanatory ambition of BSA as well: ‘[M]y account explains, as Armstrong’s does in its very different way, why the scientific investigation of laws and of natural properties is a package deal; why physicists posit natural properties such as the quark colours in order to posit the laws in which those properties figure, so that laws and natural properties get discovered together.’ Armstrong 1983: 85 is equally clear that the connection arises from ‘[t]he utterly natural idea that the laws of nature link properties with properties.’ 6 Armstrong 1983: 82 holds that universals are either monadic ‘one-place’ entities (properties) or n-adic ‘n-place’ entities (relations).

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spatially discrete entities – i.e. cup and saucer – at the same time. Now abandoning the axiom of localisation – that is, the principle that one and the same identity cannot exist in more than one place at the same time – has traditionally been taken as one of the most powerful reasons to reject immanent realism.7 But by far the most intractable difficulty that immanent realism raises for RBUIR lies elsewhere. 2.1.2. The Instantiation Principle For a number of philosophers, immanent realism offers a persuasive and moderate route through the ‘Straits of Messina’ between nominalism and platonic realism. Among those who do take a realist stance towards universals, at least, immanent realism is usually preferred to the platonic alternative. The crucial ingredient that permits naturalists to endorse it restricts the class of universals to instantiated universals.8 For every property there exists – if not at every temporal point – a particular that instantiates it. In other words, every universal must have a spatiotemporal location – no uninstantiated universals exist.9 And, applied to relations, the principle holds that every relation is a relation between terms.10 Call this the Instantiation Principle. The Instantiation Principle is standard fare for the majority11 of those who ground regularities in powers construed as universals.12 We have already noted that the ostensible motivation for developing RBUIR is the parlous state of regularity theories.13 Still, the methodological exclusion of non-spatiotemporal entities is a stance that RBUIR shares, of course, with neo-Humeanism. It is also the one that most seriously 7 To the extent that a realist theory of laws relies on it, immanent realism also seems to imply that observing instances of laws amounts to observing the laws themselves. 8 The requirement can be assumed to apply to relations as well. 9 Notwithstanding the apparent stringency of this requirement, as an eternalist or B-Theorist, Armstrong 1983: 82 claims he is entitled to qualify the Instantiation Principle by validating the existing of universals that are instantiated for any duration of time (i.e. at any temporal location in natural history). 10 David Armstrong, A Theory of Universals: Volume 2: Universals and Scientific Realism (Cambridge: Cambridge University Press 1980), p. 75. 11 Gibb 2015 has argued, however, that the majority may be wrong for thinking that realists about universals have obvious theoretical advantages over trope-theorists. 12 Realist accounts of regularities that reject realism about universals altogether take the Instantiation Principle for granted, as in the trope-theoretic strategies of Molnar, Martin, and Heil. 13 Armstrong 1983: 9: ‘[T]he criticisms … lead us toward a more satisfactory account of laws of nature, if only by showing us what a good theory of laws ought to do.’

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undermines it. Armstrong is clear that his insistence on the Instantiation Principle is based on an ideological commitment to metaphysical naturalism:14 A major reason for accepting the Principle of Instantiation is my desire to uphold, along with Realism about universals, the logically independent doctrine of Naturalism. Naturalism I define as the view that nothing exists except the single, spatiotemporal, world, the world studied by physics, chemistry, cosmology and so on.

By insisting on the Instantiation Principle, Armstrong locates universals firmly in the spatiotemporal domain as ‘repeatable features of that world.’15 2.1.3. Categoricalism Once More In §1.1.3, we saw that the empiricist outlook motivating nomic antirealism takes the nature of properties – that is, the ways things are ‘characterised’ in the world – to be wholly distinct from their causal or nomic profile. Properties have a suchness or ‘quidditas’ in the same way that some treat each substance as having a primitive ontology or ‘haecceitas.’ Nevertheless, positing metaphysically substantive relations between categorical properties does appear to offend Hume’s Principle even if it shares neoHumeanism’s categoricalist stance. But even if we are willing to follow Armstrong in positing lawmaking relations on an abductive basis (to be analysed in §2.2.1 below), the question still remains of how best to analyse the nature of these relations. RBUIR’s solution to this problem is, in effect, to claim that the necessitation relations are explanatory primitives. But this is hardly the perspicuous answer that nomic realists are looking for. Even if we are to accept it, we can still challenge the coherence of the claim that relations make a nomic difference to the world given that these too would have (so to speak) modally blank natures. There must be a contingent link between categorical relations and some other ingredient to ensure that the 14 Armstrong 1983: 82. Compare his principal motivation for a combinatorial theory of possibility in Armstrong 1989: 3: ‘The main constraint I wish to place on [this account of possibility] is that it be compatible with Naturalism. The term “Naturalism” is often used rather vaguely, but I shall understand by it the doctrine that nothing at all exists except the single world of space and time. So my objective is to give an account of possibility which is in no way other-worldly.’ 15 One corollary benefit of applying the Instantiation Principle to universals is that it ensures that all universals can in principle be ascertained a posteriori. Platonic realism, by contrast, cannot claim any direct epistemic or perceptual access to uninstantiated universals. We shall return to this issue later in Chapter 4.

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categorical relations constrain properties in the relevant lawmaking ways. Yet to claim that the necessitation relation is itself categorical would be to concede that it lacks a unique nomic profile. This implies that RBUIR’s theory of property-identity is simply not adequate to the task of explaining how a categorical relation could entail the relevant regularity. Schneider frames the worry as follows:16 Armstrong has claimed that necessitation is a relation with a unique inner nature that confers nomic necessity on the laws. If universals lack a unique inner nature then how can it be claimed that there is something special about the necessitation relation such that, when it obtains, a law has been instanced? … For one thing, [this] conflicts with his work on laws. For another, it renders mysterious the way in which universals determine resemblances and confer causal powers on the objects that have them.

This seems to be a persuasive criticism: Armstrong’s categoricalism does appear to extend to the necessitation relation, in which case RBUIR’s lawmakers are no less quidditistic than the properties it relates. A key mark of RBUIR’s success is the extent to which it can give an account of the lawmaking relation that is transparent enough to anticipate this objection without compromising its categoricalist commitments. The inability to handle this worry would provide a clear motivation for preferring the Powers Model, because – once again – if relations can exert causal power over particulars, why is it the case that properties cannot do so as well? For unless there are principled reasons why properties cannot play the causal role RBUIR assigns to relations, ontological and ideological economy considerations would urge us not to invoke anything in addition to properties to meet nomic realism’s objectives. 2.1.4. The Eleatic Principle Spatiotemporal instantiation is one of the criteria that Armstrong requires as a background assumption to his version of RBUIR. But the Instantiation Principle is connected to another doctrine favoured by naturalists, namely the ‘Eleatic Principle’ or – as it is also sometimes referred to – ‘Alexander’s Dictum.’ The idea first arises in the following remark made by the ‘Stranger from Elea’ in Plato’s Sophist:17 I suggest that everything which possesses any power of any kind, either to produce a change in anything of any nature or to be affected even in the 16 17

Schneider 2002: 590. Plato, Sophist 247 d-e.

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least degree by the slightest cause, though it be only on one occasion, has real existence. For I set up as a definition which defines being, that it is nothing else but power.

The basic claim is that every entity must make (or be capable of making) a causal difference to the world.18 Armstrong gives his reasoning as follows:19 [The Eleatic Principle] involves rejecting transcendent universals, realms of number, transcendent values, timeless propositions, non-existent objects … possibilia, possible worlds, and ‘abstract’ classes … A general argument is given against postulating any of these entities. They all lack causal power: they do not act. It is then argued that we have no good reason to postulate anything that has no effect on the spatio-temporal world.

Graham Oddie neatly captures the idea behind the criterion as requiring ‘[r]espectable entities [to] work for their living,’ adding that ‘there is no social security in Armstrong’s universe.’20 As we shall see in §2.4.1, the Eleatic Principle threatens to destabilise RBUIR very seriously when it comes to accounting for non-causal laws.

2.2. Exposition of RBUIR With these metaphysical assumptions in play, Armstrong’s theory of laws falls into place relatively quickly. We earlier summarised RBUIR as the claim that laws of nature consist in logically contingent dyadic causal necessitation relations between categorical properties. Thus, the law that all exemplifications of F are exemplifications of G consists in the nomic fact that , which is a law expressing the fact that all instantiations of universal F (i.e. all Fa … Fn) are instantiations of universal G (i.e. Ga … Gn) by means of a necessitation relation that ties F to G. So construed, RBUIR’s lawmaker is the truthmaker for subjunctive conditional statements such as . Crucially, the theory holds that necessitation relation obtaining between F-ness and G-ness is logically contingent.

18 19 20

For criticisms of the Eleatic Principle, see Oddie 1982 and Colyvan 1998. Armstrong 1978: 5. Oddie 1982: 285-6.

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2.2.1. Two Non-Inductive Inferences As Armstrong sees it, the basic argument for nomic realism is that the weaknesses of nomic antirealism are sufficiently serious to motivate nomic realism abductively – i.e. to make positing laws in the realist sense an inference to the best explanation for why an extensive regularity obtains:21 It will involve arguing that classical or extrapolative induction [from regularities to laws] is simply a particular case of abduction, where the abductive argument proceeds by arguing to a common principle (as opposed to a cause) behind the phenomena … [T]he argument goes from the observed constant conjunction of characteristics to the existence of a strong law, and thence to a testable prediction that the conjunction will extend to all cases.

So Armstrong’s principal strategy for positing laws takes the form of an inference to objective forms of natural necessity as the best explanation of the predictive success of law-statements that feature these forms in their content. As he puts it:22 The postulations of a connection between universals can provide an explanation of an observed regularity in a way that postulating an explanation of an observed regularity in a way that postulating a Humean uniformity cannot. The inference to a connection of universals is a case of an inference to the best explanation. A series of states of affairs is observed, each a case of an F being a G. No Fs which are not Gs are observed. The postulation of a single state of affairs, the law N(F,G), gives a unified account of what is otherwise a mere series … it deductively yields a prediction which enables it to be tested, the prediction that all other Fs will be Gs. It is therefore a good explanation of the phenomena. With luck, it is the best.

It is worth noting in passing that optimality plays just as central a methodological role in making the case for RBUIR as we saw it did with respect to BSA in §1.3. The basic approach, then, is this: empirical inquiry uncovers a range of regularities in the physical world; the best explanation for why some of these regularities are so extensive is that they are constrained to be that way in virtue of objective forms of natural necessity constituted by universals – that is, in virtue of the laws of nature. Let us try to illustrate Armstrong’s approach. In the eighteenth century, regularities began to be observed in the relationship between the mass of a fluid flowing through a pipe (on the one hand) and the potential energy, pressure energy, and kinetic energy of the fluid (on the other). Repeated 21 22

Armstrong 1991: 507. Armstrong 1983: 104.

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tests uncovered a fixed, proportionate relationship between these variables, a relationship that came to be accurately expressed in Bernoulli’s Theorem, which states that the mass of a non-conducting fluid in inviscid flow is equal to the sum of the three forms of energy it contains. The abductive approach to nomic realism proposes that we posit a law as the best explanation for the empirical regularity. Bernoulli’s Theorem not only describes the relationship between the relevant variables; it also captures an objective feature of the inviscid flow of a non-conducting fluid that ensures this regularity obtains. On the abductive approach, positing an underlying source of natural necessity in this way is taken to be a rational inference. But the crucial point to note is that this inference is not an inductive inference. For Armstrong, it is something akin to a Moorean fact: ‘If making such an inference is not rational,’ he asks, ‘what is?’23 Subsequent to the first inferential step, Armstrong proposes a second one from the (already inferred) existence of forms of natural necessity to the predictive power these confer, an inferential step open to empirical verification. This second inference concludes that the existence of objective forms of natural necessity entails the occurrence of future regularities of the same type as the past regularities from which these forms were first inferred.24 To return to our illustration, the justification for this second step consists in the fact that Bernoulli’s Theorem is confirmed every time the measurement of the relevant variables satisfies the mathematical connections that it expresses. Although we will scrutinise his approach in more detail in §5.2, it is worth noting briefly that John Foster deploys a similar abductive strategy to Armstrong at this juncture, though it is one that Foster himself presses in the direction of a theistic account of regularities. Like Armstrong, he suggests that the problem of induction can be solved by positing laws by means of a two-step extrapolative analysis. He takes pains to stress that since both of these steps is only extrapolative, neither should offend the inductive sceptic. From the phenomenon of regularities, it is inferred that there are entities that play an objective, lawmaking role. Foster’s second step, like Armstrong’s, consists in a second inference from the existence 23 Armstrong 1983: 53. A Moorean fact is, in the words of Lewis 1996: 549, ‘one of those things that we know better than we know the premises of any philosophical argument to the contrary.’ 24 Once RBUIR’s justificatory strategy is framed in this way, one might be tempted to suppose that it relies on circular reasoning: laws are inferred from observing putatively lawful regularities, while regularities are judged to be lawful on the basis of inferring from them that there are laws. I will not pursue this objection here, but for criticisms along these lines see Beebee 2011: §3.

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of objective lawmakers to testable predictions. He characterises this subsequent move as deductive on the basis that it is a matter of logic that if it is necessary that bodies behave gravitationally, then they always do.25 Thus Foster claims to have found a way to an extrapolative conclusion through two non-extrapolative steps – the first abductive, the second deductive. And this successfully addresses, he claims, the problem of induction, since it employs inferential methods that inductive sceptics can accept. If this basic approach does offer a successful way of positing laws in the realist sense without offending the inductive sceptic, then an empirically respectable alternative to nomic antirealism emerges that does not suffer from the latter’s explanatory inadequacies. As it stands, though, the abductive strategy only permits Armstrong and Foster to justify the existence of predictively powerful laws as the best explanation of the empirical data. What still needs to be examined, of course, is whether they can buttress this two-step method with a coherent metaphysical analysis of these laws. And, as we have already noted, the coherence of RBUIR depends almost entirely on how we are to analyse the necessitation relations that Armstrong claims we are now justified in positing.26 2.2.2. The Lawmaking Relation It is a paradoxical feature of RBUIR that although its lawmakers are logically contingent (that is, although the lawmaking relation between universals F and G might just as well have connected universals F and H), they are the sole source of the necessity in virtue of which particulars are constrained to interact causally in regular ways. One might be tempted to share Armstrong’s view that the apparent paradox is actually clarificatory. He suggests that the combination of logical contingency and quasi-causal necessity provides a solution to the Modal Hybridity Problem. On the one hand, RBUIR’s claim that it is contingent which properties are related in lawmaking ways satisfies the Contingency Intuition; on the other hand, given that properties are related in this way, it is not contingent that particulars exemplifying these properties behave in the regular ways that they do, which satisfies the Governance Intuition.

25

Foster 2004: 58. We shall see in §5.2 that Foster himself explicitly rejects Armstrong’s constructive approach in favour of a theistic version of the Dispositionalist Account. 26

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Nevertheless, for this solution to succeed an explanation is owed of how the necessitation relation between universals actually brings about the regularities it purportedly governs at the first-order level. To meet this challenge, Armstrong attempts to characterise the necessitation relation as a causal relation (though as a causal relation of a very specific kind).27 Here he draws on a controversial distinction between ‘singular’ and ‘general’ causation.28 Those who support the basic intelligibility of singular causation – so-called causal singularists – follow Anscombe in rejecting the idea (which she traces back to Hume) that every cause is an instance of an exceptionless generalisation. In other words, causal singularists reject the idea that causes are necessarily subsumable under wider nomological principles (i.e. laws, however these may be construed). As Anscombe argued, it is perfectly possible to experience two events as standing in a causal sequence without being in a position to identify the law under which the sequence is subsumable. That we cannot do so, however, should not worry us, since causation is something we can directly perceive and therefore not something for which any deeper philosophical analysis is required. Donald Davidson’s response was to introduce the notion of covering laws.29 Davidson’s claim was that although one might not be able to identify which specific laws govern any particular causal sequence, it is still possible to identify that some law ‘covers’ it. But Davidson’s response to the problem seems suspiciously ad hoc, since there are no obvious grounds for thinking that a singular causal sequence is subsumable under a set of covering laws if we are not already in a position to construe these as universal laws. It is logically possible, at least, that singular causal sequences are not governed by any laws at all (covering or otherwise); so it is also logically possible to suppose that a particular cause results in a particular effect simply by virtue of being that particular cause.30 Despite expressing some unease over causal singularism, Armstrong does deploys it as an analogy for explaining the modal character of RBUIR’s necessitation relation by claiming that the mere logical possibility of singular causation buttresses the logical possibility of singular necessitation between properties (he claims, indeed, that the former is simply an instance of the latter). If this link is granted, he argues, it is perfectly permissible to transpose purely singular necessitation from the 27 28 29 30

The causal account is set out in Armstrong 1983: 93-6. The locus classicus for this is Anscombe 1971. Davidson 1970. Anscombe 1971.

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context of particulars to the context of universals, and thereby to make sense of how one universal could necessitate another universal simply in virtue of being that universal. As we have already seen, one of RBUIR’s central theoretical virtues is the seriousness with which it takes the Modal Hybridity Problem.31 Yet the modal character of its lawmaking relations remains a puzzle. Subsequent to his original formulation of RBUIR, Armstrong did attempt to clarify his analysis by suggesting that the lawmaking relations should be construed as being similar to causal relations. ‘When like causes like,’ he claimed, ‘at the level of universals a state of affairs of type F brings about a further state of affairs of the very same type.’32 If that is correct, then it would turn out that RBUIR’s laws ultimately consist in quasi-causal necessitation relations.33 With this last theoretical piece in place, Armstrong takes the central objective of his theory to have been met: the existence of laws can be rationally inferred from hitherto uniform regularities, laws that possess the requisite degree of modal strength sufficient to sustain objective distinctions between accidental and non-accidental regularities, to supply truthmakers for subjunctive conditional statements, and to underwrite inductive reasoning.

2.3. Objections to RBUIR Armstrong’s formulation of RBUIR stands as an indisputably impressive achievement and one whose influence continues to be felt in the proliferating analytic debates on the metaphysics of lawhood that it did much to inspire. His account presupposes, as we saw in §2.1, a constellation of 31 Armstrong 1983: 78. This is an intuition that, as we have seen, BSA is forced to explain in psychologistic terms. To the extent that BSA relies on discrete natural properties alone, it cannot posit laws in the prescriptive sense that would satisfy the Governance Intuition. Such events would be treated as some of the discrete pieces that make up the neo-Humean mosaic. Thus the attribute-nominalist is ‘nailed to Hume’s cross’ with respect to laws as well. It is worth noting that Armstrong denies that resemblance nominalism is any better placed to account for identity between instantiations as a function of a network of resemblance-relations between particulars. For, strictly speaking, there is nothing that members of a class of particulars share in common (for if there were it would fail to qualify as nominalism). A member of a class might resemble other members, but its resemblancerelations to other members will always differ from every other member’s resemblancerelations to other members; according to Armstrong, this problem of ‘shifting ground’ cannot deliver the requisite degree of uniformity (cf. Armstrong 1983: 81). 32 Armstrong 1997: 230. 33 It is worth noting that Armstrong takes the necessitation relation itself to be a universal.

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closely connected metaphysical commitments – notably the Instantiation Principle and the Eleatic Principle – that should warm the heart of metaphysical naturalists. Unfortunately, however, there are a number of difficulties with his version of the Relations Model that make it difficult to accept. I now want to argue, in fact, that the Instantiation Principle is the source of many of them. If those concerns are justified, that would imply that within the dialectic of the larger debate supporters of RBUIR who reject nomic antirealism would either be left with a naturalistic version of the Powers Model or else be forced to accept one of the non-naturalistic strategies considered in the second half of this book. 2.3.1. Regress Objections It has long been recognized that the intelligibility of the necessitation relation represents the most notorious difficulty for RBUIR. It is extremely difficult to establish a coherent account of the mechanism by which universals are instantiated identically among different particulars. One obvious problem is that RBUIR’s lawmaking relations open up an infinite explanatory regress. As we saw, it is a logically contingent matter that these relations obtain. The problem is that once one grants that they do arise contingently, it is very difficult to account for relations that obtain between the relations-between-universals and the regularities among first-order particulars to which they purportedly correspond. Armstrong himself takes this first-order relation as simply another necessitation relation (i.e. one that shares the same modal value as the initial second-order relation between universals). But this invites an obvious question: on what is the necessitation relation itself dependent? There does not seem to be any satisfactory way to insulate RBUIR against an infinite and vicious regress of contingent necessitation relations.34 The regress objection grows even sharper when we ask how RBUIR’s lawmakers satisfy Armstrong’s causal criterion of existence (i.e. the Eleatic Principle discussed in §2.1.4). Necessitation relations are second-order universals. If they are to comply with the Eleatic Principle, these relations must make some causal contribution if they are to earn their ontological keep. But what could this causal relation be? If there is a causal relation, then this must consist in a third-order relation connecting the secondorder lawmaking relations, which in turn would require a fourth-order 34 Bird 2005 argues that the contingent character of RBUIR’s lawmakers generates precisely this concern.

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relation to connect it causally to another third-order relation, and so on through an infinite series of higher-order universals. Armstrong does not, unfortunately, address this objection in a satisfactory way, since he simply reiterates that the second-order lawmaking relations are brute, explanatory primitives. As far as he is concerned, there is no deeper explanation for why they possess the modal character they do. 2.3.2. Van Fraassen’s Fork This sort of response only serves to heighten the suspicion that the metaphysical link between lawmaking universals and particulars is ad hoc.35 The problem, in brief, is this: what do regularities in causal interactions between particulars have to do with patterns among relations between universals? Conversely, how could relations between universals entail causal behaviour at the level of first-order particulars? Van Fraassen holds that the two problems are structurally complicit, so that solving one of them immediately triggers the other:36 If laws of nature are identified in terms of some sort of necessity in nature which is simply postulated as fact, then there is no logical reason to think that the inference from lawlike necessity to actuality is valid. (Calling the postulated factor “necessity” or “necessitation” does not help.) If on the other hand the semantic account of law statements is so constructed that the inference in question is logically valid, then typically the truth-conditions of law statements involve something unidentifiable.

Let us refer to this dilemma as Van Fraassen’s Fork. Van Fraassen labels the first difficulty the Inference Problem: if it is a law that all Fs are Gs, on what basis are we to infer that this instance F must necessarily be an instance of G? If a satisfactory solution to the Inference Problem is found, van Fraassen argues that RBUIR must confront the Identification Problem: how can RBUIR identify lawmaking relations simply from observing the behaviour of particulars? The effectiveness of Van Fraassen’s Fork is that it draws out just how mysterious RBUIR’s lawmaking relation is. To his credit, it is a difficulty about which Armstrong is perfectly candid:37 [T]he following complaint may be made. At the end of all our explanations, this factor of necessitation remains unexplained … This reproach is just, 35 36 37

This charge is made – inter alia – by Mellor 1991: 168 and Lewis 1983: 40. Van Fraassen 1993: 412. Armstrong 1983: 92.

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I think, but the inexplicability of necessitation just has to be accepted. Necessitation, the way that one Form (universal) brings another with it as Plato puts it in the Phaedo (104d-105), is a primitive, or near primitive, which we are forced to postulate … We must admit [the necessitation relation] in the spirit of natural piety, to adopt Samuel Alexander’s phrase.

As far as RBUIR is concerned, its lawmakers are – as we have seen – brute, explanatory primitives that resist further analysis. It seems that Armstrong must stipulate that lawmaking relations entail their corresponding regularities. But, as Lewis noted, declaring that the relations have modal force does not confer modal force on them ‘any more than one can have mighty biceps just by being called “Armstrong”.’38 2.3.3. The Two-Way Traffic Problem On the Relations Model, universals are put to a great deal of modal and causal work. But the conception of universals required by the Instantiation Principle—that is, the conception that characterizes RBUIR as a species of the Relations Model—badly undermines a realist stance towards lawmaking. Central to immanent realism is the contention that universals depend existentially on the particulars that instantiate them: according to the Instantiation Principle, there are no universals that are not exemplified by an object. Within Armstrong’s metaphysical framework, this existential dependence is conveniently illustrated by what he labels the ‘victory of particularity.’ Every universal belongs to a state-of-affairs, which for Armstrong is an entity that consists in a particular (a ‘thin’ particular) that exemplifies a universal is itself, always and only, a particular (a ‘thick’ particular). Universals are separable from the states of affairs to which they belong only via a process of cognitive abstraction. In themselves, universals enjoy no independent existence whatsoever. It is important to emphasise that Armstrong’s thick particulars are the only entities that qualify as terms in causal relations, from which it follows – given the Eleatic Principle – that reality consists entirely in thick particulars. His ontology is, in effect, a retrieval of the ontology first presented in the early writings of Wittgenstein: Armstrong’s world just is the totality of atomic facts or states of affairs construed as thick particulars that stand in causal relations. Against this backdrop, it becomes remarkably difficult to see how universals – construed as merely dependent abstractions – are meant to support the metaphysical machinery that RBUIR 38

Lewis 1983: 25.

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requires. Universals – whether properties or relations – are ontologically parasitic on the particulars that exemplify them. The official story, as we have seen, is that regular causal interactions between particulars are grounded in a higher-order necessitation relation between two properties, where all three ingredients are construed as universals. But Armstrong also holds that the resulting law is itself a universal. So for every simple law – to borrow Armstrong’s notation – four universals are involved: the necessitation relation N, the two properties F and G, and a universal that, in conjunction with and subordinate to the particulars that exemplify the respective universals, constitutes a nomic state of affairs. It is this fourth universal that supplies the truthmaker for the law-statement that all particulars exemplifying F are particulars exemplifying G. So what makes it true to say that it is a law that electrons attract protons with a force inversely proportional to the square of the distance between them is that electronhood stands in the relevant lawmaking relation to protonhood to bring about, by virtue of the complex universal these three universals constitute, the nomic state of affairs accurately captured in Coulomb’s Law. But if this is the correct analysis of lawhood, we are left with a paradox. The paradox is that while the ontological traffic flows in one direction, the modal traffic flows in the other direction. That is to say, on the one hand Armstrong claims that universals depend on the thick particulars that exemplify them; but, on the other hand, lawlike interactions between thick particulars depend on the modal force supplied by the universals they instantiate. We are invited to adopt the puzzling view that, on RBUIR’s account of laws, universals are dependent on the very entities whose behaviour they are supposed to determine. 2.3.4. The Ex Nihilo Objection RBUIR’s compliance with the Instantiation Principle triggers a further objection that was initially raised by Tooley,39 and developed further by Evan Fales:40 Let us suppose our universe to have been one in which, during some initial segment of its history, all of the determinate properties falling under a given 39 Tooley 1977: 669. Cf. Swinburne 2006: 181 n.2: ‘[I]t seems possible that there should be in our universe laws about how substances which had certain properties which were in fact never instantiated would behave if they had those properties, and so [on the Relations Model] connections between uninstantiated universals.’ 40 Fales 1993: 134.

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determinable were uninstantiated. Such a state of affairs is certainly not logically impossible … It seems quite likely that, during some short span of time following the Big Bang, certain fundamental forces, and hence certain ranges of determinate properties, were absent.

Fales then claims that this scenario is fatal to RBUIR on the basis that immanent realism makes it impossible to posit the emergent property and the determinable properties under which it falls, since there could be no law governing its emergence that did not already feature it in its content. The scenario Fales invites us to imagine gives rise, then, to a fundamental problem for RBUIR:41 There must have been – or at any rate might have been – something about the prior states of affairs in our universe that brought it about that these instances of novel properties should appear when they did, something which predetermined that, at the very moment in question, these new universals would come into existence … Since Armstrong eschews relations between existents and nonexistent, and is no realist concerning mere possibilia, he cannot locate the truth-maker for the laws governing these universalcreating events in a nomological relation between the previously-existing universals and the not-yet existing determinate or determinable ones.

Let us refer to this problem as the Ex Nihilo Objection: RBUIR seems unable to explain how a property that has not yet emerged could feature in the content of the laws that regulate their first emergence, since the Instantiation Principle rules the property out of existence. RBUIR’s lawmaking relations pop into being, as it were, out of nothing. Armstrong attempts to anticipate the objection by denying that there are any laws regulating the creation of immanent universals or the lawmaking relations between them. But this seems to concede the force of the objection. Armstrong effectively declares that universals, and the nomic patterns they supposedly entail, come into existence out of nothing without laws. Again, most of Armstrong’s critics reject this on the basis that it is – at best – a mysterious and ad hoc explanatory stopping-point that introduces needless theoretical complexity. Although we will examine this claim in more detail in §4.2 below, it should already be clear why transposing RBUIR into a platonic framework would allow the Relations Model to handle the Ex Nihilo Objection relatively straightforwardly, since it could account for the initial emergence of a lawmaking relation by claiming that it exists uninstantiated prior to its emergence. By definition, of course, RBUIR does not accept 41

Ibid.

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platonic universals, and a fortiori any realist analysis of laws that presupposes them. Indeed the Ex Nihilo Objection seems to undermine any account of laws that would rely on the Instantiation Principle. Unless we decide to adopt the account set out in Chapter 3, this objection continues to exert a pressure to platonise on nomic realists with strong naturalistic commitments. 2.3.5. The Weak Instantiation Principle Armstrong recognised the difficulties that the Instantiation Principle would present for RBUIR early on. Indeed he proposed a modification that he claimed could deflect the difficulties raised against it. The modification involved extending the principle to include universals that are omnitemporally instantiated. On this weaker version of the Instantiation Principle, a universal instantiated at any temporal point in natural history qualifies for ontological admission. Call this the Weak Instantiation Principle. One potentially problematic corollary of the Weak Instantiation Principle is that it assumes the falsity of presentism, the view that reality only exists at the present ‘edge’ of time as it dynamically unfolds (the ‘A-Theory’). On a contrasting eternalist conception of time, however, properties and relations only exist in spatial terms (the ‘B-Theory’).42 Now if the Weak Instantiation Principle were acceptable, it might be possible to deflect the charge that RBUIR cannot explain the first emergence of lawmaking relation L. For one could then claim that L does not come into existence when it is first instantiated. On the B-Theory, L exists before and after the temporal slice to which its instantiation would be confined on the A-Theory. But this is conditional, of course, on L being instantiated at some temporal point. In other words, the Weak Instantiation Principle does not offer a great deal more comfort for supporters of RBUIR willing to abandon presentism, even if it does ease the pressure on RBUIR to posit uninstantiated entities to some degree. Let us consider the alleged benefits of Armstrong’s concession with respect to a simple law-statement such as . The Weak Instantiation Principle does permit this to be a law in circumstances where the Instantiation Principle would not. It permits it to be a law, for example, in a scenario: (i) where salt is not in contact with water at t but

42

See Armstrong 1983: §6.2.

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is at t-n; and (ii) where salt is not in contact with water at t but is at t+n. The trouble is, of course, that these scenarios were not the ones that created the most serious problems for RBUIR in the first place. For the Weak Instantiation Principle would still require RBUIR to rule out the existence of such a law: (i) in a possible world containing salt but no water; (ii) in a possible world containing water but no salt; and (iii) in a possible world containing water and salt where, coincidentally, the two substances omnitemporally do not come into contact with each other. A final problem with the Weak Instantiation Principle is that it effectively undercuts immanent realism’s claim to metaphysical modesty and the force of its accusation of undue mystery against platonic realism. The reason for this is that if temporality is not an objective feature of the physical world, as eternalists claim, then it should no longer be a mystery that this should be true of an abstract domain as well. It does not seem likely that presentists otherwise sympathetic to RBUIR’s basic approach would be willing to accept a four-dimensionalist theory of time as the price to pay for the Weak Instantiation Principle, especially since this is required by the alternative version of the Relations Model – that is, the platonic version considered in more detail in §4.2 below.43

2.4. Problematic Classes of Laws A separate, but no less damaging, line of attack against RBUIR is that it is very difficult to see how it can accommodate several special categories of laws that one would expect to qualify as laws on any realist account. Once again, these are objections that are substantially undercut once uninstantiated universals are accepted. The aim of the present section is to focus attention on five of these problematic classes of laws: non-causal

43 Swinburne 2013: 231-2. Bird 2007a: 52 raises a separate objection to Armstrong’s reformulation of the Instantiation Principle. He notes that it is inconsistent with Armstrong’s commitment to the Eleatic Principle, since entities that exist uninstantiated at t are not capable of entering any causal relations at t. As we shall see in §4.4.1 below, Bird himself denies there is any difficulty in supposing that causal traffic between abstract and concrete domains is possible. Facts, he claims, are abstract, but the fact that I am hungry can cause me to take an early lunch. I do not think that believing in facts commits us to believing facts as abstract entities, so I do not think his counterexample is successful. But the point for present purposes is that Armstrong cannot consistently claim that (i) platonists come unstuck when asked to explain how abstract entities can interact causally with concrete objects and (ii) an entity not instantiated at t can interact causally with a concrete object at t.

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laws, functional laws, uninstantiated laws, exclusion laws, and disjunctive laws. 2.4.1. Non-Causal Laws One of the most problematic kinds of non-standard laws for RBUIR, especially in light of its commitment to the Eleatic Principle, is the category of non-causal laws. Non-causal laws do not directly involve causal regularities, but there is no doubt that they deserve the status of laws. One instructive example of this kind of law would be the Boyle-Charles Gas Laws. These laws do not state that a change in one of the variables causes a change in another. It is true that it sets certain constraints on changes in the other two variables, but what fixes these is not causally determined by a lawmaking relation, as RBUIR would have us believe. It is much more plausible to suppose that the laws are picking out functional, mathematical relationships of co-variation. The challenge for causal versions of nomic realism, then, is to show that it is possible to accommodate these counterexamples. Richard Swinburne, whose position we will examine more closely in §5.1, shares Armstrong’s view that they can:44 [A]ll talk of non-causal laws is reducible to talk of causal laws (and initial conditions). If it is physically necessary that events of type A are correlated with events of type B, then either the former physically necessitate, i.e. cause, the latter, or conversely, or events which cause events of type A are also events that cause events of type B.

The view that all fundamental laws of nature are causal laws has been championed by a number of nomic realists.45 Yet it remains the case that a handful of well-known counterexamples undermine attempts to tie noncausal laws to a causal reductive base. For example, the Wiedemann-Franz Law states that the ratio – the Lorentz Number – between the electrical and thermal conductivity for all metals at all temperatures is (virtually) constant.46 What it does not contain is any reference to the active or passive causal powers of metal substances.47 All it purports to express are certain correlations between thermal and electrical conductivity. It does not specify a causal relationship between 44

Swinburne 1997: 92 n.17. See, for instance, Heathcote & Armstrong 1991. 46 See the discussion in Serway et al. 2005: 420. 47 Swinburne invokes powers in his analysis of laws, so his account is technically a theistic version of the Dispositionalist Account (this is discussed in more detail in §5.1). 45

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the values. Another counterexample to the causal reductive account is the Dulong-Petit Law, which states that within a specific temperature range, a solid’s heat possesses a constant universal value independently of the kind of substance that it is. In other words, it is a law that describes the co-existence or association between the properties of particular substances, and not direct causal interaction between them. Now the obvious move for a defender of causal laws at this point is to accept these counterexamples, but to deny that they are fundamental laws. All non-causal laws, as Swinburne claims above, are ultimately derivable from demonstrably causal laws. But although this rejoinder is persuasive with respect to most fundamental laws, causal accounts must still confront perhaps the most well-known example of a non-causal law that is indisputably fundamental, namely Newton’s Third Law of Motion, which states that if object x attracts object y, then y will attract x with an equal and opposite force. Crucially, this law is not derivable from Newton’s other laws. Moreover it may be true that instances of this law – gravitational, electrostatic, electromagnetic – are causal; but it is no part of its content that only causal kinds of forces are derivable from it. So it is not sufficiently clear how non-causal laws can be explained in terms of RBUIR’s lawmaking relation if the puzzling modal character of that relation is characterised as possessing a quasi-causal necessity. The existence of non-causal laws is especially embarrassing so far as Armstrong’s own overall theory is concerned, since they seem directly to contradict the Eleatic Principle (discussed in §2.1.4 above). This is a point, in fact, that Armstrong partly conceded some years later:48 It may be that the [Eleatic] Principle should be widened to allow for any irreducibly non-causal laws that there are, and so that making a difference to nomic power should be substituted for, or inserted alongside, causal power.

But the trouble with this suggested modification is, of course, that it is wholly ad hoc. It is ad hoc because it involves the amendment of an existing theory whose sole purpose is to accommodate an explanandum that could not be accommodated otherwise. It also undermines Armstrong’s claim to have addressed the objection that the modality of lawmaking relation is incoherent by characterising it as a relation of causal necessitation. On the face of it, then, to the extent that RBUIR invites us to analyse laws in primarily causal terms, or in terms that invoke notions closely analogous 48

Armstrong 1997: 42.

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to causal ones, it faces serious difficulties. As Stathis Psillos notes,49 its analysis of laws in terms of quasi-causal necessitation relations means that RBUIR concedes a significant theoretical advantage to nomic antirealism, since versions of the latter start from the premise that there are no causal or nomic connections between properties whatsoever. 2.4.2. Functional Laws Another notoriously problematic category of regularities for RBUIR is the category of functional laws. Functional laws are laws that state proportionate connections between determinable quantities – say distance or mass – such that the determinate values of each quantity are always proportionately related. They are, in effect, higher-order laws – that is, laws about laws. The Boyle Gas Law, for instance, states that there is an inversely proportional relationship between the pressure and volume of a gas at constant temperature. Similarly, the Charles Gas Law states that there is a directly proportionate relationship between the volume and temperature of a gas at constant pressure. And, as we have already seen, the Wiedemann-Franz Law states that the ratio between the electrical and thermal conductivity for all metals at all temperatures is (virtually) constant.50 Law-statements of this kind are especially resistant to the analysis RBUIR proposes. This is so regardless of whether it is committed to the Instantiation Principle or indeed to the Weak Instantiation Principle, because such law-statements implicitly quantify over values that are omnitemporally never instantiated. Since it follows that these values do not exist, it is difficult to see how RBUIR is in a position to provide a clear account of how the law-statements it purports to ground can satisfactorily state functional connections between variables even where there are determinate values. Even in modified form, the Instantiation Principle rules out infinitely many potentially determinate values that are contingently never instantiated. Uninstantiated values are, in effect, constitutive of functional laws; but in complying with the Instantiation Principle, the best that RBUIR can hope for when it comes to explaining them is to account for their ‘missing values’ by inferring what these values would be on the basis of whatever determinate values happen to be empirically available.51 49 50 51

Psillos 2002: 171. See the discussion set out in Serway et al. 2005: 420. For further criticisms of Armstrong’s account of functional laws, see Forge 1986.

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2.4.3. Uninstantiated Laws The problem of functional laws is tightly connected to the problem of uninstantiated laws.52 D.H. Mellor has noted that positing such laws brings with it ‘a very contentious consequence,’ namely that of accepting the existence of universals that do not depend on their instances.53 The most well-known of these is Newton’s First Law. The difficulty, of course, is that the law of inertia seems to be a fundamental non-derivable law. Now both Armstrong and Mellor adopt a similar solution to that proposed for functional laws. They hold that this kind of uninstantiated law can be grounded in a counterfactual analysis of instantiated laws. Mellor formulates the approach as follows:54 For if being acted on by a specific force F is a positive property, then being acted on by no such force – as opposed to zero net force – is an infinite conjunction of negative properties; and … no such entities exist.

We should note the importance here of the Instantiation Principle as a methodological constraint on Mellor’s solution and, in particular, that it requires him to rule out the existence of negative universals. He is therefore forced to conclude that uninstantiated laws simply do not exist. To his credit, Armstrong is explicit about this: if one endorses RBUIR, he concedes, then one must accept that ‘strictly there are no uninstantiated laws.’55 But this is not the same, he insists, as claiming that the theory cannot account for uninstantiated laws. Nevertheless, there is a separate class of uninstantiated laws that does not seem as susceptible to a counterfactual analysis as Armstrong and Mellor suggest. These are connected to the so-called “Tooley Cases” that Michael Tooley invokes by way of motivating his platonic alternative to RBUIR (his own version is discussed in more detail in §4.2). Tooley’s thought-experiments invite us to consider two problematic scenarios in particular. The first is the fundamental particle case. Here Tooley pictures ten particles in an otherwise empty possible world. The total number of possible relations between them is 55. We are then asked to imagine that 54 of these relations are known as laws, but that 53 of these laws differ from each other in such extreme ways that there are no antecedent conditions from which the 54th law could be inferred and specified. The 55th law is not known because the particles it involves have never interacted 52 53 54 55

Armstrong 1983: 111. Mellor 1995: 201. Ibid. Armstrong 1983: 117.

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(even though this would be physically possible).56 Tooley’s conclusion is that in these circumstances we are justified in inferring the existence of the law independently of its instantiation, even though it is not possible to specify the content of the law. But if there are uninstantiated laws, the universals that feature in their content must also exist independently of their instantiation. So, once again, this applies pressure to RBUIR to abandon the Instantiation Principle. It should also be noted that applying the Weak Instantiation Principle does not protect the analysis against the fundamental particle case, since the 55th law is omnitemporally never instantiated. The second Tooley Case is the emergent property case.57 To condense Tooley’s original account a little, picture an emergent property E constituted by a conjunction of three properties F, G, and H. It is easy to imagine that it is physically possible for three similar properties I, J, and K to produce another emergent property N, but that – as it happens – I, J, and K never combine to form the relevant nomic conjunction. But if that is correct, then the Instantiation Principle forces RBUIR to rule out N’s existence, as does the Weak Instantiation Principle. In these circumstances, claims Tooley, we are justified in positing the existence of an uninstantiated law that would regulate the emergence of N, and therefore in positing the existence of N as an uninstantiated universal on the basis that it would need to feature in the content of this uninstantiated law.58 And so, once again, the temptation to underpin the Relations Model with a platonic realist theory of universals returns. On the platonic alternative, it would be perfectly coherent to uphold the view: (i) that there are some laws that have not yet been instantiated but might be instantiated; or (ii) that some laws are omnitemporally not instantiated but would have been instantiated had the right circumstances obtained. 2.4.4. Exclusion Laws and Disjunctive Laws One consequence of the Instantiation Principle for RBUIR is that it rules out negative universals (such as the property not-F) and disjunctive universals (such as the property F-or-G). These restrictions create special difficulties for the theory when it comes to accounting for exclusion laws and disjunctive laws. Thus its rejection of negative universals blocks the 56 57 58

Tooley 1977: 669. Cf. the discussion in Armstrong 1983: 117-8. This is, in effect, Tooley’s version of the Ex Nihilo Objection discussed in §2.3.4. Tooley 1977: 685.

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most natural explanation of exclusion laws – that is, laws of the form . The example usually invoked is Pauli’s Exclusion Law, a principle that is fundamental to quantum theory, since it arises from the claim that particles within the same atom cannot be told apart – that is, they are inherently indistinguishable, a notion not recognised in classical physics. When applied to electrons, the principle states that no two electrons in the same atom can share the same set of quantum numbers.59 Stephen Mumford frames the objection from exclusion laws against RBUIR as follows:60 Armstrong initially endorsed the possibility of exclusion laws … but [because of the prohibition on negative universals] he then worried about how an exclusion law could be instantiated … Armstrong considered various ways to avoid uninstantiated (underived) exclusion laws, such as permitting higher-order ‘totality facts.’ If we had the positive laws plus the totality fact that these are all laws, then we would not need additionally specify exclusion laws to account for exclusions.

Similar problems arise from the fact that there might be disjunctive laws, as Tooley pointed out early on.61 But in rejecting disjunctive universals, prima facie RBUIR seems required to rule out the possibility that there could be such laws. Disjunctive law-statements are ones that take the form ‘it is a law that for any x, if x is F, then either x is G or x is H.’ Again, given immanent realism’s restrictive stipulations, they do not seem to qualify as laws on the basis that they posit the existence of uninstantiated universals G or H where, respectively, H and G are instantiated. In such a scenario, the Instantiation Principle once again rules these universals out, and a fortiori any laws that feature these in their content. * * * We have now evaluated one influential attempt to elaborate a persuasive realist analysis of lawlike regularities within the constraints of a naturalistic ontology. At the heart of this attempt lies the categoricalist theory of property-identity endorsed by the deflationary theories examined in Chapter 1. A crucial corollary of this theory is that the same properties 59 Serway et al. 2005: §9.4. For a helpful overview of the philosophical literature on this topic, see Massimi 2005: ch.1. 60 Mumford 2004: 91. 61 Tooley 1977: 677.

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can vary from possible world to possible world. So construed, the link between properties and the causal or nomic contributions they make is wholly contingent. On the neo-Humean approach, of course, this does not present a problem, since there are, of course, no such contributions (at least in the sense that nomic realism understands them). But if RBUIR is to qualify as a version of nomic realism, we saw that it needs to invoke a distinct metaphysical ingredient substantive enough to be assigned the lawmaking role. The lawmaking ingredient turned out to be logically contingent second-order relations between first-order universals. Once we had set out the basic elements of RBUIR itself, we turned to consider how these assumptions undercut it in a number of serious ways, including: (i) the conundrum triggered by conjoining the Inference Problem and the Identification Problem (“Van Fraassen’s Fork”); (ii) the sui generis and explanatorily primitive modal character of the lawmaking relation; (iii) the Ex Nihilo Objection; (iv) varieties of non-standard laws that the theory accommodates with difficulty; and (v) the Tooley Cases. We also saw that these objections did not lose much of their sting even when we granted Armstrong’s two central concessions, namely: (i) substituting the Weak Instantiation Principle for the Instantiation Principle; and (ii) analysing the modal character of the lawmaking relation in causal terms. Taken together, we concluded that almost every one of these arguments generated pressure on RBUIR to abandon its commitment to immanent realism in favour of a platonic strategy. We have assumed throughout, of course, the implausibility of a turn in the opposite direction towards nominalism. But perhaps we ought to make the reasons for doing so explicit for those who may be tempted by this option in the wake of RBUIR’s failure. Put briefly, the difficulties of achieving a successful nominalistic version of the Relations Model are insuperable. One would first need to settle on a nominalistically acceptable substitute for universals. One would then need to work out a satisfactory realist analysis of lawlike regularities among particulars. As Armstrong noted early on in the debate, this is a very hard challenge indeed for the nominalist to overcome:62 Because there is nothing identical in the different instantiations of the law, [the nominalist] is forced to hold a Regularity theory of law. For if he attempts to hold any sort of necessitation theory, then he can point to no ontological ground for the necessity. He is nailed to Hume’s cross.

62

Armstrong 1983: 78.

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Even if nominalism could find an entity to play the role that RBU IR assigns to universals, as some have argued,63 it is certainly not clear that it would be in a better position to meet the objections raised in the course of §2.3 and §2.4. Nominalists are almost always more committed to the naturalistic impulse animating RBUIR’s insistence on the Instantiation Principle. With one or two well-known exceptions,64 it is typically taken for granted that nominalist ontologies exclude non-spatiotemporal entities. As a general rule, most sides agree with Lewis’ observation that universals and laws amount to a ‘package-deal.’ Those tempted by nominalism may, of course, be tempted to turn back towards the metaphysical modesty of neo-Humean stances towards regularities. But we have already addressed the intractable problems that await them if they succumbed to this temptation. Others, however, may be willing to press on in the search for a realist analysis of laws by relaxing some of Armstrong’s background metaphysical commitments. In other words, the cumulative weight of the objections against RBUIR may not motivate a return to the inadequacies of deflationary accounts of laws, but rather to press on to find a more viable theory, even if this eventually means yielding to the pressure to platonise by considering a non-naturalistic formulation of the Relations Model. Before doing so, however, we must first examine the second attempt to offer a robust account of lawmaking that is consistent with naturalistic commitments, namely the version of the Powers Model that also presupposes an immanent realist theory of universals. For there will be many nomic realists with strong naturalistic sympathies who, if forced to choose, would prefer to abandon categoricalism rather than naturalism. Disillusioned advocates of RBUIR who continue to hope for a cogent version of nomic realism will want to scrutinise this second approach with care.

63 Fuhrman 1991 and Kistler 2003 represent two rare attempts to formulate the Relations Model without universals. As a general matter, very few nomic realists try to ground the uniformity, inductive strength, and counterfactual robustness of laws by invoking anything other than universals. Those that do – e.g. Molnar 2003, Martin 2008, Heil 2012 – usually advance versions of the account to be considered in the following chapter. 64 Notoriously, Quine 1948, who was willing to admit a host of non-spatiotemporal entities into his ontology (though not, it should be noted, properties or relations).

CHAPTER 3 LAWS AS POWERS: THE FRESCO PROBLEMS

We have been searching for a convincing case in support of the claim that law-statements are grounded in objective forms of natural necessity. We have been searching, in short, for lawmakers. It had become clear by the end of Chapter 1 that, in the final analysis, empiricist resistance to this approach undermined three crucial characteristics of any law-statement worthy of the name, namely its explanatory power, inductive strength, and counterfactual resilience. So Chapter 2 began the search for an account that would integrate these characteristics by examining an influential realist analysis – RBUIR – that sought to preserve the naturalistic assumptions of the antirealist stances considered in Chapter 1. In order to achieve this, we saw that RBUIR assigned the lawmaking role to relations between properties construed as immanent universals. Immanent realism appeared to deliver empiricist supporters of the Relations Model the best of both worlds. For, on the one hand, RBUIR excluded non-spatiotemporal entities from its ontology by invoking the Instantiation Principle, thereby claiming consistency with a central tenet of metaphysical naturalism. On the other hand, by including universals it was also able to explain what the deflationary accounts could not, namely the uniform character and universal scope typically associated with the regularities to which law-statements refer. Unfortunately, it quickly emerged that RBUIR was not only vulnerable to a number of serious objections, but also that the most persuasive diagnosis for these problems was its methodological commitment to the Instantiation Principle. These tensions provoked the suspicion that a fundamental incompatibility exists between nomic realism and metaphysical naturalism. The aim of the present chapter is to press these suspicions a little further, but this time with respect to the immanent realist version of the Powers Model or DISPIR. By the end of it, in fact, they will prove even more well-founded, since it will emerge that the best way for the Powers Model to preserve nomic realism is to do what Chapter 2 concluded the Relations Model should do: reject the Instantiation Principle altogether. Typically, DISPIR follows RBUIR in treating lawmakers as universals that exist only when instantiated. Occasionally, however, it is underpinned

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by less ontologically committed attribute-theories such as trope-theory. As we shall see, however, the objections that DISPIR provokes in virtue of its immanent realism apply a fortiori to these accounts. DISPIR’s chief departure from the analysis we considered in Chapter 2 is, of course, the fact that it assigns the lawmaking role to properties rather than relations. As we have seen, what permits DISPIR to do this is that where the Relations Model assigns the lawmaking role to causally potent connections between properties, every version of the Powers Model advances a theory of property-identity that takes properties themselves to be causally potent. On this view, properties are powers or capacities that dispose their bearers to interact causally with other objects given certain stimulus conditions. Law-statements are statements that describe regularities in the distribution of these dispositional properties among objects. The task of the present chapter is to examine the cogency of DISPIR. §3.1 sets out its basic structure and, in particular, whether it is even plausible to formulate the robustly ontological analysis of dispositions that it presupposes. §3.2 scrutinises a pair of widely accepted inward-facing or ‘centripetal’ identity-conditions for a lawmaking disposition, namely: (i) that it is ontologically independent from its potential manifestation; and (ii) that it is intrinsically connected to its bearer. §3.3 then considers a pair of widely accepted outward-facing or ‘centrifugal’ identity-conditions, namely: (i) the dependence of a lawmaking disposition on other dispositions that are involved in their stimulus and manifestation conditions; and (ii) the reciprocal orientation of these other dispositions towards the actual or potential manifestation of the lawmaking disposition. §3.4 sets out a thought-experiment that illustrates the contradictions arising from attempts to accommodate all four of these identity-conditions in a way that preserves consistency with the Instantiation Principle. §3.5 examines possible resolutions to the contradictions uncovered in §3.4; but since most of these require some degree of compromise with the Instantiation Principle, the chapter concludes by observing that as an attempt to establish a cogent framework for nomic realism, DISPIR is no less hamstrung by its naturalistic commitments than RBUIR. At this stage of our inquiry, our cumulative conclusion is that there are simply no options left for those who wish to combine nomic realism with metaphysical naturalism. In other words, if realist intuitions about lawlike regularities are to be preserved, uninstantiated universals must be included on the ontological inventory. Naturalists will baulk at this move; but if they do, by that point it should be clear that the burden rests with them to advance a realist analysis that is both consistent with a naturalistic

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ontology and immune to the objections raised against RBUIR in §2.3 and §2.4 and against DISPIR in §3.2-§3.4 below.

3.1. The Nature of Dispositions In order to grasp the specific difficulties facing DISPIR, we must first clarify what the Powers Model involves and, in particular, what distinguishes it from the Relations Model. The aim of this section is to position the vexed debate over dispositions within its contemporary context before charting their rapid recent explosion into contemporary debates in the metaphysics of laws. 3.1.1. Historical Context The first point to underline is that the Powers Model’s historical antecedents substantially pre-date the rise of the notion of ‘laws of nature’ in the early-modern period. Prior to the seventeenth century, so the traditional story goes, regularities in the natural world were almost always explained in terms of the causal powers that substances possessed in virtue of belonging to natural kinds. This broadly Aristotelian explanation of regularities dominated the high-scholastic conception of nature to such an extent that the metaphor of lawhood was applied very rarely indeed. As Bas van Fraassen has noted,1 Aquinas draws a distinction between proximate and ultimate grounds for natural regularities. Within his theological framework, God is the ultimate ground in the sense that he is the ultimate cause of substances and the natures they possess. But since it is their natures that account for the extensive and predictable patterns of causal interaction between objects in the physical world, it is created particulars that stand as the proximate ground of empirical regularities rather than unmediated divine agency. It is very clear that this general picture in no way holds that God imposes extrinsic connections on nature from without, but rather that he creates each individual substance with a configuration of necessary and sufficient properties – that is, its ‘nature’ or ‘essence.’ These causally potent properties dispose individuals to interact with one another in regular and predictable ways, ways that would later come to be characterised as law-sustaining.

1

Van Fraassen 1989: 4.

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It is remarkable that after such a long period of neglect, the basic elements of the high-scholastic conception now underpin an increasingly influential school of thought in the contemporary analytic debate on laws. For modern versions of the Powers Model also locate the proximate ground of natural regularities in the causally potent properties of objects. David Oderberg’s slogan that ‘the laws of nature are the laws of natures’ neatly distils the point at which this account departs from the Relations Model; but it also serves as a succinct description of the historical distinction between the ‘intrinsicist’ high-scholastic picture of regularities and the ‘extrinsicist’ conception that would emerge in the early-modern period.2 Although it is important to note, as we did in the Introduction, that some of those who now endorse the Powers Model claim that it permits them to eliminate talk of ‘laws of nature’ on the basis that it is unduly wedded to the extrinsicist view,3 we have assumed for the purposes of this study that it is legitimate to characterise versions of it as versions of nomic realism. For whatever the correct metaphysical analysis of the regularities might be, all sides must recognise the fact that – for better or worse – scientific theory has adopted the language of ‘laws of nature.’4 Classifying the Powers Model as a version of nomic realism allows us to pick out the most important point of disagreement in the current debate, namely whether law-statements describe how objects are constrained to behave in predictably regular ways, or whether they pick out purely contingent patterns in that behaviour. So if the Powers Model can be classified as a version of nomic realism in virtue of the fact that it construes law-statements in a modally substantive way, what more can be said with respect to how it achieves this? In its boldest form, the account holds that dispositions – also known as 2

Oderberg 2007: 144. E.g. Mumford 1998: 216-38; Mumford 2004: 201-5; Cartwright 2005. There is an ongoing intramural debate among supporters of the Dispositionalist Account over whether it renders a commitment to laws of nature redundant. Thus Bird 2007a: 189-203 claims that talk of laws is acceptable on the basis that they are not taken to represent an additional category of being – on the Dispositionalist Account, laws merely supervene upon distributions of ungrounded dispositional properties. But Mumford 2004: §12.3 argues that its misleading connotations make lawhood a harmful metaphor that should be discarded altogether in favour of the notion of power. The dispute is analogous to the debate within the philosophy of mind between reductionist and eliminativist attitudes towards mental states. 4 Even nomic antirealists designate some regularities as ‘laws’ – to this end, some have even argued that the Governance Intuition (discussed in §2.0 above in relation to the Modal Hybridity Problem) has nothing to do with a conceptual analysis of lawhood (see Beebee 2000: 580-3). 3

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causal powers,5 potencies,6 capacities,7 or powers-and-liabilities8 – are ontologically respectable natural properties that are not reducible to a categorical base. This thesis is often – though not always9 – accompanied by a strong essentialist thesis about the nature of properties to the effect that dispositional properties are necessarily oriented towards specific forms of causal interaction.10 On this view, there is no possible world in which salt is not disposed to dissolve in water, or in which electrons are not disposed to attract protons, or in which light is not disposed to travel faster than 299,792,458 metres per second. If the response to this point is that we can readily imagine such worlds, supporters of this strong essentialist rendition of the Powers Model will respond that what would be imagined in these scenarios are possible worlds where salt-like substances fail to dissolve in water, or electron-like particles repel protons, or photon-like particles travel at super-luminal speeds. In the heyday of positivist hostility towards dispositions, the claim that they might qualify even for the lowest reaches of an ontological inventory was so suspect that arguments were rarely advanced against it. Empiricist distaste for dispositions goes back, of course, at least as far as the criticisms raised against ‘occult powers’ by Boyle and Hume. Traditionally, dispositions were to be explained in terms of – and only in terms of – empirically observable properties. That is to say, they were to be understood in terms of the modally inert categorical properties that, as we saw in §2.1.3, underpins RBUIR’s analysis of laws. In one of the earliest attempts to turn the tide of this hostility, D.H. Mellor correctly captured the dominant attitude towards dispositions with the observation that dispositions were considered ‘as shameful in many eyes as pregnant spinsters used to be – ideally to be explained away, or entitled by a shotgun wedding to take the name of some decently real categorical property.’11 On the traditional view, salt’s solubility in water was not an ontologically ungrounded dispositional property, but rather the ascription 5 E.g. Harré & Madden 1975, a work largely responsible for rehabilitating the basic approach we will be exploring in this chapter within contemporary debates. 6 Bird 2007a. 7 E.g. Cartwright 1989. 8 E.g. Swinburne 2004a. 9 For a critique of the view that the Dispositionalist Account presupposes essentialism, see Mumford 2005, who argues that it is perfectly intelligible to accept natural kinds and causal powers without endorsing it. 10 As a result, ‘dispositional essentialism’ is often applied to as a label for the Dispositionalist Account – e.g. Shoemaker 1980; Ellis & Lierse 1994; Ellis 2001; Bird 2007. 11 Mellor 1974: 157.

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of a dispositional predicate, the truth-conditions for which consisted in counterfactual statements describing a categorical base (in the case of salt’s water-solubility, the microphysical structure of sodium chloride molecules). 3.1.2. Reductive Conditional Analyses So the purpose of linking dispositions to a categorical base was to avoid offending empiricist scruples. But it was still necessary to distinguish dispositional from non-dispositional ascriptions. For a long time the preferred solution – as we have just noted – was to ground the former in appropriately formulated counterfactual or subjunctive conditional statements. Conditional analyses of dispositional ascriptions tied the predicate in question (e.g. … is fragile) to certain stimulus conditions (e.g. being dropped on a hard surface) and to some specific outcome or manifestation (e.g. shattering). The dispositional ascription (‘this coupe of champagne is fragile’) could then be grounded in the truth of an appropriately formulated subjunctive conditional statement (‘if this coupe of champagne were thrown from my window, it would shatter’). Although the conditional analysis continues to be the standard way of handling dispositions within the neo-Humean tradition, the increasingly technical and sophisticated epicycles of the debate on this question have led several contemporary philosophers to abandon it. But scepticism towards the conditional analysis also arose as a result of a range of telling counterexamples. Taking the example of an electric wire’s conductivity, C.B. Martin introduced the notion of an electro-fink,12 an imaginary device attached to an electric wire to make it conduct electricity, but only when it detects that it is about to be touched. Left untouched, the wire would not conduct electricity. The problem for this conditional analysis of dispositions is that despite the fact that the wire is not disposed to conduct electricity, the subjunctive conditional (‘if this wire were touched, it would conduct electricity’) still turns out to be true: the electric wire is not conductive, but it is still true that if it were touched it would be live. In other words, Martin’s electro-fink provides a counterexample to the claim that every true subjunctive conditional grounds a disposition.13

12 13

Martin 1994: 3. Martin 1994: 8.

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Martin then asks us to imagine a reverse electro-fink that makes the wire go dead when it detects it is about to be touched. On this scenario, although the wire does have the disposition to conduct electricity, the relevant subjunctive conditional (‘if this wire were touched, it would conduct electricity’) is false. So the reverse electro-fink supplies a counterexample to the claim that every disposition is grounded in a true subjunctive conditional, because although the electric wire is disposed to conduct electricity, it is false that if the wire were touched it would do so. Although not fatal to the conditional analysis, Martin’s so-called ‘finkish’ dispositions have triggered a series of increasingly complex refinements to it,14 which have in turn been subjected to a number of other counterexamples.15 For the purposes of the present study, we need not explore these developments further. Their importance in relation to the Dispositionalist Analysis lies in the fact that what was once considered an orthodox and unproblematic approach to analysing dispositions is now much less widely endorsed. This has led many metaphysicians to ignore neo-Humean protests and integrate dispositional elements into their fundamental ontology as bona fide natural properties that resist standard reductive analyses. What initially appeared to be a small victory in a relatively minor dispute over the nature of properties has now opened up fresh perspectives on a vast array of philosophical topics.16 The central ambition of this neo-Aristotelian turn is to formulate a modally substantive alternative to categoricalist metaphysics. 3.1.3. The Role of Universals The Powers Model is not as such committed to construing its lawmakers as universals. In fact, a number of its leading champions reject universals altogether. Thus George Molnar takes dispositions to be tropes,17 as

14

E.g. Lewis 1997. Thus in response to the ‘reformed’ conditional analysis advanced in Lewis 1997, Bird 1998 invokes ‘masks’ (e.g. a fragile glass does not shatter when dropped because it is wrapped in protective packaging) and ‘antidotes’ (e.g. when someone ingests a poison having already ingested the right antidote). In each case, the dispositions are not grounded in the truth of the relevant subjunctive conditionals as the traditional analysis claims (respectively, ‘if this glass were dropped, it would shatter’ and ‘if this poison were ingested, it would kill’). 16 As Cross 2012: 115 notes, there are now a bewildering number of dispositionalist approaches to many different philosophical issues, including modality, causation, counterfactuals, chance, belief, knowledge freedom, and colour. 17 Molnar 2003: §1.2. 15

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do C.B. Martin18 and John Heil.19 But it is difficult to deny that realism about universals is a tempting position with which to underwrite the purportedly global and uniform scope of laws. For positing universals seems to be a price worth paying for securing several of the features typically associated with laws. By contrast, trope-theoretic accounts of dispositions as lawmakers must make do with an almost inconceivably fragmentary ontology. Since tropes are ontologically discrete entities, it would be deeply mysterious why lawmaking dispositions are distributed among objects in such pervasively regular ways, and it would be still more puzzling – as we shall explore in more detail in §3.3 – how dispositions could be ‘directed’ towards their specific outcomes. The standard response from trope-theorists is that commonalities between attributes can be explained in terms of class-membership or resemblance relations. Even if these explanations should prove convincing, however, it remains the case that tropes are unrepeatable property-instances, which means that it is equally difficult to see how these versions of the Powers Model can explain extensive and systematic repetitions in the causal interactions between objects. Trope-theoretic accounts merely exacerbate the difficulty of understanding why there should be any nomic connections at all between first-order particulars. It cannot be denied, of course, that these accounts are preferable to universals-based accounts in terms of qualitative ontological economy, since they include only one category of being (particulars) in their ontology. But it is an important point of methodology in metaphysics that gains in economy considerations must never redeem deficits in explanatory power.20 Nevertheless, even if trope-theoretic versions of the Powers Model could adequately bear the nomic realist’s explanatory burdens, it will emerge in the course of §3.2 -§3.4 below that if we are to arrive at a satisfactory account of what determines the identity of dispositions, the pressure to accommodate uninstantiated lawmakers becomes irresistible. We shall see in Chapter 4 that universals-based accounts can yield to this pressure by accommodating uninstantiated platonic universals. But no such escape-route is available to the trope-theorists. It is possible, perhaps, for them to invoke unrealised facts or states of affairs in the place

18 19 20

Martin 2008: §7.1-§7.2. Heil 2012: §5.8. E.g. Barnes 2000.

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of platonic universals. It is not, strictly speaking, unintelligible that possibilia of this kind exist.21 As Matthew Tugby has recently pointed out, however, the trouble with this solution is that it would make the Powers Model’s central commitment entirely redundant. This is because once one grants that there are unrealised states of affairs, it is simpler to assume that there are an infinite number of them; and this means that possibilia could provide a reductive explanatory base for every nomic fact that lawmaking dispositions were originally invoked to explain.22 There is no longer any need to construe dispositions in the robust, ontologically commissive way that DISPIR requires, since unrealised possibilia can meet their explanatory objectives just as well. In particular, considerations of qualitative ontological economy – one ontological category (irreducibly categorical entities) is more parsimonious than two ontological categories (irreducibly categorical entities and irreducibly dispositional entities) – would dictate that the latter should be eliminated in favour of unrealised possibilia, since this would not affect the overall explanatory power of the resulting account.23

3.2. Lawmaking Dispositions I For any version of the Powers Model to succeed, then, it is difficult to avoid the conclusion that it must construe properties as universals. But it must also, of course, offer persuasive reasons for thinking that the properties to which law-statements refer have an irreducibly dispositional character. It is not enough, though, for DISPIR to show that reductive analyses of its lawmakers fail; it must also put forward a constructive analysis that makes it reasonable to designate dispositional properties as lawmakers. The aim of this section and the next is to suggest a set of four necessary and sufficient conditions for determining the kind 21

It is worth noting that this solution would not be available to trope-theoretic supporters of the Dispositionalist Account such as Molnar who do not accept facts or states of affairs – see Molnar 2003: §2.3. 22 This, in effect, is precisely what Lewis 1986a proposes with respect to modality more generally – modal facts are reducible to possible worlds that are concrete (but nonactual) existents. 23 Tugby 2013a: 461-2. Tugby cites Whittle 2009 as an example of a theory that eliminates dispositional elements entirely in favour of a nominalist analogue of the Dispositionalist Account. Although there is no space to investigate this proposal here, there are a number of reasons why this particular account is unpersuasive.

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of dispositional properties required to perform the theoretical role of lawmaking on the Powers Model. One immediately striking feature of this quartet is that it consists in two pairs of intuitively divergent identity-conditions.24 The first pair – to be examined in this section – are intrinsic characteristics that involve nothing beyond the dispositional property itself. Let us refer to these as the ‘centripetal’ identity-conditions. The second pair – to be examined in §3.3 below – are extrinsic characteristics that appear to involve properties that are distinct from the dispositional property whose nature they purportedly determine. We can refer to these as the ‘centrifugal’ identityconditions. 3.2.1. Independence The first centripetal identity-condition for determining the identity of an ungrounded lawmaking disposition stipulates that such a disposition exists irrespective of whether or not it is ever manifested. At an intuitive level, this seems perfectly obvious: a vase can be fragile without ever breaking; kerosene is flammable even if it never comes into contact with a flame; arsenic is lethal even if it is never ingested. To illustrate this with reference to a plausible candidate for a lawmaking disposition, electrons are disposed to attract protons with an electrostatic force inversely proportional to the square of the distance between them (Coulomb’s Law). Given its realist stance towards lawmaking dispositions, DISPIR is committed to the claim that electrons retain their disposition to attract protons even if it turns out that there are electrons that never do attract protons— that is, even if an electron’s dispositional property of negative charge never manifests itself.25 Dispositions, in other words, exist independently of their manifestations to the extent that they are construed in the robustly realist sense that DISPIR requires. Where D is a disposition and ij its specific outcome, D confers a power to ij independently of 'ij-ing. Call this feature of lawmaking disposition Independence.

24 For the avoidance of doubt, references to ‘identity-conditions’ throughout this study should be treated as references to the ontological conditions constitutive of the identity of an entity rather than the epistemic conditions necessary for correctly identifying it. 25 Molnar 2003: 57. This identity-condition seems to be widely accepted. Thus on the realist side Tugby 2013a: 454 takes Independence to be a ‘central platitude’ of philosophical analyses of dispositions, while in the course of his criticisms of the realist position Psillos 2006: 141 notes that ‘the distinctive feature of powers is that they may be possessed, thought [sic] not manifested.’

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To grasp its intuitive appeal, let us imagine that Independence were false. That is, suppose that when electrons do not manifest their power to attract protons, their power to do so does not exist. But that would imply that nothing has the potential to do anything. On a realist conception of dispositions, at any rate, this yields the conclusion that only the actual is possible. But this view, historically associated with so-called ‘Megaric Actualism’,26 has been roundly rejected since Aristotle’s devastating criticisms against it.27 It amounts, in effect, to a form of wholesale, and wholly implausible, eliminativism about modal truths. If my ability to wake up does not exist when I am asleep, I can look forward to an eternal lie-in. Needless to say, all sides of the debate reject this wildly implausible result; even those who would reduce dispositions to a categorical base at least concede that dispositional statements are intelligible.28 Yet it is precisely the thesis to which we would be committed if it we were to deny Independence. For if one rejects the view that a lawmaking disposition exists even when it is not manifested, then one must also accept the unpalatable conclusion that dispositional properties pop into existence out of nothing when they are manifested and pop out of existence into nothing when they cease to be manifested. In effect, those who reject Independence are forced to reject dispositional properties altogether. This is because the only properties that exist once Independence is abandoned are occurrent properties; and to say that a property is occurrent just is to say that it is not dispositional. As it stands, then, Independence is not a controversial thesis. The difficulty comes when supporters of DISPIR try to provide an ontological analysis of unmanifested dispositions. To borrow a question from a leading critic of the realist position, what is it that dispositions do when they are not manifested?29 Crucially, Independence cuts deeply against the empiricist assumptions that motivate the Instantiation Principle. The two commitments could scarcely conflict more directly with each other: while Independence holds that dispositions exist when they are not spatiotemporally instantiated, the Instantiation Principle holds that nothing exists that is not spatiotemporally instantiated. It is puzzling, then, that some supporters of DISPIR are willing to accept the fundamental contradiction between Independence and the 26 27 28 29

Molnar 2003: §4.3.1. Aristotle, Metaphysics IX 1046 b 29-30. Psillos 2006: 138-9. Psillos 2006.

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Instantiation Principle without too much difficulty. Stephen Mumford, for instance, argues as follow:30 [I]n what, actual, does an unmanifested, elementary causal power consist? Nothing other than itself. It grounds its own manifestations. Similarly, an unobserved elementary categorical property, if such a thing there could be, would consist in nothing but itself. Powers are, then, to be regarded as actual properties that ground further possibilities.

This solution seems to have a distinctly declarative quality; but it also confuses an ontological point with an epistemological one. The confusion emerges more fully into view if we focus on an equivocation between ‘an unmanifested, elementary causal power’ and ‘an unobserved elementary categorical property.’ It is an equivocation because the problem Independence poses is not (or not only) how we could ever observe or know a dispositional property that is never exercised, but that we seem compelled – to the extent that we abide by the Instantiation Principle – to deny its existence altogether. But no such problem arises in relation to categorical properties, since there is no contradiction involved in accepting that they exist even though they are not empirically accessible. Supporters of DISPIR need to find a much more cogent solution to the tension between Independence and the Instantiation Principle. It may be clear even at this stage why those who wish to preserve the Powers Model will be tempted to abandon the Instantiation Principle altogether. For if lawmaking dispositions were held to exist independently of their instantiation – that is, if DISPIR’s underlying ontology did admit uninstantiated dispositional properties – there would be no difficulty at all in endorsing Independence as an identity-condition for dispositional properties. Abandoning the Instantiation Principle would allow the Powers Model to accommodate Independence at a single stroke. But short of rejecting Independence as an identity-condition for dispositions – a remedy tantamount to abandoning the Powers Model altogether – there is no coherent way of combining it with immanent realism. So Independence strongly suggests that as a realist analysis of laws, DISPIR fails as a philosophical analysis of lawlike phenomena. 3.2.2. Intrinsicness When we turn to the second centripetal condition, the situation does not seem to get any better for DISPIR. This identity-condition stipulates 30

Mumford 2006: 485

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that ungrounded dispositions are intrinsically connected to their actual or potential manifestations. Come what may, the flammability of a kerosene is connected to its catching fire. Whatever changes might be made to its external circumstances, what determines the fragility of a glass is partly the fact that it is connected to the actual or potential shattering of the glass. The power of an electron to attract protons is intrinsic to that electron on the basis that its ability to exercise that power has nothing to do with anything other than that electron. Call this Intrinsicness. Now it is true, as Jennifer McKitrick has argued, that not all dispositions satisfy Intrinsicness. For instance, a key can lose its power to open a door if the lock of the door is changed; an object’s disposition to elicit a particular reading on a set of scales varies according to the gravitational field in which it is located.31 Nevertheless, this would present a challenge to the Powers Model only if it was committed to the thesis that all dispositions are lawmakers. But this is not the case: some supporters of the Powers Model would in fact hold that very few dispositions qualify as lawmakers. As one of its earliest contemporary advocates notes, the dispositions that the Powers Model identifies as possible candidates for lawmakers are only those properties that are thought to exist at the fundamental level of reality, in particular the properties of sub-atomic particles – charge, spin, and mass:32 The cases where we appeal to ultimate dispositions are … limited: there are not as many ultimate dispositions as there are dispositions … The dispositions that we allow to be ultimate are therefore a limited class, examples of which would be the disposition of subatomic particles which apparently have no internal constitution that could explain their behaviour.

So the question for present purposes is not whether dispositions satisfy Intrinsicness, but whether lawmaking dispositions do so. It is fair to say that once this qualification is made, there is relatively widespread support on all sides of the debate that the Powers Model needs to show that ungrounded lawmaking dispositions at the fundamental level should satisfy Intrinsicness.33 31 McKitrick 2003: 159-60. Molnar 2003: 102-5 cites Boyle’s question regarding what properties (if any) are added to a lock at the point at which the first key is wrought to fit it. Intuitively, the creation of the key means that the lock acquires the corresponding liability being openable. But if that analysis is correct, the liability of the lock to be opened is not an intrinsic property, since it depends on how things are with something distinct from the lock. 32 Mumford 1998: 229. 33 E.g. Lewis 1997: 147-8; Johnston 1992: 234; Bird 2007a: 125.

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But the trouble for DISPIR is that it is no clearer that Intrinsicness can be satisfied given its prior commitment to the Instantiation Principle than Independence can, even if it is a little harder to see why this is the case. The basic problem is that given the Instantiation Principle, it seems perfectly possible to block the putatively intrinsic connection between lawmaking dispositions and their manifestations by altering circumstances that are extrinsic to the dispositions. If an electron were placed in a possible world in which there no protons are instantiated, then according to the Instantiation Principle no protons exist.34 But this means that the power of electrons to attract protons in such a world would also not exist. By altering conditions extrinsic to electrons, it becomes impossible for electrons to manifest a lawmaking disposition. In other words, we have changed from without the connection between the dispositions of electrons to attract protons and the manifestation of that disposition in ways that should not be possible given Intrinsicness.35 DISPIR seems forced to conclude that fundamental dispositions are no more intrinsic than the power of a key to unlock a door. Why is it, though, that Intrinsicness poses a problem specifically for DISPIR? There are at least two reasons. First, its endorsement of immanent realism – or, indeed, a less ontologically committed attributetheory – means that all kinds of modifications to the external circumstances of a lawmaking disposition are possible that would rule out the existence of the manifestation to which it is supposed to be intrinsically connected. To see this, consider how easily a lawmaking disposition could satisfy Intrinsicness if it was not required to comply with the Instantiation Principle. Imagine that the property characterizing an electron actually exercising its power to attract a proton (the ‘manifestation’ property) were an uninstantiated universal that exists irrespective of whether or not it is spatiotemporally instantiated. It easy to see that amending the Powers Model in this way means that it is now possible to preserve the intrinsic status of the link between an electron’s dispositional property to attract protons

34 If it is the case that electrons are placed in possible world w at t in which protons are not instantiated at t, the Weak Instantiation Principle (see §2.3.5 above) does not rule out the existence of protons. But I earlier argued that the Weak Instantiation Principle would be an ad hoc solution to the objections raised against RBUIR, especially for those committed to an A-Theory of time. Even if those arguments are unsuccessful, the objection can easily be reformulated as an objection from the incompatibility of Intrinsicness and the Weak Instantiation Principle by imagining possible world w* in which electrons are instantiated and protons are, omnitemporally, never instantiated. 35 For an incisive discussion of this point, see Tugby 2013a: 469-70.

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and the corresponding manifestation property. This is because the manifestation property now exists no matter what modifications we introduce to the possible world in which electrons exist. In other words, an electron’s disposition to attract protons remains determinate even in possible worlds where the environmental conditions are fixed in ways that block the specific outcome towards which the lawmaking disposition in question is oriented. Second, Intrinsicness poses a specific problem for DISPIR because unlike RBUIR, it posits a constitutive link between a lawmaking disposition and its nomic outcome. For every version of the Relations Model, however, the link between properties and the nomic outcome in which they feature is – as we have repeatedly seen – a purely contingent one, so that in other possible worlds, one and the same lawmaking relation connects entirely different properties in such a way that regularities in those worlds will be identical to those that obtain in the actual world. By contrast, the two centripetal identity-conditions considered in this section demonstrate how radically the Powers Model diverges from that account in virtue of its underlying analysis of properties.

3.3. Lawmaking Dispositions II The previous section uncovered tensions between DISPIR’s commitment to the Instantiation Principle and two conditions for determining the identity of its lawmakers. Each of these difficulties, I suggest, is sufficiently serious to refute the claim that DISPIR offers a credible basis for accepting nomic realism. But it became clear at the same time that neither tension invalidated the basic explanatory approach of the Powers Model as such, at least to the extent that the latter presupposes a realist stance towards universals. For it is open to supporters of versions of the Powers Model with a prior commitment to universals to insulate them against the tensions provoked by Independence and Intrinsicness by yielding to the pressure to posit uninstantiated universals. Does a broadly similar conclusion arise if we scrutinise the second ‘centrifugal’ pair of identity-conditions for lawmaking dispositions? I suggest that it does. But here the pressure to admit uninstantiated universals is even stronger, because where the centripetal criteria focus on lawmaking dispositions taken separately (i.e. independently of any other properties), the centrifugal identity-conditions compel the Powers Model to posit additional ontologically distinct entities.

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3.3.1. Directedness One of the most peculiar features of the Powers Model’s commitment to ungrounded dispositions is the need to consider how things stand with entities that appear to be wholly distinct from them. Consider my ability to execute a satisfactory backhand in a tennis-match. This is determined in large part by dispositional properties that, as a metaphysical matter, have nothing to do with me. In other words, no metaphysical analysis of the disposition in question would be complete if it did not refer in some way to the fact that the disposition ‘points’ towards these other dispositions. Most crucially of all, the analysis would need to account for the fact that the disposition also ‘points’ towards my actually striking the tennis-ball in the relevant way. Needless to say, the idea that the identity of any property might be constituted (in whole or in part) by connections to ontologically discrete entities flatly contradicts Hume’s Principle. Yet in a series of striking departures from this orthodoxy, a growing number of analytic philosophers have argued that the identity of an ungrounded disposition is indeed partly determined by the manifestation towards which it is oriented.36 For an electron to have the disposition to attract protons in accordance with Coulomb’s Law is for it to be directed towards manifesting that power – that is, towards actually attracting protons. On the face of it, this seems a perfectly reasonable consequence of adopting a realist stance towards ungrounded dispositions. After all, it is difficult to see how a disposition that does not dispose its bearer towards any outcome at all could be a disposition.37 Call this feature of lawmaking dispositions Directedness. Can DISPIR offer a cogent metaphysical analysis of Directedness? There are, so far as I can see, two basic ways to approach the challenge. The first would be to treat dispositions as properties that are partly constituted by a full-blooded metaphysical relation to its correlate manifestation property. The second approach depends on a controversial analogy between Directedness and the intentionality of mental states. Let us consider each of these in turn. 3.3.2. Relational Directedness On the first analysis of Directedness, what grounds the fact that a lawmaking disposition points towards its manifestation property is that there 36 37

E.g. Molnar 2003: 60. Molnar 2003: 57; Bird 2007a: 524.

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is a genuine, metaphysically substantive relation connecting them. Call this Relational Directedness. Relational Directedness would hold that a rubber-band’s elasticity is related to its being stretched; that a match’s flammability is related to its being lit; that a vase’s fragility is related to its being shattered; and so on. Since these relations provide a metaphysical basis for Directedness, this solution relieves the worry that the nature of DISPIR’s lawmakers is mysteriously indeterminate. What are we to make of Relational Directedness? Unfortunately, it seems that the only reason to recommend it is that it is more plausible that the alternative solution (to be considered in §3.3.4 below). For, as David Armstrong has noted, far from addressing the problem that Directedness raises, Relational Directedness serves only to reinforce some of the very unpalatable metaphysical consequences that appear to flow from it: [H]ow can a state of affairs of a particular’s having a property enfold within itself a relation (of whatever sort) to a further first-order state of affairs, the manifestation, which very often does not exist? We have here a Meinongian metaphysics, in which actual things are in some way related to non-existent things.38

Let us collectively refer to these criticisms as the Meinong Objection. How might supporters of DISPIR respond to it? One solution, of course, is to bite the bullet and accept its implications.39 But quite apart from its inherent implausibility, this solution would rob DISPIR of precisely what was supposed to distinguish it from the Relations Model in the first place. For the hallmark of DISPIR – and, indeed, of the Powers Model more generally – is the elimination of lawmaking relations from its ontology in favour of natural properties alone. Second, if the motivation for DISPIR’s insistence on the Instantiation Principle is consistency with naturalism, it would make no sense at all to revise its underlying ontology in order to include entities as mysterious as those the solution proposes. If one is willing to accept this solution, there seems to be no principled reason left why one should not accept a full-blooded platonic ontology rather than the hazy hybrid of a Meinongian one. One influential supporter of the Powers Model proposes just this solution in response to the Meinong Objection. Thus Alexander Bird has 38

Armstrong 1997: 79. Mumford 2004: 193 notes that while he denies that Directedness is vulnerable to the Meinong Objection, ‘even if it [was], it would not be fatal to the [Dispositionalist Account].’ 39

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claimed that the objection overlooks the fact that dispositions could satisfy Directedness in virtue of the fact that they point towards an uninstantiated manifestation property. We will explore the basic strategy of formulating the Powers Model without the Instantiation Principle in §4.4.1 below. But for present purposes, it is enough to note that whatever its merits, it is not a solution that is available to DISPIR. Indeed the only reason the problem arises in the first place is that DISPIR is committed to the Instantiation Principle.40 3.3.3. Intentional Directedness The second way of accounting for Directedness is a proposal championed by George Molnar and U.T. Place to the effect that dispositions point towards their manifestations in a manner analogous to the way mental states point towards their intentional objects. On the intentionalist theory of mental states, my belief that elephants have tusks is constituted by the fact that it ‘involves’ – in a sense that the theory bears the burden of elucidating – elephants and tusks. This, claim Molnar and Place, helps us to make metaphysical sense of how salt’s water-solubility is oriented towards its dissolution in water. Call this Intentional Directedness. Intentional Directedness entails that the difference between the dispositional and the categorical cuts deeper than a mere linguistic distinction between dispositional ascriptions and categorical predicates.41 It develops Brentano’s famous thesis that the intentional is the mark of the mental by claiming that it is also the mark of the dispositional. One attraction of this view is the ideological economy and explanatory scope it would achieve: if the case for Intentional Directedness is successful, and if this case could satisfactorily be aligned with a plausible account of mental intentionality, this view would result in a well-integrated explanation of the mental and the physical. Needless to say, this would be an impressive philosophical achievement. The trouble is that, quite apart from the obvious differences between physical properties and mental properties (assuming, of course, 40 It is worth noting that Bird 2007a: 139-46 deploys graph theory to claim that powers supervene on their positions on a graph depicting the relational structure between powers. But Bird’s graph-theoretic approach means that his theory is still more congruent with the positing uninstantiated universals, since these could provide the ontological basis for the ‘missing co-ordinates’ that are filled in on the graph model. For an early attempt at formulating this graph-theoretic approach, see Dipert 1997. 41 Mumford 1999: 216.

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that the latter are accepted as a distinct ontological category), the most obvious difficulty with Molnar’s proposal is that many philosophers of mind take the fact that intentionalist theories of mental content resist a satisfactory naturalistic analysis to be a serious philosophical problem. Indeed many would cite this feature as reason enough for rejecting an account of the mental that presupposed it. So these philosophers, at any rate, are not likely to be persuaded that it might yield by analogy a solution to the problems that Directedness presents. They might argue, in fact, that proposing Intentional Directedness amounts to an argument by way of reductio against Directedness, and therefore an argument against the claim that there are ungrounded dispositions that could sustain laws in the realist sense. In response, supporters of Intentional Directedness might claim that the fact that mental intentionality does resist naturalistic analysis is simply a reflection of the inadequacies of naturalism’s procrustean ontology. For some, naturalism may seem an illegitimate basis on which to rule out mental intentionality as a potential source of fruitful philosophical comparison with the alleged physical intentionality of lawmaking properties. This line of argument may persuade some. But it is worth that if it is pursued – that is, if naturalism is rejected as the basis for deciding the ontological admissibility of mental content – then the primary motivation for DISPIR’s commitment to the Instantiation Principle evaporates, and the way is open once again to solving Directedness with uninstantiated universals as Bird proposes. 3.3.4. Reciprocity Let us now turn to consider a second striking implication of DISPIR’s commitment to ungrounded dispositional properties, namely that their identity is determined at least as much by other dispositional properties that feature among the stimulus conditions for them, properties that are – as it were – reciprocally directed towards the nomic outcome towards which the original property is directed. For without these other properties, the putative lawmakers would not attain the specific outcome towards which they are directed. Unfortunately, it turns out that this second centrifugal identity-condition provokes at least as many theoretical difficulties as Directedness itself. We have already seen that the identity of a disposition is constituted by the manifestation that it is a disposition for. But let us now consider the scenario from an entirely different perspective. In metaphysical terms, my dispositional ability to execute a

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satisfactory backhand shot in a tennis-match depends not only on the fact that it is directed towards my actually executing the shot, but also on indefinitely many other dispositional properties that are also reciprocally directed towards the manifestation of the disposition in question. In other words, whether or not I have the ability to strike a tennis-ball in the relevant way also depends on dispositional properties that are themselves directed towards my actually doing so. Indeed the claim that I have the ability in question would be simply unintelligible were it not for the implicit assumption that these other properties were directed in this way. After all, I could not exercise the ability were it not for the tensibility of the tennis-racket, or the elasticity of the tennis-ball, or the grip of my tennis-shoes on the surface of the court. To return to our standard scenario, on closer inspection it emerges that an electron’s disposition to attract protons cannot be the only disposition on the scene. For if electrons are to exercise their disposition to attract protons, it is necessary for protons to be disposed to be attracted by electrons. For the event to occur in a manner consistent with Coulomb’s Law, these dispositions must be aligned with each other. We can say that if electrons are ‘directed’ towards protons, protons are reciprocally ‘directed’ towards electrons: they are both ‘reciprocal disposition partners.’42 In other words, the exercise of a power requires stimulus conditions and manifestation conditions that typically involve many other powers.43 Call this Reciprocity. Reciprocity may strike us as a strange identity-condition for an ungrounded dispositional property. But consider the implications for DISPIR if it did not subscribe to Reciprocity. Let us try to imagine, that is, a scenario in which electrons have the power to attract protons but protons do not have the corresponding power to be attracted by electrons. We might try to do so; but we could never succeed. For it would not only be nomologically impossible for electrons to attract protons under these circumstances, but conceptually impossible too. It is simply not possible to conceive of a scenario in which electrons attract protons but protons are not attracted to electrons. As it happens, Reciprocity is a basic corollary of the overall metaphysical vision that a commitment to ungrounded dispositions implies. Lawlike regularities consist not in lone powers exercising themselves on an inert environment, but rather in the simultaneous exercise of multiple 42 43

Martin 2008: 3. Williams 2010: 87-9.

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powers within a structure of mutually connected dispositions.44 Once this is grasped, it is possible to see that Reciprocity in fact follows trivially from Directedness, since the distinction between them is just a function of how we go about analysing the instance of a purported regularity. So if we begin by analysing an electron’s disposition to attract protons, we must then ask how protons must be reciprocally disposed in order to be attracted by electrons. If, by contrast, we begin by analysing a proton’s disposition to be attracted to electrons, we then turn to the reciprocal disposition electrons must possess in order for protons to be disposed in this way.45 Notwithstanding the ‘centripetal’ character of the identity-conditions discussed in §3.2, it is hard to deny that, as an ontological matter, dispositional properties come bundled together. That is to say, for any power to be exercised it seems that other powers must be partnered with it. Dispositions enjoy reciprocal connections with each other. The importance of Reciprocity to DISPIR emerges when one notes that some advocates DISPIR explain laws in terms not only of powers, but also liabilities.46 The metaphysical analysis of lawlike regularities that DISPIR proposes requires it to treat the simultaneous exercise of innumerably many distinct powers sufficiently coordinated to bring about highly specific and pervasively regular outcomes. Water’s power to dissolve salt is, it turns out, only a partial condition in salt’s dissolving in water with lawlike regularity. For the regularity must also consist in salt’s power to be dissolved in water; in the power of the air particles to move at sufficient 44 Different labels have been used for the ontology that Directedness and Reciprocity implies – e.g. Martin 2008: 22 (‘a web or net of readiness’); Mumford 2004: 182 (‘an interconnected web’); Armstrong 1997: 255 (‘a power net’). 45 Williams 2010: 88 makes essentially the same point in the context of causation when he illustrates Reciprocity by asking us to imagine a rock striking a glass, noting that ‘[w] hen considering causation we tend to focus on a single salient feature of the cause, treating it as the cause, thereby downgrading the importance of the other factors involved. And yet without those other factors ‘the’ cause could not have produced the effect. We say that it is the rock that broke the glass. The rock is the subject … but when powers are the source of causal action, the rock does not act upon the glass, the two act together. It follows that it is a mistake to single out a single feature and treat it as the cause in the first place.’ 46 The terminological distinction between ‘powers’ and ‘liabilities’ is one adopted by Swinburne 2004a in his own account of laws. But it seems to me that framing dispositional pairs in this way is not especially helpful, since it risks obscuring Reciprocity altogether by implying that there is an asymmetric relationship between (say) water’s ‘power’ to dissolve salt and salt’s ‘liability’ to be dissolved in water. But in fact the latter is no less necessary a condition for the dissolution of salt in water than the former. Martin’s language of ‘mutuality’ between multiple dispositions that ‘partner’ with one another more accurately expresses the basic thought behind Reciprocity.

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velocity to prevent the water from freezing; in the power of hydrogen atoms to form covalent bonds with oxygen atoms; and so on. The conjunction of Directedness and Reciprocity gives rise to what has been labelled ‘the problem of fit.’47 The metaphysical analysis undertaken in §3.2 and §3.3 of what determines the identity of a simple but plausibly fundamental lawmaking disposition – that is, the power of an electron to attract a proton in accordance with Coulomb’s Law – has led us to uncover a vast network of interconnected dispositions. It is a network – a ‘powers net’ or ‘web of readiness’ – that exhibits an almost unimaginable degree of interconnectedness between the dispositional properties that are supposed to provide the metaphysical ground for lawlike regularities. As Martin puts it, the Dispositional Account implies that ‘nature comes in package deals.’48

3.4. The Fresco Problems We have now seen that conjoining the Instantiation Principle with each of the four identity-conditions discussed in §3.2 and §3.3 provokes four unpalatable dilemmas for DISPIR. For the sake of clarity, let us rehearse these once again in summary form: a lawmaking disposition could not exist independently of its manifestation given that the Instantiation Principle requires DISPIR to deny the existence of non-occurrent manifestations; (ii) a lawmaking disposition could not be intrinsically linked to its manifestation given that modifications to the external conditions of the disposition could prevent the manifestation, but in the absence of the Instantiation Principle it could be intrinsically linked to its manifestation regardless of the modifications since the manifestation would exist uninstantiated; (iii) a lawmaking disposition could not be directed towards its manifestation, since the Instantiation Principle entails that non-occurrent manifestations do not exist; and

(i)

47 Williams 2010: 90. Tugby 2013a picks up on a difficulty very close to this one, though he frames it in terms of the inconsistency between Intrinsicness and Directedness. Both suggest that a platonic theory of properties could provide a way out for those committed to ungrounded dispositions, a proposal we will pursue at greater length in Chapter 4. 48 Martin 2008: 3.

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(iv) a lawmaking disposition can only be manifested if other dispositions are not present, but these dispositions could not be reciprocally directed towards its manifestation, since the Instantiation Principle entails that non-occurrent manifestations do not exist. In the face of these difficulties, some supporters of the Powers Model have suggested that it requires an underlying ontology of a vast network of interconnected dispositions that has been dubbed ‘powers-holism.’49 Before we consider whether these solutions are coherent within a naturalistic ontology, we must first consider a more global kind of objection to DISPIR that threatens to undermine DISPIR still more seriously than the tensions noted in (i)-(iv) above. 3.4.1. A Thought-Experiment To see why the four identity-conditions set out in §3.2 and §3.3 form an inconsistent quartet given the Instantiation Principle, consider the following thought-experiment. Suppose that an earthquake devastates the town of Assisi, and that many centuries later an archaeological team excavates the long-forgotten ruins of the Basilica di San Francesco. The team uncovers some – but not all – of the pieces from the fresco sequence in the Upper Basilica narrating the life of St. Francis. Each of the uncovered pieces depicts a self-contained artistic scene from the saint’s life. As the excavation progresses, however, enough of these pieces are uncovered for the team to form the reasonable conclusion that: (i) what initially appeared to be discrete works of art in fact formed part of a larger artistic vision; and (ii) the gaps that are inferred in the narrative sequence from the uncovered pieces indicate not that these scenes were never painted, but rather that they are still missing or destroyed. The scenes on the fresco-pieces represent DISPIR’s lawmakers. Analogues to the four identity-conditions considered in §3.2 and §3.3 can be elaborated as follows. Independence is captured by the fact that the intelligibility of a scene depicted on one of the pieces is not affected by whether or not it is under the rubble, just as the existence of a lawmaking disposition is not affected by the fact that it is not manifested. Intrinsicness can be represented by the thought that the intelligibility of the scene on a fresco-piece is not affected by any other discovery the team could 49

Williams 2010.

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make, just as a lawmaking disposition’s connection to its manifestation is not affected by modifying its external circumstances. These would be the analogues to the centripetal identity-conditions. As for the centrifugal identity-conditions, the equivalent to Directedness would be the fact that as more fresco-pieces emerge, it becomes clear that many of the scenes can only be fully understood in the context of their relation to other scenes. For example, although one fresco-piece seems to depict a self-contained scene of St. Francis as a wealthy man, another fresco-piece is discovered that depicts him celebrating a life of poverty. The meaning of the first scene is enhanced when viewed alongside the second one once we grant that an underlying narrative connects the two scenes: when we observe the former, we now do so in anticipation of the latter. Similarly, Directedness tells us that the nature of a lawmaking disposition is determined – at least in part – by the specific outcome towards which it points. Its identity is constituted by something discrete from it.50 Once again, what constitutes a disposition is what it is a disposition for. Trivially, this captures Reciprocity too: just as we can observe the first scene in anticipation of the second, we can also understand the significance of the second scene by situating it in relation to the first. Framing the scenario in this way makes it easier, I suggest, to see where the tensions with the Instantiation Principle lie. This is because the team has made the only sensible inference: there were once many frescopieces that together depicted a coherent and integrated narrative. But notice that this is the equivalent of inferring from an analysis of the identity-conditions of lawmaking dispositions that uninstantiated properties exist. That is, it is the equivalent of denying the Instantiation Principle. To find an analogue to this denial in our thought-experiment, it would be as if the team declared that the only fresco-pieces ever painted were those that happened to have been discovered,51 or that it was sheer coincidence that, taken together, the scenes could be interpreted as an integrated, organic whole. In fact, the scenario does not quite illustrate just how implausible this second claim really is. For while it might be possible to imagine some of 50 I should note that the thought-experiment might encourage us to think that the Fresco Problems capture the epistemic difficulty of establishing the nature of lawmaking dispositions; this would be mistaken, since the problem is whether or not their identity can be settled as an ontological matter given the Instantiation Principle. 51 This, in effect, is the analogue to the ‘Megaric Actualist’ solution to Independence – discussed in §3.2.1 above – to the effect that only the actual is possible.

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the scenes accidentally fitting together, it would be impossible for a disposition to be directed towards a manifestation and for that manifestation to be the specific outcome of some other disposition, since salt’s disposition to dissolve in water and water’s disposition to dissolve salt are two sides of the same conceptual coin.52 3.4.2. Two Unsuccessful Solutions It is a profoundly puzzling feature of the most sophisticated and influential defences of the Dispositional Account that they overlook the implications of the Fresco Problems to the degree that they do. Martin, for example, chooses simply to state the difficulties rather than solve them:53 The readiness of something’s disposition … may fully exist although its disposition partners and mutual manifestations do not. As such, dispositions are not relations. A disposition can exist although its manifestation, or even its reciprocal disposition partners, do not. Salt in a world lacking H2O would have many of its readinesses unfulfilled. Among the non-actual reciprocal disposition partners for which it would have actual readinesses would be ones that would be simple and very different or complex with a very different mix from those in our world. There could be a realist model for what we need for modality in this.

But what could this ‘realist model’ be if not one that admitted entities that existed outside spacetime? Given that Martin relies on tropes rather than universals, the answer to this must presumably force an appeal to unrealised states of affairs rather than uninstantiated universals. As we saw in §3.1.4 above, however, this move ultimately renders the dispositional elements in Martin’s proposed ontology entirely obsolete. In any event, his remarks make it no clearer how DISPIR could evade the Fresco Problems than a trope-theoretic version of the Powers Model could. Simply stipulating that arsenic is lethal in a possible world in which there is no one with a corresponding disposition to die as a result of ingesting it fails to address the difficulty DISPIR faces. For recall that, given the Instantiation Principle, the disposition that is meant to partner reciprocally with the arsenic’s disposition to kill does not exist. So Martin simply begs the question against those who object to the coherence of DISPIR as a realist analysis of laws.

52 53

I owe this point to Williams 2010: 91. Martin 2008: 6.

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Stephen Mumford comes much closer to uncovering the Fresco Problems when he devises a similar scenario:54 The world is more analogous to a jigsaw puzzle [than Lewis’s vast mosaic – see §1.1.2 above]. Each jigsaw piece can fit with the rest in only one way. It can connect with a number (all) of its neighbouring pieces but its shape and colouring allow only a single place for it in the complete picture. Furthermore, the entire sum of pieces will fit together only in one way to form one picture. The puzzle has a single solution due to the complexity of its interconnections … It is impossible to life two pieces out of the complete picture and swap their places … In this sense, the place in the whole picture is necessary to the piece. The metaphor is inexact in a few ways. The most significant ones are that each piece still has intrinsic qualities, which you could describe if you found a single piece that was separated from the rest of the puzzle, and each piece still has a self-contained identity … The point of the inexact metaphor, however, is to illustrate some of the important features of the holistic view of the world. The world is a single whole, composed of properties whose essence and identity are determined by their place in that whole.

It is important to note that the thought-experiment we have considered avoids the inexactness in Mumford’s jigsaw metaphor, since it does feature an analogue to the centripetal identity-conditions (Mumford’s ‘intrinsic qualities’) where the jigsaw puzzle does not, because the fresco-pieces do depict self-contained scenes. But despite the fact that Mumford correctly concludes that analysing dispositions implies a holistic ontology that contrasts very sharply with the atomistic ontology implied by Lewis’ categoricalism, he fails to see that the picture collapses once uninstantiated universals (in the case of DISPIR) or unrealised possibilia (in the case of trope-theoretic versions of the Powers Model) are excluded from that ontology.55 Like Martin, he seems indifferent to the fundamental contradiction between positing connections between a lawmaking disposition and its manifestation and stipulating that the existence of the disposition in no way depends on any other property:56 We can say merely that a property’s identity is fixed by the (causal) role it plays in relation to other properties. Though its identity is fixed by relations with other properties, its existence has no ontological dependence on those properties … The power and its manifestation are distinct existences between which there are de re connections. 54

Mumford 2004: 184. I am assuming that Mumford is an immanent realist about universals, but it is difficult to find an explicit statement in his writings to this effect. It is clear enough, though, that he rejects uninstantiated properties and unrealised states of affairs, and that is enough for the objection to hold. 56 Mumford 2004: 171. 55

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In short, it is difficult to make any sense of an idea that both Martin and Mumford take largely for granted. How can the identity of a property be determined by its causal connection to other properties even though its existence is entirely independent of it? The Fresco Problems draw out deep and puzzling contradictions between the centripetal pair of identityconditions and the centrifugal of identity-conditions that emerge to the extent that the Powers Model refuses to lift metaphysical naturalism’s injunction against uninstantiated universals. This central contradiction means that, in the final analysis, we should reject attempts to elaborate the Powers Model from within the confines of a naturalistic ontology. * * * This chapter has argued that if the Powers Model is to succeed, the Instantiation Principle must be rejected. For there seems to be no other way of analysing its lawmakers in a way that renders their identity determinate. The attraction of a platonic ontology is that it would allow the Powers Model not only to defend the coherence of each of the four identity-conditions, but also to explain how the conflicting pairs of identity-conditions might be integrated in a coherent way. So it appears that for all the differences we have stressed between RBUIR and DISPIR, the shortcomings of each account independently point us in the direction of precisely the same solution. If we are to continue the search for a realist analysis of laws, the time has come for us to scrutinise more carefully the implications of succumbing to the pressure to platonise. For the source of almost all our woes so far could not, I suggest, be more clear: naturalism has failed to deliver.

CHAPTER 4 THE TURN FROM NATURALISM: TWO PLATONIC STRATEGIES

We have now examined the two most plausible naturalistic cases in support of a realist conception of regularities in the natural world. Each depended on the assumption that universals exist. This should not surprise us: it is no accident that realist accounts of laws in the last few decades have emerged in tandem with an equally vigorous renewal of confidence in the existence of universals. As we have already noted, the reason for this dialectical alignment is that universals deliver some of the most critical ingredients in any realist theory of laws, in particular the alleged objectivity, generality, repeatability, and universality of lawlike regularities in nature. Yet it has also emerged that the tactic of positing the kind of universals RBUIR and DISPIR each propose incurs at least as many theoretical costs as the benefits they were supposed to confer. Some of these costs were borne by RBUIR alone, others by DISPIR alone, while some threatened to undermine both accounts. We have conceded that these objections are convincing enough to reject nomic realist strategies that are underwritten by immanent realism. Now this does not, of course, entail platonic realist alternatives. For, faced with this prospect, committed naturalists may now be tempted to abandon the search for a viable realist analysis of lawmaking in favour of nomic antirealism. But if deflationary approaches did not themselves present profound problems of their own, we would never have initiated that search in the first place. So the proposal that animates the remainder of this book is that we accept the failure of theories that rely on the Instantiation Principle warrant rejecting it altogether as a methodological constraint. If we wish to preserve a commitment to universals – and it will be clear by now why nomic realists should wish to do so – platonic realism quickly follows in light of the difficulties that confronted immanent realism in Chapter 2 and Chapter 3. The purpose of the present chapter is to assess whether a platonic theory of universals relieves any of the theoretical tensions identified in Chapter 2 with respect to the Relations Model and in Chapter 3 with respect to the Powers Model. We have already noted, after all, that these

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tensions appeared to generate a pressure to platonize. What happens, then, if each account surrenders immanent realism and succumbs to the pressure to platonize? Let us begin, though, with two general reasons why nomic realists might be tempted to take up a platonic strategy. The first reason arises by analogy with a classic argument for scientific realism, while the second offers a variant on the so-called ‘indispensability arguments’ for the existence of mathematical objects advanced by Quine and Putnam in the 1970s. In §4.2, I turn to consider Michael Tooley’s attempt to elaborate the Relations Account within a platonic realist framework – a position we shall designate as RBUPR – with a view to determining how successfully his strategy escapes the objections raised against its immanent realist counterpart in §2.3 and §2.4. We shall see that although RBUPR can handle these objections in a sufficiently promising way to be taken seriously as a realist proposal, it also generates a number of difficulties – explored in §4.3 – that did not confront RBUIR. Given these difficulties, in §4.4 I proceed to analyze the benefits that result from developing the Powers Model within the framework of a platonic ontology. It turns out that this version of the theory – a position we shall label DISPPR – does indeed clear up many of the objections raised against DISPIR in the course of §3.2, §3.3, and §3.4. §4.5, however, I show that DISPPR is vulnerable to many of the same difficulties that undermine RBUPR. Finally, in §4.6 I consider the weight of metatheoretical objections against both platonic transpositions and concludes that in light of the fact that it is debatable – at the very least – whether these have the upper hand in explanatory terms, the ungainliness and undue complexity of their theoretical commitments should make us hesitate still further before endorsing either of them. The ultimate failure of these two platonic strategies forces us to consider the only sort of explanation still left untouched by that stage, namely theistic strategies. A full assessment of this non-naturalistic alternative in the course of Chapter 5 and Chapter 6 will eventually lead us to consider renditions of the Relations Model and the Powers Model that eliminate universals altogether.

4.1. Platonic Lawmaking: The Metaphysical Framework The problems that the Instantiation Principle provokes for nomic realism have persuaded several philosophers – theorists who are predominantly, it should be stressed, committed naturalists in other respects – that a

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coherent account of laws cannot succeed if it does not invoke platonic properties.1 But before we are in a position to evaluate these accounts, we must first settle on a working definition of platonic realism. In its most basic form, it construes properties and relations as universals that exist in an abstract domain prior to and independently of their instantiation in concrete particulars. Most would also agree that platonic universals exist necessarily if they exist at all.2 If universals do exist in an abstract domain, then on most definitions of abstractness they would also exist outside space and time and be causally inert. 4.1.1. Indispensability Arguments In addition to accommodating the objections that flow from the Instantiation Principle in Chapter 2 and Chapter 3, it may be possible to offer more constructive support for combining platonic realism with nomic realism by drawing on the kind of argument sometimes advanced in support of ‘Scientific Platonism.’3 One might also appeal to Putnam’s ‘no-miracles’ argument for scientific realism:4 The positive argument for scientific realism is that it is the only philosophy that doesn’t make the success of science a miracle. That terms in mature scientific theories typically refer … that the theories accepted in mature science are typically approximately true, that the same term can refer to the same thing even when it occurs in different theories – these statements are viewed by the scientific realist not as necessary truths but as part of the only scientific explanation of the success of science, and hence as part of any adequate scientific description of science and its relations to its objects.

A nomic realist variant of this argument might claim that platonic realism is warranted on the basis that, in the absence of platonic universals, it is a miracle that regularities have the predictable and uniform character that they do. A central weakness of RBUIR, for instance, is that it makes laws depend on wholly contingent facts about which universals are instantiated at any point in space and time. As we have already seen, Armstrong’s proposal to adopt the Weak Instantiation Principle does address this objection to some degree, but only if we are prepared to endorse eternalism. 1 Tooley 1977: 685-6; Tooley 1987: 72-5; Forrest 1993; Fales 1990; Bigelow & Pargetter 1990; Brown 1991; Bird 2007; Tugby 2013. 2 For an argument that this is especially true of platonic realists who wish to develop a realist theory of laws, see Tugby 2013b. 3 Bigelow & Pargetter 1990: §1.1. 4 Putnam 1975: 73.

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As we saw in §2.3.5, this commitment will exact unacceptably high price for some. And, as we have also seen, Armstrong’s concession still does not accommodate the plausible thought that some laws are omnitemporally never exemplified. Arguments of this kind in support of platonic realist approaches to laws are not wildly implausible. Although he is otherwise critical of Tooley’s platonic version of the Relations Model, Ted Sider accepts that, as it stands, the analogy from the argument for scientific realism is a perfectly reasonable one. Positing the lawmaking relation between universals may be acceptable for the purposes of what else it clarifies.5 But the problem with motivating an argument for platonic realism this way is that it is an argument for realism about concrete rather abstract entities. That is to say, it is an argument in favour of the existence of entities that are in principle accessible to empirical inquiry. So even if the ‘no-miracles’ argument were successful – and many deny that it is6 – then the most one could infer from it is that it is legitimate to posit the existence of entities that are unobserved but in principle detectable. This detectability criterion is crucial: I can detect that someone has been in my sitting room from footprints on the carpet, even if I cannot observe the person directly. So there seems to be a clear and intuitive distinction to be made between (on the one hand) positing spatiotemporal entities to clarify a scientific theory – i.e. entities that in principle play some causal or functional role – and (on the other) positing abstract entities to which there is in principle no epistemic or perceptual access. Some have been willing to go as far as to posit abstract entities if an idealized science quantifies over them. This draws on the well-known criterion of ontological commitment he deploys to justify realism with respect to certain mathematical objects on the basis that they feature in our best scientific theories. Indeed Putnam himself explicitly extends the ‘no-miracles’ argument to include abstract mathematical objects (i.e. entities that are in principle undetectable):7 I believe that the positive argument for realism has an analogue in the case of mathematical realism. Here too, I believe, realism is the only philosophy that doesn’t make the success of science a miracle. 5 Sider 1992: 14: ‘While it would be nice to have a more complete account of its workings, we may view the introduction of the necessitation relation as a theoretical posit, analogous to the positing of subatomic particles in physics to account for various data.’ 6 See, for instance, Lipton 2004: 196-8, who argues that it is guilty of committing the so-called ‘base-rate’ fallacy. 7 Putnam 1975: 73.

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It might also be argued that since law-statements form part of our best scientific theories – such as those considered in §2.4 above – and since these quantify over universals that are not instantiated, Quine’s criterion commits us to the existence of these entities. Now indispensability arguments for laws grounded in platonic universals are likely to prove at least as controversial as indispensability arguments for mathematical objects; but I shall now suggest that to the extent they posit an abstract domain that is capable not only of grounding a robust realism about laws, but also of providing an ontology for their mathematical content, advocates of platonic theories are in a position to claim a greater degree of explanatory unity and ideological economy than their immanent realist counterparts. 4.1.2. A Mathematical Ontology for Laws The foregoing arguments suggest some of the reasons for adopting a platonic strategy to laws as a result of its inclusion of attributes into its ontology (specifically, properties and relations). But it is important to underline that it is also considerably strengthened by the fact that it suggests a solution to one of the most familiar problems in the philosophy of mathematics, namely the applicability of abstract mathematical objects to the physical world.8 The reason for this is straightforward: the ontology that underpins platonic versions of nomic realism would accommodate the apparently ineliminable mathematical content in lawstatements in a much more plausible and less ad hoc way than theories that reject an abstract domain. It is, after all, almost impossible to formulate a statement of scientific law in a way that entirely avoids reference to mathematical entities. All things considered, a theory of laws that accounts for lawlike regularities as well as their mathematical content should be preferred to one that does not. Take, for the sake of simplicity, Newton’s gravitationၕ law, central to which is the inverse-square function.9 What is especially striking is that this function operates in laws that have

8 This is a problem that Wigner 1967 famously labelled the ‘unreasonable effectiveness’ of mathematics. 9 I use this example on the assumption that it is to this law that the nomic realist is committed if she is committed to any law. It is true of course that the gravitational law operates only within the framework of classical mechanics, but since the mathematical content featured in quantum laws is considerably greater than any featured in the gravitational law, this enhances indispensability arguments for the existence of abstract entities.

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very different applications.10 Thus in the field of optics, the law governing the propagation of light states that the decrease in luminosity is inversely proportional to the square of the distance between the lightwaves and sound-waves and their respective point source. Likewise, in the field of acoustics, decreases in sound pressure are inversely proportional to the square of the distance between the sound-waves and their point source. In the field of electrostatics, Coulomb’s Law holds – as we have repeatedly seen – that the quantity of electrostatic charge between two charged objects is inversely proportional to the square of the distance between them. Taken together, these very different examples highlight how difficult it is to make sense of the idea that the inverse-square function is not located in an abstract domain. Even if we could provide a convincing nominalist reduction of the function – a fictionalist one, perhaps11 – this would still not explain why it is applicable across so many discrete branches of the empirical sciences. One important generic advantage that platonic strategies have over rival accounts, then, is that they can add mathematical entities – such as the inverse-square function – to their ontology at a relatively low additional cost. An ontology that integrates both laws and their mathematical content would make these theories much more economical and explanatorily powerful than their immanent realist counterparts, which struggles to accommodate into its ontology truthmakers for mathematical statements.12 4.1.3. Regress Concerns Any theory that presupposes platonic realism faces, of course, the difficulty of explaining the exemplification tie between universals and particulars. Different regress arguments have famously been advanced against it. As Ryle noted long ago in relation to the ‘Third Man’ Argument in Plato’s Parmenides, the exemplification problem is problematic for the same reason that Bradley found relations to be problematic.13

10 For a discussion of the applicability of the inverse square principle, see e.g. Steiner 1998: 35-6. 11 An excellent recent defence of mathematical fictionalism is Leng 2010. 12 Armstrong himself opts for an Aristotelian account of numbers – see Forrest & Armstrong 1987 and Armstrong 1997: 178-80 – but few empiricists have followed him down this road. 13 Ryle 1939.

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Bradley’s famous objection to relations was that they trigger an infinite – and vicious – explanatory regress: logically prior to x and y being related to each other, there must be a relation R between them such that xRy. But if that is so, we must then ask what relates x to R and R to y. If the response is that, respectively, R’ relates x to R and that R’’ relates y and R, it is easy to see why a regress threatens so that the nature of the exemplification tie between universal and particular is rendered forever indeterminate. This regress objection can be applied to universals in general, not just relations. If a square bricks exemplifies squareness, there must be some metaphysical tie between the particular and the universal. But then it seems that we are forced to characterize this tie by invoking a universal that it exemplifies, and so on ad infinitum.14 The upshot of these objections is that if exemplification is characterized as a relation, then it must be distinguished from the kind of relations to which Bradley objected. It looks as if the platonic realist has to claim that exemplification relations are primitive particulars (non-repeatable property-instances, perhaps – i.e. tropes) that do not themselves exemplify second-degree properties. In terms of ideological parsimony, this is hardly a satisfactory outcome; but it is one that we may end up preferring in light of the difficulties immanent realist accounts encountered in Chapter 2 and Chapter 3.15

4.2. Platonizing the Relations Model The aim of this section is to set out a platonic realist version of the Relations Model by examining the account elaborated by Michael Tooley. It will stress the ways that the platonised version – RBUPR – addresses many of the difficulties that confront its immanent realist counterpart. As we shall now see, platonic realism offers genuine explanatory gains to the supporter of the Relations Model.

14 Not all regresses are vicious, of course. If it is true that snow is white, it is true that it is true that snow is white, and it is true that it is true that it is true that snow is white, and so on ad infinitum. This is not a vicious regress, because it is not one that forever defers an explanation. The regress before us now, however, is one that passes the explanatory buck along an infinite series. 15 Thus Strawson 1959: 167; Fales 1990: 138-9; and Moreland 2001: 116.

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4.2.1. Varieties of Platonic Realism Tooley develops by far the most well-known version of RBUPR.16 Tooley himself distinguishes three main options for platonic realism. He labels the first option factual platonic realism. This is the view that universals are independent of particulars but exist contingently. He terms the second option moderate platonic realism, which simply adds to factual platonic realism the thesis that independent but contingent universals can also include universals constructed out of other universals (such as structural universals or conjunctive universals). Tooley rejects this second conception primarily on metatheoretical grounds, choosing instead to adopt factual platonic realism to support his version of RBUPR. Tooley also sets out a third conception: strong platonic realism. This is the position most widely recognised as platonic realism. Strong platonic realism, he claims, is to be distinguished from the other two by virtue of its claim that universals are necessary existents, since it denies that any universal is dependent in any way on any contingent feature of the world: universals exist as a matter of necessity.17 On strong platonic realism, if universals exist necessarily, then so too do the relations between them. It therefore follows that a version of the Relations Model that adopts this kind of platonic realism must treat natural laws as governing entities as a matter of metaphysical necessity. As it stands, then, this approach offers the converse response to the Modal Hybridity Problem from that proposed by BSA. For where the latter resolves the problem in favour of the Contingency Intuition, the former does so in favour of the Governance Intuition. The claim that the nomological structure of the actual world might have been otherwise must simply be abandoned where the Relations Model is combined with strong platonic realism, notwithstanding the pull of the Contingency Intuition. But Tooley claims that this unwelcome consequence does not follow from versions of the Relations Model that adopt factual platonic realism or moderate platonic realism. This is because, unlike strong platonic realism, both treat universals as contingent existents. Thus universals are independent of the particulars that might or might not instantiate them – and so exist in a transcendent, non-spatiotemporal realm – but the question of which universals happen to populate that realm, and how 16 Tooley 1977; Tooley 1987. Similar versions can be found in Swoyer 1982, Fales 1990, and Fales 1993, even if these also differ in some important respects – see the discussion of hybrid platonic strategies in §4.3.4 below. 17 Tooley 1987: 119-20.

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these universals are related in lawmaking ways is an entirely contingent matter. In Tooley’s view, then, the proponent of either of these modally weaker versions of platonic realism is able to accommodate the Contingency Intuition in a way that the strong platonic realist cannot. But why does Tooley think these weaker versions resist treating laws as metaphysical necessary? The central advantage of positing contingent transcendent universals, he claims, is that it undermines one of the main historic objections raised against platonic realism:18 [A]ccording to the Factual and Moderate versions of Platonic realism, what universals exist is a contingent matter. This difference is important in the present context; for given that the commitment to necessarily existent entities is, for many philosophers, one of the most unappealing features of Strong Platonic realism, it is essential to notice that the expression ‘Platonic realism’ is here being used to cover positions that are free of that commitment.

But the argument that one can render platonic universals palatable by weakening their modal strength is a puzzling one. For the central problem involved in positing these entities is not their necessary modal status. Rather, naturalists reject abstract entities on the basis that they are not spatiotemporal and/or that they do not enter into causal relations. They are much less motivated to do so by the question of their modal status: realism about abstract entities might commit one to the metaphysical necessity of the number 7, but also to the contingent status of Shakespeare’s A Winter’s Tale. Tooley’s suggestion that construing platonic universals as contingent does not appear to remove the central obstacle that stands in the way of accepting them. 4.2.2. Tooley’s Indispensability Argument Our discussion of RBUIR in Chapter 2 has already hinted at the basic shape of Tooley’s argument for RBUPR. It starts from the reasonable intuition that if there had been a slight difference in natural causes that led to the instantiation properties and relations constitutive of laws, there would have been a corresponding difference in how the universals came to be instantiated. Universals that are instantiated might not have been instantiated – the actual patterns of instantiation that we find among universals arise entirely as a contingent matter. Tooley insists that had these patterns not been instantiated, there would still have been laws governing 18

Tooley 1987: 120.

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their possible instantiation. The challenge for RBUIR is to explain what makes this counterfactual true given that uninstantiated universals are excluded from its ontological inventory. Tooley’s view, in effect, is that the challenge cannot be met: what makes the law-statement true is the actual existence of the universals over which it quantifies. He illustrates the point with the following thought-experiment:19 Suppose that materialism is false, and that there is, for example, a nonphysical property of being an experience of the red variety. Then consider what our world would have been like if the earth had been slightly closer to the sun, and if conditions in other parts of the universe had been such that life evolved nowhere else. The universe would have contained no sentient organism, and hence no experiences of the red variety. But wouldn’t it have been true in that world that if the earth had been a lot farther from the sun life would have evolved, and there would have been experiences of the red variety? If so, in virtue of what would this subjunctive conditional have been true? Surely an essential part of what would have made it true is the existence of a certain psychophysical law linking complex physical states to experiences of the red variety. But if the truthmakers for laws are relations among universals, it could not be a law in that world that whenever a complex physical system is in a certain state, there is an experience of the red variety, unless the property of being an experiences of the red variety exists in that world. Thus, if [the Relations Model] is correct, one can describe a slightly altered version of our world in which there would be uninstantiated, and hence transcendent, universals.

Tooley’s intuition is that hypothetically ‘missing’ universals should not affect the existence of a law governing the nomic behaviour of particulars that do in fact instantiate these universals. But since the Relations Model holds that laws just are relations between universals, the only way of making sense of this claim is to postulate universals (and relations between them) that would exist regardless of whether the right causal conditions obtain to trigger their instantiation. In other words, on factual platonic realism universals are indispensable theoretical posits for formulating the best version of the Relations Model. 4.2.3. So Long, Meinong It is implausible to think that Tooley’s alien universals – that is, properties that hitherto have no instances – would not interact in lawful ways with actual instances of universals if they were ever instantiated. But this counter-intuitive conclusion seems to be forced on realist accounts 19

Tooley 1977: 685.

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that take every universal to be an instantiated universal. In §3.3.2, we noted the objection that Armstrong levels against Relational Directedness as an attempt by supporters of DISPIR to account for the orientation of a dispositional property towards its corresponding manifestation property. Yet this seems to invite a tu quoque objection, since the problem of alien universals seems to highlight a similar vulnerability in his own account. To see this, consider a variation on the scenario first raised by Tooley.20 The aim, we will recall, is to ensure that the Relations Model can accommodate the intuitively plausible possibility that the causal behaviour of alien properties would be governed by laws if they were instantiated.21 The suspicion is that its preferred ontology prevents RBUIR from grounding the truth of this subjunctive conditional. Since RBUIR relies on the Instantiation Principle, the scenario seems to force us to entertain relations between instantiated universals and possible but non-existent entities. Yet this, of course, is precisely the Meinong Objection we saw Armstrong himself raise against Relational Directedness in §3.3.2. Given RBUIR’s categoricalism, one might have thought that it would unaffected by problems raised specifically against DISPIR. For categoricalism appears at first glance to insulate RBUIR against the objection from Independence against lawmaking dispositional properties on the basis that it assumes from the outset that all natural properties – or, at least, all fundamental natural properties – are occurrent properties. Manifestation is already built into the properties that RBUIR invokes. The difficulty is that properties are not – indeed, as we have repeatedly underlined, could not be – the lawmaking ingredient on which RBUIR relies. And with respect to relations RBUIR does appear to confront structurally similar difficulties to those that undermined DISPIR. Here, RBUIR faces a dilemma: either relations are categorical or they are not categorical. If they are categorical, then they could not perform the lawmaking role that RBUIR assigns to them. If they are not categorical, then they are – wholly or partly – dispositional relations.22 The point is that RBUIR’s lawmaking 20

Tooley 1977: 669. Others who have raised this objection include Schneider 2002 and Handfield 2005. 22 Handfield 2005: 460 frames this version of the Meinong Objection against RBUIR as follows: ‘[The lawmaking relation] is akin to a disposition to make first-order properties dispositional. If this does not suffice to convince you that the apparent category mistake of calling [it] a dispositional universal is warranted, then [a] weaker conclusion will suffice: [it] may not be a power or disposition, but it is essentially such as to bring about non-actual states of affairs under non-actual but possible conditions. As such, it is just as modally inverted as a first-order disposition or power.’ 21

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necessitation relations seem to involve non-existent possibilia in just the same way that Directedness and Reciprocity imply with respect to DISPIR’s lawmaking dispositions. After all, RBUIR claims that its lawmaking relations bring about non-existent states of affairs under non-existent conditions. It may be that this tu quoque version of the Meinong Objection does not apply to RBUIR with quite the same force as it does to DISPIR. But even though the identity of the disposition being soluble in water is not partly determined via Directedness to the manifestation property of being dissolved in water, RBUIR still grounds the disposition in the microphysical structure of sodium chloride molecules together with applicable physical and chemical laws. But how, on RBUIR, can these laws prescribe the character of not-currently-occurrent and/or omnitemporally-neveroccurrent regularities? To the extent that they do, the position must involve reference to alien but possible regularities in much the same way as DISPIR does. It is here, of course, that a platonic transposition of RBUIR can rescue the Relations Model. For RBUPR posits laws that exist as logical relations between transcendent ante rem universals. Thus law-statements and counterfactuals involving ‘alien’ properties and ‘alien’ laws are determined by existing but uninstantiated universals: this would seem to solve the Meinong Objection as far as the Relations Model is concerned. The platonic version of the Relations Model envisages a contingent network of logical necessitation relations between abstract universals, which allows it to underwrite the explanatory power of laws that involve unrealised but possible states-of-affairs: laws involving alien universals, vacuous laws, probabilistic laws, functional laws, and uninstantiated laws.

4.3. Objections to Platonizing the Relations Model The theoretical advantages that RBUPR enjoys over RBUIR are considerable. Yet even philosophers who lack a doctrinaire commitment to naturalism are unlikely to be persuaded that the explanatory gains of this platonic alternative fully offset the costs of abandoning the Instantiation Principle. For the theory raises several kinds of difficulties. We can group these into three distinct categories: causal problems, epistemological problems, and metatheoretical problems. Ironically, almost all of the objections spring from RBUPR’s introduction of a fundamental ontological division between concrete and abstract. In other words, what equips

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RBUPR with the resources to handle the objections raised by RBUIR is precisely what triggers most of the objections against it. 4.3.1. Sharpening Van Fraassen’s Fork As we saw in §2.3.1, one of the most well-known objections to RBUIR points to the puzzle of how its lawmaking relations bring about states-ofaffairs. But I suggest that it is even harder for its platonic realist counterpart to explain the almost unimaginable degree of isomorphic fit between networks of lawmaking relations in an abstract realm and the causal regularities they purportedly govern in the concrete realm.23 Nancy Cartwright distils these two related objections succinctly:24 [W]e need some account of why when abstract properties relate in the way they must given what they are, the systems that instantiate them relate in some corresponding way. In fact we need more than that. For we not only want the relations in the empirical world to hold whenever the abstract ones do; we also want the fact that the abstract relations hold to be what makes the empirical relations hold. That story is lacking [on RBUPR].

So both versions of the Relations Model seem to be extremely vulnerable to Van Fraassen’s Fork – that is, to the conundrum that the Inference Problem cannot be solved without triggering the Identification Problem, and vice versa. Armstrong subsequently tries to meet this objection by identifying relations between typed states-of-affairs as a species of the causal relation between tokened states-of-affairs. But this modification gives the Relations Model a distinctly platonic cast, as Armstrong himself concedes:25 A law … is a causal connection between state-of-affairs types. It is a ‘direct’ connection between these state-of-affairs types, that is, between universals. It does not hold between universals via their instances. This direct connection may suggest Platonism. Universals, whether instantiated or uninstantiated, stand above the flux and certain relations between the universals ‘govern’ their instances, lay down the law, to the instances.

He goes on immediately to deny that he is advocating RBUPR, but for all his protests to the contrary, Armstrong specifies that lawmaking connections depend not on tokens but on types. But if this is the case, what 23 On this second point, see Carroll 2008: 71: ‘It is awfully convenient that the universals should line up so nicely in Plato’s Heaven, doling out lawfulness to exactly the regularities that are laws. But why should we believe that they really do line up so nicely?’ 24 Cartwright 2005: 128. 25 Armstrong 1997: 226.

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existence could they have, given the Instantiation Principle? It is very difficult to see how they have any ontological basis at all. At the same time, Armstrong continues to claim that universals are tied to bare particulars and that there is a ‘victory of particularity’ over the instantiated universal.26 Leaving aside the merits of Armstrong’s response in defence of RBUIR, it is clear enough that RBUPR cannot invoke it to blunt Van Fraassen’s Fork. In fact, as we have seen, substituting platonic universals for immanent universals makes these problems much sharper given the problem of understanding how traffic between abstract and concrete is possible on platonic realism. This is because the lawmaking relation between platonic universals on RBUPR is a purely logical one. It is just about intelligible for Armstrong to characterise the nature of the lawmaking relation between universals as analogous to the nature of the causal relation between particulars. But the point is that Tooley cannot avail himself of Armstrong’s escape, because on his view lawmaking relations are, as an ontological matter, wholly discrete from the causal domain. We saw in §4.2 that there are a number of ways in which introducing a distinct ontological domain does make the Relations Model a more attractive analysis. In the case of Van Fraassen’s Fork, however, it seems that the decision to platonise opens up an even greater explanatory deficit than RBUIR does. For, as we have seen, it is one thing to be persuaded by Armstrong that lawmakers are quasi-causal connections between immanent universals that are tokened in the particular instances of a law. It is quite another to be persuaded that such a connection exists in an abstract domain. The promising dialectical move for RBUPR is the stress it places on the ontological distinction between concrete and abstract. Yet it is also precisely this move that threatens most to undermine it, since it decouples the Relations Model’s lawmakers still further from the regularities they are supposed to govern. 4.3.2. The Second-Order Humeanism Objection Another objection to RBUPR undercuts it from a different direction. Recall that the main reason Tooley endorses factual platonic realism is that it permits the platonist to posit uninstantiated but contingent universals. As we have seen, he holds that removing the criterion of metaphysical necessity 26

This is, in essence, the Two-Way Traffic Problem discussed in §2.3.3 above.

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for universals eliminates the reason that most reject them. Problems arise, though, when one asks what explains the contingent network of lawmaking logical relations. If its explanation for first-order concrete regularities is that they instantiate contingent arrangements of higher-order abstract universals, it seems obvious that RBUPR is solving one set of problems only by replicating them at a higher level. It is hard to avoid the suspicion that the contingency of Tooley’s platonic universals is anything more than brute stipulation. Tooley cannot simply declare that there is an abstract arrangement of lawmaking relations that are isomorphic with some physical regularities. In the spirit of Lewis’ humorous retort to Armstrong, RBUPR can no more confer the right kind of necessity on its platonic relations by stipulative decree than calling someone ‘Tooley’ can make him adept at handling tools. In effect, then, RBUPR offers us a neo-Humean mosaic at the level of universals, according to which it is simply a brute fact that the network of logical lawmaking relations exists.27 Different laws could obtain in other possible worlds, and it is just a cosmic coincidence that a given law holds in certain worlds but not in others. On this account, hydrogen might have had an atomic number of 124, neutrons might have been positively charged, and an increase in the pressure of a gas at constant volume might always be accompanied by a decrease in its temperature. It is chance that relations hold between properties in a lawmaking way. 4.3.3. Hybrid Platonic Strategies Some platonic strategies are harder to classify, since they seem to locate the lawmaking role in both properties and relations. Thus in his realist manifesto for causation and platonic universals,28 Evan Fales takes the Ex Nihilo Objection to be a factor motivating the adoption of a strong necessitarian analysis of laws according to which the lawmakers are ostensibly identified as metaphysically necessary relations between properties (where both relations and properties are construed as platonic universals).

27 For a slightly different but related criticism, see O’Connor 2008: 51, who argues that second-order Humeanism arises because the existence of the lawmaking relation is inferred from the constant conjunction of first-order regularities. 28 Fales 1990. Other examples of this approach would be Swoyer 1982 and Tweedale 1984.

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Yet in a recent critique of imagined theistic transpositions of the Relations Model, he also assigns the lawmaking role to properties.29 Here, law-statements are grounded, as in his earlier work, in metaphysically necessary truths about the nomic profile of objects. His basic stance endorse Shoemaker’s arguments for a causal structuralist theory of propertyidentity.30 So Fales posits uninstantiated properties that, when instantiated, are essentially disposed towards specific forms of causal interaction in addition to uninstantiated relations that, when instantiated, also fix specific forms of causal interaction between their relata. The main problem with Fales’ approach is a metatheoretical one, because it argues both for irreducibly causal properties and a metaphysically necessary lawmaking relation connecting properties. But it is not clear what explanatory benefits this hybrid strategy brings that would be commensurate with the additional costs it incurs in terms of multiplying kinds of explanatory primitive. After all, Fales’ account does not obviously have the edge over rival accounts in explanatory terms; and so economy considerations can and should apply when evaluating it in relation to these accounts. When we do undertake a comparative assessment, however, it seems obvious that even when compared with other platonic theories it does not stand up well. The hybrid view is certainly less economical in ideological terms, since it advances an additional kind of theoretical primitive (thereby breaching qualitative ideological economy), together with a much higher number of theoretical primitives (thereby breaching quantitative ideological economy) than either RBUPR, which confines the lawmaking role to necessitation relations, or DISPPR, which confines it to dispositional properties. For these reasons, we can leave this hybrid account to one side.31

4.4. Exposition of DISPPR Although realist analyses of laws that invoke a platonic ontology in support of lawmaking dispositions are rare, there is some evidence that supporters of the Powers Model have begun to recognise the explanatory inadequacies of DISPIR and so to succumb to the pressure to platonise. Partly as a result of the rapid proliferation of versions of the Powers Model in recent years, the tendency to ground these either in immanent 29 30 31

Fales 2010: §3.1. Shoemaker 1980. For similar criticisms, see Jacobs 2007: 125-7.

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realism or trope-theory is now being exposed to much closer scrutiny.32 So the literature does now feature one or two attempts – albeit tentative ones – to undertake a platonic transposition of DISPIR. 4.4.1. Bird’s Account Perhaps the most sophisticated example of this approach is the position advanced by Alexander Bird. Formally, he insists that advocates of the Powers Model can remain neutral on the question of choosing between DISPIR and DISPPR. But it is clear that he takes DISPPR very seriously as an alternative to DISPIR, and that he does so on the basis of at least some of the worries raised in Chapter 3. One reason for this is that he forcefully rejects Intentional Directedness – described in §3.3.3 above – as a way of accommodating Directedness and Reciprocity in compliance with the Instantiation Principle. Indeed, since he joins most other advocates of the Powers Model in rejecting the Meinongian implications of Relational Directedness, the platonic strategy appears to be the only option remaining. To repeat: Bird’s official line is that DISPIR and DISPPR are equally persuasive. Nevertheless, on closer inspection he does show some hostility towards immanent realism, and in particular towards the intelligibility of multiply localized individual universals. Enforced compliance with the Instantiation Principle is, Bird claims, a mere ‘failure of nerve’ on the part of the immanent realist. So construed, universals seem no less mysterious than the platonic realist’s exemplification relation. But Bird argues that the exemplification relation is not mysterious. Causal links between abstract and concrete domains, he claims, are perfectly intelligible. His central argument for this is the purported causal efficacy of facts:33 Facts exist outside space and time. That is clear for the facts that salt dissolves in water or that the universe is infinite or that Charles is the son of Elizabeth. And facts explain things. So, contrary to Aristotle, entities outside space and time can explain. Furthermore, since universals are components of facts, we can see how universals, though also outside space and time, can contribute to explanations.

So Bird rejects the worries over the causal efficacy of abstract universals on the basis that the causal criterion for abstractness is misplaced. The criterion is misplaced, Bird suggests, because there are other examples of abstract entities that play causal roles. Facts regularly bring about 32 33

E.g. Williams 2010; Ingthorsson 2012; Tugby 2013a. Bird 2007a: 51.

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effects. Since facts are abstract objects, the causal efficacy criterion for abstractness is misplaced. The causal efficacy criterion should not, he claims, apply to necessary objects. If that is correct, DISPPR’s lawmakers would be exempt from having to satisfy the Eleatic Principle (discussed in §2.1.4 above). Indeed Bird thinks this exemption is what permits his version of DISPPR to be classified as naturalistic. What are we to make of this argument? Its central weakness, I submit, is its assumption that facts are abstract entities. Nominalists resisting DISPPR do so because it posits abstract universals; they reject these broadly on the grounds that they are non-naturalistic. So they are unlikely to be persuaded to posit them on the basis that facts are abstract objects, because they will almost always reject this second ontological thesis as well. That is, Bird assumes facts are abstract objects, but that is to beg the question against those who do not take talk of facts to be ontologically commissive. 4.4.2. Regress Objections Bird focuses much attention on a range of regress objections against the Powers Model. One objection claims that it is not possible to identify a dispositional property without invoking another dispositional property. The identity conditions for this property, however, must in turn be satisfied by appealing to another dispositional property, thus setting off an infinite regress. Bird’s solution is to concede that the Powers Model is guilty of a circularity, but to deny that it is a vicious one. He does this by suggesting that on DISPPR, laws are embedded in networks. These networks are constituted by the patterns of lawmaking dispositional properties or – to cite his own term – ‘potencies.’34 This solution therefore bears a close resemblance to Martin’s ‘power nets’ described in Chapter 3. In contrast to Martin, however, Bird claims that these nomological patterns obtain between universals rather than tropes. And, crucially, Bird is willing to concede that the network of universals is a platonic one. If he is correct to claim that laws supervene on second-order universals, then it is possible to see how the various problems that arose in §3.2 and §3.3 in relation to the individual identity-conditions of lawmaking dispositions might be handles. But it also shows how the Powers Model might reconcile the centripetal identity-conditions (Independence and Intrinsicness) with the centrifugal ones (Directedness and Reciprocity), and thereby point the way to a solution of the Fresco Problems. 34

For the reasons behind this terminological preference, see Bird 2007a: 45 n. 40.

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4.4.3. Identity-Conditions Resolved How convincingly, then, does DISPPR accommodate the four features of lawmaking dispositions outlined in §3.2 and §3.3 taken separately? And how successfully does DISPPR handle the Fresco Problems? Let us begin by tackling the first question. Recall that the four identity-conditions for lawmaking dispositions triggered four separate tensions with DISPIR’s commitment to the Instantiation Principle. We noted that these contradictions together provided a strong cumulative motivation for DISPIR to abandon the Instantiation Principle in favour of DISPPR. In the case of Directedness and Reciprocity, we saw that there were two different ways of responding to the Meinong Objection: Relational Directedness and Intentional Directedness. The first option was simply to accept the implications of the centrifugal criteria and accept that dispositions are in fact related to their manifestations, but without characterising the latter as fully-fledged universals. The difficulties of pursuing this solution for any view that rules out the existence of manifestation universals that are not instantiated (either presently or omnitemporally) do not need to be restated. As we have seen, very few philosophers are willing to endorse this position, and for good reason. The second approach is to argue that physical objects display the kind of intentional character typically associated with a particular theory of mental content. Although taken seriously by some, we concluded in §3.3.3 that this option makes questionable explanatory gains at substantial theoretical costs. But DISPPR now offers us, of course, a third option, according to which the connection between disposition and manifestation is taken to be an ontologically respectable relation between existing universals. Since this theory proposes to drop the Instantiation Principle altogether, on this view manifestation universals that are not presently or omnitemporally instantiated exist in the robust sense that a realist analysis of laws requires. Since they are capable of being ontologically substantive relata, explaining Directedness and Reciprocity in terms of metaphysical relations between dispositional universals and manifestation universals is much less problematic than it was prior to rejecting the Instantiation Principle. If DISPPR’s lawmakers unqualifiedly exist, they can serve as bona fide candidates determining the identity of powers by satisfying Directedness and Reciprocity. Dispositional properties are ‘directed’ or ‘partnered’ on the basis of their relative positions in an abstract structure of causal powers. More specifically, DISPPR also neutralises the threat from the centripetal identity-conditions for dispositions – that is, Independence and

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Intrinsicness. In the case of Independence, recall that the problem was how lawmaking dispositions could exist independently of their manifestation given the Instantiation Principle. We saw that it is simply not credible to suppose that ungrounded dispositions pop into existence when manifested and cease to exist when no longer manifested, as we saw that Megarian Actualism claims. Lawmaking dispositions must have an ontological standing prior to and independent of their manifestations. DISPPR solves this problem at a single stroke, because once one grants its underlying ontology, dispositions just are entities that exist regardless of any concrete exemplification. In the case of Intrinsicness, the problem was that it seemed possible to block the manifestation of a purportedly intrinsic disposition by altering circumstances extrinsic to its bearer if the Instantiation Principle is presupposed. As we saw in §3.2.2, supporters of DISPIR must confront the puzzle that salt’s solubility in water is simply not an ontologically determinate property in waterless possible worlds. Supporters of DISPPR, by contrast, can coherently claim that lawmaking dispositions satisfy Intrinsicness. Salt’s water-solubility is partly determined by its connection to a manifestation universal . Salt’s power to dissolve in water is ontologically determinate whether or not it is in a waterless world (i.e. whatever changes might be made to its external environment). So, on DISPIR, Intrinsicness seems to be preserved. 4.4.4. Assisi Revisited It also appears that DISPPR is in a position to solve the Fresco Problems that undercut its immanent realist counterpart. These uncovered the contradictions that arise once one tries to reconcile the four identity-conditions taken together into a single integrated account of the nature of a lawmaking disposition. Bird argues that the Powers Model has a theoretical advantage over the Relations Model in that the latter requires relations between universals (and therefore, if we accept the tu quoque version of the Meinong Objection discussed above, between non-existent possibilia). He claims that the Powers Model, by contrast, can satisfy Directedness and Reciprocity without invoking any relations. Bird frames the argument as follows:35 Now the invocation of a law of nature does involve a relation to something else, for the law is [on the Relations Model] itself a relation between 35

Bird 2007a: 107.

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universals, and … the law will involve universals … However, for the property realist, these universals are genuine, actual entities…The essence of a potency does involve a relation to something else … As in Armstrong’s case this entails that there is a possibilium that is the manifestation of the potency. But … we do not need to invoke any relationship to that possibility in order to explain either the nature of the potency or the nature of the fact of its being instantiated by a particular.

So Bird is able to reject the Fresco Problems, but although he does not state this expressly – notwithstanding his earlier charge that DISPIR’s refusal to invoke platonic universals was ‘a failure of nerve’ – the only reason he is in a position to do so is that he is willing to endorse DISPPR.36 This version of the Powers Model supplies the underlying ontology required to resolve the central Fresco Problem, namely how lawmaking dispositions could combine the centripetal and centrifugal identity-conditions.

4.5. Objections to Platonizing the Relations Model DISPPR addresses an impressive number of the objections raised against DISPIR in Chapter 3. But the central worry with the approach it proposes is that it simply moves the bump along the rug. For it is difficult to see how it does not shoulder an equally heavy explanatory burden in relation to the higher-order network of platonic dispositions. What explains, for instance, why this network obtains in the first place? And why is it that there is an almost inconceivably extensive isomorphism between the network and the first-order particulars that partly instantiates it? It is true, of course, that the platonic dispositionalist can claim that his fundamental ontology does not itself need an explanation in order to be a better explanation of lawmaking dispositions than DISPIR. The cogency of an explanation does not depend on its own capacity to be explained: if the explanation for my failure to attend an appointment was that my train was delayed, you do not need to know why my train was delayed to have a good explanation of my failure to attend. But it does mean that we must look carefully at what supporters of DISPPR are inviting us to assume, namely that there exists a vast network of what are, in the final analysis, brute ontological posits that are all tied together by necessary relations. The solution brings us uncomfortably close to F.H. Bradley’s doctrine of 36 As I have already noted, Bird 2007a: 55 insists (somewhat implausibly, I suggest) that nothing in his account depends on whether immanent realism or platonic realism is adopted.

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internal relations, the refutation of which by G.E. Moore was one of the founding moments of analytic philosophy.37 4.5.1. Identity-Conditions Once More Introducing platonic dispositions does solve the problem of how dispositions can exist unmanifested (Independence) and how no changes extrinsic to dispositions can affect what they are dispositions to do (Intrinsicness). It also explains how dispositions can be determined by relations to non-occurrent manifestations (Directedness and Reciprocity). The trouble is that DISPPR also faces serious objections on this front. Basic among these is that, as we have already seen in the case of RBUPR, uninstantiated universals are abstract. And again, the causal inertia of these entities makes it mysterious how a platonic structure of dispositions could possess a sufficiently causal character for DISPPR to explain regularities. Consider Nancy Cartwright’s complaint against RBUPR:38 Abstract relations are not the kinds of things that can make other things happen; they are not the kinds of things that have powers … If [they] are to figure in an account of what makes things happen in the empirical world, some outside force is required to make them relevant. They may serve as God’s blueprints for what he brings about in the world, but they cannot bring about things themselves. What Platonists call ‘laws’ as well as what empiricists call ‘laws’ need God and his direct control of the world if these are to be laws at all.

These criticisms are well-placed. But given DISPPR, we can raise exactly the same objection against platonic lawmaking dispositions that Cartwright herself raises against platonic lawmaking relations. There is no special reason to suppose that properties but not relations can determine regularities from a platonic heaven. On platonic realism, properties and relations are uninstantiated universals one and all. The only way we can envisage a domain of uninstantiated dispositions making regular causal differences to nature is if we have a better metaphysical story to tell about how traffic is possible between abstract and concrete. 4.5.2. An Expensive Fresco The basic impulse behind the Fresco Problems is how to reconcile the ontological discreteness of dispositions with the fact that they can be 37 38

Moore 1919-1920. Cartwright 2005: 126 (italics mine).

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determined by their position relative to other dispositions in the network. On the face of it, as we suggested in §4.4.5, DISPPR seems to be capable of solving this. It claims that since the interconnections between dispositions exist necessarily, there is no problem of fit between ‘directed’ dispositions and their ‘reciprocal’ partners. Concrete dispositions fit together with each other when exercised, and this instantiates the fit between platonic universals. There is a ‘fresco’ structure that exists in an independent, non-spatiotemporal abstract domain. Although this might appear to dissolve the Fresco Problems – by positing, in effect, a a platonic fresco – the question can be simply reformulated for DISPPR at the second-degree level: why are the fresco-fragments arranged in an intricate abstract structure? It seems that the dispositional network is the ideological primitive of the theory. So DISPPR offends ideological economy by invoking infinitely many explanatory primitives that exist necessarily for no reason at all. It breaches qualitative ideological economy because it introduces a new ontological category (abstract universals); and it breaches quantitative ideological parsimony because most will claim that if there are platonic universals, there are infinitely many of them. 4.5.3. Modal Worries Another reason to be suspicious of DISPPR is that it is very difficult to see how it satisfies the Contingency Intuition. If the lawmakers are abstract universals, then it is plausible to suppose that, given their ontologically discrete, independent existence, they exist necessarily. If platonic dispositions exist necessarily, it follows trivially that the configuration of the network is necessary as well. That means that one simply cannot make sense of the Contingency Intuition (i.e. that the laws of nature might have been different). So DISPPR exacts a heavy intuitive cost as a solution to the Modal Hybridity Problem. We have seen that DISPPR boasts a number of advantages over DISPIR. An infinite network of platonic dispositions sustains regularities. The diverse but intricately interwoven platonic universals are DISPPR’s lawmakers. Laws of nature are regularities in the arrangement of the dispositional network. And if the identity of a dispositional property is exhausted by its relations to other properties (manifestation properties and reciprocal properties), then all that is needed to ground the truth of counterfactuals involving laws in a world is a single dispositional property. For the identity of that one property would be constituted entirely

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by its position within the vast network of possible ties that connects all of the dispositional properties in that world, regardless of the fact that only one link in that network is instantiated.39 If a lawmaking power just is a node in the single nomic network encompassing physical reality, then commitment to the one entails commitment to the other. Indeed one advocate of this line suggests that this gives the Powers Model an advantage over the Relations Model on the basis that it does not generate a pressure to platonise:40 If one accepts that dispositions are occurrent properties whether or not they are manifested, it may be tempting to say that laws are in a sense actual, whether or not they are actualized. This would amount to the idea, offered here merely as food for thought, that uninstantiated but possible relations “exist” in potential form, standing by to be realized under appropriate circumstances.

The trouble with Chakravartty’s suggestion is that it effectively restates the difficulties that motivated DISPPR in the first place, because what he is pointing to in this passage is an ontology of laws that comes very close to construing them as Meinongian objects. A robust platonic realism about dispositions seems far more preferable to an ontological twilight zone where things are ‘standing by’ to exist. Still, it is hard to avoid the conclusion that there is very little to distinguish between (on the one hand) Molnar’s ‘intentional’ objects, Chakravartty’s ‘standing by’ entities, and Bird’s possibilia, and (on the other hand) Meinong’s subsisting objects, a point that R.D. Ingthorsson has stressed:41 Arguably, the sense in which Meinongian objects are necessary but nonexistent beings is very close to the sense in which Bird’s possibilia necessarily exist but do not necessarily ‘occur.’ Indeed, it is not too far-fetched to ascribe to Molnar the same view, notably that the objects of an unmanifesting power must be somehow real since they are distinct from the power and something to which the power is directed, but they lack being in the sense of non ‘occurring’ at any particular place or particular time. In any case, the objects postulated by Bird, Molnar, and Meinong to resolve the problem of directedness to objects that are not located in space-time, are all, in one way or the other, abstracta. They just disagree about the existential status of such abstracta.

So even if its supporters were willing to bite the Meinongian bullet and posit a more ontologically robust platonic dispositional network, DISPPR is still left with the problem of how the identity of its lawmaking 39 40 41

Chakravartty 2007: 146-7 Chakravartty 2007: 147. Ingthorsson 2012: 11.

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dispositions is ever fixed. If the identity of a power is to be wholly determinate, then it should be possible to determine all its connections of ‘directedness’ to other dispositions in the network. But this is not possible, because to know the determinate location of a power in the network means knowing the location of other dispositions, which in turn are determined by their connections to other dispositions, and so on ad infinitum. It is reasonable, then, to conclude that DISPPR accommodates the identity-criteria and solves the Fresco Problems only at the cost of a platonic ontology of dispositions whose identity is, in the final analysis, no more determinate than the identity of DISPIR’s dispositions.

4.6. Generic Objections Up to this point, we have analysed the weaknesses of RBUPR and DISPPR separately. But there are, of course, a number of problems that confront any theory that endorses a platonic ontology. The aim of this final section is to assess whether these objections are strong enough to undercut the explanatory gains that platonic strategies confer relative to their naturalistic counterparts. 4.6.1. Exemplification One of the most common objections to platonic realism, of course, is the puzzling status of the exemplification tie between abstract universals and the concrete particulars that instantiate them. In an effort to ward off regress objections and the Third Man Argument, platonic realists generally insist that the link is an ideologically primitive posit (in much the same way, in fact, as the lawmaking relation is treated as primitive by supporters of RBUIR). They point out that every attribute-theory invoked to underpin nomic realism will at some point need to rely on an entity that resists further analysis. Trope-theorists must posit relations of compresence as ultimate; resemblance nominalists posit resemblance relations, class-nominalists posit class-membership; and so on. The fact that platonism is also forced to turn its explanatory spade somewhere should not, therefore, count against it. 4.6.2. A Benacerraf Dilemma In Chapter One we briefly noted an epistemological problem for every platonic strategies. The problem is, in effect, a nomological variation of

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a famous objection that Paul Benacerraf posed for realists about mathematical objects.42 Benacerraf begins with the assumption that a ‘reasonable’ epistemology assumes that there is a causal component involved in knowledge-acquisition. But this immediately raises a problem for those committed to the existence of mathematical objects (numbers, functions, sets, and so on). The basic puzzle relates to how cognitive access to the content of law-statements is possible if that content is wholly or partly abstract, and therefore incapable of standing in causal relation with our epistemic faculties. It is worth reiterating that the Benacerraf Dilemma arises only for those who accept that knowledge of abstracta involves some kind of causal component, since a standard criterion for abstract entities is that they are causally inert if they exist at all. So far as I am aware, the problem has not been applied specifically to RBUPR. The problem is how we can come to know about laws involving abstract objects if we combine the causal efficacy criterion of abstractness with a causal theory of knowledge. Since Benacerraf formulated this argument, the problem has usually been framed as an epistemic dilemma. But it is worth noting that there is no reason in principle why RBUIR and DISPPR would not face parallel dilemmas with respect to: (i) the semantics of law-statements where a causal theory of reference is presupposed; (ii) the possibility of perceptual access to law-governed behaviour between particulars where a causal theory of perception is presupposed; and (iii) the possibility of explanatory success in connecting lawlike behaviour among particulars (explananda) to laws (explanations) given a causal account of explanation. Each of these background assumptions about the role causality plays in our access to reality is no less reasonable than Benacerraf’s assumption that epistemic access involves a causal element. This generic epistemological objection to platonic strategies has been countered in a variety ways.43 On the one hand, some are willing to endorse a highly controversial a priori account of epistemic access to abstract lawmaking relations or dispositions44 on the basis that modern physics provides good evidence for rejecting a causal account of knowledge-acquisition altogether.45 Others, on the other hand, have suggested that epistemic access to platonic lawmakers arises from a direct acquaintance with 42 43 44 45

Benacerraf 1973. Carroll 1994: 162 n.2. E.g. Brown 1991. Brown 2012: ch.5.

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them (i.e. not only by means of their instantiations).46 But it is difficult to deny that either of these epistemological solutions to Benacerraf-style objections to RBUPR and DISPPR have commanded widespread acceptance. We are forced to conclude, then, that quite apart from the bloated ontological commitments and explanatory puzzles that platonic realism confers on the accounts, an equally powerful reason for rejecting them is the epistemic barrier that an abstract ontology erects around their respective categories of lawmakers. 4.6.3. Classifying Economy Objections Platonic strategies are also generally rejected on the basis of their extravagance. These are metatheoretical objections, whose basic thrust is that platonic strategies offend against important criteria for theory-selection. One might ask, though, why principles of metatheoretical economy are applicable in the first place. If they are, what is the appropriate way to weigh them as factors when choosing between competing metaphysical theories? These questions would require another study to be adequately addressed. But since they will recur, let us briefly consider them a little more closely. There are a number of different arguments for why theories should treat metatheoretical economy as an important methodological goal. Some rationalist approaches take the preference for economy to be a priori. Richard Swinburne claims that it is an ‘ultimate a priori epistemic principle that simplicity is evidence for truth.’47 This can be characterised as simplicity at the explanatory level – that is, at the level of ideological economy. Critics of economy principles stress that their relevance varies significantly from context to context. So while local economy arguments might be permissible, global ones might not be.48 More pertinently, J.J.C. Smart has detected illicit theological freightage in the appeal to simplicity:49 There is a tendency, then, for us to take simplicity, in some obscure objective sense, as a guide to metaphysical truth. Perhaps this tendency derives 46

E.g. Fales 1990: 163. Swinburne 1997: 1. 48 Sober 1990: 77: ‘I believe that philosophers have hypostasised parsimony. When a scientist uses the idea, it has meaning only because it is embedded in a very specific context of inquiry … The philosopher’s mistake is to think that there is a single global principle that spans diverse scientific matters.’ 49 Smart 1984: 121. 47

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from earlier theological notions: we expect God to have created a beautiful universe.

Whatever its original source, most philosophers and scientists would agree that aesthetic criteria can and do play an important role in theoryselection. Although the method is defeasible, the criteria operate as a form of filtering system, guiding its users towards more persuasive philosophical analysis. There are, after all, far fewer methodological principles available to the metaphysician than to the scientist. What few there are broadly overlap with those used when weighing up scientific hypotheses: explanatory (especially predictive) power, fertility in other areas, economy in the number of theoretical ingredients (entities and axioms) and explanatory primitives, internal coherence, and so on. Now since metaphysical theories do not deal directly in empirical data, these virtues clearly cannot be applied in the same way. But let us consider how some of these metatheoretical criteria might apply to the platonic strategies on the basis considered in the present chapter. 4.6.4. Ontological Economy There are two basic kinds of economy a theory can show: ontological and ideological. A theory is economical in the first sense if it has a short ontological inventory. But there are in fact two inventories. Quantitative ontological economy relates to the numbers of entities that a theory posits, whereas qualitative economy is concerned with counting the kinds of ontological categories of entities. David Lewis famously rejected quantitative ontological parsimony with the thought that once one has posited an ontological category, it does not matter how many examples there were of it: ‘qualitative parsimony is good in a philosophical or empirical hypothesis; but I recognise no presumption in favour of quantitative parsimony.’50 Despite some resistance,51 most would agree with Lewis that quantitative parsimony should not weigh – or should weigh very lightly – in the process of theory-selection. If that is right, there is no need to reject RBUPR and DISPPR in favour of their immanent realist equivalents simply on the basis that they posit indefinitely greater numbers of entities. As we have seen, Tooley claims that RBUPR does not offend economy principles on the basis that uninstantiated properties are required for 50

Lewis 1973: 87. Nolan 1997 argues with some force that, from a historical point of view, quantitative parsimony has played an important role in the selection of some scientific theories. 51

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nomic realism to be sufficiently explanatory. If a realist account of laws requires such properties in order to provide satisfactory explanations of lawlike regularities, then economy considerations do not apply. But Tooley is highly restrictive with respect to the number of universals he is willing to posit. He takes a ‘sparse’ view of uninstantiated properties, according to which the only uninstantiated properties it is permissible to include in one’s ontology are those involved in the actual content of laws. Like Armstrong, he rejects disjunctive and negative universals. Tooley might then argue that since the number of ontological primitives on RBUIR is coextensive with universals that feature in laws, his version of RBUPR will fare better at the fundamental level of explanation than theories that rely on particulars alone (the best recent formulation of resemblance nominalism, for example, depends on an infinite number of concrete possible worlds).52 But tailoring the second-degree level to fit the nomic structure of the world is a very artificial move. Although it may be an acceptable move for platonic strategies in terms of quantitative ontological economy, it cuts against the metatheoretical principle discussed in §4.6.6 below. Lewis argued that the most important criterion in theory-selection is qualitative ontological economy. And here it is difficult to deny that platonic theories do not seem to fare well. For RBUPR and DISPPR posit abstract universals in addition to concrete particulars. That is to say, they each add a distinct ontological domain that immanent realist theories reject. How might platonic realists respond to this objection? It might be claimed that immanent realist theories posit exactly the same number of distinct ontological categories: concrete particulars and immanent universals. Platonic theories can also rehearse the objections against the multiple localisability of universals. So it is not obvious, perhaps, that platonic strategies for laws are in worse shape than rival theories. Nevertheless, even if categories do differ on other ontologies, the distinction between platonic posits and concrete regularities as ontological categories is considerably sharper. 4.6.5. Ideological Economy The second kind of metatheoretical economy we should consider is ideological economy. This has been helpfully characterised as the degree to which a theory is unified around the fewest brute, explanatory 52

Rodriguez-Pereyra 2002: §5.4.

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primitives.53 This is driven in part, as Oliver notes, from the ‘aesthetic’ features of an ideologically economical theory. As we saw in the case of BSA in Chapter 1, this theoretical virtue features heavily when it comes to assessing the optimal balance between simplicity and strength in systematic descriptions of hitherto observed regularities. Like ontological economy, ideological economy also takes qualitative and quantitative forms. Roughly, a theory is ideologically economical in the quantitative sense if it minimises the number of entities at the fundamental level of explanation. A theory is ideologically economical in the qualitative sense if it minimises the number of kinds of entity that represent the theory’s explanatory primitives.54 Are RBUPR and DISPPR more ideologically economical analyses of laws in either of these two senses? If applied in the quantitative sense, the answer is not especially encouraging. At explanatory bedrock, for example, DISPPR is forced to posit uncountably many entities since, only an infinitesimally small section of the network of lawmaking dispositions is exemplified in the actual world. So measured against this criterion, it is hard not to conclude that DISPPR is an especially costly thesis in terms of quantitative ideological economy. But what if we measure it against its qualitative counterpart? The answer is that platonic strategies fare rather better. For one might argue, as I have already suggested in relation to the mathematical content of laws in §4.1.2 above, that both RBUPR and DISPPR score highly in terms of qualitative ideological economy by giving us a more unified explanation of laws than its rivals.55 Another example where platonic strategies fare well on this criterion is in relation to classes of non-standard laws. As we saw in §2.4, RBUIR is forced to introduce some suspiciously ad hoc modifications to accommodate functional and uninstantiated laws. RBUPR, by contrast, can account for all of these laws with a single explanation (the same applies, in fact, with respect to DISPPR). An integrated network of platonic universals, tied together by lawmaking relations, supplies all the otherwise missing values in a functional law such as masses and distances that, as a matter of contingent fact, have never featured as values in any instance of the law of gravitational attraction.

53

Oliver 1996: 3. Cowling 2013 provides a detailed and sophisticated assessment of the methodological role of ideological economy. 55 Some have argued that unification is the definitive hallmark of explanation – see in particular Friedman 1974 and Kitcher 1989. 54

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The difficulty for RBUPR is that it derives this unifying explanatory power by positing entities that make the explanatory connection between its lawmakers and the regularities they purportedly ground a great deal more opaque. It can only explain concrete regularities by grounding them in abstract relations. Moreover, by grounding non-contingent regularities in relations between universals that obtain contingently, RBUPR shifts the bump in the rug, because we can then simply reformulate the original question: what explains the nomological network of relations at the level of universals? The worry is that RBUPR does not have an explanation for why the platonic universe of lawmaking relations just happens to be configured in the way reflected in concrete regularities. So what RBUPR gains in qualitative ideological economy by unifying the explanation around abstract universals, it seems to lose in terms of overall explanatory power. 4.6.6. Nihil Ad Hoc A final metatheoretical concern is the extent to which positing platonic universals offend what we might term the principle of nihil ad hoc. For some philosophers, this principle weighs much more heavily than parsimony concerns. A central justification in Rodriguez-Pereyra’s case for resemblance nominalism, for example, is that it avoids breaching it.56 Theories that invoke contingent uninstantiated universals with the sole purpose of achieving an explanatory aim are, all things considered, less persuasive than theories that do not. The challenge this presents to RBUPR and DISPPR will be obvious, since their platonic posits are not part of an existing metaphysical framework, but rather theoretical novelties introduced specifically to deal with the difficulties raised by their immanent realist counterparts. We are searching, however, for a theory that can integrate the relevant explananda with resources that are already assumed to be part of that theory’s background metaphysical framework. Provided it is comparable in terms of explanatory power, then all other things being equal this will be more attractive as a theory than a background metaphysical framework that needs to be revised in specific ways. * * *

56

Rodriguez-Pereyra 2002: 210-1.

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We have now analysed a range of arguments for adopting platonic strategies in support of a viable theory of nomic realism, a stance that had begun to appear distinctively unattractive by the end of the previous chapter. In particular, we surveyed the theoretical strengths and weaknesses of two platonic versions of the Relations Model (RBUPR) and the Dispositionalist Account (DISPPR), before raising generic metatheoretical objections to this basic approach. We concluded that RBUPR and DISPPR present powerful solutions to many of the objections raised against their counterparts in Chapter 2 and Chapter 3 respectively. But we also saw that the basic strategy of positing platonic lawmakers involves metatheoretically expensive moves that generate serious explanatory problems of its own – causal, epistemological, and modal. It is now time to take stock. In the first half of this book I attributed the failure of the best naturalistic attempts to account for laws in the realist sense to their insistence on a strict application of the Instantiation Principle to the most plausible candidates for lawmaking – that is, universals. But it is now clear that abandoning that requirement altogether yields theoretical gains that are largely offset by the explanatory and metatheoretical costs that platonic strategies bring with them. It looks as if we need a realist theory of laws that can eliminate the difficulties universals generate without introducing an abstract domain and without sacrificing the explanatory benefits that universals confer. One thing, at any rate, is now clear: if we are to continue our inquiry any further, there is only one category of alternative theories that remain: theistic ones.

CHAPTER 5 DIVINE LAWMAKING AND CAUSAL POWERS

The first three chapters of this study argued that, strictly construed, metaphysical naturalism was inadequate to the task of formulating a realist account of lawmaking. The previous chapter then took up the challenge of providing such an account within a non-naturalistic theoretical framework by attempting a straightforward substitution of immanent universals for platonic universals with respect to both the Relations Model and the Powers Model. Notwithstanding the undoubted advantages that platonic strategies conferred on these two approaches, it soon emerged that each reformulation was vulnerable to a range of objections distinct from, but no less substantive than, those that had confronted the versions it was hoped they would improve. One central complaint animating these objections was that, in the final analysis, neither strategy successfully elucidated the relationship between their respective lawmakers and the causal behaviour of the objects they purportedly determined. Second, it emerged that there was no reason to suppose that either RBUPR or DISPPR was any less immune to objections affecting platonic ontologies more generally. We noted, for example, that an epistemological worry from the philosophy of mathematics also applied to these two accounts of laws. A variation of Benacerraf’s objection showed that it was far from clear on either account how epistemic (and, perhaps, perceptual) access to abstract lawmakers could be possible given the plausible assumption that the acquisition of knowledge involves – at least to some degree – a causal component. These explanatory difficulties substantially offset the genuine theoretical gains RBUPR and DISPPR made in relation to the immanent realist counterparts analysed in Chapter 2 and Chapter 3 respectively. As a result, it was difficult not to conclude that the net explanatory strength of the four theories examined thus far was approximately the same, and that given the disproportionate increase in metatheoretical commitments that platonic ontologies entail, RBUIR and DISPIR appeared preferable given their comparative metaphysical modesty. We are finding it remarkably difficult to find compelling reasons to adopt any of the realist analyses of laws that have been advanced since

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the revival of the debate over laws began four decades or so ago. This is an unsettling development. For Chapter 1 concluded that the best sense we can make of the central role assigned to law-statements in scientific theorizing is that they pick out objective forms of necessity in the physical world, forms of necessity that constrain reality to behave in predictably regular ways. If we are unable to support these intuitions with a lucid metaphysical analysis of lawmaking, there is no longer any reason to trust our widespread pre-theoretical convictions that there is an objective distinction between accidental and non-accidental regularities, or that there is an ontological ground for claims about how an object would behave in a counterfactual scenario, or that it is rational to infer unobserved regularities on the basis of those already observed. It is true that, if our inquiry were to halt here, we would not be required to embrace nomic antirealism instead. After all, it is obvious that for as long as we are searching for an account that genuinely explains the intuition that there is an irreducibly modal basis for lawlike regularities, no account that takes this intuition to be fundamentally misguided will prove more palatable than the failed realist alternatives. Nevertheless, neoHumean scepticism towards lawmaking does now appear considerably more attractive than it once did. So we seem to be confronted with an unpalatable choice: we must either adopt an approach that ultimately fails to explain laws in satisfactorily realist terms, or else refuse any attempt to explain it at all. We have, in other words, reached an impasse. So far as I can tell, there remains only one basic approach yet to be explored: the theistic approach. Now the turn to theism may, of course, offend still more scruples than the turn to platonism did in the previous chapter. But it is not an abrupt turn. For we have already given the naturalistic approach a scrupulously fair hearing. And we have carefully scrutinised the only plausible nontheistic alternative to the naturalistic approach. So unless we are willing to accept the costs of abandoning the inquiry altogether, there is no reason in principle why we should not consider the theistic approach as well. This task is the burden of the present chapter, which begins with a critical exposition of Richard Swinburne’s realist analysis of lawmaking in terms of the powers and liabilities of substances before turning to consider the theistic account offered more recently by John Foster. While each of these accounts turns out to be more promising than the other four theories we have considered, the first half of the chapter concludes that they are not persuasive as they stand. Nevertheless, §5.3 develops a thought

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stimulated by the critical assessment of Foster’s account: perhaps the central obstacle for nomic realism is not the decision regarding what kind of universals should be invoked to underpin it, but rather the decision to invoke universals in the first place. To test this idea, I consider in particular U.T. Place’s attempt to formulate a non-theistic version of nomic realism within a nominalist theory of attributes that substitutes universals for concepts and predicates. I then enumerate the most serious objections to this approach in order to show how they illuminate by contrast the strengths of adopting the basic strategy within a theistic framework, a task that will be undertaken more fully in Chapter 6.

5.1. Theistic Nomic Realism I – Swinburne’s Account For more than three decades, Richard Swinburne has defended the view that law-statements are best construed in terms of regularities in the causal powers and liabilities of substances, and that theism provides the most probable overall explanation for why there should be such regularities at all.1 As we shall see, Swinburne’s account is in fact a species of the Powers Model. More precisely, its basic structure differs very little from DISPIR, since it also presupposes an immanent realist theory of universals. Nevertheless, this section argues that although its theistic shape considerably enhances the explanatory power and scope of Swinburne’s account, in the end it is not enough to insulate it against the central objections raised against DISPIR in Chapter 3. 5.1.1. A Basic Overview As with the other versions of the Powers Model we have examined, Swinburne denies that lawmaking is extrinsic to objects. Lawmaking is a ‘constitutive aspect’ of objects and their causal interactions. The causal behaviour of objects is what it is in virtue of the properties they possess or – more precisely – in virtue of the causal powers and liabilities they possess:2 Laws of nature are then just regularities – not of mere spatiotemporal succession (as with Hume), but regularities in the causal powers (manifested 1 Swinburne 2004a: 26-35; 277-88; Swinburne 2004b; Swinburne 2006; Swinburne 2013: 6-8; 125-33. 2 Swinburne 2004a: 33.

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and unmanifested) of substances of various kinds. That heated copper expands is a law is just a matter of every piece of copper having the causal power to expand, and the liability to exercise that power when heated. As a matter of contingent fact, substances fall into kinds, such that all objects of the same kind have the same powers and liabilities. The powers and liabilities of large-scale things (lumps of copper) derive from the powers and liabilities of the small-scale things that compose them (atoms; and ultimately quarks, electrons, etc.).

Swinburne stresses that the basic explanatory structure of his version of the Powers Model is independent of the theistic framework in which he locates it. But he does argue that if God is the metaphysical source of laws, then this is because God establishes what substances there are and endows them with whatever causal powers and liabilities they possess. This account makes up the core of Swinburne’s first teleological argument from the intrinsic probability, given theism, of the universe featuring extensive regularities in the behaviour of the objects it contains. If theism rather than naturalism were true, there is a significant a priori probability, he contends, that there would be lawmakers of the kind that the Powers Model posits,3 and ‘[hence] the operation of laws of nature is evidence – one strand of a cumulative argument – for the existence of God.’4 As it happens, Swinburne does not claim that the argument from the probability of temporal order depends on the particular account of laws he proposes.5 In his view, the same explanatory difficulties bedevil any non-theistic analysis of lawlike regularities. Thus he argues, as we did in Chapter 1, that BSA might equip nomic antirealists with a method of describing what regularities there are, but that it cannot provide a fundamental explanation of why lawlike regularities obtain given the ontology that underpins it.6 Deflationary approaches to laws fail to explain the undeniable degree of success that characterises inferences from past to future observed regularities:7 If we were to adopt [nomic antirealism], the conformity of all objects to laws of nature being just the fact that they do so conform would have no further cause except from outside the system. If there were no God, it would be a highly improbable coincidence if events in the world fell into kinds in such ways that the simplest extrapolation from the past frequently yielded 3

Swinburne 2004a: 154-66. Swinburne 2004a: 166. 5 Swinburne 2004a: 34: ‘[T]he argument of this book does not depend on my preferred account of laws of nature.’ 6 Swinburne 2004a: 30-1; 160. 7 Swinburne 2004b: 299. 4

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correct predictions. There are innumerable logically possible ways in which objects could behave today, only one of them being in conformity with the simplest extrapolation from the past. If, on the other hand, God causes the behaviour of physical things, then the coincidence is to be expected …

Turning to the Relations Model, he concedes that although naturalistic formulations of it do offer some explanation of lawlike phenomena, it is ultimately an incomplete explanation. More specifically, Swinburne argues against RBUIR as follows:8 [RBUIR does not explain] why there should be universals connected to each other before they are instantiated [i.e. the Ex Nihilo Objection discussed in §2.3.4], and why – if there is a universe, and so some universals must be instantiated – should quite a few universals be instantiated in such a way as to form a whole system of laws of nature. There might be many universals that were instantiated without bringing any other universals with them, so that there was no predictable effect of the instantiation. But on [the Relations Model] virtually all universals are connected to other universals. And there might be universals, but only ones of kinds instantiated once or twice in the history of the universe, rather than ones like ‘photon’ or ‘copper’ that are instantiated often and so can be used for useful prediction. And, again, the mathematical connections between the universals—for example, between the masses of bodies, their distance apart, and the gravitational attraction between them—might be of such complexity as never to be inferable from the past behaviour of objects.

Finally, although – as we have just noted – Swinburne denies that the Powers Model presupposes there is a God who constrains the causal behaviour of objects, he does contend that there is no reason why, given naturalism, there is any reason to expect objects to be disposed to behave in the regular ways that they are disposed to behave. On naturalism, it is an extremely improbable coincidence that physical objects should fall into a very small number of kinds, membership of which confers on these objects identical configurations of lawmaking dispositions:9 Such a coincidence cries out for explanation in terms of some single common source with the power to produce it. Just as we would seek to explain all the coins of the realm having an identical pattern in terms of their origin from a common mould, or all of many pictures having a common style in terms of their being painted by the same painter, so we should seek to explain all physical objects having the same powers in terms of their deriving them from a common source. So again, on [the Dispositionalist Account], as on [the Relations Model] (and a fortiori on the Humean account), it is very improbable that there would be in a Godless universe 8 9

Swinburne 2004a: 161. Swinburne 2004a: 164.

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laws of nature sufficiently simple for rational beings to extrapolate from past to future with normal success.

Swinburne’s teleological argument from the relative probabilities of temporal order given theism or naturalism is, I suggest, a plausible one. But it is important to distinguish it from the theistic proposal we will be considering in Chapter 6. Ultimately, which will argue that to the extent the Powers Model is the most persuasive realist account of laws, the analysis of lawmaking dispositions that most plausibly accommodates the quartet of identity-conditions set out in Chapter 3 is the one that construes them in terms of God’s conceptual and causal powers. As we shall see, however, Swinburne’s own account is no more successful at explaining how lawmaking dispositions satisfy Independence, Intrinsicness, Directedness, and Reciprocity – whether individually or collectively – than the non-theistic immanent realist theories explored in Chapter 2 and Chapter 3. 5.1.2. Analyzing Divine Causation If laws are to be explained in basic terms by reference to the autonomous dispositions of objects, an obvious question that arises is the nature of God’s ongoing causal contribution to lawmaking once objects come into existence according to their respective kinds. In other words, what is that distinguishes Swinburne’s theistic version of DISPIR from a deistic version of DISPIR? The brief answer to this worry is that Swinburne takes divine agency to be a continuing cause of the lawmaking powers and liabilities of substances. If God were to cease to cause properties in objects, he claims, the physical world would cease to exist. But Swinburne does not specify precisely how God does continually sustain lawmaking dispositions. In fact, for all his emphasis on the primacy of causation, Swinburne is conspicuously silent on the question of whether and to what extent God concurs with creaturely causes. Indeed, if we accept the taxonomy of positions on the precise relationship between divine agency and natural causation set out by Alfred Freddoso,10 it would not be at all accurate to classify his position as concurrentist. God conserves – by means of a ‘basic action’ – every concrete substance together with all of its causal powers and liabilities; but this in no way entails how these powers and 10 Freddoso levelled precisely this accusation in response to a paper given by Peter van Inwagen – the oral exchange is summarised by van Inwagen 1988: 215 n.4.

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liabilities are exercised, which yields the rather surprising result that, against the backdrop of the mediaeval debate, Swinburne’s conception of divine agency amounts to a weak form of deism. 5.1.3. DISPIR Once More As we have seen, Swinburne claims that his teleological argument from temporal order can in principle be formulated irrespective of the particular theory of laws that is presupposed. This broadly parallels the approach adopted in the course of this study. In §1.4, for instance, we explored the merits of a theistic formulation of BSA and concluded that it was a somewhat more promising explanatory solution than the non-theistic alternative. We will also examine what theoretical advantages accrue to transposing the Relations Model into a theistic framework in §6.3 and §6.4, before analysing a very different theistic version of the Powers Model in §6.5 and §6.6. For present purposes, however, let us scrutinise his proposal more closely, and consider in particular whether his analysis of lawmaking dispositions – or, to borrow his preferred terminology, powers and liabilities – successfully shields itself against the problems we encountered in relation to DISPIR in Chapter 3. We have already noted that Swinburne adopts an immanent realist theory of universals. He rejects platonic realism on the basis of what he takes to be its undue mystery and theoretical complexity. It is misleading, he insists, to stipulate by ‘linguistic fiat’ that uninstantiated universals exist.11 He rejects for similar reasons theistic attempts to identify properties with God’s concepts, a position to which we shall return in greater detail in the following chapter. Universals, he claims, exist only to the extent that they comply with the Instantiation Principle:12 Properties are only manifested in the concrete way in which substances exist when they are instantiated in substances … Properties occur or are manifested,

11

Swinburne 1994: 8. Swinburne 1994: 8. It is puzzling that at one point Swinburne describes properties as ‘timeless things instantiated from time to time in substances’ (Swinburne 2013: 28). The best sense I can make of this remark is that when properties are not instantiated, they are temporal but not spatial parts of their bearers (as described, for instance by Lewis 1986: 205). But it seems unlikely that Swinburne himself could subscribe to this given his commitment to a tensed theory of time. So it is difficult to see how the reference to universals as ‘timeless things’ can be understood ontologically in a way that is consistent with immanent realism or how it avoids introducing the degree of mystery and complexity Swinburne aims to eradicate. 12

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and may then be said to exist, when and only when they are instantiated in substances. Redness only exists when there are red things.

With these basic ingredients in place, it becomes clearer that Swinburne’s realist account of laws is scarcely distinguishable from DISPIR as we evaluated it in Chapter 3. The only substantive difference between DISPIR and DISPPR (on the one hand) and Swinburne’s theistic version of DISPIR (on the other) is that as far as the former is concerned, there is no deeper explanation for the pervasive patterns in the distribution and interconnection of dispositions among objects.13 As far as the latter is concerned, by contrast, there is a deeper – and, in Swinburne’s view – simpler explanation for this fact: dispositions of objects are the proximate lawmakers, while God is the ultimate lawmaker.14 Nevertheless, as we have already noted, Swinburne takes this theistic modification to be independent of the basic structure of the account he advances. So while it is crucial with respect to his cumulative argument for the existence of God, his version of DISPIR ‘does not presuppose that there is a God who operates in this way.’15 At this point, then, an obvious question arises: if the theistic framework within which Swinburne elaborates his version of DISPIR does not affect it as it stands, on what basis can it be defended against the array of objections raised against it in Chapter 3? After all, the only reason we were motivated to consider theistic options in the first place was the hope that one of these might provide a way through the difficulties we have already encountered. But if the theistic version of DISPIR brings with it the same problems as the naturalistic version, then we are no nearer to reaching our goal of establishing a plausible case for nomic realism. Let us examine more carefully, however, the analysis that Swinburne offers of his lawmaking dispositions. The first point to note is that he does not accept that there are ungrounded dispositions. This represents an important point of departure from the majority of those who support the Powers Model. As we saw in Chapter 3, these philosophers typically 13 As Mumford 1998: 219 concedes, at the fundamental level, the regularities that dispositions sustain are ‘ultimate truths’ about the physical world: ‘These are ultimate facts about the world in virtue of being truths for which there is no further explanation. It is thus unanswerable why the basic laws of nature are as they are and not otherwise. In other words, it is unanswerable why it is a world with these laws that is actual instead of one of the many other possible worlds which have different laws.’ Mumford specifically excludes appeals to ‘supernatural’ explanations. 14 Note that to all intents and purposes, this is the position Aquinas endorses – see Adams 2013: 3-7. 15 Swinburne 2004a: 34.

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presuppose that all natural properties are dispositional,16 while others claim that at the fundamental level there are both dispositional natural properties and categorical natural properties.17 But we also encountered a theory of property-identity that treated the categorical and dispositional as two ‘aspects’ of one and the same natural property.18 In order to evaluate Swinburne’s own version of DISPIR, we must first establish which – if any – of these different accounts of property-identity he is relying on when he assigns the lawmaking role to dispositional properties. As it happens, Swinburne is well-known in the literature on dispositions for advancing an argument against Sidney Shoemaker’s view that all there is to the identity of every property is the causal role it is disposed to fill (including properties such as shape and location that are generally considered to be categorical).19 Swinburne’s objection to this view is that if it were true, it would be impossible to have epistemic access to these properties. If the nature of a property is its causal potential to bring about another property, he claims, then it is a mystery how we ever come into epistemic contact with any property at all. More recently, he has illustrated the objection using the analogy of a government official whose only powers are to appoint other officials, whose only powers were to appoint still more officials, and so on ad infinitum; if a state’s executive were structured this way, he claims, nothing would ever get done.20 So whatever account of lawmaking dispositions Swinburne presupposes, it is emphatically not one that construes them as pure, ungrounded powers. Now he cannot, of course, reject dispositions altogether without undercutting his preferred theory of laws. That is to say, he is not in a position to analyse them reductively along the lines of the conditional analysis discussed in §3.1.2. The only available alternative, it seems, is the one that takes the distinction between categorical and dispositional to exist only at the level of the roles a property plays rather than at the level of properties themselves. And yet Swinburne rejects this view as well:21 One could attempt to avoid [the epistemic regress] by saying that while the only properties of substances are their powers, we can distinguish between 16 E.g. Mumford 2004; Bird 2007a. This is sometimes referred to as ‘dispositional monist’ or ‘pure powers’ view. 17 Ellis 2010: 138-41 refuses to reject categorical properties on the basis that the best objection against them – namely, that they presuppose quidditism – fails. 18 E.g. Martin 2008: 63-9; Heil 2012: §§4.2-4.4; Jacobs 2011: §3. This is usually known as the ‘powerful qualities’ view. 19 Swinburne 1980 responding to Shoemaker 1980. 20 Swinburne 2013: 26. 21 Swinburne 2013: 26.

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different events (involving different powers) … by their different ‘aspects’ or ‘modes of presentation.’ One could say that when a surface has a certain powers, there are not two distinct events of it being red and reflecting light of such-and-such wavelength (which are the same event), but we can pick out that same event by different ‘modes of presentation’ or ‘aspects’ (e.g. its visible colour and the reflected wavelength). But that is just to multiply ontological categories unnecessarily. For ‘a mode of presentation’ or an ‘aspect’ of an event is just as much a real characteristic of an object as any property. And nothing is left out and much is clarified if we say that visible redness and reflecting light of a certain wavelength are both properties of the surface.

Although he frames the view by reference to events, it is clear that this objection would apply with equal force to the hybrid view of propertyidentity proposed by C.B. Martin and John Heil, according to which one and the same property can exhibit both categorical aspect and a dispositional aspect. We can refer to this as the Mixed View. Swinburne’s point is that since the dispositional role that a property plays is a way of characterising an object, it just is a property. The same principle applies to the categorical role of a property. In short, he holds that there is no reason to conflate two roles within a single property when each role does the kind of distinct metaphysical work normally considered sufficient to classify it as a property. So Swinburne purports to reject the Mixed View. And, as we have already noted, he cannot endorse a fully-fledged categoricalist account of the nature of properties without abandoning his account of laws in terms of powers and liabilities. But without a clear view of how he proposes to analyse the entities that purportedly play the lawmaking role, it is extremely difficult to evaluate his overall account of laws in a satisfactory way. Even if we grant for the sake of argument that Swinburne takes a stance towards dispositions that is sufficiently realist to underwrite his theistic version of DISPIR (whatever the precise details of that position may be), it remains unclear why we should prefer his account to the version of DISPIR that we rejected in Chapter 3. For instance, the tension that the Instantiation Principle triggers between Intrinsicness and Directedness also arises on his own account, even if it is a tension that he appears to accept without further analysis:22 [T]here are properties which things have intrinsically that concern how they could or would interact with other things under certain circumstances. In particular, causal powers are like this. The power to lift a 100-pound weight, 22

Swinburne 1994: 33 (italics mine).

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although it in some sense concerns a relation which I might have to some other thing, is on my definition a monadic property, because it does not concern a relation to any actual thing – my having this causal power is to be distinguished from my exercising it. (I could have it without there ever being any 100-pound weights or anything else.)

Given his explicit commitment to immanent realism, the contradictory character of this position is as evident as it was when we considered similarly stipulative reconciliations of Intrinsicness and Directedness offered by Martin and Mumford in §3.4.2. It is also worth noting a second example: Swinburne is explicit that the nature of a lawmaking disposition – or ‘power’ – is constituted in part by Independence:23 The power to exert such and such a force is a property possessed by an individual whether or not it ever exerts it or whether there are any other actual individuals on which it can exert it.

But what answer does he provide to the question (raised in §3.2) to the effect that Independence flatly contradicts the Instantiation Principle? As far as I can tell, the tension is left untouched. 5.1.4. A Preliminary Assessment In Swinburne’s theistic formulation of DISPIR, the appeal to God as ultimate lawmaker considerably enhances the overall explanatory power of his realist approach relative to its naturalistic rivals. For on naturalistic approaches, there is indeed a relatively low a priori probability that there would have been pervasively regular distributions of small numbers of interconnected dispositions among objects fixed by virtue of their membership in relatively few kinds. And, as we have already noted, naturalists concede that they cannot provide any further explanation for why these regularities obtain rather than any others.24 Nonetheless, it is difficult to see how the superior explanatory strength of a theistic version of DISPIR is relevant in the absence of a clear analysis of the proximate lawmakers that it invokes and, in particular, the tensions between identity-conditions for these lawmakers that follows from immanent realism. Since he does not provide such an analysis, we are forced to conclude that Swinburne’s preferred theory of laws in terms of the powers and liabilities of substances ultimately fails.

23 24

Swinburne 1995: 389. Mumford 1998: 219.

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5.2. Theistic Nomic Realism II – Foster’s Account John Foster proposes a second theistic account of laws that broadly resembles Swinburne’s analysis.25 The aim of this section is to set out the basic contours of this proposal with a view to exploring Foster’s criticisms of the role played by dispositions in non-theistic versions of the Powers Model relative to the role they play in his own constructive proposal. We will see that the balance between the explanatory strengths and weaknesses of Foster’s account are broadly similar to those enumerated in relation to Swinburne’s account in §5.1. Finally, the section will devote careful attention to one especially distinctive feature of Foster’s constructive case, namely his apparent willingness to abandon a realist stance towards universals altogether. This basic move sows the seed for the central constructive proposal of this study, to be formulated and assessed in Chapter 6. 5.2.1. A Basic Overview Imagine a box filled with a hundred balls, fifty of which are white and fifty of which are black. And suppose that fifty balls are randomly selected from the box and that every one of the selected balls turns out to be white. Now it would be possible to explain, with respect to each individual selection, why one ball rather than another was selected simply by appealing to the different physical forces operative in the box at the time it was picked out. In one sense, then, it would be possible to explain the final outcome of all fifty selections in terms of the sum total of explanations for each individual selection. But such an explanation would be entirely useless as an explanation of why the selected balls collectively exemplify a regularity. It would simply not explain why the ostensibly random selection was made up entirely of white balls rather than a random mixture of white ones and black ones. For Foster, the central hallmark of a successful philosophical analysis of laws is the extent to which it can explain a lawlike regularity as a regularity, and not as an aggregate of the ontologically discrete instances of that regularity. That is to say, the chief explanatory objective for any theory of laws is to account for the collective behaviour of objects in the physical world. As we saw in Chapter 1, even in its most sophisticated 25

Foster 1982; Foster 2004.

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forms the neo-Humean purports to explain the astonishing fact that fifty white balls were randomly selected from the box by aggregating together the explanations for why each selection was made. And, indeed, Foster scarcely engages with the strand of descriptivist views that – as we saw in Chapter 1 – do not even step up to the explanatory challenge that the nomic realist sets for himself. But Foster does devote considerable scrutiny to Armstrong’s version of RBUIR, and in the course of doing so raises a number of serious criticisms against it.26 Since we have already addressed the difficulties this account faces in some detail in the course of §2.3 and §2.4 let us leave these to one side for present purposes and focus instead on his critique of naturalistic versions of the Powers Model. These criticisms, together with his brief criticisms of nomic antirealism (‘non-nomological’ theories) and RBUIR (‘nomological theories’), preface his constructive theistic account, which we will examine in due course. 5.2.2. The Mixed View of Lawmaking Dispositions Foster offers three main arguments for rejecting the Powers Model. The first argument he raises targets the way in which it proposes to connect dispositions to a categorical base.27 The only way to explicate the connection between a disposition and its categorical base, claims Foster, would be to invoke lawful connections between a disposition and its categorical base. But it is immediately obvious that to the extent that dispositions are invoked to provide a foundational account of why there are any lawful connections in the first place – as of course the Powers Model purports to do – this proposal is hopelessly circular. It is rare to find supporters of the Powers Model willing to embrace this circularity. Many endorse the Mixed View’s explanation of the problematic link by collapsing the dispositional and the categorical into a single ‘dual-aspect’ property (already discussed in §5.1.3 above).28 26

Foster 2004: 94-110. It is worth noticing that he takes for granted the view – satirised, as we saw in §3.1.1 above by Mellor 1974: 157 – that every disposition must be wedded to an ontologically reputable categorical property. That is to say, he does not even consider at this point versions of the Dispositionalist Account that take lawmakers to be metaphysically robust properties that are not to be explained away in terms of their connection to a reductive categorical base. 28 E.g. Heil 2003: ch. 11 and Martin 2008: ch. 6. Armstrong 1997: §16.3 offers a lucid critique of the double-aspect position from a categorical monist perspective. 27

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Supporters of this view might legitimately point to the many difficulties that undermine alternative analyses of dispositional properties – in particular, theories that treat fundamental properties either as irreducibly categorical or as irreducibly dispositionalist – and conclude that the strangeness of their proposed posit is amply outweighed by the objections that can be levelled at theories that take properties to be only dispositional or only categorical. But in the final analysis, the Mixed View’s proposal is a decidedly ad hoc move that requires us to introduce a puzzling and unnecessary category of ‘hybrid’ property in order to explain something that two ordinary properties could do just as well. A still more substantive objection to the Mixed View is that it makes no metaphysical distinction between the dispositional and categorical roles of a putatively lawmaking property. If the difference between them is purely a conceptual one, then we are forced to confront an unpalatable paradox. For it then looks as if we are being asked to accept that one and the same property grounds its modally substantive aspect (i.e. its dispositional mode) and its modally inert aspect (i.e. its categorical mode). But this seems very difficult to do. Suppose it is true, as Heil suggests,29 that a ball’s being spherical is a categorical property. In virtue of possessing this property, the ball also possesses the dispositional property being movable. No doubt this provides a plausible analysis of some properties. Perhaps it even provides a convincing account of those fundamental properties identified as lawmakers on the Powers Model. But it is one thing to claim that an object is movable in consequence of the fact that it is spherical; it is quite another to claim that being spherical and being movable are one and the same property. The most we can conclude from Heil’s example is that there are categorical properties, that there are dispositional properties, and that these are tied together in ways that can only be explained by invoking the very lawful connections that the Powers Model was supposed to elucidate. So it seems to me that Foster’s second objection to the Powers Model – confined though it is to the version that presupposes the Mixed View of dispositions – is as well-founded as Swinburne’s. His first objection, moreover, had already ruled out the alternative proposal of drawing a robust distinction between dispositions and their categorical base on the basis that this solution also tacitly relies on the lawful connections it is supposed to explain. So within the parameters of Foster’s own discussion, it seems that the only way to salvage the Powers Model would be to take 29

Heil 2010: 66-8.

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up a realist stance towards dispositions as ungrounded, bona fide properties. But this approach, of course, is precisely the one we considered at length in the course of analysing DISPIR in Chapter 3 and DISPPR in Chapter 4. Indeed had either of those analyses proved promising, we would not now be scrutinising theistic alternatives. Now Foster shares Swinburne’s basic contention that, in the absence of theistic support, the Powers Model is explanatorily inadequate even if it invokes ungrounded – or, to borrow his own description, ‘autonomous’ – dispositional properties rather than the Mixed View of properties that both reject. We have already stressed that, in Foster’s view, an adequate explanation of lawlike regularities is one that explains them as regularities. But this, he claims, is precisely what no naturalistic rendition of the Powers Model could hope to achieve:30 [T]he putative explanations [that any naturalistic version of the Powers Model] envisages do not explain what needs to be explained. They do not explain what needs to be explained, because they only account for the behaviour and causal influence of objects taken separately, and not for why the separate modes of behaviour and causal influence collectively exemplify a regularity. And the reason why they do not explain the latter is that they do not explain why different objects of the same intrinsic type have the same dispositions.

At first glance, this objection might stem from Foster’s ambivalent attitude towards universals, which we shall this in more detail in §5.2.4 below. Given this ambivalence, we might be tempted to think that if Foster were less sceptical about universals, he would be in a position to recognise that it is a relatively short step from treating universals as natural properties to treating them as classes of natural properties as well. Many supporters of the Powers Model would indeed hold that universals ground natural kinds that confer on their members identical configurations of properties, including but not necessarily limited to lawmaking dispositional properties. It is not that realism about dispositional universals entails realism about natural kinds. But the two positions are sufficiently congruent that many supporters of the Powers Model have been willing to endorse them as a package. For if dispositional properties are universals, then this would explain, for example, why sub-atomic particles that exemplify negative charge are disposed to attract sub-atomic particles that exemplify positive charge. Nevertheless, we can still ask why so many sub-atomic 30

Foster 2004: 115.

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particles of the same type are disposed to interact causally in absolutely identical ways. In order to address this difficulty, some advocates of the Powers Model are willing to endorse a robust realism about natural kinds. E.J. Lowe, for example, goes so far as to ground law-statements in kindmembership:31 [I]ndividual objects possess their various ‘natural’ powers in virtue of belonging to substantial kinds which are subject to appropriate laws – these laws consisting in the possession by such kinds of certain properties (in the sense of universals), or in the standing of kinds in certain relations to one another.

With kinds and universals on the ontological books, one might suppose Foster’s perplexity to be misplaced. Indeed, anticipating this sort of objection is what motivates many versions of the Powers Model to invoke universals and kinds in the first place. We have repeatedly observed that many nomic realists adopt universals to explain lawlike phenomena in the physical world. But Foster’s criticisms now show us that the strategy of identifying putatively lawmaking properties as universals is not in itself sufficient to explain why universals inhere in objects of the same generic type. Given this explanatory deficiency, it is not in a position to explain on its own terms why objects are collectively disposed to behave in regular ways, and cannot therefore explain regularities as regularities in a way that is consistent with what Foster takes to be the hallmark of a successful realist analysis. Nevertheless, if we were tempted to suppose that Foster’s criticisms depended on a rejection of universals and kinds that most naturalists who support the Powers Model would not endorse, we would be mistaken. For he goes on to target a weakness that arises irrespective of whether realism about universals and kinds is presupposed, namely that they cannot even explain why objects taken separately are disposed towards specific causal interactions over time:32 Thus if B is a particular body, the proposal assigns a gravitational disposition to B at all times of its existence; but it does not offer an explanation of why B is, in this respect, uniform in its dispositions over time, and so does 31 Lowe 2006: 127. Cf. Ellis & Lierse 1994 and Ellis 2001: 6: ‘[C]ausal laws all ultimately depend on the causal powers of things belonging to natural kinds, and the manners and circumstances of their displays … causal laws can only be found in areas concerned with natural kinds of objects, properties, or processes.’ 32 Foster 2004: 115. He goes on to reject for similar reasons naturalistic theories that seek to explain regularities by finding something within the natural order that causally accounts for them (Foster 2004: 116-20).

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not, in any way that provides what was needed, explain why B is regular in its gravitational behaviour over time.

It turns out, then, that Foster accepts none of the accounts of the nature of dispositions as adequate to the task of providing a coherent case for nomic realism. He rejects reductive views that ground them in a categorical base as question-begging and the Mixed View for exactly the same reason. And, finally, he claims that eliminating the categorical dimension altogether by treating dispositions as ‘autonomous’ properties explains neither why objects collectively behave in regular ways nor even why any single object is disposed to behave in regular ways over time. 5.2.3. The Indispensability of Lawmaking Dispositions Given the strength of Foster’s objections to the Powers Model, it is somewhat surprising to find that he takes dispositions to be indispensable to his constructive theistic proposal. In fact, where Swinburne explicitly makes room for alternative accounts of lawmaking, Foster takes the stronger line that a dispositional analysis of lawlike phenomena is ‘nonnegotiable’ and that any theistic account of regularities must be consistent with it. Paradoxically, Foster’s reasons for emphasising this line contrast sharply with Swinburne’s regress argument against dispositional monism, since he holds that rejecting the view that physical objects have dispositions is a recipe for global scepticism:33 [O]ur belief in physical dispositions is not one that we could afford to relinquish. For if we did, we could no longer preserve an acceptable account of the nature of the external reality and our relationship to it. Thus if we denied their possession of dispositions, we could no longer think of material objects as having powers to affect our senses; and, without their possession of such powers, there would be nothing in our relationship to such objects which equipped us to perceive them … The upshot is that if we were to abandon our belief in physical dispositions, we would have to abandon our belief in a physical universe altogether…

We may recall that Swinburne objected to construing lawmaking dispositions in the robust, ungrounded sense on the basis that if every property were a disposition to bring about another property, there would never be any occurrent mental states. If there were never any occurrent mental states, we could not know anything. Since we do know things, not every property is dispositional in character. 33

Foster 2004: 165.

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But where Swinburne argues against dispositional monism from our knowledge of things, Foster argues against dispositional reductionism from our perception of things. If there were no dispositions, objects would never be disposed to appear to our senses. If this were the case, we would never perceive anything. Since we do perceive things, every perceptible property is a disposition. These two arguments are not strictly at odds with each other: Swinburne claims that at least some properties – that is, properties to which we have epistemic access – are not dispositional, while Foster claims that at least some properties – that is, those properties to which we have perceptual access – are dispositional. The task of untangling this dialectical tension would take us too far afield. It is worth noting it, however, as evidence of just how opaque the metaphysical connection is between the categorical and the dispositional on both their accounts. Foster is no less indifferent to the problems we raised in Chapter 3 than Swinburne himself. For example, he is content to combine his ontologically committed stance towards ungrounded lawmaking dispositions with Independence:34 [T]he presence of a disposition does not depend on there being occasions when the disposition is exercised; nor, when there are such occasions, is the presence of the disposition exhausted by the totality of events that occur on them. Thus if something is fragile, it is so even if it is never subjected to the kind of impact that would make its fragility manifest.

Elsewhere Foster briefly discusses the possibility of taking dispositions to be ungrounded properties as a possible alternative to grounding them in a categorical base. It seems clear that he endorses the latter view, but it is striking that at least one of the reasons for that endorsement is, in effect, the tension between Intrinsicness and Directedness that confronts DISPIR in light of its commitment to the Instantiation Principle (i.e. precisely one of the tensions uncovered by the Fresco Problems in §3.4): I just cannot see how the intrinsic properties of physical objects … could sustain dispositional properties in this way. Take … the case of gravity. We are being asked to suppose that there are things about the intrinsic natures of the space and forms of matter that exist in the actual world which, as a matter of strict necessity, oblige bodies to behave gravitationally. But if the relevant properties really are purely intrinsic – purely to do with what the space and forms of matter are like in themselves [i.e. Intrinsicness], and not directly to do with how [objects] are disposed to behave or causally interact [i.e. Directedness], there seems to be no way of understanding how they could play this sort of role. 34

Foster 2004: 162-3.

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This is as good a summary as any of why Intrinsicness presents such an intractable problem for DISPIR. Now we saw that, for all its problems, DISPPR was capable in principle of accommodating this identity-condition. It is absolutely clear, however, that Foster would reject the solution DISPPR proposes. For although he does not specifically consider it, he does (for example) reject axiological explanations of the universe for their appeal to abstract entities on the basis that these would exist independently of the causal realm. In other words, it is safe to infer that Foster would not have invoked DISPPR in an effort to resolve the tension between Independence and his implicit commitment to the Instantiation Principle (a tension he does not actually notice), or the tension between Intrinsicness and Directedness (a tension he does notice), or indeed any of the other tensions uncovered in §3.2, §3.3, and §3.4 that he does not discuss. 5.2.4. Foster’s Fork We are now in a position to ask the following question: in what specific ways does Foster insulate his theistic version of the Powers Model against the objections he himself raises against naturalistic versions? At the heart of his solution to the problem of laws is the contention that the only way to explain regularities as regularities is that they are causally imposed on the physical world as regularities,35 and that they are so imposed in a way that no natural factor could plausibly explain:36 [T]he point is not just that there is no direct empirical evidence to suggest that regularities are ever brought about by natural factors in that kind of way. It is also that that kind of causation would be wholly out of keeping with all that we empirically know about how the world works. It might be suggested that … we could think of the regularities as causally sustained, as regularities, by aspects of the global structure of the world … But the only remotely plausible way we could think of this as working would be to suppose that it is aspects of the structure of the world at a time that causally dispose things to behave in the same regular ways at different times.

Since the causal imposition of regularities as regularities can only be explained in non-naturalistic terms, and since platonic solutions are ruled out on the basis that these do not invoke the concrete entities that would

35 36

Foster 2004: 158-9. Foster 2004: 119.

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be needed to explain how regularities are causally imposed, Foster infers that the only explanation is a theistic one.37 Dialectically, he develops an argument for the existence of God by presenting the non-theist with a dilemma. Let us label this dilemma Foster’s Fork. Briefly put, the argument claims that each ‘prong’ of Foster’s Fork prods us ultimately towards a theistic conclusion.38 He begins with the observation that every philosophical attempt to analyse physical regularities is confronted with two basic options: either it construes them as laws or it rejects the notion as fundamentally incoherent in favour of an alternative.39 The first prong of Foster’s Fork emerges when we analyze basic regularities as laws; for we must then account for how regularities are causally imposed as regularities. And, as we have just seen, so far as Foster is concerned there is no credible way for the naturalist to do so. The Powers Model, naturalistically construed, cannot account for regularities in the dispositional behaviour of objects as regularities in their collective behaviour. They cannot even account for the fact that objects are disposed in the relevant ways over time.40 Similarly, a causal account, naturalistically construed, cannot explain either regularities as regularities or the diachronic character of regularities other than by appealing to laws of nature, which simply restates the problem that it was supposed to solve.41 The only solution, claims Foster, is to appeal to a non-naturalistic causal origin for the imposition of regularities as regularities – that is, as regularities in the collective behaviour of physical objects over time. At this stage, claims Foster, the inference to divine agency seems irresistible. The second prong of Foster’s Fork begins with the claim that it is extremely tempting to abandon the very idea of laws as incoherent, principally on the basis of their perplexingly hybrid modal character. It is difficult to overstate the centrality of this problem for Foster: it is, in fact, the primary motivation for his abandonment of every previous attempt to make sense of lawlike regularities. Given its centrality, it is important that we have it clearly in view. The problem is easy enough to state. On the one hand, unless we accept the deflationist critique, we will hold that 37

Foster 2004: 120-7. Foster 2004: 160-1 sets out a condensed version of the argument. 39 I suspect, therefore, that Foster would have objected to the practice I have adopted in this study of applying the label ‘nomic realism’ to any analysis that treats the referents of law-statements as modally substantive entities. 40 Foster 2004: 114-5. 41 Foster 2004: 116-20. 38

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regularities possess some degree of modal force. For clearly no analysis of laws could describe itself as a nomic realist analysis if it characterised all regularities as wholly contingent and treated the modality intuitively associated with law-statements exclusively in epistemic terms. On the other hand, it seems implausible to suppose that laws are forms of strict necessity, where this is taken to cover logical (or ‘narrow’ logical) and metaphysical (or ‘broad’ logical) kinds of necessity. Foster asks us to imagine possible worlds that are ‘compositionally relevant’ to the actual world, worlds that feature all the basic ontological and categorical ingredients needed for identical instances of a particular law in the actual world – say, Kirchoff’s Laws – to be possible. Now in compositionally relevant possible worlds, we could readily imagine that Kirchoff’s Laws fail to obtain. That is, we could readily imagine a possible world with exactly the same basic ontology as the actual world, but in which electrical circuits behaved differently. The very character of laws seems, then, to occupy a point on the modal spectrum midway between pure contingency and strict necessity. The Modal Hybridity Problem provides strong grounds for completely rejecting the notion of laws where these are construed as objective forms of non-strict necessity – or (in other words) for accepting the ‘second’ prong of Foster’s Fork. But once we do so, Foster insists, there is only one way to explain regularities in non-nomological terms, namely by appealing to the kind of necessity that the causal account envisages, and specifically to the version of the causal account that attributes the imposition of regularities as regularities to a free divine agent. For Foster, this is the only way in which the Modal Hybridity Problem (first raised in §2.0) can be solved, for it is only on this view that one can make sense of why apparently necessary regularities in the actual world could fail to obtain in another (compositionally relevant) possible world. In other words, the second prong of Foster’s Fork forces us towards the same theistic conclusion as the first. What are we to make of this argument? Foster’s Fork might put some pressure on realist analyses of laws that fail to provide satisfactory solutions to the Modal Hybridity Problem. For example, we saw in §2.3 that one of the central difficulties facing RBUIR was the primitive, brute modal character of the lawmaking relations it posits. Armstrong implies that the modality he invokes for this account falls between logical necessity and brute contingency; in the end, he shifts towards the view that laws have a quasi-causal modal force. The point is that the kind of necessity Armstrong stipulatively builds into RBUIR’s lawmaking relation

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– the central plank of his case for nomic realism – is at best unfamiliar, and at worst entirely opaque. Similarly, one might think that the Powers Model ignores the Modal Hybridity Problem altogether by satisfying the Governance Intuition at the expense of the Contingency Intuition. The reason for this is the strong essentialist assumptions that it makes: its lawmaking properties ground the same regularities across all possible worlds. On this view, possible worlds in which samples of argon gas did QRWKDYHDPHOWLQJSRLQWRIíƒ&ZRXOGQRWEHVDPSOHVRIDUJRQ gas; the intuition that its melting point might vary across possible worlds is taken to be an illusory and unreliable guide to possibility. By contrast, if we are willing to grant with Foster that the ultimate lawmaker is a personal being who freely and rationally decides on the particular distribution of laws in the actual world, then the attractions of this model for nomic realists who insist a solution must be found to the Modal Hybridity Problem are undeniable. For if there is a being who causally imposes regularities on the physical world as regularities in this way, then the Governance Intuition makes sense: God causes the world to behave in the generic ways he prescribes. But if Foster’s thesis is true, it is also easy to see why the Contingency Intuition seems so reasonable, since a free agent could have selected a slightly different package of prescriptions with respect to other possible worlds. Unfortunately, however, Foster’s model leaves far too many objections unanswered. In particular, his theistic case for nomic realism suffers from the same deficiencies as those we encountered with respect to naturalistic versions of DISPIR in Chapter 3 (and, indeed, with respect to Swinburne’s theistic version of DISPIR evaluated in §5.1). This is the case regardless of whether we prefer to develop his solution in ‘nomological’ terms (i.e. to infer a theistic conclusion from the otherwise puzzling modal hybridity of laws) or whether we prefer to do so in ‘non-nomological’ terms (i.e. to infer a theistic conclusion from otherwise puzzling uniformities in the collective and diachronic behaviour of objects where it is presupposed that laws cannot account for these). For once we probe more deeply into the mechanics of Foster’s solution, it is extremely unclear how we should envisage God’s causal imposition of regularities resulting in the creation of laws. As we have seen, he takes dispositions to be indispensable features of the physical world, but he rejects the view of dispositions as ungrounded in favour of the traditional view that grounds them in a categorical base. In other words, he rejects the Powers Model by ruling out the possibility of lawmaking dispositions. How, then, does he explain the connection between

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dispositions and their categorical base? As far as I can tell, with a considerable degree of vagueness:42 We must conclude that God creates the universe by directly creating its initial state, and by making provision for its subsequent history by prescribing the systematic ways in which its state at any given time is to give rise to its states at subsequent times. This will ensure that God imposes certain regularities on the universe as regularities, thereby creating laws; and the creation of laws will, in the standard way, furnish material objects with their dispositions.

It is not clear to me what Foster means by the claim that, as he puts it elsewhere,43 God ‘prescribes the modes of transition’ after having directly created the universe in its initial state. He unpacks this phrase with the remark that ‘[a]ll we are to suppose is that God intentionally causes it to be the case that the universe develops along the relevant lines – in accordance with the relevant modes of transition, and so in conformity to the relevant forms of regularity.’44 But I just cannot see, given Foster’s ontological commitments, how the universe could develop in this way without God directly sustaining at every moment the link between each lawmaking disposition and its corresponding categorical base. This is something he denies, however, claiming instead that God imposes regularities ‘leaving open all the details of how things conform to them.’45 Yet something has to sustain this link in an ongoing way. We have noted and accepted Foster’s argument that no naturalistic factor could fill this role; and we have separately made a case against the only nonnaturalistic alternative to divine agency in the previous chapter (one that it is reasonable to assume Foster would share). So the logic of his case presses us towards the conclusion that God causally sustains the link between every disposition and its categorical base directly. But if this is the final outcome of Foster’s account, it is difficult to see how it can be distinguished from occasionalism. Occasionalism is, as Alfred Freddoso has convincingly argued,46 a surprisingly difficult outcome for orthodox theists to avoid. But we can safely presume that is not a result Foster would have endorsed. If we are to avoid it, we must draw at least two lessons from his ultimately unsuccessful account. First, we cannot establish a convincing case for nomic realism if we cannot first show how putatively 42 43 44 45 46

Foster 2004: 165. Foster 2004: 154. Ibid. Ibid. Freddoso 1988; Freddoso 1991; Freddoso 1994.

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lawmaking dispositions ground regularities, where regularities are construed – in the way Foster convincingly shows they must be – as diachronic regularities in the collective behaviour of objects. Second, we also cannot achieve our goal if we cannot show how dispositions sustain regularities so analysed without themselves being grounded in anything that would require us to invoke the very lawlike connections they were invoked to explain. 5.2.5. The Rejection of Universals It seems, then, that although Foster has helped us to clarify the explanatory objectives of this study, we are no closer to finding a successful realist analysis. We had, after all, already concluded that naturalistic strategies were unworkable; and we were already close, in our analysis of DISPPR, to a resolution of the tensions that undermine accounts of the nature of lawmaking dispositions (at least one of which Foster cites as a reason to reject the Powers Model completely). Nevertheless, rather than abandon Foster’s account altogether, I wish to focus on a single striking detail that emerges from it. It is a feature that does not affect in any significant way the substance of his overall theory. It contains a clue, however, that – suitably developed – may eventually help us to formulate a cogent case for nomic realism. We have repeatedly observed in the course of our inquiry that, for all their differences, most cases in support of nomic realism construe properties and relations as universals. We have also seen that this commitment is at once the source of their greatest strength and their greatest weakness. On the one hand, universals secure the degree of uniformity typically associated with laws. On the other, the problems posed by including the Instantiation Principle make it tempting to abandon it altogether, and with it the uniform character of lawful regularities that universals were supposed to explain. Yet Foster avoids positing universals altogether. His brief remarks on the topic suggest, at least, that he rejects them to the extent they are to be treated as entities. But what does he mean by ‘entities’? We might be tempted to think that he means to reject the more robust form of realism about universals – i.e. platonic realism. But this cannot be reconciled with the fact that he makes the remarks in the course of his critique of RBUIR (that is, the immanent realist version of the Relations Model). Indeed Foster expressly states that RBUIR ‘has to be realist about universals [as entities] … and to hold that reference to them must feature in the

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philosophically fundamental description of how things are.’47 What makes it difficult to identify precisely where Foster stands on the question is that he also claims to reject nominalism on the basis that properties and relations are irreducible ingredients of reality. But he goes on to note that he shares the nominalist’s distaste for the reification of properties and relations. If pressed to make a final assessment, I think it is difficult for us to avoid the conclusion that – for all his protests to the contrary – Foster does ultimately endorse a nominalist position. But which nominalist stance does Foster adopt? At first he comes close to adopting predicate-nominalism by substituting universals for linguistic items. On this view, particulars resemble each other solely in virtue of the fact that they are subjects to which the same predicate is attributable. Here is the crucial passage:48 I am inclined to think that, although shape-properties are a fundamental ingredient of physical reality, their presence is to be ultimately understood predicatively, rather than ontologically – as a matter of objects being, for example, cubic or spheroid or ovoid … [I]n the final philosophical analysis, I am inclined to think that our understanding of the nature of properties and relations has to be in terms of what it is for things to be propertied and related, and that this is something which is captured by the use of predicates rather than by reference to certain kinds of abstract entity.

If it were accurate to characterise Foster as a predicate-nominalism in this way, this would have still more serious implications for his analysis of laws, not least because it would commit him to the highly implausible view that regularities – construed as regularities causally imposed by divine agency – ought to be analysed in linguistic terms, and this would be tantamount to abandoning the attempt to find a realist analysis of laws altogether. Nevertheless, as if anticipating this objection, Foster then goes on to deny that the applicability of common predicates is constitutive of properties and relations.49 Despite the ambiguity that attends Foster’s constructive alternative to the kind of robust ontological commitment to universals that has characterised almost every other case for nomic realism we have considered, 47

Foster 2004: 97. Foster 2004: 98-9. For an extended discussion of predicate-nominalism, see Armstrong 1978: 11-24. 49 Foster 2004: 99: ‘I should … stress that I am not suggesting that the presence of properties and relations in the world is in some way dependent on the existence of the corresponding predicates. Predicates are simply what are needed to express what the presence of properties and relations ultimately amounts to.’ 48

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I suggest that his ambivalence towards universals is one that we should take seriously. For we have seen that, time and again, positing universals has thwarted our attempt to arrive at a compelling solution to the problems that lawlike phenomena present. In the case of RBUIR and DISPIR, the problems arose from immanent realism’s commitment to the Instantiation Principle. But we then saw, in the case of RBUPR and DISPPR, that abandoning it in favour of an abstract domain of platonic universals introduced at least as many explanatory puzzles as it was supposed to resolve. It is now time to conclude, I suggest, that realism about universals – immanent and platonic – is a strategy that, in the final analysis, consistently promises nomic realists more than it ever delivers. If we are to abandon that commitment, though, where else are we to turn? We shall begin to address this question more fully in §5.3 below. 5.2.6. A Final Assessment In the course of this section and the previous section, it has emerged that for all the undeniable improvements their accounts make to non-theistic versions of nomic realism in terms of overall explanatory power, neither Swinburne nor Foster provides a fully satisfactory analysis of the lawmaking dispositions that underpin them. Needless to say, this has worrying implications with respect to our quest for a convincing case for nomic realism. Indeed pursuing either of the two theistic strategies we have considered threatens to envelop that quest in a dialectical circle. For the motivation for turning to theism sprang from the theoretical inadequacies of naturalistic versions of the Relations Model (Chapter 2) and the Powers Model (Chapter 3), together with the fact that the most persuasive nonnaturalistic alternatives to theism pay a disastrously high metatheoretical price for negligible explanatory gains (Chapter 4). Although Swinburne and Foster each propose a theistic solution, they are no less committed to the same methodological constraints that undermined DISPIR enough to motivate the turn to platonic realism in Chapter 4 – that is, the Instantiation Principle. It is true, of course, that any theistic account of laws must invoke at least one non-spatial entity. There is therefore a non-trivial sense in which their model is more weakly committed to the Instantiation Principle than RBUIR and DISPIR, since each of the latter includes spatial location as part of the price of ontological admission. But, as we have seen, their common commitment to the Instantiation Principle triggers the problems that generated the pressure to platonise. The success of the present inquiry depends, then, on finding

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a solution that maintains the basic advantages of RBUIR and DISPIR without returning to the impasses of Chapter 2 and Chapter 3. The remainder of this study is devoted to arguing that this dialectical circle can be broken. If the argument is to succeed, one ingredient in the unsuccessful accounts needs to be eliminated without undermining the central contention of nomic realism: universals. In keeping with the strategy that we have adopted throughout, the following section considers one way of subtracting universals in a manner consistent with a naturalistic ontology. Although this strategy fails, its failure will help us to see the comparative strength of the theistic variation, and so to motivate an ontology for nomic realism that rids us entirely of universals, and with them the host of intractable problems they have provoked in the course of the inquiry so far.

5.3. Conceptualist Strategies We began this study with the assumption that realism about universals and realism about laws were, in effect, structurally complicit metaphysical positions.50 That is to say, we repeatedly assumed that the success of nomic realism depends on whether or not a coherent account of universals could be found. Now it is true that we have not explored in detail every competing merit of immanent realism and platonic realism. But we have carefully considered the implications of each of these stances with respect to the specific question of laws. And at almost every turn, fundamental theoretical problems arose when these implications were examined. Still, if it is finally conceded that neither immanent realism nor platonic realism supports nomic realism, what alternatives are left? It seems to me that there is only one basic approach remaining that has any genuine prospect of underwriting the nomic realist position, and that is to assign the theoretical role that universals were supposed to play in developing the case for nomic realism to the conceptual activities of a cognitive being. And if we are to adopt this highly controversial proposal, then we are faced with a choice: we must either effect this substitution in relation to the conceptual activities of human beings – a position I shall refer to as secular conceptualism51 – or as products of the mental 50 It has briefly considered trope-theoretic approaches endorsed by Molnar 2003, Heil 2012, and others; but it found that these failed to satisfy some key desiderata. 51 I here follow Leftow’s terminological practice of using ‘secular’ to designate anything ontologically distinct from God (or, as he puts it, ‘non-God-involving’ – see Leftow 2012: 83).

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activity of a supremely rational being – a position I shall refer to as theistic conceptualism. 5.3.1. The Incredulous Stare Invoking divine concepts to perform the explanatory work ordinarily assigned to universals in realist theories of laws may well provoke cries of obscurum per obscurius from those already opposed to the theistic hypothesis. Even opponents of nomic antirealism may see such a move as a reductio ad theologiam, and conclude that if invoking divine concepts as lawmakers is the price to be paid for nomic realism, it would be better to cease the search for it altogether. But let us scrutinise this imaginary objection more closely. If the criticism is that theistic conceptualism is insufficiently economical from a metatheoretical point of view, then its supporters can point out – as we did in relation to platonic strategies in §4.6.3 above – that economy principles should only eliminate posits that are explanatorily redundant to a theory. Are divine concepts redundant in this sense? Part of the point of structuring our inquiry in the way that we have – that is, by undertaking exhaustive assessments of existing non-theistic options (naturalistic and non-naturalistic) at the outset – was to anticipate precisely this kind of objection. For the structure of my argument has been intended to underline as forcefully as possible that the theistic proposals we have turned to consider in this chapter and the next cannot now be attributed to an unreflectively doctrinaire preference for theism, but rather to the fact that every other solution we have explored thus far has failed. As far as I am aware, the different versions of the Relations Model and the Powers Model analysed in Chapter 2, Chapter 3, and Chapter 4 collectively exhaust the non-theistic approaches available to the nomic realist. Moreover, the theistic strategies assessed in §5.1 and §5.2 represent by far the most substantive and sophisticated of the small handful of contemporary theistic accounts that exist.52 Given the charge-sheets that have now been drawn up against each of these six accounts, we can hardly dismiss theistic conceptualism as a metatheoretically extravagant solution to a problem for which adequate alternatives are available.

52 Ratzsch 1987 motivates a theistic case for nomic realism very powerfully by claiming that theism underwrites subjunctive conditional statements more plausibly than its rivals; but, as it stands, his constructive account is too brief and inconclusive to be fully persuasive.

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If the immediate reaction to a theistic conceptualist analysis of laws is straightforward incredulity, then we need add very little to David Lewis’ response to those who treated his modal realism to an ‘incredulous stare’:53 The proper test [of common sense], I suggest, is a simple maxim of honesty: never put forward a philosophical theory that you yourself cannot believe in your least philosophical and most commonsensical moments … The incredulous stare is a gesture meant to say that modal realism fails the test. That is a matter of judgement and, with respect, I disagree. I acknowledge that my denial of common sense opinion is severe, and I think it is entirely right and proper to count that as a serious cost … I still think the price is right, high as it is. Modal realism ought to be accepted as true. The theoretical benefits are worth it … Provided, of course, that they cannot be had for less.

As I have already remarked, the advocate of theistic conceptualism is in a dialectically similar position to the advocate of modal realism. Each thesis amounts to a ‘severe’ rejection of widely held beliefs; and each thesis will elicit incredulity from several quarters. But just as Lewis can claim that the theoretical benefits of modal realism are worth the price of these costs, so too can the theistic conceptualist insist that the promise of his case for nomic realism comfortably offsets whatever counterintuitive costs it might incur. And just as Lewis can note that the success of modal realism depends on the absence of a comparably explanatory but less costly alternative, so too can the theistic conceptualist point – at this stage in the study – to the fact that we have already searched hard for comparably explanatory but less costly alternatives. At this point, moreover, we would do well to recall ourselves to the fact that the most costly theoretical posit common to the theories examined thus far has been universals. Realism about universals, as we have seen again and again, has been a costly position not only in terms of ontological economy (qualitative and quantitative), but also in terms of the endless explanatory problems it has generated. So it would be odd, to say the least, if we failed to consider a theory that promised to deliver the explanatory objectives for which universals are invoked without incurring a corresponding cost. It is the central contention of the following chapter that one version of what I shall term theistic nomic conceptualism can do just this.

53

Lewis 1986: 135.

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Nevertheless, if we are to make good on the claim that the theoretical benefits of theistic conceptualism are not available more cheaply elsewhere, there is one final option to be considered before we turn to it: secular conceptualist strategies. As it happens, cataloguing the difficulties of these strategies before assessing their theistic counterpart serves the overall argument of this study rather well, since their weaknesses illuminate by contrast the considerable strengths of the theistic alternative. 5.3.2. Objections to Secular Conceptualism The problem that arises immediately for secular conceptualist strategies is that they appear flatly to contradict a self-evident feature of the way human beings negotiate the world. For we can and do configure our conceptual schemes incorrectly. The conceptual scheme in which phlogiston played an explanatory role not only contradicted the conceptual scheme that came to reject it, but also the way the world is. For the reason phlogiston was inconsistent with the subsequent conceptual scheme was that the latter offered a truer account of mind-independent reality. It is extremely difficult to make sense of this distinction, however, if we accept the thesis that reality is constituted by whatever conceptual scheme we apply to it. The second objection to secular conceptualism begins from two plausible assumptions. The first is that there are uncountably many items in reality that could be targeted by human concepts, but which as a matter of fact never are. The second is that there are uncountably many items in reality to which we could not have any conceptual access in principle, for the simple reason that our cognitive faculties are inherently limited, as Christopher Peacocke notes:54 It can, for instance, be true that there are concepts human beings may never acquire, because of their intellectual limitations, or because the sun will expand to eradicate human life before humans reach a stage at which they can acquire these concepts. ‘There are concepts that will never be acquired’ cannot mean or imply ‘There are mental representations which are not mental representations in anyone’s mind.’ If concepts are individuated by their possession conditions, on the other hand, there is no problem about the existence of concepts that will never be acquired. They are simply concepts whose possession conditions will never be satisfied by any thinkers.

54

Peacocke 2005: 169.

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Now Peacocke is correct to claim that there are concepts that human beings could not possess or will never in fact possess. He is also correct to claim that it is incoherent to suppose that those concepts that could never or will never be grasped might be mental representations. But it is not clear why these objections do not apply with equal force to his own position. On a secular account of the nature and ontology of concepts, at any rate, it is clearly not possible to tie concepts that could never be possessed or are never possessed to cognitive agents. So Peacocke must introduce a strong ontological distinction between concepts and conceptpossessors and stress that we only come to acquire concepts once certain possession conditions are met. Yet what is the ontological status of concepts on the resulting account? Peacocke appears to concede an independent ontological standing to infinite numbers of concepts whose possession conditions either could never be met or are never met. This results not only in an extremely bloated ontology, but also one that contains very unusual entities indeed: free-floating concepts that are never be possessed by any cognitive agent. A third difficulty with secular conceptualist strategies is that they do not explain how concepts could perform the unifying role of universals. Realists appeal to universals, for example, to ground putatively objective similarities between members of divisions or categories. Yet what determines membership cannot be a function of how we happen to carve reality up. This is not simply a different way of framing the first objection, although there is ample historical evidence that we can – and often do – fail to pick out objective distinctions in nature. It is rather to point out that if anything does constitute the natural unity of a species, it is implausible to suppose that the ontological basis for this is a concept in the mind of a species that evolved much later (and, indeed, one that might never have existed at all). A fourth objection can be raised against secular conceptualist strategies with respect to causation. The difficulty is that the conceptualist is committed to the idea that explanatory traffic between concepts and causes is one-way – that is, that it is our concepts that organise which causes bring about which effects, and never the other way round. Secular conceptualists must hold that the causal behaviour of every concrete particular depends on the way we organise it conceptually. Now there are, of course, all sorts of circumstances in which it is obviously correct to claim that concepts precede causes in the order of explanation. The concepts that feature in this sentence are explanatorily prior to the causal processes that led to its appearance on the page; patents are filed prior to the physical appearance

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of the prototype; the plot of a play is conceived before it is staged; and so on.55 But as a global explanation of causal behaviour in nature – which is, after all, our present concern – the analysis to which secular conceptualism is committed seems wildly implausible. Indeed it is difficult to imagine even the most dedicated Kantian accepting an account of concepts that yields this kind of result. This final objection is especially acute in relation to those who subscribe to the Eleatic Principle, because if one holds – with Armstrong and many others – to a causal criterion of existence, then on the secular conceptualist view nothing exists that does not depend on the concepts you and I possess. And this, to say the least, is an extremely counterintuitive and unwelcome consequence. 5.3.3. Secular Nomic Conceptualism – A Case Study So the obstacles ranged against secular conceptualism seem very substantial indeed. But it is worth pausing for a moment to observe just how much more difficult it would be to combine secular conceptualism with a realist analysis of laws. One recent attempt to do so by U.T. Place conveniently highlights the dangers facing would-be secular nomic conceptualists. Place’s conceptualism is motivated by a deeply ambivalent attitude towards universals. He appears to concede that there must be universals or ‘features’ to ground resemblances between particulars, but then goes on to claim that these are simply functions of whatever classificatory scheme is applicable to these particulars. He even concedes the possibility that uninstantiated universals might exist, but only in the sense that there might be concepts that no concrete particular satisfies.56 That is to say, for Place universals (and kinds) are simply mental states, products of mental abstraction from concrete particulars. The process of abstracting properties and relations generates certain taxonomies, which are in turn embedded within the semantic structure of a natural language. For example, to claim that a cherry instantiates redness amounts to the claim that there are languageusers who apply the linguistic token redness on the basis of criteria consistent with the possession and application of a concept that individuates red particulars within a shared conceptual framework. On Place’s view, then, universals are not so much abstract objects as abstracted entities. It is useful to distinguish here between universals that 55

Note that if concepts could not precede causes, theistic conceptualism could not get started. This is because it holds that God forming the concept is explanatorily prior to God willing whatever causal sequences ultimately terminate in the existence of pineapples. We shall discuss this in more detail in the following chapter. 56 Place 1993: 56.

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are construed as abstract in the epistemological or ‘Lockean’ sense from those that are abstract in the ontological or ‘Quinean’ sense. For some immanent realists, the abstract character of universals derives from the fact that they are unsaturated entities or, put differently, entities that have no existence independently of the states of affairs they (wholly or partly) constitute. Universals ‘exist’ only in the rather limited sense that they feature in our mental content once abstracted from the particulars to which they belong.57 Now if we do accept this distinction, it may be possible to classify Place’s theory of laws as a version of DISPIR on the basis that he is committed to universals in the attenuated Lockean sense. If this conclusion is correct, however, it is difficult to reconcile it with Place’s claim that given his theory of property-identity, laws cannot be construed as objective states of affairs. For laws, he claims, should be reduced to law-statements (or ‘formulae’) that pick out certain commonalities between the ‘features’ of concrete particulars:58 [T]he source of the philosopher’s claim to authority in matters of ontology derives from an understanding of the process whereby linguistic utterances acquire the dispositional property of depicting a reality beyond themselves … [W]hat experience tells us, I suggest, is not that, in order to accommodate [unusual phenomena], we need to add new categories of existent to our ontology or abandon old ones. It is rather that in these areas we have passed beyond the proper scope of natural language into a domain where only the language of mathematics has literal application. For a conceptualist this conclusion is no embarrassment. It simply emphasizes the mind-dependent character of and consequent limitations of our conceptual scheme. It confirms the view that it is a mistake … to project that conceptual scheme onto reality by postulating universals and laws of nature as something more than convenient ways of classifying particulars and characterising the way particular relations between particular situations resemble one another.

This passage succinctly sets out just how severe are the consequences of Place’s conceptualism for nomic realism. Indeed it comes close to a version of linguistic positivism: nomic necessity is de dicto and supervenes on the semantic structure of whichever natural language a particular lawstatement happens to be expressed in. And yet, paradoxically, Place takes causal necessity to be a de re modality that is empirically observable. He grounds this necessity, moreover, in the dispositional properties of an object: it is the brittleness of a glass, he claims, rather than its microstructural base that accounts for its counterfactual resilience. 57

Armstrong 1983: 90-1. Place 1996: 52-3. Note his subsequent remark (at 54) that ‘[I] would be uncomfortable with the claim “that the world is a world of situations or states of affairs,” if that is taken to imply that there is one uniquely correct way of carving up the world into situations.’ 58

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So Place combines a secular conceptualist reduction of universals with a realist stance towards dispositions as lawmakers. This is, to say the least, an idiosyncratic theory of laws. But it should be stressed that it is not the idiosyncrasies themselves that make this particular account untenable. It is rather that Place’s position brings with it all the theoretical weaknesses of secular conceptualism. In the first place, we are given no reason to think that his analysis of laws is true. On his analysis, the most that can be claimed of (say) a statement of Pauli’s Exclusion Principle is that it is correct with respect to the classificatory scheme within which it is embedded, and consistent with the semantic rules that the statement employs. This presents, of course, a familiar but profound sceptical challenge to secular conceptualism more generally. For however fine-grained the conceptual scheme that mediates sense-experience to us, and however widely it might be endorsed by those who share that conceptual scheme, there could never be any basis for it in reality that did not tacitly assume a vantage point that was independent of the methods with which the scheme was first devised. So Place’s account stands as an instructive warning before we move on in the next chapter to examine a very different conceptualist case for nomic realism. He mistakenly assumes that a functionally antirealist stance towards universals need not undermine a realist stance towards lawmakers, which he identifies as dispositions. But on Place’s view, resemblances in the nomic profiles of properties can and should be explained predicatively: lawlike regularities ultimately consist in the fact that they satisfy certain linguistic terms within a particular conceptual scheme; more precisely, lawlike connections between dispositions supervene on the conceptual connections constitutive of this scheme. In short, the modal strength of Place’s lawmakers does not derive from anything independent of human cognitive capacities and linguistic practices. And since it is the contention that lawmakers do have the kind of independence that chiefly defines nomic realism, it is difficult to see how Place’s claim that his account is a version of nomic realism can be sustained. * * * This chapter began by pursuing the two most cogent contemporary attempts to advance a theistic case for nomic realism. In contrast to the platonic strategies evaluated in Chapter 4, these accounts placed a promising and relatively unproblematic emphasis on the role of causation in their account of laws. But their shared commitment to the Instantiation

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Principle meant that they were stymied from advancing the inquiry any further than the stage it had already reached by the end of Chapter 3. But at the end of our assessment of Foster’s analysis, the following thought presented itself: what if we were to develop a case for nomic realism that abandoned universals altogether? More specifically, what if we were to replace universals with concepts? If universals were not properties that belonged to their bearers (as immanent realism claims) nor entities that existed independently of them (as platonic realism claims), we might want to construe universals as products of the mental activities of cognitive beings. True to the methodological practice adopted more generally in this study, we began by exploring ways to develop this account in non-theistic terms. In particular, we examined a bold attempt to elaborate a realist account of laws within a secular conceptualist framework. We concluded that the prospects of secular nomic conceptualism were dim. It is now time to consider the two theistic alternatives.

CHAPTER 6 THE MAKER’S MIND: DIVINE CONCEPTS AND NATURAL ORDER

We have now evaluated permutations of the two basic realist analyses of lawlike phenomena: the Relations Model and the Powers Model. So far, however, none of these approaches has yielded a persuasive account of how best to construe regularities in the physical world. Moreover, when we turned to consider two leading theistic proposals in the previous chapter, it turned out that the explanatory gains these undoubtedly conferred were undercut by the same difficulties that had earlier forced us to reject the immanent realist version of the Powers Model. Nevertheless, in the course of assessing the second theistic account, we began to suspect that a principal source of the difficulties undermining realist analyses was the widespread commitment to the existence of universals however construed; and this in turn led us to consider whether a substitute could be found for universals that would preserve their explanatory power without incurring their substantive theoretical and metatheoretical costs. In particular, Foster’s marked ambivalence towards universals prompted us to ask whether it would be possible to ground nomic realism in a nominalist ontology. We began to examine two kinds of nominalism in particular: predicate-nominalism and concept-nominalism. Brief analyses of these positions, however, quickly uncovered their inadequacies, inadequacies that became painfully apparent when we examined U.T. Place’s attempt to draw on both positions in support of his version of the Powers Model. For all of its obvious weaknesses, however, the basic theoretical substitution that secular conceptualism1 proposes boasts an ancient pedigree in the intellectual traditions of monotheism. The difference is that where secular conceptualism replaces universals with human concepts, theistic concept-nominalism replaces them with ideas in the mind of God. 1 For the purposes of the present argument, I assume that nothing of significance depends on the difference between ‘concept-nominalism’ and ‘conceptualism.’ Some philosophers, however, use the former term to designate a specific stance towards attributes (properties, relations, kinds) and the latter term to denote a more global thesis about the nature of reality as a whole.

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Historically, the most well-known versions of this approach are to be found in the writings of Augustine,2 Aquinas,3 and Leibniz.4 Yet enthusiasm for it among contemporary analytic philosophers of religion has been in evidence for some time.5 The principal attraction of this strategy is that it promises to accommodate within a single integrated theory many intuitions motivating realism and nominalism that would otherwise sharply diverge. To take an already familiar example, realists about universals typically insist that they are required in order to provide an objective basis for resemblances among particulars, whereas antirealists will often reject them on the basis that it is incoherent to posit any entity that is located in multiple places at the same time (in the case of immanent realism) or in a distinct, empirically inaccessible ontological domain (in the case of platonic realism). As many theistic philosophers have noted, however, the theoretical intuitions of both sides are satisfied by theistic conceptualism. God’s mind provides the objective basis for laws that the realist is searching for, but in a way that requires neither a commitment to multiply localised entities nor the introduction of an abstract domain.

2 For references, see page 8, note 16 above. Augustine’s transmutation of Platonic forms into divine ideas was in part a defensive strategy deployed to neutralize the risk that the former would undermine divine aseity and divine sovereignty. For a critical comparison of the Augustinian position with the ‘theistic activism’ of Morris & Menzel 1986 (discussed below), see Werther 1989. 3 For references, see page 8, note 17 above. Comprehensive discussions of the relevant texts can be found in Wippel 1993; Boland 1996: 195-273; and Doolan 2008. 4 See page 8, note 18 above. An increasing number of philosophers of religion drawing on theistic conceptualist position with an explicitly Leibnizian stamp – see, in particular, Leftow 1989; Pruss 2002; Pruss 2011 (see note below). 5 The literature on theistic conceptualism has grown considerably since it was first revived as a strategy four decades or so ago. See, for instance, the theistic conceptualist construal of universals in Wolterstorff 1970: ch. 12, logical necessity in Adams 1974 and propositions in Plantinga 1982 (indeed Plantinga 2007 extends the strategy to include numbers and sets as well). Other stances worth noting are Loux 1986, who proposes a theistic conceptualist account of attributes; Morris & Menzel 1986, who suggest there is nothing in the platonic domain that could not in principle be substituted for God’s intellective activities; Menzel 1987 argues that if set-theory provides adequate foundations for mathematics, then sets can be substituted for collections in the divine mind; Leftow 1989 advances a theistic conceptualist version of Leibniz’s cosmological argument; Welty 2006 endorses a theistic account of propositions and possible worlds, arguing that theistic conceptualism is the best way to accommodate these; Leftow 2006 offers a powerful argument that universals should be substituted for God’s concepts; Dummett 2006: 96-109 argues for a similar solution to the problem of verification conditions for sentences; and, finally, Pruss 2002, Pruss 2011, and Leftow 2012 argue that God’s mind (together with God’s concrete causal powers) provides the most comprehensive and metatheoretically economical ground for modal truth. For criticisms against conceptualist arguments for God’s existence more generally, see Smith 1984 and Oppy 1993.

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The question before us in the present chapter, however, is whether this kind of conceptualist approach can be pressed into the service of a theistic case for nomic realism. Notwithstanding the historical and contemporary precedents for substituting universals (and other abstract objects) for divine ideas, so far as I am aware no one has examined the implications of applying this strategy specifically to current debates in the metaphysics of laws.6 What follows is an attempt to put this right, and to argue that theistic conceptualism offers a far more promising solution to the problems that have occupied us in this study than its marginal status in those debates would suggest. §6.1 rehearses some general considerations relevant to the motivation for theistic nomic conceptualism, sets out the basic explanatory framework, and anticipates the objection that it entails an unacceptable degree of ontological commitment. §6.2 then examines whether a convincing metaphysical analysis of divine concepts is available, since if no such analysis is available then plainly no theory that relies on them can hope to succeed. §6.3 undertakes a transposition of the Relations Model into a theistic conceptualist framework by replacing lawmaking relations with divine concepts; it then enumerates the explanatory advantages that accrue to this version and raises some objections to it that, I argue, irretrievably undermine it. §6.4 performs the same exercise with respect to the Powers Model by substituting lawmaking dispositions for divine concepts. It shows how the explanatory power of Powers Model is considerably enhanced once it is situated within the framework of theistic nomic conceptualism.

6.1. Divine Conceptualism: Some General Considerations Before attempting to transpose the two basic realist approaches to laws into a theistic conceptualist framework, we must first consider whether the basic ontology on which this proposal relies resists the objections raised against secular conceptualism in the previous chapter. The aim of this section is to argue not only that theistic conceptualism successfully meets these objections, but that its lean body of metaphysical commitments 6 I was pointed in this direction, however, by Leftow 2006: 327-8. Dumsday 2014 proposes a solution to the problem of dispositional properties (construed as universals) that partly resembles the approach proposed here; but Dumsday mistakenly characterises this as a version of the cosmological argument, and so fails to draw out the potential of this approach with respect to developing a theistic conceptualist case in support of nomic realism.

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broadly preserves the central theoretical advantage of secular conceptualism.7 6.1.1. Solutions to Secular Conceptualism Turning back to the objections raised against secular conceptualist strategies in §5.4, consider how the failure of these strategies illuminate by contrast the strength and promise of the theistic alternative. The first objection noted that secular conceptualists cannot explain what accounts for the fact that many of our conceptual schemes fail to capture reality.8 This cannot be the case, however, with respect to God’s conceptual scheme. This is not simply because it is logically impossible for an omniscient being to misapply a concept; it is also because anything distinct from God that could satisfy a concept has its ultimate causal origin in the concepts informing his creative actions. Theists are committed, after all, not only to the view that God is omniscient, but also to the view that he is the ultimate causal origin of everything distinct from himself. The second objection against secular conceptualism took its cue from what seems to be a reasonable premise, namely that there are many – indeed infinitely many – aspects of reality that omnitemporally fail to satisfy secular concepts. But again, the theistic alternative dissipates this objection at a single stroke. Traditionally conceived, God is an omniscient being, from which it follows that there could not be any aspect of reality that both satisfied a concept and failed to satisfy God’s concept of it.9 The third objection held that secular concepts fail to ground objective similarities between members of a naturally unified class. But this difficulty also disappears once God’s concepts are in play, because membership of a kind or class of natural individuals is definitively settled by what God conceives this to be.10 As George Bealer concedes, 7 On this point, see Robinson 2011: 257-8: ‘Treating the Platonic realm as an intellect and not as a collection of inert abstract entities enables one to preserve the virtues of a variety of theories about the world of abstracta … The abstract objects by which [God] thinks are creations of a mind, like fictions, but, unlike fictions, are essential to the constitution of the reality that is thought about.’ 8 Some of the standard examples deployed in support of scientific realism include phlogiston and ether – see Psillos 1999: 177-88 for a discussion of the implications of these for the antirealist position. 9 As Leftow 2006: 339 puts it: ‘[T]here is nothing a thing could be of which God would not have a concept.’ Leftow goes on to note that this would be the case even if God lacked concepts of possible existents. 10 Since I hold that God is timeless, my use of the word ‘prior’ refers only to logical priority.

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every conceptualist reduction of universals points towards a theistic conclusion:11 My arguments [against nominalism and conceptualism] would fail if, for every logically possible circumstance, everything object there – in particular, every object that is not among the objects that actually exist – is nevertheless such that God right now has an actual idea that would apply uniquely and rigidly to that object. Thus, a necessary condition for the truth of nominalism or conceptualism is not only that God exist but also that God have ideas of a kind that in principle we could not have and, indeed, that we could not know what it is like to have.

Theistic conceptualism also blocks the fourth objection, according to which secular conceptualism cannot make causation itself depend on how human beings conceptually organise sense-experience. We conceded that secular concepts can – and very often do – precede causal actions. But as a global thesis of how natural objects causally interact with each other, secular conceptualism is not a promising strategy. Yet, once again, on theistic conceptualism the problem simply does not arise: any and every object distinct from God that can stand in causal relations is the product of causal processes originating in what God conceives and causes them to be. Our analysis in §5.3.2 and §5.3.3 of how much secular conceptualism gets wrong illuminated by contrast how much theistic conceptualism can get right. And if it was correct to conclude that realism about universals creates more problems than the theoretical benefits it confers, then short of turning to trope-theoretic or nominalist strategies (which would, as we noted in §2.5, suffer from many more difficulties than realism provokes), theistic conceptualism is – so far as I can tell – the only plausible candidate left standing. Still, even those who accept the inadequacies of the alternatives will baulk at what they perceive to be the metatheoretical extravagance and undue mystery of theistic conceptualism. There will, indeed, be theists who prefer the accounts advanced by Swinburne and Foster as considerably more economical and perspicuous than one that invokes uncountably many divine concepts to which we have no obvious epistemic access. These are important objections that we must examine more closely. 6.1.2. The Metaphysical Framework It is all very well to propose that universals should be eliminated in favour of divine concepts. But how exactly is this substitution supposed 11

Bealer 1993: 27-8.

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to work? Well, the solution is straightforward and – it seems to me – wholly consistent with uncontroversial theistic commitments. In condensed form, the theistic conceptualist proposal is this: reality is what God conceives and wills reality to be. This simple formula encodes a complete theory of attributes – properties, relations, kinds – that meets every explanatory objective for which nomic realists invoke universals. Let us consider these three aspects in turn. The reductive analysis of properties proposes to eliminate universals altogether in favour of the way God conceives and wills that a particular should be characterised. God conceives that and wills that it be so, such that Px. A theistic conceptualist of the law-governed behaviour of electrons would hold that electrons are negatively charged because God conceives, wills, originates and sustains that electrons be negatively charged. On this view, electrons do not ‘exemplify’ the ‘property’ of negative charge in the sense that an immanent realist or a platonic realist would understand this. For, strictly, no properties are exemplified on the theistic conceptualist proposal. God conceives of every possible way that electrons could be characterised. If negative charge is part of an electron’s essence, then there is only one metaphysically possible way for God to conceive of electrons (once he has conceived of them and brought them into existence). If negative charge is not part of its essence, there are infinitely many numbers for God to conceive of electrons. Either way, God wills that his conceiving that be satisfied. And, since God is an omnipotent being, it is logically impossible for him to will anything to occur that does not occur, so that the relevant divine volition entails whatever causal process is required to bring it about that electrons are negatively charged.12 Taken together, God’s conceiving and willing supply the necessary and sufficient conditions for electrons to bear every characteristic that belongs essentially to them. Given this way of describing it, one might be tempted to think that the foregoing reductive analysis describes a composite or sequential action in the divine mind. In reality, however, what grounds the fact that electrons are negatively charged is a single occurrence: 12 The volitional element here is important, because – as Leftow 2012: 432-4 explains in his criticisms of the intellectualist position advanced in Loux 1986: 510 – God’s mere belief that electrons are negatively charged cannot in itself ground the fact that electrons are negatively charged. To see this, note that prior to the existence of electrons God could not have had the belief that electrons are negatively charged, since God cannot have false beliefs. For God’s mental life adequately to account for the way a thing is, he must also will that it exist. God’s willing that his conceiving that be satisfied is all that theistic conceptualist’s analysis of Px requires.

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conception and volition – together with whatever causal processes these jointly entail – constitute a single, indivisible event in God’s mental life. With this analysis in place, corresponding reductions of relations and kinds quickly follow. Thus relations are constituted by the fact that God conceives that and wills this to be so, such that xRy. So too with kinds: the fact that created particular x is a member of kind K is determined by the fact that God conceives that and wills this to be so, such that x is a member of K. What grounds the fact that particular x is an electron is God conceiving that and God willing that be causally satisfied. So theistic conceptualism has all the metaphysical resources the nomic realist could need to develop a framework for laws. But those who prefer the explanatory structure of the Relations Model will assign the lawmaking role to ‘relations’ as theistic conceptualism parses these, while those inclined towards the Powers Model will assign it to ‘properties’ as these are analysed on this approach.13 Once the substitution of relations or properties for lawmaking universals (as the case may be) has been made, the theistic conceptualist analysis of laws follows the basic formulation that each of these two accounts sets out. 6.1.3. Ontological Commitment If the basic metaphysical framework set out in §6.1.2 strikes us as rather baroque, I suggest that this is a trick of perspective. Although it is, to be sure, an unfamiliar line given the overwhelmingly naturalistic climate of analytic philosophy, it is difficult to deny that the position presupposes a remarkably lean body of ontological commitments. At any rate, it does not offer an account of laws that is obviously less economical or any more mysterious than the theistic accounts we evaluated in §5.1 and §5.2. Indeed I suggest that we can advance a much bolder claim: theistic nomic conceptualism is capable of doing considerably more of the nomic realist’s explanatory work than the appeal of these accounts to divine causation alone and at considerably less metatheoretical cost. After all, many non-theists are committed to concepts, even if there are substantive disagreements over the correct ontological analysis of 13 Although we have not discussed this alternative at length, it is easy to see how a realist analysis of laws in terms of natural kinds – see e.g. Ellis: 2001: 229-58 and Lowe 2006: 156-73 – might be elaborated along theistic conceptualist lines. See the discussion in §5.2.2 above.

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these. Secular conceptualism tries to press these into the service of explanatory work for which others invoke other categories (universals, tropes, classes, and so on). Now we explored at some length in §5.3 the reasons for supposing that these moves are misguided. But if secular conceptualism was comparable to universals-based accounts in terms of its explanatory power, it would be difficult not to prefer it to these accounts on metatheoretical grounds. But at least as many metatheoretical advantages accrue to theistic conceptualism.14 For any theistic solution to a metaphysical problem already prices God in to its overall metatheoretical cost. If God is already part of the metaphysical picture, then so too are his concepts, volitions, causal powers, and so on; and if these can stand in for ontological categories that non-theists are forced to introduce into their explanatory scheme, economy considerations alone should compel theists to endorse theistic conceptualistm, and make it (at the very least) an attractive and plausible solution for non-theists.15 To illustrate this point by way of comparison, one crucial reason that nomic realism developed so quickly among analytic philosophers was the recovery of realist confidence in universals.16 In other words, as soon as universals made it back onto the ontological books, they emerged almost immediately as core components in realist theories of laws that they partly motivated. So nomic realists with logically independent reasons to believe in universals are not only entitled to invoke them in support of their account of laws: it would have been deeply puzzling if they had done anything else. But the same basic principle applies to theistic conceptualism: it would make no sense for theists to develop a solution to nomic realism without drawing on their antecedent ontological commitments; and this methodological principle applies a fortiori if these existing commitments are expensive commitments. At least some theists who baulk at the perceived excesses of theistic conceptualism are willing to draw on other theistic commitments to resolve a metaphysical problem – most obviously, of course, when appealing to 14 I owe this point to Leftow 2012: 301: ‘Concept nominalism’s claim to economy rests on its ridding us of kinds of entity: there are concepts anyway, and so with universals dropped, there are fewer kinds of things in its heaven and earth than are dreamt of in Russell’s philosophy.’ 15 Thus, once again, Leftow 2006: 348-9: ‘[I]f one is a theist, God and His concepts are there anyway, and so every kind of entity one uses them to replace is one less kind of thing in one’s ontology.’ 16 It is not a coincidence that this was largely inaugurated by Armstrong 1978 and Armstrong 1980.

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the existence of God as the best explanation of a whole range of different features of the human experience and the natural world. But if the principle applies in the case of belief in the existence of God, then it should also apply in the case of whatever commitments that this belief brings with it. If one is minimally committed to the existence of God, then one also believes – at the very least – that he has a mental life of some sort. Similarly, if one is minimally committed to the existence of God as monotheistic traditions conceive him to be, then – as a general matter – one should be comfortable with the idea that he is the ultimate metaphysical origin of everything distinct from himself. And this includes, of course, the physical world. Now once one conjoins these two credally orthodox commitments – God as minded, God as creator of everything non-divine – it seems reasonable for theists to infer that some aspect of God’s mental life accounts (at least in part) for every aspect of what he creates. If God is capable of filling an explanatory role for which non-theists need to invoke other additional entities – universals, tropes, nominalistically acceptable substitutes – then economy considerations should restrain all theists from positing these in addition to their fundamental metaphysical posit. 6.1.4. Benacerraf Dismissed The platonic strategies examined in Chapter 4 were persistently undermined by a variation of Benacerraf’s dilemma for mathematical realists (see §4.6.2 above). But it might be objected that locating the substitute for universals in the mind of God creates at least as many epistemological difficulties as platonic realists do by locating universals in an abstract domain. Alvin Plantinga has claimed, however, that theistic conceptualism makes it much clearer how epistemic access to its posits is possible than platonic realism does. Plantinga claims that God’s mental items are causally related to God in something like the way a thought is related to the mind that thinks it. In God’s case, however, it is not only mental items that stand in causal relations to God – created cognitive beings do as well. In principle, then, it is perfectly intelligible to posit distal causal chains between God’s mental life and our own epistemic faculties in a way that platonic strategies cannot.17

17 Plantinga 2003: 232-3 (I am grateful to Plantinga for clarification of his views on this point).

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One problem with Plantinga’s approach is that it does not account for the direction of causal traffic between God, his concepts, and the epistemic faculties of human beings. Let us assume that causation is transitive: if x causes y and y causes z, then x causes z, if only indirectly. But this does not mean that if x causes y and x causes z, y causes or is caused by z. If God causally determines which concepts he has as well as causing cognitive creatures to exist, it does not follow that divine concepts and human creatures stand in a direct causal relation.18 One point in support of Plantinga’s suggestion, however, is that the theist does still gain an important theoretical advantage over the platonic realist, namely that there is no causal barrier in principle between divine concept and cognitive creature. There is such a barrier, however, between abstract platonic lawmakers and concrete regularities. Not even God could make abstract entities enter into causal relations, since most philosophers would analyse these not only as causally inert, but as necessarily causally inert. So Plantinga’s suggestion lays down the metaphysical conditions for a coherent theory of divine illumination, whereas nomic platonists who treat properties as abstract objects in the ‘Quinean’ ontological sense must fall back on the implausible claim that we have an a priori epistemic ‘grasp’ of these objects. Leftow suggests a similar theistic solution to the Benacerraf Problem with an illuminationist twist.19 He urges that perfectbeing considerations indicate why theists should expect there to be epistemic access to the relevant entities. There is an obvious reason why a morally perfect being would ensure that his creatures might in principle gain cognitive access to his concepts. For this kind of access would confer obvious epistemic goods, evolutionary and otherwise, on the ways in which we negotiate the physical world. Taken together, the causal story Plantinga and Leftow offer renders it intelligible – at the very least – that causal traffic (i) can in principle move between theistic nomic conceptualism’s lawmakers and cognitive creatures and (ii) does in fact move between them. For it is reasonable to suppose both that an omnipotent being could bring this about and that a morally perfect being would bring it about. 6.1.5. Theistic Nomic Realism Once More Let us now compare the basic elements of theistic nomic conceptualism against the position we labelled theistic nomic realism in §5.1 and §5.2. 18 19

I owe this point to William Lane Craig. Leftow 2012: 74-5; 527-8.

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It is clear that the explanatory structure of theistic nomic conceptualism departs in significant ways from these accounts. But it is hard to see what metaphysical commitments it presupposes in addition to those that these accounts presuppose. Neither Swinburne nor Foster denies, of course, that God is a minded being who conceives and wills; and neither denies, of course, that God is the ultimate causal origin of physical reality. Yet the conjunction of these two uncontroversial claims is all that the theistic conceptualist’s analysis requires. There is no additional need to invoke a separate ontological category of universals, together with the intractable problems that undercut realist stances towards them, once God’s concepts are on the ontological books. Indeed given that it eliminates universals altogether, theistic nomic conceptualism makes considerable gains in terms of qualitative ontological economy relative to Swinburne’s immanent realism. Before we evaluate that claim, however, we must see if we can find a plausible analysis of what it is for God to have concepts in the first place and, if so, whether these concepts could carry off the explanatory work that most nomic realists assign to universals. In the following section, then, let us turn to three accounts in the contemporary literature of the nature and ontology of concepts in general to see if these might elucidate the nature and ontology of divine concepts in particular.

6.2. The Nature and Ontology of Divine Concepts No single study could hope to distil the complex and varied philosophical literature on concepts. But it is possible, I think, to pick out three broad currents of opinion in contemporary approaches. These are: (i) the semantic account; (ii) the representationalist account; and (iii) the abilities account. The aim of this section is to outline some of the merits and difficulties of each of these positions, before setting out why the theistic conceptualist should construe divine concepts in line with the third account. 6.2.1. The Semantic Account The semantic account of concepts takes its cue from Frege’s well-known distinction between ‘sense’ and ‘reference.’ In very general terms, the view treats concepts as entities that mediate between mind and world.20 20 Given this mediating role, Frege’s label for concepts as constituents of ‘thoughts’ is highly misleading.

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Concepts are constituents of propositions that characterise reality for cognitive, language-using beings. Frege construed concepts as free-floating ‘unsaturated’ entities primarily in the hope of resolving some notorious puzzles in the philosophy of language, such as the problem of explaining how two terms can co-refer but not be substituted for each other in a truth-preserving way. For instance, although the singular terms ‘Superman’ and ‘Clark Kent’ have the same referent, the statement is trivially true in a way that the statement is not. Frege’s solution was to invoke ‘senses’ – in our example, and – that each ‘present’ the same referent in distinct ways.21 Taking these ‘senses’ to feature as constituents of their propositions would show that the reason the second statement is not trivial is that it conjoins two distinct entities, two distinct ‘ways’ of picking out the same referent. Fregean senses also purport to solve the semantic puzzle of how it is possible for sentences that refer to nonexistent entities to be meaningful. Thus the reason that propositions such as are meaningful is that the singular term picks out a concept even though everyone (except, perhaps, the fictionalist) agrees that Zuleika Dobson does not exist. Perhaps the most serious objection to the semantic view is that it treats concepts as abstract entities.22 We have already considered in Chapter 4 the problems that arise for versions of nomic realism that are founded on an abstract ontology, so I shall not rehearse them again here. It is true that Frege repeatedly stressed that since ‘senses’ had a purely functional character (in particular, the explanatory function of connecting referents to their truth-values), they should not be understood in an ontologically commissive way, but rather as incomplete entities pending their inclusion as constituents in a proposition.23 But this distinction has generally been regarded as controversial. Indeed, if the semantic account can successfully 21 Strictly speaking, Frege himself did not use the term concepts for ‘senses’ but rather for the referents of predicates. But since contemporary defenders of his approach refer to ‘senses’ as concepts, this is how I shall use the term – on this point, see Margolis & Lawrence 2007: 566. 22 One influential contemporary defender of the Fregean view is explicit on this point: see Peacocke 1992: 99. It is also a central assumption of the argument developed by Sutton 2004, who defends a version of the representationalist view (though to the extent that Sutton is committed to types of mental representations, he also seems to be committed to abstract entities). Cf. Margolis & Lawrence 2007: 564-6. 23 The problems this view faces are in some ways analogous to those faced by the immanent realist, who also claims that universals are ‘unsaturated’ entities without any ontological standing independent of their instantiation in a particular.

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deny that it implies concepts are abstract objects in the traditional sense, then it is left with an additional existential domain of unsaturated entities that is somehow neither abstract nor concrete. So whether concepts are abstract in the traditional sense or occupy this hybrid realm, qualitative ontological economy dictates that we opt for an account of concepts that confines itself to concrete entities alone. These difficulties affect the semantic account of concepts tout court. But perhaps the most salient objection to it as an account of God’s concepts is that it is entirely unmotivated. Trivially, God cannot fail to distinguish which co-referring terms can be substituted for each other in truthpreserving ways: since he directly apprehends every truth that it is possible to apprehend, the statement that is no less trivially true for him than the statement that . Similarly, God has a concept of every entity that could ever be picked out with a linguistic term, since God knows every possible linguistic term. But quite apart from the fact that the semantic account would be entirely unmotivated as an account of divine concepts, there is also the suspicion that concepts qualify as abstract or hybrid entities, so that it would then be necessary for theistic nomic conceptualism to explain why these do not undermine orthodox commitments to God’s aseity and sovereignty – that is, to explain how God could ever have created necessarily existing, non-spatiotemporal, and causally inert entities. 6.2.2. The Representationalist Account In contrast to the first account, the representationalist account adopts a strictly empiricist stance towards concepts that relies in part on its rejection of alternatives that take concepts to be independent of sense experience. The view encompasses a wide spectrum of positions, but these typically anchor concepts in some aspect of perceptual experience.24 Developments in cognitive neuroscience have continued to sustain the popularity of the representationalist view, despite the fact that it has been subjected to telling criticisms in recent years.25 24

For a sophisticated recent defence of the representationalist view, see Prinz 2002. One problem is that Representationalism seems to trigger an infinite – and probably vicious – regress as soon as one asks how we first come to possess concepts in the way the representationalist claims we do. Much of the plausibility of the representationalist account derives from trading on the parallel between the way we acquire concepts and the way we acquire sensory data. But this does not explain why we are disposed to acquire and organize concepts in the first place. 25

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In any event, given its distinctively empiricist stamp, advocates of the representationalist account are unlikely to take seriously a theistic account of concepts. Moreover, the idea at the heart of the representational view – that we acquire concepts from perceptual experience – is not one that translates very easily into an account of divine concepts. Should this concern the theistic conceptualist? It is true that, as an immaterial being, God does not possess the requisite perceptual apparatus to acquire and construct concepts in the way this view supposes. But as an omniscient being, God has no need for concepts of this sort in the first place. God possesses every concept it is possible to possess, and he does so without relying on any intervening mechanism of concept-acquisition. As an omniscient being, God does not need to represent anything to himself: nothing capable of being represented could fail to be already cognitively present to him. As we noted above, since God is the ultimate origin of everything distinct from himself, there is no aspect of empirical reality that does not feature somewhere in God’s mental content prior to being created.26 6.2.3. The Abilities Account If both the first and second accounts we have examined are unmotivated, what of the third account? The motivation for the abilities account of concepts is predominantly a negative one. It stems from Wittgensteinian suspicions that rival approaches illicitly hypostasise concepts as mental particulars. Advocates of the abilities account claim that it avoids this by explaining concepts in terms of the diagnostic capacities of cognitive beings. So to say that I have the concept is simply to say that I am capable in principle of inferring that shoes come in different sizes, that I can distinguish shoes from peaches, that I can identify brogues and sandals as kinds of shoe, and so on.27 As an account of concepts, it suffers 26 One challenge motivating the representationalist view is formulating a suitably physicalist account of our conceptual apparatus that could explain how neurological connections in the brain run orthogonally to rational inferences in the mind. But this explanatory demand does not arise with respect to God’s concepts, since there could be no symmetry between the neurological and the rational in God’s mental life. In the first place, God neither has a physical mind nor one that is grounded in anything physical. But second, even if he did, given divine omniscience, God does not make rational inferences in any event, in which case there would be nothing for divine neurological connections to parallel even if he did have a physical mind. On this point, see Leftow 2012: 302, who cites Aquinas, Summa Theologiae, q.14 a.7 and q.19 a.5. 27 Kenny 2010: 105-6: ‘We may use “concept” as a term for the specific abilities that are particular exercises of the universal capacity that is the mind … Abilities and exercises are individuated by their possessors and their exercises, but they are distinct from both. The

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some of the same difficulties faced by the first two accounts. In particular, if concepts consist in cognitive capacities, then there are uncountably many concepts that elude – either as a matter of fact or in principle – our intellectual grasp. Nevertheless, theistic conceptualists can respond in the same way as that proposed in §6.1.1 above: there is nothing that could in principle satisfy a concept that does not in fact satisfy a divine concept. A more troubling worry for supporters of the abilities account is that it is not clear how to determine precisely which abilities it is necessary and sufficient for a cognitive agent to have in order to qualify as possessing a concept. Well, if God exists, then he has whatever abilities it is necessary and sufficient to have in order to qualify for the possession of any concept it is possible to possess. At one level, this means that the theistic conceptualist is not in an obviously better position to describe which capacities constitute which divine concepts than the proponent of the abilities account is to describe which capacities constitute which human concepts. But this worry need not prevent a version of nomic realism from being formulated in terms of divine concepts. For these could be treated as theoretical placeholders: the divine concept is constituted by whatever epistemic abilities God must exercise – though we know not which – for it to be true to state that he possesses . One immediate attraction of the abilities view is its pragmatist resistance to the speculative character of the two rival accounts. Its scepticism towards the latter’s reification strategies means that it avoids the bloated ontology of the semantic account and the regress worries that attend the representationalist account. This is one of the reasons why some version of the abilities account is now widely accepted by the majority of contemporary theorists.28 But there is also an obvious reason why theistic nomic conceptualists who support the Powers Model might prefer this third account, namely that it would yield a remarkably streamlined and integrative account of lawmaking. This is because possessing a mental ability to ijamounts to much the same thing as being disposed towards ij-ing. If the proximate ground for regularities is the way in which physical objects are disposed towards specific forms of causal interaction, and if the ultimate ground possessor of an ability is what has the ability … Which ability we are talking about, on any occasion, is explained by specifying what would count as an exercise of that ability.’ 28 See, for instance, the observation by Fodor 2000: 27: ‘What’s really happened … just about everywhere … where meaning and content are the names of the game, is a new consensus about what concepts are … [modern theorists] are all likely to agree on this: concepts are capacities; in particular, concepts are epistemic capacities.’

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for these physical dispositions is the matrix of mental dispositions that God exercises in creating physical reality, then the theistic conceptualist version of the Powers Model (discussed in §6.5 below) can claim to be a more theoretically unified proposal than many of its rivals.

6.3. Divine Concepts and Lawmaking Relations The aim of this section is to transpose the Relations Model into a theistic conceptualist framework. Let us henceforth refer to this version of nomic realism as RBUTC. Although what follows represents – so far as I am aware – the first substantive attempt to formulate this kind of account since non-theistic versions of RBUIR and RBUPR were first proposed, Leftow observes in passing that RBUIR’s difficulties provide an obvious motivation for RBUTC. As part of a wider case for his version of theistic conceptualism, he notes that the Instantiation Principle undermines the counterfactual resilience of law-statements. He cites the thought-experiment – devised, as we have already seen, by Tooley – that invites us to imagine a scenario in which life on earth had never evolved. In such a scenario, claims Tooley, it must be possible to say that if life had evolved, organisms with the relevant brain states would have undergone the phenomenal experience of redness.29 That is to say, an account of laws is needed that is realist enough to underwrite counterfactual claims about what psychophysical laws would have brought about had life evolved (assuming, for the sake of argument, that there are such laws). The thought experiment is designed to exert a counterintuitive pull not only on the nomic antirealist, but also on nomic realists committed to the Instantiation Principle. But Leftow astutely notes that theists should discard RBUPR in favour of RBUTC:30 [T]he universal phenomenal redness must exist even if no experiences of red ever do. But God could provide for such laws. Natural necessities could rest entirely on God’s concepts and volitions. Perhaps the reason these brain states must give rise to those experiences, even if there are no brains, is that God would allow no other result.

It seems reasonable to infer from these brief remarks that Leftow has RBUTC in mind.31 There are infinite networks of concepts in God’s mental 29

Tooley 1987: 114; for his earlier version of this difficulty, see Tooley 1977: 668-9. Leftow 2006: 328. 31 I should stress that I do not think Leftow himself would actually endorse any variation of the Relations Model. 30

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life that it is metaphysically possible for God to will to be instantiated. If categoricalism is to be preserved on the theistic account, the nomic work must be done not by the particulars that satisfy divine concepts, but by the relations between them. The question that subsequently presents itself is this: what could these relations be? More precisely: how, if at all, is a distinction to be drawn at the level of God’s concepts between the Relations Model’s lawmakers – relations linking categorical properties and the Powers Model’s lawmakers, namely properties that possess their own intrinsic causal and nomic profile. 6.3.1. Exposition of RBUTC To distinguish itself from dispositionalist alternatives, RBUTC needs to treat divine concepts as substitutes for categorical properties. As we shall see in §6.4 below, DISPTC itself does not need to proceed any further, since on this view any fundamental ‘property’ that features in a law satisfies the divine concept just if it disposes its bearer to behave causally in determinate ways given the appropriate stimulus conditions. But RBUTC does need to do more, since it must explain why regularities obtain in the causal behaviour of the particulars that satisfy divine concepts. What is needed is some suitable substitute in God’s mental make-up for the lawmaking relations posited by RBUIR and RBUPR. Whatever the correct solution to this is on RBUTC, the answer must consist in something more than substituting n-adic connections between divine concepts for corresponding n-adic necessitation relations between properties. As a theistic account, RBUTC must operate within its own strictures. Minimally, it involves a commitment to the standard divine attributes, including omniscience. RBUTC is, in other words, committed to the view that logically prior to creation, God apprehends every connection that could possibly obtain between every concept that it is possible to possess. So God apprehends infinitely many more concepts and connections between concepts than any that could ever be tokened in the nomological structure of the actual world. If RBUTC’s lawmakers are connections that God apprehends between concepts he entertains, some additional ingredient is required. What might that ingredient be? It is, presumably, the volitional content that the relevant connections possess. From among the infinitely many possible networks of connections between concepts that he entertains, God wills a single one of these to be actualised. It is important to underline here that since RBUTC builds in a categoricalist theory of property-identity,

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it is not the case that God directly wills anything with respect to how particulars – or, more precisely, their ‘properties’ – satisfy his concepts. For the crucial lawmaking ingredient on RBUTC – as on every version of the Relations Model – must be whatever grounds the connections between the characteristics of particulars rather than the characteristics themselves. Let us consider how this would work in the case of Coulomb’s Law. God possesses the concept and the concept . He notes the infinitely many lawmaking ways in which these two concepts can be connected, and the infinitely many lawful regularities that would arise if he willed those connections to be satisfied when creating the physical world. As it happens, the connections that God wills to be satisfied at the sub-atomic level between and just are the ones that, through a posteriori inquiry, we express through Coulomb’s Law. Now this analysis is, of course, a defeasible one that could and should be modified as our scientific understanding of the behaviour of electrons and protons develops. As the history of science has demonstrated over and over again, we must accept that Coulomb’s Law may be an inaccurate analysis of the conceptual matrix that grounds regularities in the electrostatic behaviour of sub-atomic particles that God wills to be satisfied. So it may well be the case that Coulomb’s Law is only the best analysis of electrostatic attraction we can currently hope for given the resources available to us. But this no more undermines the basic approach that theistic nomic conceptualism proposes than it would any other metaphysical analysis of lawlike regularities. If scientific knowledge develops in a way that contradicts what is currently assumed to be a law, or in a way that relativises the law to a specific field, then the metaphysical analysis would no longer be applied to what was once taken to be a lawful regularity. But it would not in any way destabilise the analysis itself. This last point raises an important methodological principle that should defuse the familiar objection that theistic solutions are only advanced to plug gaps in existing scientific theorising, solutions that become redundant as soon as this theorising develops. It should be clear, though, that in every salient respect, theistic accounts of laws – including RBUTC and DISPTC – can accommodate developments in scientific theory in just the same way as non-theistic accounts. Metaphysical analysis of regularities (nomic realist or otherwise) begins only at the point where scientific inquiry ends. This is not to deny, of course, that one’s metaphysical stance will affect how one construes the results of that inquiry in

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fundamental ways. But it is relatively rare that empirical findings in themselves have an impact on a particular metaphysical stance.32 The crucial question is, rather, the degree to which a theistic theory such as RBUTC measures up against its rivals as a metaphysical analysis of the data on which all sides agree. And here, I now wish to suggest, RBUTC overcomes at least three of the objections that undercut its non-theistic alternatives. Let us consider each of these in turn. 6.3.2. Blunting Van Fraassen’s Fork We have already seen that both RBUIR and RBUPR face a dilemma triggered by a conjunction of the Inference Problem and the Identification Problem, a dilemma we labelled Van Fraassen’s Fork in §2.3.2. But Van Fraassen’s Fork is not a dilemma that confronts RBUTC. If this is correct, then if one is not persuaded by any version of the Powers Model, and if one takes the majority view that Van Fraassen’s Fork does undermine RBUIR and RBUPR, there would be strong motivation for preferring RBUTC as the most attractive version of nomic realism. To see why this is the case, let us briefly rehearse the dilemma that Van Fraassen’s Fork presents for the Relations Model. The objection claims that RBUIR and RBUPR cannot explain how it is possible (i) to identify patterns in the behaviour of particulars as lawful connections between universals (the Identification Problem) and (ii) to infer those behavioural patterns from the posited connections (the Inference Problem). Thus if one insists the Identification Problem can be solved (as Armstrong does) on the basis that it is possible to perceive an event directly as lawful in the way Anscombe claimed that it is possible – pace the Humean tradition – to perceive instances of causation.33 If so, the Inference Problem arises: the 32 There are exceptions, of course, to this general principle. Thus I take it that the B-Theory of time would not be as widely accepted by philosophers as it is today had it not been for Einstein’s gravitational field equations (whatever the merits of the claim that these equations do underwrite eternalism). Similarly, it is likely that the renewal of interest in the viability of the NDOƗPcosmological argument is at least partly a consequence of the Hawking-Penrose singularity theorems. But even drawing these two metaphysical conclusions from scientific theory is hardly uncontroversial. 33 Armstrong & Heathcote 1991. Armstrong 1993: 422 lays out his own solution to the Identification Problem as follows: ‘It is at this point that, I claim, the Identification problem [sic] has been solved. The required relation is the causal relation, the very same relation that is actually experienced in the experience of singular causal relations, now hypothesized to relate types not tokens. There is of course no question of proof that this hypothesis is true. It is rather a postulation that recommends itself because of its explanatory power.’ Cf. Anscombe 1971 for the case in support of the perceivability of (singular) causation.

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Relations Model owes an explanation of why regularities that are identified as laws are entailed by the lawmaking relation that it posits as their metaphysical ground. Now I do not think RBUTC is in a significantly better position than its rivals to solve the Identification Problem. It is true, perhaps, that RBUTC’s independent commitment to the existence of a maximally perfect creator of physical reality may confer a slight explanatory advantage (provided, of course, it can show that the commitment was well-grounded). For this might provide some reason to think that, given the existence of such a being, it was a priori more probable that cognitive beings would emerge capable of identifying regularities as lawful. But this sort of response would do little to satisfy the inductive sceptic, since the inference from lawlike to lawful regularities can always be blocked given sufficiently strict empiricist constraints. Still, the hard objection that Van Fraassen’s Fork raises is not that the Relations Model relies on an illicit inference from regularities to laws. It is rather that it cannot justify that inference (i.e. solve the Identification Problem) at the same time as making the converse inference from laws to regularities (i.e. solve the Inference Problem). Once one sees that the objection arises from the structural complicity of the two problems, I suggest that the superior theoretical strength of RBUTC emerges more fully into view. For on this account, of course, the problem of rendering the entailment relation between connected universals and empirical regularities intelligible never arises in the first place. The reason for this is simple: RBUTC eliminates universals altogether from the ontology underpinning RBUIR and RBUPR.34 As long as the theist can infer the existence of laws from regularities, he is free to infer that regularities reflect a pattern of connections between concepts in God’s mind rather than between universals. What closes the gap between divine concepts and the empirical regularities that satisfy them is that each shares the same ultimate metaphysical origin. God’s concept is a token and not a type. Both and the salt in my kitchen are each 34 It may be objected at this point that the elimination of universals means that it is not credible to classify RBUTC as a species of the Relations Model. By way of brief response, the validity of this objection stands or falls on the extent to which the substitution of divine concepts for universals succeeds. My claim – following Morris & Menzel 1986 and Leftow 2006 – is that the former can do all the explanatory work of the latter, including the role assigned to universals in RBU. Proponents of the Relations Model apply the label laws to relations-between-universals even though they do not believe in laws as ontologically irreducible entities. So I think it is legitimate to describe RBUTC as a version of the Relations Model even if it rejects universals.

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a terminus of causal paths that share a common origin: God. RBUTC explains the law that salt dissolves in water by first positing a specific connection between God’s pre-creative concept and his precreative concept . The nature of this connection is such that, when conjoined to the appropriate divine volition, it is physically necessary that every physical token dissolves in every physical token of . 6.3.3. Solving the Second-Order Humeanism Objection The earlier analyses of RBUIR and RBUPR demonstrated the vulnerability of both accounts to the Second-Order Humeanism Objection. That objection claimed that the Relations Model is no less descriptivist than the nomic antirealist accounts it rejects. Let us recall for a moment how that objection arose. One overarching motivation for the Relations Model is nomic antirealism’s refusal to accept that putatively uniform regularities in the physical world demand a substantive metaphysical explanation. Nomic antirealism holds that nothing explains why some regularities are more extensive than others; the most extensive regularities may be plausible candidates for inclusion as axioms in an optimally systematised description of the world, as we saw in §1.3. But this inclusion never amounts to an explanation of why they are extensive. Indeed it could not, since the inclusion is logically parasitic on the logically prior fact that they are extensive. On nomic antirealism, predictable regularities in nature do not confer predictive power on theories that include them because they are included as axioms in an optimally systematized description; they are included as axioms because they confer predictive power on theories that include them. Nomic realists seek to explain why this is so. But the Second-Order Humeanism Objection claims that the Relations Model shrinks from the explanatory task no less than deflationary accounts do. The only difference is that it does so at the level of universals rather than particulars. That is to say, although the Relations Model offers an explanation of lawlike regularities at the first-order level by invoking lawmaking configurations between second-order universals, it does so at the cost of shifting the explanatory bump to the second-order level. The Relations Model must either turn its explanatory spade at the second-order level – and provide a plausible reason for why it does so – or else set off on a infinite and vicious regress of ever-higher necessitation relations, each of which explains how it entails the regularity on the level beneath it by invoking the modal strength of the relation on the level above it.

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Moreover, if the conclusion is that the Relations Model tacitly assumes the neo-Humean tradition’s ‘vast mosaic’ at the level of universals, it is an extremely costly one. After all, deflationist accounts of laws grounded in a first-order mosaic can at least be credited for their qualitative and quantitative ontological economy. But the Relations Model confers an apparently illusory explanatory gain in return for introducing: (i) a distinct kind of metaphysical entity; and (ii) given the explanatory regress that ensues if the Relations Model tries to escape the Second-Order Humeanism Objection, infinite numbers of them. Does the situation improve for the Relations Model once it is transposed into a theistic conceptualist framework? I suggest that it does. The legitimacy of infinite regresses is a familiar feature in the dialectical landscape of natural theology. So far as I am aware, however, the regress that purportedly threatens the Relations Model as a result of the SecondOrder Humeanism Objection is not one that theists have sought to block by an appeal to God. What triggers the regress in the first place is, as we have seen, that if the Relations Model is to avoid invoking ever-higher necessitation relations, it is forced to stipulate lawmaking configurations among second-order universals that entail regularities among particulars. To prevent the regress from being triggered, RBUTC would need to explain why lawmaking concepts are configured as they are in the divine mind or for why no such account can be given. Can RBUTC explain, for instance, why the divine concepts , , and are connected in proportionate and lawmaking ways, in a way that RBUIR and RBUPR cannot? It seems to me that if there were facts about the structure of God’s mental life, then these would be more plausible candidates for halting an explanatory regress than brute second-order universals. First, RBUTC would be free to deploy reasoning familiar from teleological arguments to explain why God decreed that the relations between , , and should be uniformly tokened in the physical world, namely to provide conditions suitable for the evolutionary processes that would ultimately give rise to beings capable of relating freely to him. Second, RBUTC could claim there is no deep explanation of why God willed that some of his conceptual connections should be tokened by created objects in the way described in Newton’s Second Law; other configurations might have served his purposes just as well. And, as we have seen in the course of revisiting Van Fraassen’s Fork, RBUTC’s explanation of why its lawmakers entail regularities is just the fact that God decrees that the relevant conceptual connections be tokened at the level

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of particulars. If these are the connections he has willed to be tokened, then these regularities must obtain, since it is metaphysically impossible for the will of an omnipotent being to be thwarted. Finally, if these responses do not satisfactorily address the SecondOrder Humeanism Objection, RBUTC is still in a much better position to handle the regress than its rivals. Perhaps RBUIR or RBUPR could reject the idea that any further explanation is needed of why n-order necessitation relations entail n–1-order regularities beyond noting that n+1-order necessitation relations entail that they do. Now I doubt that this move would satisfy those who would press the Second-Order Humeanism Objection. But if it does, RBUTC can at least claim, in a way that avoids the ad hoc posit of a secular lawmaking relation, why there need not be an upper limit to its hierarchy of lawmakers. If God is omniscient, then it is trivially true that he possesses infinitely many concepts. RBUIR and RBUPR, by contrast, are forced to posit infinite levels of universals as a tailored response to the Second-Order Humeanism Objection; if not, they must simply stipulate that lawmaking stops at the level of second-order relations between first-order universals. So RBUTC is entitled to claim that its solution is less ad hoc than these alternatives. And although this is a more global point in favour of theistic conceptualism, it is worth noting at this point that RBUTC can also claim a greater degree of qualitative ontological economy on the basis that it does not include anything other than particulars in its account.35 6.3.4. Solving the Ex Nihilo Objection Another reason for preferring RBUTC to its non-theistic alternatives is the strength of its response to the Ex Nihilo Objection raised against RBUIR in §2.3.4. The complaint was that RBUIR could not explain how conditions obtain under which lawmaking relations between universals are first instantiated. RBUIR could not appeal to other laws to explain the origination of a new law, since these laws would need to specify which universals were to feature in the content of the new law. But given the Instantiation Principle, these universals do not exist independently of their instantiation, and so they could not be specified in laws governing the creation of a new law. RBUIR was, then, committed to the idea that 35 In terms of quantitative ontological economy, RBUTC would seem to be on a par with RBUIR and RBUPR whether or not a regress is triggered. But there may be reasons for thinking that quantitative economy should not be a factor in theory-selection, or at least that it should count for less than other metatheoretical virtues.

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laws originate in the absence of any prior conditions and without any underlying ontology: laws emerge, as it were, out of nothing. Let us assume that theistic accounts can offer some intelligible account of how God could have created a universe ex nihilo with determinate lawmaking relations between categorical properties. RBUTC would then gain an obvious advantage over RBUIR in that it is already committed to the existence of an entity with the requisite power and motivation to bring about lawmaking relations in the absence of the relevant background conditions, conditions that RBUIR cannot invoke without contradicting itself.

6.3.5. The Occasionalist Threat The chief difficulty for RBUTC is the internal tensions it generates for the theistic position. In particular, if theists wish to preserve a credally orthodox account of God’s causal role in the physical world, I suggest that RBUTC should, in the end, be avoided. The problem emerges most fully into view when we recall that it is underpinned by categoricalism. RBUTC denies that created objects possess any intrinsic causal or nomic properties. As a species of the Relations Model, it holds that the source of all causal behaviour is entirely extrinsic to the objects contained in it. What, then, does RBUTC identify as the extrinsic connections that sustain causal behaviour? As a theistic account, I suggest that RBUTC cannot plausibly identify these connections with anything other than God’s volitional decrees. But if this is correct, RBUTC opens up the threat of occasionalism, the view that God is the cause of every possible effect. Is there any way that RBUTC could block the occasionalist threat? The challenge for RBUTC is to interpose between God and physical reality metaphysical entities that would be suited to the lawmaking role that RBUIR and RBUPR assign to necessitation relations. One way of achieving this might be to adopt an antireductionist view of laws. On this view, laws are ontological primitives that exist independently of anything else and that cannot be reduced to or explained in terms of anything else, so that an empty duplicate of the actual world would be identical to it in every nomic respect.36 The trouble with this strategy, however, is that it 36 One recent example of an antireductionist account is provided Maudlin 2007: 18: ‘My analysis of laws is no analysis at all. Rather I suggest we accept laws as fundamental entities in our ontology … the notion of a law cannot be reduced to other more primitive notions.’ See also the position set out in Carroll 1987, Carroll 1994, and Carroll 2008. This kind of view is distinctive for its reliance on the distinction between realism and reductionism. In effect, it claims that one can combine realism about laws with reductionism

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threatens to undermine traditional theistic commitments to divine sovereignty and divine aseity. As the creative source of every existent distinct from himself, God is the only ontological primitive. So a theistic account consistent with credal orthodoxy should resist the view that laws are ontological primitives. Alternatively, RBUTC might invoke exactly the same necessitation relations as RBUIR and RBUPR. On this view, the extrinsic connections would be identified – with Armstrong and Tooley – as ideological primitives that just do constrain their relata to interact causally in uniform ways. The idea here would be that by integrating either one of these approaches, the theist can adopt the Relations Model in a way that mediates God’s direct involvement in laws to the point at which the threat of occasionalism is averted. The problem with this approach is that it eliminates at a single stroke many of the explanatory advantages that the theist’s account seemed to bring with it. After all, the theist who grants the existence of ideologically primitive necessitation relations obviates any further explanatory appeal to God; and if God does not need to feature in the metaphysical analysis of laws, then it is difficult to see why he should not be ruled out altogether. 6.3.6. Evaluation of RBUTC We have now considered one attempt to transpose nomic realism into a theistic conceptualist framework. We concluded that RBUTC makes at least two significant improvements to non-theistic versions of the Relations Model. First, it gives supporters of that account a way of blunting Van Fraassen’s Fork, a problem that had undermined both RBUIR and RBUPR. Second, it offers a promising solution to the Ex Nihilo Objection raised against RBUIR without incurring the difficulties that undercut RBUPR’s solution involving how causal traffic is possible between the abstract realm of lawmaking relations and the concrete realm of lawful regularities. Nevertheless, RBUTC also implies a conflict with credally orthodox conceptions of how causal labour is divided between divine agency and natural causes. In particular, we concluded that the advocate of RBUTC would find it hard to resist identifying the lawmaking relation directly about laws: thus the Relations Model is no less reductionist for being a species of nomic realism, since it explains the existence of laws by appealing to something other than laws (i.e. universals).

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with divine volitions, which would, in effect, turn RBUTC into a version of occasionalism. This was because the alternatives to doing so involved either following the antireductionist approach of positing laws as ideological primitives, or following RBUIR and RBUPR in treating laws as quasi-causal relations between properties. But it was concluded that these strategies left the theistic dimension of RBUTC explanatorily redundant, for if one is willing to meet the explanatory demands of the nomic realist by positing one category of primitive entities, one would not want to compound the theoretical cost of one’s model by including God as well. Despite its initial promise relative to the alternatives, then, RBUTC ultimately falls short as a successful version of nomic realism. Let us now turn, though, to examine whether a theistic conceptualist account of the Powers Model fares any better.

6.4. Divine Concepts and Lawmaking Powers It is worth noting, by way of preliminary remark, that the theistic explanation of lawlike phenomena along the lines considered in this section are hardly without precedent. Indeed the dominant scholastic account of regularities in nature was based on a combination of Aristotelian naturalism – in particular an ontology of causal powers – and perfect-being theology.37 It is ironic, then, that nomic realists who reject the Relations Model in favour of the Powers Model to escape the theological associations of the former seem unaware that the latter was the mainstream theological approach until the seventeenth century. The principal aim of this section, however, is to examine whether this historical model can be formulated in a way that addresses the objections against DISPIR and DISPPR. It will emerge that a theistic conceptualist version of the Powers Model – hereafter DISPTC – suggests some very promising ways in which each of these objections can be met. 6.4.1. Exposition of DISPTC Once divine concepts are substituted for universals, the basic explanatory structure of DISPTC differs very little from the explanations advanced by its non-theistic alternatives. Regularities have an objective basis in the 37 Adams 2013 provides a helpful overview of the role of powers in the philosophies of nature advanced by Aquinas, Scotus, and Ockham.

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causal powers that objects possess; and although some supporters of the Powers Model have objected to characterising these regularities as laws,38 the account ensures that law-statements have referents that are modally substantive and therefore meet this study’s criteria for lawmakers. The central difference on this account is that the proximate lawmakers are particulars that satisfy God’s dispositional concepts. That is to say, they are not entailed or causally brought about by extrinsic connections between properties that, on RBUTC, would be grounded in connections between divine concepts. The crucial question for DISPTC is whether or not its substitution of divine concepts for dispositional universals (immanent or platonic) can improve the Powers Model in a way that insulates it against the objections raised against it in §3.2-§3.4 and §4.5. Let us see if it achieves this goal. 6.4.2. Solving Independence The first kind of objection to DISPIR claimed that it could not give a perspicuous account of the four identity-conditions for dispositions taken separately. The second kind of objection – the Fresco Problems – claimed that even if it could do so, it would not be able to explain how to integrate the identity-conditions collectively into its realist analysis of laws. These objections combined to impose on DISPIR a dialectical pressure to platonise. But it turned out that even though DISPPR could handle these difficulties better than DISPIR, it did so only at considerable theoretical cost, leaving almost as much unexplained as DISPIR itself. The test, then, for DISPTC is whether it can overcome the objections to DISPIR in a way that avoids the shortcomings of DISPPR. Let us briefly remind ourselves of the four criteria that we would typically expect a power to satisfy. Independence expressed the intuition that a power to do something was in good ontological standing irrespective of whether that power was ever exercised: a match has the power to light a piece of paper even if it never lights it. Intrinsicness recorded the intuition that at least with respect to fundamental properties, a power to do something is not affected by anything distinct from that power: a match has the power to light a piece of paper even if it is placed in a paperless world. Directedness held that every power is a power to bring about a result that is determinate and ontologically distinct from it: a match has the power to light a piece of paper (together with a delimitable 38

Mumford 2004: ch. 10.

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number of other things) because that power involves lighting the piece of paper – the match’s power is in some sense directed towards this result. This analysis seemed intuitively correct, since a power without any specified target does not seem to be any power at all. And once Directedness was granted, Reciprocity quickly followed: a match has the power to light a piece of paper because the piece of paper has the correlate liability to be lit, a liability that is itself directed towards being lit as a result of the match’s correlate power being exercised. Now we saw in §3.2-§3.4 that problems arose not as a result of the identity-conditions per se, but rather as a result of DISPIR’s attempt to combine these with a commitment to the Instantiation Principle. For if it is assumed that dispositional universals (or, indeed, dispositional tropes) exist only when they are spatiotemporally instantiated, it becomes very difficult to make sense of each of the identity-conditions. It then emerged in §4.4 that although few philosophers have endorsed (or even considered) this solution, abandoning the Instantiation Principle would make each of the identity-conditions of lawmaking dispositions a good deal more coherent. But DISPPR also generates some especially vexing causal, modal, and metatheoretical difficulties. DISPTC, by contrast, offers supporters of the Powers Model a very similar way out, but – crucially – in a way that largely avoids these difficulties. For it can hold that a lawmaking disposition satisfies each of its identity-conditions just to the extent that it satisfies God’s concept of what it is to be that lawmaking disposition. Thus God’s concept of the disposition exists regardless of whether or not it is ever manifested. That is to say, on DISPTC lawmaking dispositions also satisfy Independence. On DISPTC, a fragile glass that never breaks is still disposed to break under the relevant circumstances on the basis that the glass is such that it satisfies God’s concept of fragility. 6.4.3. Solving Intrinsicness Can DISPTC offer a solution to the problem that Intrinsicness presents? There are good reasons to suppose that it can. To return to our example, on DISPTC a fragile glass would still be fragile even if one altered the external conditions by placing it in a possible world in which it could not break. The metaphysical basis for the fragility of the glass is that it satisfies God’s concept regardless of any extrinsic modifications that could be introduced. Now at this point one might raise an obvious objection to this suggestion. If it is claimed that dispositions belong intrinsically to their bearers,

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then how could their identity be bound up with how things are with God? Given Intrinsicness, a glass’s disposition to break under certain circumstances is surely to do with how things are with the glass. It seems odd to claim that a disposition is intrinsic when its identity depends on a connection to something that lies outside it. And yet this is precisely what DISPTC seems to claim by proposing that lawmaking dispositions satisfy Intrinsicness in virtue of its connection to a concept in God’s mind.39 Leftow lays out two ways in which DISPTC can meet this objection.40 A crude, but intuitively plausible, account of an intrinsic power is that it is a power whose identity is determined by whatever is spatially internal to its bearer: intrinsic powers, then, are interior powers. On this view, Intrinsicness holds that a power belongs to its possessor regardless of how things stand outside its bearer’s spatial limits. So the objection to the claim that divine concepts satisfy Intrinsicness on DISPTC assumes that they involve something exterior to the bearer of a power. Divine concepts exist in the mind of God, and therefore outside the spatial limits of the power’s bearer: how, then, could they determine the identity of a (non-divine) intrinsic power where this is understood as a power spatially interior to its bearer? What are we to make of this assumption? To examine the objection more closely we need to assess how best to construe divine omnipresence. Scripture41 and perfect-being considerations42 agree that omnipresence is a divine attribute. It can be taken to imply that God exists in every spatial location or in no spatial location.43 If he exists in every spatial location, how does this affect Intrinsicness? On this view God exists as much within the match as he does outside it, and so too do his concepts. As Leftow notes, this need not imply that God is a part or a property of the match. It is simply that God’s presence within the match is a fact that is intrinsic to it.44 If, on the other hand, God has no spatial location, then nor do this concepts; so the problem of whether the concept that the match’s 39

Foster 2004: 163-4. Leftow 2006: 340-3. 41 E.g. Psalm 139:7-10. 42 e.g. Anselm, Monologion 20-23. 43 Anselm wrestles with precisely this tension, and does not ultimately offer us a satisfactory explanation. Thus he claims in Monologion 20 that God exists ‘ubique et semper, id est in omni loco vel tempore,’ but in Monologion 21 that ‘impossibile est ut [deus] sit ubique et semper.’ For a detailed discussion of these texts, see Wierenga 1988. 44 Leftow 2006: 341: ‘This is not surprising. Relations to things within an item’s skin count as intrinsic to the item. We ordinarily focus on parts and perhaps properties as intrinsic … If there is a God who is everywhere, though, these are not the only items.’ 40

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power satisfies is inside or outside the match disappears.45 Only if there is a sound reason for supposing that God’s concept of the power lies outside the match do we have a sound reason for supposing that the power is not intrinsic. But if God is omnipresent in the sense that he exists in no spatial location, there is no such reason. A more sophisticated account holds that a property is intrinsic if and only if it is independent of anything accompanying it.46 On this view, the match’s power to light paper is intrinsic if and only if the match has the power whether or not there exists anything distinct from it. Here there seems no way of construing divine concepts as intrinsic: God is distinct from the match, and the match has the power to light paper if it exists in a possible world in which God does not accompany it (i.e. exist). But applying the definition to our example shows immediately what is wrong with it. For there is no possible world in which God does not exist. And, indeed, Langton and Lewis are careful to specify that the notion of accompaniment only relates to contingent entities that are distinct from the property under scrutiny. So provided the theist accepts that God’s existence is metaphysically necessary, the analysis goes through. A lawmaking disposition can be determined by God’s concept of it in a way that is consistent with Intrinsicness however divine omnipresence is construed, provided only that God is held to be metaphysically necessary. 6.4.4. Solving Directedness and Reciprocity Third, DISPTC makes sense of how a power could be directed to nonexistent circumstances (Directedness). The directed character of a power is settled by the fact that God entertains the concept of that power in relation to his concept of any other power that its manifestation involves. God thinks of his dispositional concept as directed in the appropriate way to his correlate dispositional concept . So any particular that satisfies the first divine concept enjoys a legitimate metaphysical connection to anything satisfying the second divine concept. is directed towards the manifestation concept even if I never happen to pour the salt on my kitchen-table into the glass of water on my kitchen-table. Furthermore, 45 The same reasoning applies a fortiori if we follow Anselm’s suggestion in Monologion 23 that omnipresence should be understood as the claim that God is in all existing things rather than in all places. 46 Langton & Lewis 1998: §4.

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since is also ‘reciprocally’ directed towards the manifestation concept , DISPTC shows that Reciprocity can be satisfied too. Where DISPTC differs from DISPPR is that it is not left with the awkward task of explaining how one section of an infinitely large network of powers in an abstract domain is so closely interwoven – or, indeed, interwoven at all – with the network of powers in the physical world. DISPTC’s greatest explanatory advantage over DISPPR is that it does not invoke an abstract domain if the causal criterion of abstractness is in play: God’s concepts consist in bundles of causally potent epistemic capacities. DISPTC’s explanatory advantage is that it can account for the isomorphism between God’s conceptual network of powers and the network of powers that actually obtain in the world. Logically prior to creation, God entertains every configuration of powers there could possibly be and wills one of these to obtain with respect to the actual world by willing whatever causal sequences are needed to bring the selected configuration about. As soon as one grants that the powers of an object are what they are in virtue of the fact that God grasps them to be so, each of the individual difficulties attending the four identity-conditions begins to dissipate. Still, a realist theory of lawmaking along the lines DISPTC proposes cannot succeed until it can offer a solution to the difficulty of accommodating these identity-conditions in collective terms. Let us turn now to consider whether DISPTC offers an equally promising way to resolve the Fresco Problems. 6.4.5. Assisi Restored The central challenge that the Fresco Problems presented was how best to integrate all of its relevant identity-conditions into a coherent analysis of a disposition’s nature. For lawmaking dispositions plausibly possess both centripetal features (Independence and Intrinsicness) and centrifugal features (Directedness and Reciprocity). The difficulty was inescapable for DISPIR in light of its prior commitment to the Instantiation Principle (and, a fortiori, for any supporters of the Powers Model more weakly committed to the objective existence of attributes). But we also saw in §4.5 that although DISPPR offers a partial solution to the Fresco Problems by positing an abstract network of lawmaking dispositions, it failed to provide reasons – or, at least, reasons whose strength was commensurate with DISPPR’s substantial metatheoretical costs – for supposing that this network could ground lawful interactions among concrete particulars.

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It is here that the superior theoretical strength of DISPTC emerges sharply into view. For as we saw in the previous section, DISPTC grounds the identity-conditions of a lawmaking disposition in the conceptual matrix that God willed to be satisfied with respect to the physical world. DISPTC therefore solves the Fresco Problems in much the same way as DISPPR does, since the concepts he possesses clearly do not depend ontologically on whether they happen to be satisfied in the physical world. To see how DISPTC addresses the Fresco Problems, let us return once again to the power of electrons to attract protons. As we have seen, on the Powers Model, the truthmaker for a law-statement such as is the fact that every electron is intrinsically disposed to attract protons, given certain stimulus conditions. In contrast to the Relations Model, no other metaphysical ingredient is required. Transposed into the framework that DISPTC proposes, the lawmaking disposition ceases to be a dispositional universal, but rather a first-order concept that God possesses, which when satisfied – i.e. when a particular comes to possess it – disposes its bearer towards a specific causal outcome. Given the conclusion reached in §6.2.3 that concepts are best construed as abilities, this analysis amounts to the claim that God possesses every cognitive ability necessary for exhaustively determining what it would be for something to be negatively charged. So the reason that electrons are negatively charged is just that God ensures that his concept is included in the volitional content informing every causal sequence he initiates that issues in the existence of electrons. Since it is part of the identity of a lawmaking disposition that, once it is manifested, its bearer exhibits a particular kind of nomic behaviour, that behaviour is what it is in virtue of the fact that it satisfies God’s concept of behaving that way. The divine concept of the disposition will always be connected in the appropriate way to the divine concept of its manifestation. But notice that in explanatory terms, DISPTC provides a much more powerful solution to the Fresco Problems than the one DISPPR proposes. This is because, once again, theistic nomic conceptualism eliminates a fundamental ontological barrier between an abstract realm of lawmakers and a concrete realm of regularities. On DISPTC, then, a disposition to attract protons is part of the identity of an electron even if that disposition never in fact manifests itself, because the manifestation universal is neither ruled out of existence (as DISPIR implied) nor located in a causally inert platonic realm (as DISPPR proposed); rather, lawmaking dispositions satisfy Directedness and Reciprocity in virtue of the fact that God conceives them as involving other concepts he possesses that ground their

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manifestations (e.g. the divine concept is conceptually tied to the divine concept ; to ; to ; and so on). Laws turn out to be nothing more than the ways in which God conceives objects to be disposed towards causal interactions for any combination of stimulus conditions that obtains. * * * As a second attempt at a theistic conceptualist version of nomic realism, DISPTC has proved a good deal more promising than RBUTC. For although both DISPTC and RBUTC each successfully counter the objections levelled against their respective non-theistic counterparts, DISPTC steers more clearly away from the threat of occasionalism, principally because it follows Aristotelian naturalism in locating the lawmaking modality in natural objects themselves rather than in the connections that confer a nomic profile on them from without. To put it another way, all God had to do to create the laws of nature was to create objects disposed towards a determinate range of causal interactions given certain stimulus conditions. What it means for God to create such an object is simply that he brings into being a concrete particular that satisfies a particular configuration of his dispositional concepts. Scientists then formulate a set of defeasible law-statements describing regularities in the causal interactions between these objects. But it is the ways in which concrete particulars satisfy divine concepts that fixes the way laws are, not the extrinsic relations that connect them contingently together, as RBUTC proposed. DISPTC preserves the Powers Model’s characteristic insight that laws of nature are laws of natures. But our inquiry has now concluded that the nature of a thing contributes to the regularities that law-statements describe in virtue of the fact that it satisfies the complex of concepts in God’s mind in virtue of the myriad causal processes that brought it into existence. God, then, is the ultimate source of what laws there are, but not in anything like the top-down sense so forcefully rejected by neoHumeans and neo-Aristotelians alike. God creates objects and endows them with dispositions; and these dispositions sustain laws in exactly the way that the Powers Model proposes.47 To repeat: it is the task of the natural sciences to establish, through a posteriori inquiry, what these regularities are. Nothing in the proposed 47 This, at least, would be the case given a bare-substratum theory of objects. On a bundle-theory of objects, God would create objects by creating all the properties that constitute them.

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case for a theistic analysis of laws is formally inconsistent with a fundamental commitment to methodological naturalism. But we have, at long last, found a way to overcome the contradictions arising from arguments in support of nomic realism that sought consistency with metaphysical naturalism through a stringent application of the Instantiation Principle. Moreover, we have done so in a way that avoids the difficulties undercutting platonic solutions without any of the metatheoretical excesses to which these solutions committed us. In the final analysis, then, all that DISPTC is required to posit at the fundamental metaphysical level is a single concrete particular possessed of every mental power required to form whatever concepts stand as the referents of law-statements, together with the causal powers to ensure that these concepts are satisfied in the way that these law-statements describe.

CONCLUSION

We have now reached the end of a difficult quest for an analysis of lawlike regularities in the physical world that is at once internally coherent, explanatorily powerful, and metatheoretically attractive. The arguments examined in the course of our search have cumulatively pressed us towards elaborating a realist theory of natural laws in terms of the mental life and causal powers of God. To those convinced that the centrality of lawhood to scientific inquiry had long ago banished supernaturalistic explanations of the natural world, this may seem a disquieting development. Since metaphysical naturalism continues to be a dominant orthodoxy in contemporary philosophy, such a reaction would hardly be unsurprising. Nevertheless, it was precisely to anticipate this disquiet that we began the inquiry by paying close attention to the best naturalistic analyses of lawhood before turning to platonism and theism as alternatives. The central philosophical puzzle that lawlike phenomena present is the Modal Hybridity Problem – that is, the problem of reconciling the intuition that the laws of nature might have been otherwise (the Contingency Intuition) with the intuition that the regularities that scientific statements of law describe are not merely accidental (the Governing Intuition). How one responds to this problem largely determines whether one will endorse a realist theory of lawhood or a deflationary one. As I argued in Chapter 1, accepting the dilemma’s first horn erases the explanatory strength of lawhood entirely. On the deflationary view, the most promising way of securing the distinction between lawful and accidental regularities is to suggest that the former have a theoretical role in an optimally systematized description of the world and that the latter do not. Conversely, we saw in Chapter 2 and Chapter 3 that those who take the dilemma’s second horn bear the burden of identifying some ingredient in the natural world – or, as we explored in Chapter 4, a platonic heaven – that grounds lawful regularities in a sufficiently objective way while leaving room for the Contingency Intuition. We saw that by invoking God’s libertarian agency – the theologically uncontroversial claim that God could have acted otherwise than he has – theists can dissolve this central dilemma at a single stroke. They can accommodate the Contingency Intuition with the straightforward observation that God was free to originate different laws from the ones

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he actually brought about. They can preserve the Governing Intuition by arguing that the difference between law-governed patterns of behaviour can and merely accidental regularities consists in the fact that divine intent and agency underwrites the objective modal strength of the former. In other words, theists have the resources to avoid the Humean insistence that there is no halfway point between brute contingency and logical necessity. Accounting for the weak modality of natural necessity is an advantage that accrues to every theistic account, including those considered in Chapter 5. But the theistic conceptualist approach advanced in Chapter 6 provided metaphysical resources for resolving a series of theoretical difficulties that rival theistic options could not. In the first place, by substituting lawmaking universals – whether construed as extrinsic relations or intrinsic dispositions – for items in God’s mental life, the proposal enjoyed clear advantages over naturalistic renditions of the Relations Model and the Powers Model. In particular, it accounted for several classes of laws that were much less easily assimilated by rival versions and it explained how the emergence of the first lawmakers could have been a law-governed process. Moreover, when weighed against its leading non-naturalistic rival, the proposed solution avoided ungainly platonic solutions that struggled to elucidate how abstract lawmakers could govern the natural world from a platonic heaven. In sum, adopting the theistic conceptualist framework means that realists pay a cheaper metatheoretical price for a more cogent realist account of lawhood, an account that supports the central intuitions about laws of nature with which our inquiry began: their weak modal force, inductive strength, explanatory power, and counterfactual resilience. Although that basic framework left open the question of whether to identify relations or powers as lawmakers, it became clear that to adopt the categoricalist ontology that the Relations Model presupposes would pressure theistic supporters of this approach to analyze God’s causal interaction with physical world in occasionalist terms. Since eliminating creaturely causation in this way would fundamentally undermine a wide range of doctrinal commitments, I suggested that this would be an imprudent option for orthodox theists to pursue. When applied to the Powers Model, however, it emerged that theistic conceptualism can be reconciled more easily to theories of divine causation that make room for the autonomy of creaturely causes. On this account, nature is not mechanical but organic: it teems from below with causal energies of its own. Natural objects are intrinsically oriented to those forms of behaviour that law-statements

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aim to codify and not – as the Relations Model implies – constituents of a passive ontological landscape animated by extrinsic connections imposed from above. So in the course of searching for a philosophically viable realist stance towards lawlike regularities we have uncovered a nomological argument for classical theism, an argument that has received scant attention in the annals of natural theology. Where might we locate it on the traditional landscape of theistic arguments? It is not a law-specific version of the cosmological argument, though some theists may wish to explore the claim that if laws are grounded in a network of powers that is (so to speak) dispositional all the way down, then positing a fully actual divine being offers the best way to halt an otherwise infinite and vicious explanatory regress. But it is it not – or not quite – a law-specific version of the teleological argument either. Formulating the Powers Model did require us to construe the teleological characteristics of lawmaking dispositions as objective; to that extent, it would be accurate to classify the argument that theistic conceptualism is the best explanation for these features as a species of teleological argument. Nonetheless, we should recall ourselves to the fact the proposed solution to the Powers Model begins from premises that differ considerably from those that typically provide the basis for teleological arguments. We did not, for example, need to infer our conclusions from contested claims regarding the purportedly irreducible complexity of biological phenomena or the life-permitting character of fundamental cosmological constants. In recent years, a consensus has emerged among metaphysicians in favour of the Powers Model that the goal-directed features of dispositional properties (‘Directedness’ and ‘Reciprocity’) are real and irreducible. As we have seen, theories that attempt to explain these features by grounding them in teleologically blank categorical properties simply restate the problem, since they cannot explain what governs the interactions between the two kinds of property without invoking the very lawlike regularities they were supposed to explain. For all that, to classify this book’s conclusions as a teleological argument would be to forget the chief impetus for its investigation, which was to find a theory of lawhood that could accommodate our most fundamental pre-philosophical intuitions about the patterned regularities we observe in the natural world. It would also fail to do justice to the fact that the difficulties that led us to adopt theistic nomic conceptualism were not confined to elucidating the teleological characteristics of lawmaking dispositions. For we were equally motivated by the challenge of finding an explanation

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of these features that could also resolve dialectically independent puzzles regarding the ontological status of unexercised dispositions (‘Independence’) and the standard view that lawmaking dispositions are intrinsic properties (‘Intrinsicness’). Finally, we saw that theistic nomic conceptualism compares very favourably with rival versions when judged against metatheoretical criteria that are widely (if not universally) endorsed by analytic philosophers, in particular the qualitative and quantitative varieties of ontological and ideological parsimony, consistency with our best scientific findings, compliance with the principle of nihil ad hoc, and consonance with Moorean intuitions about lawhood, including the Contingency Intuition, the Governance Intuition, and intuitions regarding the objective reality of the distinction between lawful and accidental regularities. Neo-Humeans sympathetic to the deflationary accounts criticised at the outset of this inquiry may, of course, chalk up the theistic implications of the Powers Model as another reason for rejecting realism altogether. But, as we have seen, classical theism provides neglected but powerful solutions for realists who wish to deflationism’s profoundly counterintuitive implications, but who recognise the weaknesses of the naturalistic and non-naturalistic options available to them. That is a conclusion that can be welcomed by anyone committed to the objective existence of the lawful regularities that order the world around us.

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INDEX

abduction/abductive inference: 32, 40, 43-5 Abrahamic monotheism: 2-3, 7, 159 abstract objects: 108, 116, 154, 161-2n, 168, 171 actualism/Megaric Actualism: 73, 110 Adams, Marilyn McCord: 130n, 184n Adams, Robert: 160n Al-Ghazali: 2n Anscombe, Elizabeth: 6, 46, 177 Anselm: 187-8 antirealism: antirealism about universals: 156, 160 causal antirealism: 27 nomic antirealism: 5, 11-12, 14-15, 17, 32-3, 35, 37, 40, 43, 45, 48, 57, 63, 66n, 91, 124, 126, 135, 150, 174, 179 scientific antirealism: 162n antireductionism: 21, 182, 184 Aristotle: 3 Aristotelianism: 38, 65, 96n, 184, 191 Neo-Aristotelianism: 4, 69, 191 Armstrong, David: 16n, 36-62, 79, 83n, 93, 94, 96n, 101, 103-5, 111, 119, 135, 143, 147n, 154-5, 166n, 177, 183 atomic facts: See states of affairs A-Theory of time: 25, 53, 76 Aquinas, Thomas/Thomism: 8, 65, 130n, 160, 172n, 184n aseity: 160, 171, 183 Augustine: 8, 160 Ayer, A.J.: 6n-7n Barnes, E.C.: 70n Bealer, George: 162, 163n Beebee, Helen: 28n-30n, 44n, 66n Benacerraf, Paul: 15, 16n, 115-7, 123, 167-8 Best-System Analysis of Laws/BSA: 12, 19-30, 32-3, 37-8, 43, 47, 98, 120, 126, 129

Bigelow, John: 93n Bird, Alexander: 3n, 22n, 48n, 54n, 66n-67n, 69n, 76n, 78n, 79, 80n, 81, 93n, 107-8, 110-11, 114, 131n Black, Robert: 14n Boland, Vivian: 8n, 160n Boyle Gas Law: 55, 57 Boyle, Robert: 67, 75 Bradley, F.H.: 96-7, 111 Brown, James Robert: 93n, 116n B-Theory of time: 25, 53, 177 Callender, Craig: 20n-23n Carroll, John: 21n-22n, 103n, 116n, 182n Cartwright, Nancy: 16n, 66n-7n, 103, 112 categoricalism: 14-16, 36-7, 40-41, 62, 88, 101, 175, 182 categorical properties: 15n-16, 35-7, 42, 67, 74, 131n, 136, 175, 182, 195 causal power(s): 2, 3, 7-8, 412, 55-6, 65, 67, 74, 109, 123, 125, 126, 128, 132-3, 138, 160, 166, 184-5, 192 causation: 25, 27, 46, 69, 83, 105, 141, 153, 156, 163, 177, 194 Divine Causation: 128, 165, 168 Chakravartty, Anjan: 114 Clark, Errin: 3n Cohen, Jonathan: 20n-23n Colyvan, Mark: 42n Contingency Intuition: 36, 45, 98-9, 113, 144, 193, 196 Coulomb’s Law: 51, 72, 78, 82, 84, 96, 176 counterfactuals: 16, 18-19, 30, 33, 36, 58, 62n, 63, 68, 69n, 100, 102, 113, 124, 155, 174, 194 Cowling, Sam: 120n Craig, William Lane: 8n, 168n Cross, Troy: 69n

210

INDEX

Davidson, Donald: 46 deduction/deductive inference: 20, 21n, 23, 29, 43, 45 deflationism: 16, 18, 21, 26, 33, 35, 60, 62-3, 91, 126, 142, 179-80, 193, 196 Descartes, René: 4, 201, 204 determinism: 29 Dipert, Randall R.: 80n direct acquaintance: 116 directedness: intentional directedness: 80-1, 107, 109 relational directedness: 78-9, 101, 107, 109 DISPIR (immanent realist version of the Powers Model): 63-5, 71-4, 76-85, 87-9, 91-2, 101-2, 106-7, 109-11, 113, 115, 123, 125, 128-33, 137, 1401, 144, 148-9, 155, 184-6, 189-90 See also: Powers Model DISPTC [theistic conceptualist version of the Powers Model]: 175-6, 184-92 See also: Powers Model dispositions/dispositional properties: 2-3, 14-15, 45, 55, 64-78, 80-88, 102, 106, 108-16, 120, 127-140, 144-6, 148, 156, 161, 174, 185-7, 189-191, 194-6 divine concepts/divine conceptualism: 8, 150, 159, 161, 163, 168-9, 171-5, 178, 180, 184-5, 187-8, 190-1 divine ideas: 7, 8n, 160-1 Doolan, Gregory T.; 8n, 160n Dretske, Fred: 37 Dulong-Petit Law: 56 Dummett, Michael: 160n Dumsday, Travis: 161n Eleatic Principle: 41-2, 48, 50, 54n, 55-6, 108, 154 Ellis, Brian: 15n, 67n, 131n, 138n, 165n empiricism: 2, 7, 12-13, 20, 23, 29, 40, 63, 67-8, 73, 96, 112, 171-2, 178 epistemic access: 15-17, 21, 116, 131, 140, 163, 167-8 Ex Nihilo Objection: 51-3, 59n, 61, 105, 127, 181, 183

Fales, Evan: 51-2, 93n, 97n-98n, 1056, 117n Fodor, Jerry: 173n forces/physical forces: 36, 51-2, 56, 58, 72, 133-4, 180 Forge, John: 57n Forrest, Peter: 93n, 96n Foster, John: 7, 32, 44-5, 124-5, 134-48, 157, 159, 163, 169, 187 Foster’s Fork: 141-3 Foster, M.B.: 4 Freddoso, Alfred: 128, 145 Fresco Problem(s): 63, 84, 86-89, 108113, 115, 140, 185, 189-190 Friedman, Michael: 120n Fuhrman, André: 62n Gibb, Sophie: 39n Gierre, Ronald N.: 16n God: 2, 4, 6-8, 26-32, 36, 65, 112, 118, 126-130, 133, 142, 144-5, 149, 154, 159-60, 162, 163-9, 171-6, 178-191, 193-4 Goodman, Nelson: 18-9, 23, 25 Governance Intuition: 36, 45, 47n, 66n, 98, 144, 196 Haecceitas: 40 Handfield, Toby: 101n Harré, Rom: 3n, 67n Harrison, Peter: 4n Hawthorne, John: 14 Heil, John: 3n, 15n, 39n, 62n, 70, 131n2, 135n-6, 149n Henry, John: 4n Hume, David: 2, 11-13, 20, 24ff, 46-7, 61, 67, 125 Humeanism/Neo-Humeanism: 6, 11ff, 35, 37, 39-40, 43, 47, 61-2, 68-9, 104-5, 124, 127, 135, 177, 179-81, 191, 194, 196 Hume’s Principle: 12, 13, 14, 17, 20, 21, 24, 26, 28, 29, 31, 33, 40, 78 Identification Problem: 49, 61, 103, 177-8 incommensurability: 23, 30

INDEX

Independence criterion: 72-4, 76-7, 85-6, 101, 108-10, 112, 128, 133, 140-1, 185-6, 189, 196 induction: 43-45 Ingthorsson, R.D.: 107n, 114 Instantiation Principle: 39-41, 48, 50-4, 57-64, 73-4, 76-7, 79-81, 84-7, 89, 91-3, 101-2, 104, 107, 109-10, 122, 129, 132-3, 140-1, 146, 148, 174, 181, 186, 189, 192 See also: Weak Instantiation Principle Intrinsicness criterion: 74-77, 84n, 85, 108, 110, 112, 128, 132-3, 140-1, 185-9, 196 isomorphism: 32, 111, 189 Jacobs, Jonathan: 15n-16n, 106n, 131n Johnston, Mark: 75n Kail, P.J.E.: 13n Kenny, Anthony: 172n Kistler, Max: 23n, 62n Kitcher, Philip: 120n La Forge, Louis de: 2n Lamont, John: 3n Langton, Rae: 188 lawmakers: 1, 3, 6, 35-6, 41-2, 45, 48, 50, 63, 69-71, 75, 77, 79, 81, 85, 89, 104-5, 108-9, 113, 116-17, 121-3, 126, 130, 133, 135-6, 144, 150, 156, 168, 175, 180-1, 185, 190, 194 laws: disjunctive laws: 55, 59-60 exclusion laws: 55, 59-60 functional laws: 55, 57-8, 102, 120 fundamental laws: 29, 31, 55-6, 84 natural laws/laws of nature: 7, 14, 16, 20-1, 36, 38-9, 42-3, 49, 55, 65-6, 98, 113, 125-8, 130n, 142, 155, 191, 193-4 law-statement: 1n, 3, 17-20, 36-7, 43, 51, 53, 57, 60, 63-4, 66, 71, 95, 100, 102, 106, 116, 124-5, 138, 142-3, 155, 174, 185, 190-2, 194 Leftow, Brian: 8n, 27n, 149n, 160n62n, 164n, 166n, 168, 172n, 174, 178n, 187

211

Leibniz, G.W.: 8, 32, 160 Leng, Mary: 96n Lewis, David: 13-15n, 20-1, 28n-32, 38, 44n, 49n-50, 62, 69n, 71n, 75n, 88, 105, 118-9, 129n, 151, 188 Lierse, Caroline: 67n, 138n Lipton, Peter: 94n Locke, John: 15, 155 Loewer, Barry: 20n, 23n logical empiricism: 2, 12 Loux, Michael: 8n, 160n, 164n Lowe, E.J.: 138, 165n Malebranche, Nicolas: 2n, 28n Margolis, Eric: 170n Martin, C.B.: 3n, 15n, 39n, 62n, 68-70, 82n-83n, 84, 87-9, 108, 131n, 132-3, 135 Massimi, Michela: 60 materialism: 100 mathematical content [of laws]: 95-6, 120 mathematical objects: 92, 94-5, 116 Maudlin, Tim: 182n McKitrick, Jennifer: 75 Meinong Objection: 79, 100-2, 107, 109-10, 114 Mellor, D.H.: 3n, 49n, 58, 67, 135n Menzel, Christopher: 160n, 178n methodological naturalism: 192 Mill, John Stuart: 19-21 Modal Hybridity Problem: 36, 45, 47, 66, 98, 113, 143-4, 193 Molnar, George: 3n, 39n, 62n, 69, 71n73n, 75n, 78n, 80-1, 114, 149n Moore, G.E.: 16n, 44, 112, 196 Moreland, J.P.: 97n Morris, Thomas: 160n, 178n Mumford, Stephen: 3n, 22n, 60, 66n67n, 74, 75n, 79n-80n, 83n, 88-9, 130n-131n, 133, 185n Murphy, Mark C.: 6n Nadler, Stephen: 2n, 28n naturalism: 4-5, 7-8, 26, 33, 37, 40, 62-4, 79, 81, 89, 102, 123, 126-8, 184, 191-3 natural kinds: 18, 23, 65, 67, 137-8, 165

212

INDEX

natural laws/laws of nature: 7, 14, 16, 20-1, 36, 38-9, 42-3, 49, 55, 65-6, 98, 113, 125-8, 130n, 142, 155, 191, 193-4 natural necessity: 2-5, 12, 32, 43-4, 63, 174, 194 natural philosophy: 3-4 natural properties: 14, 16, 20, 24-5, 27, 35, 38, 47, 67, 69, 79, 101, 131, 137 natures: 2-3, 40, 65-6, 140, 191 necessitation relation: 37-8, 40-2, 45-8, 50-1, 57, 94, 102, 175, 179-83 Newton, Isaac: 4, 56, 58, 95, 180 Newton’s First Law: 58 Newton’s Second Law: 180 Newton’s Third Law: 56 Nolan, Daniel: 118n nomic realism: 2-3, 5-7, 11, 15n-16n, 26, 27n, 30-1, 33, 35, 37, 41, 43-4, 55, 61-4, 66, 77, 92, 95 115, 119, 122, 125, 130, 134, 139, 142n, 14451, 155-7, 159, 161, 166, 168, 170, 173-4, 177, 183-4, 191-2 nominalism: 39, 47, 61-2, 119, 121, 147, 159-60, 163, 166n ‘no-miracles’ argument: 93-4 nomological structure: 28, 36, 98, 175 non-naturalism: 27n, 37, 48, 62, 92, 108, 123, 141-2, 150, 194, 196 Oakley, Francis: 4n occasionalism: 2n, 8, 26n-27n, 28, 33, 145, 182-4, 191 O’Connor, Timothy: 105n Oddie, Graham: 42 Oderberg, David: 3, 66 Oliver, Alex: 120 omnipresence: 187-8 ontological commitment: 94, 117, 145, 147, 161, 165-6 Oppy, Graham: 160n Osler, Margaret: 4n Ott, Walter: 4n panpsychism: 9 parsimony [as a criterion for scientific theories]: 6, 97, 113, 117n, 118, 121, 196

Peacocke, Christopher: 152-3, 170n Perler, Dominik: 2n philosophy of religion: 7-8, 160 Place, U.T.: 80, 125, 154-6, 159 Plantinga, Alvin: 160n, 167-8 Plato: 41, 50, 96, 103 platonism (about natural laws): 5, 8, 27, 35ff, 93, 103, 115, 124, 193 positivism: 11 possibility: logical possibility: 46 nomological possibility: 2 Powers Model: 3, 5, 15, 37, 41, 48, 62-7, 69-72, 74-80, 85, 87-89, 91-2, 106-8, 110-11, 114, 123, 125-9, 130, 134-9, 141-2, 144, 146, 148, 150, 159, 161, 165, 173-5, 177, 184-6, 189-91, 194-6 See also: DISPIR and DISPTC predictive power: 18, 44, 118, 179 Prinz, Jesse: 171n Projectivist Regularity Theory: 18, properties: dispositional properties: See dispositions uninstantiated properties: 86, 88n, 106, 118-9 Pruss, Alexander: 160n Psillos, Stathis: 17, 19n, 57, 72n-73n, 162n Putnam, Hilary: 92-4 qualities: 4, 14-5, 88, 13n quidditas/quidditism: 3, 14, 40-1, 131n Quine, W.V.O.: 62n, 92, 95, 155, 168 Quinn, Philip: 27n Ramsey, Frank: 20-1 Ratzsch, Del: 7n, 150n Read, Rupert: 13n realism: immanent realism: 35-6, 38-9, 50, 52, 54, 60-4, 74, 88n, 91-2, 95-7, 107, 110-11, 118-9, 121, 123, 125, 128-9, 133, 146, 148-9, 155, 157, 159-60, 164, 169-70 nomic realism: 2-7, 11-12, 14-16n, 26-27n, 29-33, 35-7, 40-1, 43-4,

INDEX

53, 55, 61-4, 66, 70, 77, 91-3, 95, 115, 119, 122, 125, 130, 134-5, 138-9, 142-51, 155-7, 159, 161, 164-6, 168-70, 173-4, 176-7, 179, 183-4, 191-2 platonic realism: 8, 39, 40n, 54, 59, 91ff, 129, 146, 148-9, 157, 160, 164, 167-8 scientific realism: 27n, 39, 92-4, 162n Relational Directedness: See directedness Relations Model: 3-5, 15, 35-7, 48, 50-2, 54, 59, 61-3, 65-6, 77, 79, 91-2, 94, 97-8, 100-104, 106, 11011, 114, 122-3, 127, 129, 146, 148, 150, 159, 161, 165, 174-80, 182-4, 190, 194-5 RBUIR [immanent realist version of the Relations Model]: 35-65, 67, 76n-77, 89, 91-3, 99-104, 115-6, 119-20, 123, 127, 135, 143, 146, 148-9, 174-5, 177-84 RBUPR [platonic realist version of the Relations Model]: 92, 97-9, 102-106, 112, 115-23, 148, 174-5, 177-84 RBUTC [theistic conceptualist version of the Relations Model]: 174-185, 191 Rescher, Nicholas: 8n Richman, Kenneth: 13n Robinson, Howard: 162n Rodriguez-Pereyra, Gonzalo: 119n, 121 Rutherford, Donald: 8n Ryle, Gilbert: 96 scepticism: 2n, 16, 24-6, 29, 31, 68, 124, 139, 173 Schaffer, Jonathan: 4n Schmaltz, Tad: 2n, 28n Schneider, Susan: 28n, 41, 101n School of Immanence: 2-3 School of Imposition: 2-3 Schopenhauer, Arthur: 26 Schrenk, Markus: 22n, 28n scientific realism: See realism

213

secular conceptualism: 149, 152-4, 1567, 159, 161-3, 166 sense-experience: 12-13, 20, 22, 29, 156, 163 Serway, Raymond: 55n, 57n, 60n Shakespeare, William: 99 Shoemaker, Sidney: 67n, 106, 131 Sider, Ted: 94 simplicity [in philosophy of science]: 21-4, 30-2, 95, 117, 120 singularism/causal singularism: 46 Smart, J.J.C.: 117 Smith, Quentin: 160n Sober, Elliott: 117n sovereignty (divine): 160, 171, 183 states of affairs: 38, 43, 50, 52, 70-1, 87-8, 101n, 102-3, 155 Steiner, Mark: 96n Strawson, P.F.: 97n supervenience: 13 Sutton, Jonathan: 170n Swartz, Norman: 4n Swinburne, Richard: 7n, 25, 51n, 54n6, 67n, 83n, 117, 124, 125-34, 136-7, 139-40, 144, 148, 163, 169 Swoyer, Chris: 98n, 105n theism: 2n, 4-8, 11-12, 26-9, 31-3, 44, 45n, 55n, 92, 106, 122, 123ff, 148, 150, 175-8, 180-4, 188, 190-96 thick particulars: 50-1 Tooley, Michael: 37, 51, 58-61, 92-4, 97-101, 104-5, 118-9, 174, 183 tropes: 69-70, 87, 97, 108, 166-7, 186 Tugby, Matthew: 71-72n, 76n, 84n, 93n, 107n Tweedale, Martin: 105n uninstantiated laws: 55, 58-9, 102, 120 universals: contingent universals: 98, 104 immanent universals: 52, 63, 104, 119, 123 platonic universals: 53, 70-1, 93, 95, 99, 104-5, 111, 113, 120-1, 123, 148 van Fraassen, Bas: 16n, 22n, 49, 61, 65, 103-4, 177-8, 180, 183

214

INDEX

van Inwagen, Peter: 28n, 128n Vetter, Barbara: 3n Ward, Barry: 19n Weak Instantiation Principle: 53-4, 57, 59, 61, 76n, 93 Welty, Greg: 8n, 160n Werther, David: 160n Whitehead, Alfred North: 2, 3n-4n

Wiedemann-Franz Law: 55, 57 Wierenga, Edward: 187n Wigner, Eugene: 95n Williams, Neil E.: 82n, 83n-85n, 87n, 107n Wilson, Jessica: 13n Wippel, John F.: 8n, 160n Wolterstorff, Nicholas: 160n

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