Powers, Parts and Wholes: Essays on the Mereology of Powers 1032288574, 9781032288574

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POWERS, PARTS AND WHOLES

This volume offers a fresh exploration of the parts–whole relations within a power and among powers. While the metaphysics of powers has been extensively examined in the literature, powers have yet to be studied from the perspective of their mereology. Powers are often assumed to be atomic, and yet what they can do—and what can happen to them—is complex. But if powers are simple, how can they have complex manifestations? Can powers have parts? According to which rules of composition do powers compose into powers? Given the centrality of powers in current scientific as well as philosophical thought, recognizing and understanding the ontological differences between atomic and mereologically complex powers is important, for both philosophy and science. The first part of this book explores how powers divide; the second part, how powers compose. The final part showcases some specific study cases in the domains of quantum mechanics and psychology. Powers, Parts and Wholes will be of interest to professional philosophers and graduate students working in metaphysics, philosophy of science and logic. Christopher J. Austin is a postdoctoral research fellow in the ‘Mistakes in Living Systems: A New Conceptual Framework for the Study of Purpose in Biology’ project at Reading University. His specialization is in Metaphysics and Philosophy of Science. He is the author of Essence in the Age of Evolution: A New Theory of Natural Kinds (Routledge, 2018). Anna Marmodoro holds the Chair of Metaphysics in the Department of Philosophy at Durham University, and she is concomitantly an associate member of the Faculty of Philosophy of the University of Oxford. She specializes in two research areas: metaphysics and ancient, late antiquity and medieval philosophy. Her latest monograph is Forms and Structure in Plato’s Metaphysics (2021). Andrea Roselli has been part of the Oxford-based Mereology of Potentiality research group for the last three years while being a postdoctoral research associate at Durham University. He specializes in metaphysics, the philosophy of science and the philosophy of time.

Routledge Studies in Metaphysics

Neo-Aristotelian Metaphysics and the Theology of Nature Edited by William M. R. Simpson, Robert C. Koons, and James Orr Death, Determinism, and Meaning Stephen Maitzen A Case for Necessitarianism Amy Karofsky E.J. Lowe and Ontology Edited by Miroslaw Szatkowski A Map of Selves Beyond Philosophy of Mind N. M. L. Nathan Meaning and Metaphysical Necessity Tristan Grøtvedt Haze Relational Passage of Time Matias Slavov Political Identity and the Metaphysics of Polities Edited by Gabriele De Anna and Manuele Dozzi Powers, Parts and Wholes Essays on the Mereology of Powers Edited by Christopher J. Austin, Anna Marmodoro, and Andrea Roselli For more information about this series, please visit: https://www.routledge.com/RoutledgeStudies-in-Metaphysics/book-series/RSM

Powers, Parts and Wholes Essays on the Mereology of Powers Edited by Christopher J. Austin, Anna Marmodoro, and Andrea Roselli

First published 2024 by Routledge 605 Third Avenue, New York, NY 10158 and by Routledge 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2024 selection and editorial matter, Christopher J. Austin, Anna Marmodoro, and Andrea Roselli; individual chapters, the contributors The right of Christopher J. Austin, Anna Marmodoro, and Andrea Roselli to be identified as the authors of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-28856-7 (hbk) ISBN: 978-1-032-28857-4 (pbk) ISBN: 978-1-003-29883-0 (ebk) DOI: 10.4324/9781003298830 Typeset in Sabon by SPi Technologies India Pvt Ltd (Straive)

Contents

Notes on Contributors

vii

Introduction 1 CHRISTOPHER J. AUSTIN, ANNA MARMODORO, AND ANDREA ROSELLI

PART I

Parts of Powers 1 Carving Up the Network of Powers

9 11

A. J. COTNOIR

2 Parts and Grounds of Powers: A Logic and Ground-Theoretic Mereology for Power Ontologies

42

ROBERT C. KOONS

3 Complex Powers: Making Many One

61

CHRISTOPHER J. AUSTIN

4 Powers as Mereological Lawmakers

83

MICHAEL TRAYNOR

5

Determinable Dispositions NICKY KROLL

96

vi Contents PART II

Composition of Powers

109

  6 What There Is and What There Could Be: Mereology, Causality and Possibility in an Ontology of Powers

111

SOPHIE R. ALLEN

  7 What Can Causal Powers Do for Interventionism? The Problem of Logically Complex Causes

130

VERA HOFFMANN-KOLSS

  8 Collective Powers

142

XI-YANG GUO AND MATTHEW TUGBY

  9 The Special Power-Composition Question and the Powerful Cosmos

167

JOAQUIM GIANNOTTI

10 The Composition of Naïve Powers

185

MICHELE PAOLINI PAOLETTI

PART III

Power Mereology in Science

207

11 Quantum Dispositions and the Simple Theory of Property Composition

209

MATTEO MORGANTI

12 Dispositions, Mereology and Panpsychism: The Case for Phenomenal Properties

227

SIMONE GOZZANO

Index 245

Notes on Contributors

Sophie R. Allen is a lecturer in philosophy at Keele University and a supernumerary fellow in philosophy at Harris Manchester College, Oxford. She specializes in metaphysics, the philosophy of science and the philosophy of mind, taking a particular interest in meta-metaphysical and methodological questions. Within metaphysics, she primarily focuses on classification, causation, laws of nature and modality. She has written papers on the implications of properties being causal powers for theories of persistence, modality and possible worlds, the hard problem of consciousness and the conceivability argument. She is the author of A Critical Introduction to Properties (2016). A. J. Cotnoir is a senior lecturer in the Philosophy Department at the University of St Andrews and a member of the Arché Philosophical Research Centre. He researches primarily in metaphysics and is especially interested in mereology, identity, individuation and unity. He is a co-author (with Achille C. Varzi) of the recent Mereology and co-editor (with Donald L. M. Baxter) of the collection Composition as Identity. He enjoys applying formal systems from philosophical logic and the occasional foray into the philosophy of religion. Joaquim Giannotti is a postdoctoral researcher and the principal investigator of the FONDECYT de Iniciación en Investigación project (No. 112200300) ‘Dual Aspect Essentialism: A Scientifically Responsible Metaphysics of Fundamental Properties’ at the Universidad de Chile. He is also a research associate at the ERC-funded project (Grant No. 757295) ‘FraMEPhys: A Framework for Metaphysical Explanation in Physics’, based at the University of Birmingham. His work primarily focuses on metaphysical grounding and the ontology of powers. He has published papers exploring and defending non-orthodox views about topics in leading journals, including Philosophical Studies and Synthese.

viii  Notes on Contributors Simone Gozzano is a professor of philosophy of mind and metaphysics at the University of L’Aquila (Italy). He works on themes such as mind– body relation, mental causation and the metaphysical nature of phenomenal states. He is the author of four books (in Italian), co-editor (with Chris Hill) of New Perspectives on Type Identity and (with Francesco Orilia) Tropes, Universals, and the Philosophy of Mind. He has published a number of papers on scholarly journals. Xi-Yang Guo presently teaches part-time in the Philosophy Department of Durham University, from which he received his PhD in 2017. His thesis covered the metaphysics of properties, facts, modality and metametaphysics. He was supervised by Sophie Gibb and Matthew Tugby with the support of an AHRC scholarship. Vera Hoffmann-Kolss is an associate professor of Philosophy at the University of Bern. Her current research focusses on interventionist causation and Bayesian causal models. She is also interested in the metaphysics of properties, mental causation, and the recent debates on ontological vagueness and hyperintensionality. She has published a number of papers on these topics and a book on the distinction between intrinsic and extrinsic properties. Robert C. (“Rob”) Koons is a professor of philosophy at the University of Texas at Austin and earned his MA from Oxford University and his PhD from the University of California, Los Angeles. He is the author or co-author of five books, including The Atlas of Reality with Timothy H. Pickavance (2017) and Is Thomas’s Aristotelian Philosophy of Nature Obsolete? (2022). He is the co-editor of four anthologies, including The Waning of Materialism (2010) and Classical Theism (Routledge 2023). He has been working recently on an Aristotelian interpretation of quantum theory and defending and articulating hylomorphism in contemporary terms. Nicky Kroll is an associate professor and the chair of philosophy at Franklin and Marshall College. He works in the philosophy of language and metaphysics, focusing on the nature of potentiality and process and how they are encoded in natural language. His work appears in the Oxford Studies in Metaphysics, Linguistics and Philosophy, Philosophical Studies, Erkenntinis, Natural Language Semantics and others. Matteo Morganti is a professor of philosophy at the University of Rome Tre, where he teaches courses in logic, reasoning, general philosophy of

Notes on Contributors  ix science, epistemology and the philosophy of physics. His research activity focuses on issues related to our knowledge of the physical world; in particular, he has written on the problem of scientific realism and on topics in the metaphysics of science, as well as on naturalism and the methodology of scientific metaphysics. Besides several articles in international peer-reviewed journals and edited volumes, he has authored Combining Science and Metaphysics (2013). Michele Paolini Paoletti is an assistant professor at the University of Macerata (Italy). His main research interests cover metaphysics and the philosophy of mind. He has written extensively on the ontology of relations and powers, as well as on ontological emergence and dependence. His books include The Quest for Emergence (2017) and the collection Philosophical and Scientific Perspectives on Downward Causation (Routledge, 2017, co-edited with Francesco Orilia). Michael Traynor is presently an independent researcher focusing on metaphysics, specifically of persistence, parthood, the nature of time and identity, modality, powers and laws, often through a methodological and epistemological lens. He completed his PhD, Modal Arguments, Possible Evidence and Contingent Metaphysics, at St Andrews in 2017, under the supervision of Katherine Hawley and Aaron Cotnoir, during which time he was a member of the Arche Philosophical Research Centre. He has published articles in Thought, Proceedings of the Aristotelian Society and Synthese. Matthew Tugby is a professor of philosophy at Durham University. His research focuses on issues at the intersection of contemporary metaphysics and the philosophy of science, including the topics of properties, powers, laws, teleology, causation and modality. Matthew is the author of the 2022 monograph Putting Properties First: A Platonic Metaphysics for Natural Modality, which develops a metaphysics of science based on Platonic realism about properties.

Introduction Christopher J. Austin, Anna Marmodoro, and Andrea Roselli

This collection of original essays addresses a new topic in the ever-growing literature regarding the metaphysics of powers1 – the mereology of powers: the part–whole relations existing within a power and among powers. Given the centrality of powers in current scientific, as well as philosophical, thought, recognising and understanding the ontological differences between atomic and mereologically complex powers may prove crucial in developing powers ontologies. Powers are usually assumed to be simple, atomic entities, and yet they are often assumed to have complex manifestations. Consider, as an example from daily life, the disposition of a vase to break: it can manifest that ‘breaking’ in a number of ‘ways’, ways that differ both qualitatively and quantitatively (it can crack slowly, quickly splinter, explosively shatter, etc.). There are metaphysicians who hold that (some) powers in nature are ‘multi-track’, namely individuated by more than one type of stimulus/triggering condition and more than one type of manifestation, in contrast with the ‘single-track’ powers, which are individuated by one pair of stimulus/triggering conditions and type of manifestation. Introducing this distinction does not, however, address the research question that inspired this collection: multi-track accounts, we submit, simply organise the complex manifestation of certain powers into ‘tracks’ but do not explain how this complex manifestation derives from the power. What is needed, we think, is an account of the internal complexity of such powers. Can we try to explain it in terms of parts of power? This volume offers fresh explorations of the hypothesis that there are parts–whole relations within a power (Part I) and among powers (Part II), as well as showcasing two examples of power mereology in the context of the philosophy of science (Part III). In the first chapter, ‘Carving Up the Network of Powers’, Aaron Cotnoir shows how a systematic and thorough mereology of powers can be built, strengthened and defended. Cotnoir assumes an interconnected network of powers as the underlying metaphysical basis of the world and considers a number of ways of ‘carving up’ regions of that network. Each approach DOI: 10.4324/9781003298830-1

2  Christopher J. Austin et al. generates a unique, possible mereology of powers. In the case of the ‘subcollection method’, the mereology of powers considered is based on subsets and generates arbitrary complex powers, whereby every complex power is a region of the network. Cotnoir builds on these premises a mereology based on substructures and discusses some problems that might arise from this view. He then presents the ‘clustering method’, in which he focuses on the weakest points of connection in the network of powers – cutting across the fewest connections so that the network is partitioned into its most interrelated clusters. The author finally introduces the ‘coordination method’, which attempts to group nodes in a way that minimises multitracking, and a ‘bisimulation method’ borrowed from the computing sciences. Cotnoir’s conclusion is that the carving approach to complex powers can be theoretically fruitful for different researchers with differing philosophical commitments. In the second chapter, ‘Parts and Grounds of Powers’, Robert C. Koons develops a nominalist version of a powers theory in which the concept of ‘grounding’ (a form of constitutive determination that the author precisely defines in the chapter) lies at the base of a mereology of facts, whereby powers are equivalence classes of a sui generis, dispositional version of conditional facts that are said to be ‘power-equivalent’ when they are mereologically coincident. The author advances an extreme nominalist position: a version of power ontology in which powers and (neo-)Aristotelian forms are not reified and the ontology consists only of ordinary objects and their integral parts. Koons then shows how to defend this extreme nominalist position, one would be forced to adopt either pandispositionalism or the powerful quality theory so that powers can be identified with equivalence classes of concrete entities. Building on these conceptual grounds, Koons develops a fact-based mereology of powers in which powers can have other powers as their manifestation. The author then proceeds to describe a first model in which all causal powers are assumed to be mutually concordant – where, in other words, no entity has two powers with conflicting manifestations relative to the same conditions. He concludes by showing how we can include ‘free’ powers (free in the sense that they can fail to manifest on occasion) in this fact-based mereology. The third contribution to this collection, ‘Complex Powers’ by Christopher J. Austin, is a metaphysical investigation of the possible characteristics and the conceptual requirements of a mereology of powers. In particular, the author argues that in order to develop a mereology of powers as standardly intended in the current literature, we need to find a delicate balance between the metaphysics of emergence, wherein wholly unique and irreducible entities are created, and the fusion of properties, wherein the coming together of entities form a new, although not entirely novel, entity. Austin takes as his key study what he calls ‘complex powers’ – powers that have multiple stimuli and/or multiple manifestations,

Introduction  3 which he claims are, in fact, most of the normal, ‘everyday’ powers with which we are all familiar. His idea is to examine what sort of mereological relations might suffice in order to properly characterise the metaphysical constitution of such powers. After a first important part in which it is shown how conceptualising the complexity of powers in terms of part–whole can be promising and potentially problem-solving, Austin examines the conceptual minutiae involved in various possible mereological frameworks – touching on everything from emergence, top-down causation, and fusion. All these strategies, he claims, are unable to characterise complex powers sufficiently. While he does not offer a definitive account of the mereology of complex powers, the clear laying-out of the problem itself sets the ground for promising future work in the direction of a mereology of complex powers. In the fourth chapter, ‘Powers as Mereological Lawmakers’, Michael Traynor explores an analogy between mereological principles and laws of nature, proposing a view according to which mereological principles are not ‘topic-neutral’, and therefore, the principles of a mereology of powers should have a sui generis nature, given the novel field of application. The  author develops a mereology tailored to power structuralism which includes the view that power ontologies underlie object-metaphysics or process-metaphysics, supplying structures from which objects and processes are derived. Traynor argues that, in this context, a mereology of powers could help develop a novel conception of mereological laws, such that the latter are underwritten by powers, much as laws of nature are underwritten by powers in the dispositionalist tradition. In keeping with the Eleatic stance positing power as metaphysically fundamental, the opposed traditions of necessitarian and contengentist dispositionalism concerning natural laws then extend their claims to rule over the mereological realm – we may corre­ spondingly take mereological laws to hold necessarily or contigently – each bringing with it associated strategies for dealing with supposed counter examples to one’s preferred set of mereological principles. Finally, Nicky Kroll concludes the first part of the book, with his ‘Determinable Dispositions’, going in a different direction altogether with respect to the issue of the complex manifestation of some powers. The author argues that, just as desires can be non-specific (such as the desire to do something tonight, without wanting specifically to go to a pub, or to a concert, or to the theatre), dispositions can be non-specific, or ‘determinable’. The author argues for determinable dispositions, which are nonspecific dispositions to manifest in some, non-determined way. Kroll favours an ontology of determinable dispositions because of its simplicity and (alleged) theoretical superiority over other competing theories, in, for example, explaining the nature of probabilistic dispositions (such as the disposition of a coin to land on one of its two sides) or multi-track dispositions (where fragility, for example, is a determinable disposition to break)

4  Christopher J. Austin et al. or dispositions in progress (an event in progress is disposed to bring about a resultant event at a certain, non-determinate point in time). The ontology Kroll proposes constitutes a novel framework for modelling the metaphysical complexities of dispositions which, in utilising the determinate– determinable relation, differs radically from the mereological approaches to composition that are explored elsewhere in this volume. The second part of this book discusses whether and how powers can compose within and among themselves. In the first chapter, ‘What There Is and What There Could Be: Mereology, Causality and Possibility in an Ontology of Powers’, Sophie R. Allen thoroughly analyses different philosophical possibilities for a mereology of powers in connection with what she calls both ‘direct’ and ‘indirect’ composition. In the case of direct composition, the part and the whole are instantiated by the same individual or are not instantiated. In the case of indirect composition, the part and the whole are instantiated by distinct individuals such that one individual is a proper part of another. Allen suggests that the most viable account of direct composition is one which ultimately focuses on the essentially (causally) productive nature of powers that determines what a power can do in the future. In support of this, the author argues that there are some important similarities in the context here laid out between the part–whole relations which hold between powers and those which hold between objects, events, and some abstract entities. In the second contribution of this section, ‘What Can Causal Powers Do for Interventionism? The Problem of Logically Complex Causes’, Vera Hoffmann-Kolss argues that interventionism and causal powers theories may be less distant from each other than is often assumed. Interventionists typically do not commit themselves to views about what causation really is, satisfied instead in elucidating how causal relations can be empirically discovered, described, and ultimately, manipulated. Causal powers theorists, on the contrary, typically aim to describe the metaphysical structure of causation that underpins the operations of the world. Hoffmann argues that interventionism, itself a successful enterprise, can benefit from incorporating considerations about causal powers. Interventionist theories of causation were originally designed to capture the way in which causal relations are discovered and described by practising scientists: if the data under investigation show certain patterns, these patterns can be given a causal interpretation. This approach is typically neutral about ontological questions. Hoffmann shows how interventionism plausibly needs at least some ‘metaphysical input’ in order to adequately represent the salient causal structures in the world and argues that interventionist theories could benefit from the metaphysical edifice which causal power theories provide. The next chapter, ‘Collective Powers’ by Xi-Yang Guo and Matthew Tugby, deals with the problem of how a powers ontology can coherently

Introduction  5 incorporate both low-level powers (such as the charge of an electron) and high-level powers (such as the fragility of a glass). While it is usually considered desirable to have an ontology of ‘ground-level entities’, Guo and Tugby show how it is possible to preserve an ontological commitment to higher-level powers as plurally instantiated by simple substances and grounded by the lower-level powers. In doing so, the authors develop an interesting vision of the part–whole relation in a dispositional context and give some compelling examples of its functioning in the context of a powers ontology. Guo and Tugby then offer an original way out of some longstanding problems regarding the instantiation of higher-level powers with respect to causal exclusion. For example, they argue that the species of composition involved between higher- and lower-level powers is plural rather than mereological and that this makes higher-level powers readily defensible against causal exclusion concerns. Finally, they argue that the composition of higher-level powers places no further explanatory demands on those internal structures. While Hoffmann claimed that the powers of a single bearer are parts of one another, the authors here support a mereology of multiple-bearer powers (as opposed to single-bearer powers), where a power of an individual can be a part of a power of another individual, if the first individual is part of the second individual. In the fourth contribution to this section of the book, ‘The SpecialPower Composition Question and the Powerful Cosmos’, Joaquim Giannotti presents and defends the existence of the ‘powerful cosmos’, composed by all the compossible powers instantiated. Giannotti presents this picture of the fundamental structure of the universe by re-examining the classic ‘special composition question’ in a dispositional context. He suggests that a ‘moderate’ answer, according to which powers compose objects when they form a physically united and metaphysically unified structure, is the most coherent option for a mereology built up from a powers ontology. The author, building on some considerations in the field of the philosophy of science, puts this moderate answer to the test in the context of an ontology rooted in the powerful cosmos. He ultimately argues that the powerful cosmos is the best conceptual foundation for a power mereology by offering several metaphysical, empirical, and methodological upshots for embracing the view. In the final essay in this group, ‘The Composition of Naïve Powers’ Michele Paolini Paoletti presents his version of the so-called naïve view of powers. According to the naïve view of powers, there is a one-to-one correspondence between powers, their bearers, their manifestations, and activations, on one hand, and causes, effects, and causal processes, on the other. The advantage of this view is that it makes it easy to single out powers and their features by taking into account which causal processes take place and the entities involved in them, as specific causal processes are

6  Christopher J. Austin et al. accounted for by specific powers. However, the naïve view of powers seems to disallow the mereological composition of powers. In an effort to remedy this, Paolini Paoletti presents his own account of the composition of powers – one grounded in the distinction between component and derivative powers. An element that is particularly interesting in Paolini Paoletti’s piece (along with Koons’s) is that it considers cases in which pandispositionalism is not adopted, and the ontology can then include elements that are not powers – categorical properties, processes, and so on. This opens a whole new spectrum of possibilities: it might be held, for example, that a categorical property is part of a dispositional one or that a power is a part of the individual instantiating it (in a ‘powerful bundle theory’ fashion). While most of the contributions in this volume take a pandispositionalist perspective, these other compositional possibilities are potentially fruitful hypotheses which offer promising directions for future work. In the third and final part of this collection of essays, two philosophers of science showcase two different empirical explorations of power mereology. In his ‘Quantum Dispositions and the Simple Theory of Property Composition’, Matteo Morganti discusses the characteristic of some properties included in the best available description of microphysical reality and claims that these properties are dispositional in nature. He then proceeds to show how in entangled quantum systems there are composite physical systems whose properties are more than merely the sums of the properties of their parts. Morganti proposes to adopt a refined version of ‘metaphysical coherentism’, wherein certain groups of entities may ground or depend on themselves in the sense that each of them requires the existence of all the others to be what it is. In this sense, the plurality of all the entities is the full ground of each entity, and each entity partially grounds itself and each one of the others (in other words, a layered metaphysical structure that has a fundamental basis is rejected). Morganti then shows how this background would help make sense of dispositional composition in an empirical context. His arguments are, ultimately, in favour of a power mereology in a coherentist framework. In particular, he suggests that this model can capture a fundamental fact about the complex properties of quantum entangled systems, namely that there are modal connections between entities in which not only the simpler properties of the parts determine the more complex properties of the whole but the former are, in turn, also affected by the latter. Finally, in the last chapter, ‘Dispositions, Mereology and Panpsychism’, Simone Gozzano conceptualises phenomenal properties, such as pain, in  terms of mereologically complex powers. Gozzano considers protopanpsychism: the view that fundamental entities have properties that are ‘precursors’ to consciousness and that they can collectively constitute consciousness in larger systems. For those familiar with the powers literature,

Introduction  7 this utilisation of the ‘Brentano thesis’ will be readily familiar. The author makes the case that this view is able to easily incorporate mereological composition within an ontology of dispositional properties. After offering a series of arguments that protophenomenal properties cannot be merely categorical in nature, Gozzano makes the interesting claim that dispositional properties standing in particular mereologically significant relations can be used to model the way in which consciousness both arises and persists. Given the centrality of powers in the current metaphysical debate, recognising and understanding the ontological differences between atomic and mereologically complex powers is important. This book’s chief aim is to fill this important lacuna in our understanding of the metaphysics of powers. There are already, of course, important contributions to the development of new theories in both mereology and the metaphysics of powers. However, none of these focuses on the intersection between the metaphysics of powers and the metaphysics of parts and wholes. We hope to have contributed with a step forward in this promising direction. Note 1 Although some philosophers prefer one term to the other for various conceptual reasons, we use power and disposition interchangeably here.

Part I

Parts of Powers

1 Carving Up the Network of Powers A. J. Cotnoir

According to the Humean paradigm: ‘the world is a vast mosaic of local matters of particular fact, just one little thing and then another’ (Lewis 1986 xi). There are no necessary connections between distinct entities, and so everything not related by identity (or mereology) is modally free. According to this picture, fundamental properties are categorical: they are perfectly natural intrinsic properties instantiated by spacetime points. Everything else is derivative of that. Dispositional properties or powers (e.g. fragility, solubility, electric charge, etc.) involve what an object does (which properties it manifests) in certain stimulus conditions and importantly what an object would do in various similar circumstances. That is, powers have modal connections that help characterise them. A failure to reduce these modal connections (by a conditional analysis or similar) would disrupt the Humean picture. One tradition in metaphysics seeks to develop theories of powers in an attempt to undermine Humeanism and build a rival comprehensive view of the world. Over time, that tradition has gained steam, and work in this area reached a fever pitch in the last decade, with an explosion of work on dispositions, powers, and potentialities.1 In this corpus, powers are often assumed to be partless or mereologically simple. This isn’t much of a surprise – in order to put pressure on the Humean programme, powers should be fundamental – in the sense of not being reducible to other non-­ powerful qualities. And it is often assumed that fundamental entities are mereological ‘atoms’ or simples.2 But that assumption is not forced; indeed, there’s growing recognition that the question of whether powers themselves are structured mereologically is independent of the question of whether they are reducible. Moreover, powers are complex: they often have complex stimulus conditions and complex manifestations. One of the core aims of this collection is to investigate how to explain this complexity and whether it is feasible to do so mereologically. While I don’t have committed views on whether the world is ‘ultimately’ categorical or dispositional,3 the mereological issues that powers raise are DOI: 10.4324/9781003298830-3

12  A. J. Cotnoir interesting in themselves and ripe for formal investigation. Mereological thinking is typically guided by two core metaphors: building versus carving. According to the building picture, things are built up or constructed from their fundamental parts, and to be a different thing is to be built up from different parts. This approach tends to proceed from bottom to top, from part to whole. A ‘Builder’ might ask the question of mereological complexity for powers as follows: ‘How can complex powers be built up from fundamental ones?’ The carving picture is different. It sees things as the result of separating or carving some underlying ‘space’ or structure according to more or less natural ‘joints’. It tends to approach things from a top-­to-­bottom direction, from whole to part. A ‘Carver’ might ask the question of mereological complexity for powers differently by wondering: ‘How can the space of all-­powerful qualities be subdivided in its most natural ways?’ In this chapter, I’ll take a carving perspective; my starting point is to characterise the underlying space as an interconnected network of powers along the lines of Bird (2007a, 2007b) and Tugby (2013). I then consider several ways of carving the network:4 1. the subcollection method, which generates arbitrary complex powers 2. the clustering method, which attempts to carve only along the weakest points of connection 3. the coordination method which attempts to group nodes in a way that minimises ‘multi-­tracking’ (in a sense to be explained) Each of these approaches generates a mereology of powers, some standard and others non-­standard: each with its own formal behaviours, each with its virtues and vices. In a spirit of helpful collaboration, I aim to develop these options sequentially, noting various features and issues but without any attempt to defend or reject them. One’s metaphysical views about powers ought to drive the choice of mereology, not vice versa. It is often claimed that many basic mereological principles are topic-­ neutral (applying to anything of any ontological category whatever) and analytic (true by virtue of mereological terms like part and compose)5 and, as a result, are beyond meaningful debate. While it seems clear that fruitful mereological theorising is not just restricted to material objects, I don’t think we can be antecedently assured that the correct mereology for, say, properties will match (in every detail) the part–whole theories we find elsewhere. The case for analyticity of many mereological axioms is ­ ­overstated anyhow.6 In metaphysics, as elsewhere, a productive ­methodology is an abductive one: which mereological theory is correct will often be a result of the typical holistic criteria for theory choice. We should not hold fixed any mereological system but, rather, discover which mereological principles are most suited to the theoretical applications at hand.

Carving Up the Network of Powers  13 Here’s the plan of the chapter. In the first section, I begin by characterising the network of powers as a directed graph, looking at options explored by Bird (2007b) and modifications of that approach by Tugby (2013). I then put forward my own preferred approach, which represents the network of powers via labelled transition systems, and explore its benefits. I also raise a problem with individuating nodes of the network structurally, sometimes called the ‘vicious regress problem’. In the second section, I develop several approaches to carving up the network based on subcollections. I consider the simplest approach to a mereology of powers based on subsets: each complex power is simply a region of the network, showing that the resulting mereology is bog-­standard classical mereology. I then extend that view to incorporate the manfiestation relation, based on the idea of induced subgraphs. Finally, I briefly summarise a method from Mormann (2009, 2010) for a different application, which builds a mereology based on ­substructures. I then note some drawbacks to the approach. In the third section, I tackle the clustering method and develop a new mereology of powers based on cutting across the fewest connections, partitioning the network of powers into its most interrelated clusters. In the fourth section, I consider a different perspective on carving that attempts to cut across many connections in ways that group coordinating manifestation tracks. This generates the set of weak and strong components of a graph. Finally, I borrow a method from the computing sciences which partitions the network according to a very robust type of coordination called ­ ‘­bisimulation’. I conclude by offering my preferred perspective and some suggestions for future work. Characterising the Network What are dispositional properties? McKitrick (2018, 8) lists the following five marks of dispositionality. A property is a disposition if it . has some characteristic manifestation m; 1 2. is such that some circumstance t will trigger m; 3. can be possessed without m occurring; 4. is instantiated by things of which a conditional of the form ‘if it were subject to circumstances t, it would exhibit manifestation m’ is generally true; and 5. can be accurately characterised with an expression of the form ‘the disposition to produce manifestation m in circumstance c’. McKitrick sees these marks as jointly sufficient for being a disposition (even though not individually necessary). So, powers are marked by their ability to connect triggers with manifestations. Indeed, many theorists

14  A. J. Cotnoir represent powers as functions from triggers to manifestations7 or by representing a power’s causal profile as a pattern of the triggering/manifestation relation between other powers in the network. As you can imagine, this approach naturally lends itself to a graph-­theoretic modelling, with connections between triggers and manifestations represented by arrows or arcs. Bird (2007a, 2007b) develops the first graph-­theoretic way of modelling powers.8 Modifications and adaptations are given by Tugby (2013). I’ll proceed slightly more formally than either of their presentations, noting choice points along the way. Graphs and Constraints

A two-­layered directed graph is a triple ⟨V, Am, At⟩ of sets, with Am ⊆ V × V and At ⊆ V × V. The elements of V are vertices – we interpret these as fundamental powers. What exactly we should mean by ‘fundamental’ here is up for theorists to debate,9 but for our purposes, we view fundamental powers are mereologically simple.10 The elements of Am are manifestation arcs, and elements of At are triggering arcs. For an arc a = v → w, we call v the source and w the target of a. The targets of arcs in Am are manifestations, and the targets of arcs in At are triggers.11 Strictly speaking, it is also desirable to associate each arc in Am with a corresponding arc in At to display which manifestation of a power occurs under which of its triggers. Bird (2007b) does this by graphically displaying the associated arcs using the same colour. For now I ignore colourings of the graph since (ultimately) my system avoids any need for them.12 For convenience, we also introduce notation for referring to all manifestations (triggers) of a given power, as follows. For vertex v ∈ V:

• The m-­out-­neighbourhood of= v is vm→ {w | v, w ∈ Am }. (This is the set of manifestations of v.)

• The m-­out-­degree of v is the cardinality of vm→, written | vm→ |. • The t-­out-­neighbourhood of = v is vt→ {w | v, w ∈ At }. (This is the set of triggers for v.)

• The t-­out-­degree of v is the cardinality of vt→, written | vt→ |. We can similarly define converse notions:

• The m-­in-­neighbourhood of = v is vm← {w | v, w ∈ Am }. (This is the set of powers of which v is a manifestation.)

• The m-­in-­degree of v is the cardinality of vm←, written | vm← |. • The t-­in-­neighbourhood of= v is vt← {w | v, w ∈ At }. (This is the set of powers for which v is a trigger.)

• The t-­in-­degree of v is the cardinality of vt←, written | vt← |.

Carving Up the Network of Powers  15 A vertex that is not a source for any targets is called a sink. An m-­sink would be a vertex where vm→ is empty. This would correspond to a powerless power. Are there any such things? While not explicitly stated, Bird (2007b) assumes there are no such powers. Manifestation: Each vertex must be the source for at least one arc in Am; for all v ∈ V, the m-­out-­degree of v is non-­zero. Tugby (2013, 26) argues, ‘This clearly has to be the case, since if a node did not bear a manifestation relation, then it could not be said to represent a disposition given that dispositions are characterised by their manifestation relations.’ But is that right? Perhaps a disposition could be characterised by being unmanifestable, by standing in no such relations? One (controversial) type of unmanifestable disposition would be dispositions with only impossible manifestations.13 If one had particularly strong reasons (empirical or otherwise) to accept such things, believing that impossible manifestations are part of our best total theory, then one would expect such a theorist to include these properties in their inventory of the world. And if such impossible manifestations are an essential part of characterising a disposition, then they should appear on the graph as a vertex along with a corresponding arc. In this way of setting things up, the set of manifestation arcs will no longer represent only the possible manifestations but, rather, all manifestations (possible and impossible). In either case, the Manifestation Constraint will be satisfied. There are other ways we might have unmanifestable dispositional properties. We have been supposing that powers are linked to causal profiles – that is, we have been treating them as sparse properties in the usual sense. But we needn’t hold that all powers are sparse; we might endorse abundantism about dispositional properties.14 Some such abundant properties might not be linked up to any causal profile – that is, they may not have any possible manifestation. Highly gerrymandered properties might be an example and epiphenomenal properties generally. This perspective would put pressure on the Manifestation Constraint only if such abundant-­and-­ unmanifestable properties were required to be simple powers. But defenders of abundant powers don’t seem to view them this way; they rather see them as non-­fundamental powers, complex powers or properties that just come along ‘automatically’ with others. Such properties are not required to feature as a vertex of the graph and so need not appear in V, falling outside the scope of the Manifestation Constraint. Notice, I do not also impose the reverse constraint, which would read: each vertex must be the target for at least one arc in Am; for all v ∈ V, the m-­in-­degree of v is non-­zero. Vertices with an in-­degree of 0 are called sources. That is, we are allowing powers which are not themselves the

16  A. J. Cotnoir manifestation of any other power in the world. I concur with Tugby (2013, sec. 7) that there’s no reason to rule them out. So each fundamental power must have one manifestation. Can it have more? The next constraint imposed by Bird (2007b) answers negatively. Single-­Track: Each vertex must be a source for at most one arc in Am; for all v ∈ V, the m-­out-­degree of v less than or equal to one. This constraint, when combined with the previous one, yields that the manifestation relation is a total function. It effectively claims that all simple powers are single-­track. Single-­track powers have a single type of manifestation whenever triggered, while multi-­track powers are capable different types of manifestations in different triggering circumstances.15 In our notation, if | vm→ | = 1 then v is single-­track; if | vm→ | > 1, then v is multi-­ track. The distinction corresponds to a long-­standing dispute between powers theorists, single-­trackers and mutli-­trackers. Single-­trackers think that all powers are keyed to a single type of manifestation and that putative cases of multi-­track powers are conflations of some sort or another. Multi-­trackers have challenged this in several ways.16 The Single-­Track Constraint, however, does not require a rejection of the existence of any multi-­track powers whatsoever; it only requires that any multi-­ track powers are complex. Bird (2007a, 21ff) suggests that multi-­track powers are equivalent (or, in some way, reducible to) a logical complex of single-­track powers. Whether such a claim is true is a substantive philosophical question which we ought not decide in advance. But for our purposes, it is worth noting that defenders of multi-­tracking do not insist that any simple powers are essentially multi-­track; rather, most are willing to concede that the multi-­track powers familiar from many sciences might (for all we know) be derivable from collections or conjunctions of fundamental single-­track powers.17 Still, if a powers theorist wants to insist that fundamental powers can be multi-­track, the constraint can be dropped. (For simplicity, we will proceed with the constraint.18 As we will see, it will turn out that several of the ways to generate mereologically complex powers leads to them having multiple manifestations.) One can introduce the Trigger version of the Manifestation Constraint, which claims that every power has a trigger. (NB: the asterisk following a constraint indicates that the constraint is not ultimately imposed by our preferred framework.) Triggering*: Each vertex must be the source for at least one arc in At; for all v ∈ V, the t-­out-­degree of v is non-­zero.

Carving Up the Network of Powers  17 This constraint rules out any fundamental powers with spontaneous or untriggered manifestations. Molnar (2003, 81–87) argues that a fundamental particle’s disposition to ‘decay’ into another particle is untriggered yet often manifested; similarly, he contends that gravitational mass is a spontaneous disposition which is manifested continuously. Indeed, the possibility of powers which lack triggers would seem to be the default view.19 Examples of untriggered powers from fundamental physics – perhaps the sciences generally – have a strong claim to being fundamental, and so we have good reason to drop this constraint. A quick side note: as with manifestation relations, we also do not impose the Reverse Trigger constraint, which would read: each vertex must be the target for at least one arc in At; for all v ∈ V, the t-­in-­degree of v is non-­ zero. That is, we are allowing powers which are not themselves the trigger for any other power in the world. I concur with Tugby (2013, sec. 7) that there’s no reason to rule them out. Actually, Bird (2007b, 532) imposes the stronger trigger constraint that each power has exactly one trigger. Single Triggering*: Each vertex must be the source for exactly one arc in At; in our notation: for all v ∈ V, the t-­out-­degree of v is one. This would rule out powers with multiple fundamental triggers, each of which is sufficient for a manifestation of that power. Now if we accept that fundamental powers are single-­track, then there cannot be more than one manifestation for any power. But why think that manifestation is always triggered under the same conditions? Couldn’t there be two distinct triggering circumstances, each of which is sufficient? I leave this for powers theorists to decide and so do not impose Bird’s Single Triggering Constraint. This leads us to the issue of ‘reciprocal powers’ and ‘mutual manifestation’. Martin (1993) points out that for some powers, they and their triggers should count as being triggers for one another. An example might be salt’s solubility in water and water’s ability to dissolve salt. The idea is that the interaction of the two powers jointly or mutually triggers the same manifestation. Now, it may well be that all powers are in reciprocal groups of triggers as Martin (1996) and Tugby (2010) contend. It is for this reason that Tugby (2013) expressly rejects the Single Triggering Constraint as it fails to accommodate reciprocal groups of triggers, all of which produce the same manifestation. Tugby also advocates for wider revisions to the framework by doing away with the arcs in At altogether. He writes, Asymmetric ‘stimulus’ relations must be eradicated, because on the view being proposed none of the dispositions in a reciprocal group are

18  A. J. Cotnoir privileged as being either that which is the stimulating factor, or as being that which is stimulated. All dispositions in the group are equally crucial for the manifestation. … Indeed, nothing at all like stimulus relations are needed in the modified graphs, since the arrangement of manifestation relations alone will indicate which properties are reciprocal partners: they will be the properties that are directed towards a common manifestation. (Tugby 2013, 30) Tugby advocates for dropping At and instead indicating mutual manifestation partners by connecting them with symmetric edges.20 While it’s true that dropping At is an elegant simplifying assumption, I think the reasons for abandoning triggers altogether are too quick. For one thing, one might wish to accept that while some powers involve reciprocity, not all do. For another thing, there is a distinction between distinct powers which each are sufficient to bring about the same manifestation (compare cases of causal overdetermination) versus distinct powers which act together and are only jointly sufficient to manifest the same thing (as in reciprocal pairs). Simply having two manifestation arcs directed towards a common vertex will not distinguish between these two cases. One would need some way of displaying graph-­theoretically which powers count as joint versus individual triggers for a given manifestation. There are several ways to achieve this.21 My preferred way to proceed is given in the next section. Labelled Transition Systems

A labelled transition system is a triple ⟨V, Am, T⟩ of sets, with Am ⊆ V × T × V.22 The elements of V are vertices as before. The set T is a set of labels representing the triggers of the given manifestation arc. The set Am now α contains triples ⟨v, α, w⟩ – which we write as v → w – representing the manifestation relation between a power and its manifestation under a specific trigger. We have dropped the distinction between m-­arcs and t-­arcs and are now operating only with labelled m-­arcs. For each vertex and label, we can count up the α-­labelled arcs as follows: α

→ • The α-­out-­neighbourhood of v is v= { w | v → w ∈ Am } (This is the set α

of manifestations of v triggered by α.)

• The α-­out-­degree of v is the cardinality of vα→. α • The α-­in-­neighbourhood of v is = vα← { w | w → v ∈ Am }. (This is the set of powers of which v is a manifestation triggered by α.)

• The α-­in-­degree of v is the cardinality of vα←.

Carving Up the Network of Powers  19 We can then define the general out-­neighbourhood (v→) and in-­neighbourhood (v←) by unioning together the α neighbourhoods for all labels α in T. The generic out-­and in-­degrees are defined as the corresponding cardinalities. As with directed graphs, labelled transition systems (LTSs) can meet additional constraints. I will impose the two unstarred constraints from before: Manifestation and Single-­Track. Two things follow from this. First, the Manifestation Constraint alone entails that the LTS contains a cycle. That’s because all acyclic digraphs have at least one vertex with an out-­ degree of 0 (Bang-­Jensen and Gutin 2007, 13). Second, we also have the following constraint. Deterministic: For every v ∈ V and each α ∈ T, v can be the source for α at most one arc v → w in for all v ∈ V, the α-­out-­degree of v less than or equal to one. α

LTSs that satisfy this constraint are called ‘deterministic’, securing that → is a partial function. This restricts LTSs to only those that represent scenarios in which no power can have more than one manifestation with the same trigger. This seems to me to be eminently plausible independently. But we are already committed to it, since it follows from the Single-­Track Constraint which, recall, states that the general out-­degree of any vertex at most one. It is instructive to consider a final constraint which will not impose. Executable*: For every v ∈ V and each α ∈ T, v must be the source for α at least one arc v → w in Am; for all v ∈ V, the α-­out-­degree of v non-­zero. LTSs which satisfy this constraint are called ‘executable’, and it would guarantee that every power is manifested at least once under every trigger. This is obviously far too strong. Given some power, only some conditions trigger manifestations, and some conditions do nothing. For a given v, if α there is a manifestation arc v → w, we will say that α is enabled for v, following standard terminology. Recall that the Manifestation Constraint is strictly weaker, saying that each power has some trigger or other which is enabled for it. Untriggered Powers

What about untriggered powers then? Since the LTS requires each arc to have a label, if every label represents a trigger, doesn’t this rule out untriggered powers? Well, yes. We can easily modify the system by allowing one label in T to represent the ‘empty trigger’, the state where nothing happens. By convention, we’ll use the label ‘∅’.

20  A. J. Cotnoir Reciprocal Powers

Reciprocal powers can easily be represented by arc labels if we permit the set of vertices to be among the labels. Two powers, v and w, which are v w each triggers for each other would correspond to arcs v → x and w → x. This can be made more complex besides. If T is allowed to contain subsets of V, powers which jointly trigger a given manifestation can be repre{v , w } sented: u → x. (An indeed, letting the full powerset of V be contained in T would bring in ∅ in any case.) It’s worth highlighting another point of flexibility of the LTS set-­up: we don’t have to take triggers to be powers. Some powers theorists (e.g. Williams 2019) take triggers not to be powers but rather object-­involving states of affairs. Neither Bird’s system nor Tugby’s system can accommodate this view, whereas mine can. My approach is new to the powers literature, but I think it has several virtues. First, it simplifies the graph-­theoretic element by including only one set of arcs and eliminating any need for colouring arcs to coordinate triggers and manifestations. Second, it is flexible enough to be able to represent Bird’s system and Tugby’s system without much modification, and it can also handle other approaches that they cannot. Third, LTSs are extremely important and familiar structures in the computing sciences, and as a result, there are lots of formal tools already developed in that discipline ready for application here. Identity Conditions

I’ve been skirting a large issue regarding the identity conditions of powers, an issue that has been the primary motivation for the graph-­theoretic approach. What if all properties are powers? What if there is, in the end, no such thing as a categorical property? What if it’s just powers ‘all the way down’? This view is called ‘pandispositionalism’ or ‘power monism’ and has been held by various theorists in different ways.23 There’s an open issue for power monism: how could powers be identified? What are their identity conditions? After all, there’s a vicious regress problem lurking in the shadows: if powers are identified by their (possible) triggers/manifestations, and those triggers/manifestations are just other powers, which are, in turn, identified by their triggers and manifestations, and so on, how do powers’ identity ever get off the ground (Lowe 2006)? A going solution is structuralism – the view that a power’s identity is entirely determined by its place in the network of triggers and manifestations. Structuralism views a power’s identity as a holistic matter, connected with its causal profile which essentially involves any other power it interacts with. It suggests that there is

Carving Up the Network of Powers  21 nothing more to a power’s identity than its dispositional profile. The graph-­theoretic approach was originally developed by Bird (2007b) as an attempt to solve this regress problem. If structuralism is going to serve as a solution to the regress problem, we need each power to be determined by its place in the network, so each vertex in V must be uniquely identifiable by its place in the structure. One way to ensure this is to stipulate that there there must be no way to permute the vertices in V while preserving the structure of arcs in Am.24 More specifically, we require there to be no non-­trivial automorphisms of the graph. An automorphism is a structure-­preserving bijection from the graph to itself, so f : V ↦ V such that

• surjective: for all y ∈ V there exists some x ∈ V with f(x) = y. • injective: f(x) = f(y) only if x = y • structure-­preserving: for all u, v ∈ V, if ⟨u, v⟩ ∈ Am then ⟨f(u), f(v)⟩ ∈ Am. The identity function mapping every vertex to itself is the trivial automorphism. Bird (2007b) suggests that requiring the following constraint on acceptable graphs would solve the regress problem. Asymmetry: No non-­trivial automorphisms on the graph exist. Some graphs are like this, and many others are not. Graphs with this property are (unhelpfully) called ‘asymmetric’.25 The Asymmetry Constraint approach is pretty strong; it severely limits the sorts of structures that can be models of the web of fundamental powers.26 What’s really going on is that every aspect of the structure of the graph is relevant to the identity of the nodes. A given vertex is identified by not merely which other power(s) it manifests (its m-­out-­neighbourhood) but also which power(s) it is the manifestation of (its m-­in-­neighbourhood), and, of course, all those sets’ member’s neighbourhoods, and so on. For what it’s worth, Bird eventually endorses a different constraint (involving downstream subgraphs) which restricts attention only to a given node’s m-­out-­neighbourhood, suggesting that it’s only really the manifestation of a given power that is essential to its identity. ‘What is essential to a power is what it does – not what brings it about’ Bird (2007b, 531). I expect different powers theorists will take different stances on this issue. I will not develop a structuralist approach to the identity of powers within the LTS approach, although I expect the philosophical issues to be similar. One potential difference is that the set T will either need to be given independent identity conditions (as it would if labels represent states of affairs rather than powers), or else T should be defined relative to the identity

22  A. J. Cotnoir conditions of powers (as it would be if labels include all and only the subsets of V). Anyway, I won’t discuss this further here. Despite its original structuralist motivations, in my view, the usefulness of the graph-­theoretic approach is separable from the vicious regress problem and the issues about property identity for power monism. The graph-­ theoretic approach, and indeed the slight modification to labelled transition systems, is a powerful tool for representing powers and their interconnections, and the role that triggers and manifestations play in connecting them.27 The LTS approach to modelling results in a picture of powers composing a vast highly interconnected network. Each point in the network is a simple power, characterised by its place in the network. Since powers are properties, we are naturally led to the idea that the network of powers constitutes a qualitative space, bringing powers theorists into contact with other property theorists who characterise properties as forming an abstract space of qualitative variation (e.g. Gärdenfors 2000; Cowling 2014; Cleani 2019). This standpoint invites the main question for the remainder of this chapter: How can we view complex powers as the result of carving up that space? Subcollections As I’ve mentioned, some single-­trackers (e.g. Bird 2007a, 21ff) suggest that we can treat any putative multi-­track power as a collection of single-­track powers. Williams (2019, 83) suggests the converse – that we can treat any collection of single-­track powers as a multi-­track power. The simplest idea for carving up the network of powers is the subcollection approach: complex powers are modelled by collections of simple powers, parts of powers can be modelled as subcollections. Subsets

Given an LTS ⟨V, Am, T⟩, we simply consider the power set ℘(V) without the empty set. Then the subset relation ⊆ on ℘(V) can be interpreted as the parthood relation for complex powers, and it is guaranteed to satisfy all the axioms of classical mereology. Using ‘P’ for the primitive parthood predicate, we define as follows: Proper Parthood PPxy :≡ Pxy ∧ x ≠ y Overlap Oxy :≡ ∃z ( Pzx ∧ Pzy ) Fusion Fϕ x :≡ ∀z (ϕ → Pzx ) ∧ ∀y ( ∀z (ϕ → Pzy ) → Pxy ) The first is a standard definition to the effect that a proper part is any part distinct from the whole. The second states that things overlap whenever they have at least one part in common. As for the third, it defines the fusion

Carving Up the Network of Powers  23 of the φs as the least upper bound relative to P of the objects satisfying φ, corresponding to the familiar lattice-­theoretic notion of supremum.28 The first conjunct states that x is an upper bound of the φs, while the second states any (other) upper bound includes x as a part. Now for the axioms. A1

∀xPxx

Reflexivity

A2

∀x∀y((Pxy ∧ Pyx) → x = y)

Antisymmetry

A3

∀x∀y ∀z((Pxy ∧ Pyz) → Pxz)

Transitivity

A4

∃zφ → ∃ xFφx

Unrestricted Fusion

A5

∀x∀y(¬ Pxy → ∃ z∀w(Pwz ↔ (Pwx ∧ ¬ Owy)))

Remainder

A1–A5 axiomatise classical mereology.29 The first three axioms, A1, A2, and A3, state that P is a partial order. The next axiom, A4, is actually an axiom schema. It states that, for any satisfiable open formula φ with just z free, a fusion of the φs exists. The last axiom, A5, states that whenever x is not itself part of y, there is always something – a remainder of y in x – that has as parts all and only those parts of x that don’t overlap y. That the set of non-­empty subsets satisfy A1–A5 is due to a fact noted by Tarski (1929): every model of atomistic classical mereology is isomorphic to a powerset of its atoms.30 On this view, complex powers are just regions of qualitative space, arbitrary portions of the network.31 Okay, you might think, but what about the manifestation relation? How does that work for complex powers? And if it doesn’t work, then can we realistically call subcollections powers at all? These are good questions. One might attempt to attempt to recover the manifestations of a given collection of powers in the following way. Subgraphs

We treat set of powers like {u, v} as analogous to a conjunctive property. What are the manifestations of a conjunctive power under a given trigger? Presumably, each of the conjuncts’ manifestations for that trigger (if any). An object that has both powers u and v will elicit the manifestations of u in u’s triggering circumstances and the manifestations of v in v’s triggering circumstances. Formally, let V′ be a non-­ empty subset of V. And let A′m be t {x → z ∈ Am | x ∈ V ′} which is the set of all arcs stemming from members with any label t (and T′ is the set of all labels present in A′m). Then ⟨V′, A′m, T′⟩ is called an induced subgraph of ⟨V, Am, T⟩.32 Then the set of manifestations of V′ under a given trigger – the α-­out-­neighbourhood of V′ – is α → V′= { z | x → z ∈ A′m } . α

24  A. J. Cotnoir On this way of representing powers, a conjunctive power manifests the manifestation of one of its conjuncts only under the relevant trigger. But there might be many different triggers for the conjunctive power, so it will be (unsurprisingly) multi-­track. Some conjunctive powers will be particularly natural, namely those modelled by collections V′ such that all members of v are enabled under exactly the same trigger α. In this case, V ′α→ will be the entire collection of manifestations under any trigger. So all arcs will point to the very same collection – this complex power will be, in effect, single track.33 Other conjunctive powers may be less natural. So far, so good. But the proposal is not ideal in a couple of ways.

Disjunctive Powers?

One issue is that we cannot define the general out-­neighbourhood of V′ (under any trigger) as the union:  α ∈T V ′α→. This outputs a big collection composed of all the manifestations of any power in V′ under any trigger. Remember, we are reading collections of powers as conjunctive, and so this big collection would be highly conjunctive property! We want that V′ has F among its manifestations and G among its manifestations, not that it has F ∧ G as one of its manifestations. Clearly, this is the wrong result. In order to define the general out-­neighbourhood, what we would need is a way of representing what the manifestations of a complex power would be under a highly disjunctive trigger (namely, the disjunction of all triggers!). And we don’t have an easy way of representing that. Even if we grant that conjunctive powers make sense (and behave in the ways described), what would disjunctive powers even be, and what would they have as their manifestations? Answers to these questions are not obviously forthcoming.

Mereology

The mereology of induced subgraphs is exactly as before. By defining parthood as subsethood, the induced subgraphs are ordered by the ⊆-relation here as well. So parthood for complex powers satisfies A1–A5. While subcollections have a very nicely behaved mereology, the approach is too simplistic. It doesn’t tell us what the manifestations of a complex power are. Subgraphs are a little more complex, and their mereology still standard, but they face some limitations as well. The bigger issue with either approach is arbitrariness: complex powers might be completely disparate, gerrymandered, and explanatorily pointless. It’s hard to see how these should be considered powers at all. Recall what Lewis (1983) said,

Carving Up the Network of Powers  25 Because properties are so abundant, they are undiscriminating. … Almost all properties are causally irrelevant, and there is nothing to make the relevant ones stand out from the crowd. Properties carve reality at the joints – and everywhere else as well. If it’s distinctions we want, too much structure is no better than none. (p. 346) For arbitrary subcollections, it would seem better to follow Molnar (2003), who takes collections of powers to be properties, only some of which are complex powers. But which ones are those? According to the carving picture, the most unified regions of the network. Before modelling this idea with the clustering approach, I want to take a quick detour through the notion of a substructure of a graph before picking up our main thread. Substructures

Mormann (2009, 2010, 2012) has put forward some very general and abstract methods for constructing mereologies based on category-­theoretic ideas. I won’t attempt to explain the entire programme here, but his formal approach can be adopted for graph-­theoretic purposes.34 When discussing identity conditions, we looked at automorphisms on a graph. Here we need a related idea of homomorphisms. A homomorphism from graph ⟨V, A⟩ to a graph ⟨W, B⟩ is a function f : V ↦ W that preserves arcs:

• structure-­preserving: ⟨x, y⟩ ∈ A entails ⟨f(x), f(y)⟩ ∈ B. Note, neither V and W nor A and B need be related in any other way. A monomorphism is an injective homomorphism.

• injective: f(x) = f(y) only if x = y Despite f mapping one graph into a different graph, there’s a sense in which a monomorphism gives us a substructure of a graph. The idea is that first graph has the same structure as the image of f in the second graph. The monomorphism identifies the relevant structural connections regardless of the underlying vertex set.35 Substructures are identified up to isomorphism, meaning that two equivalent monomorphisms define the same substructure. Using mereological vocabulary rather loosely, we can treat a part of a graph as represented by an equivalence class of monomorphisms.36 Mereology?

According to Mormann (2009, 338), under mild conditions, this relation of parthood is a partial order (satisfying our A1–A3) and under stronger

26  A. J. Cotnoir conditions it is a lattice (satisfying our A4).37 The upshot would seem to be that there’s a systematic way of treating substructures of a graph as parts, and they have a somewhat standard mereological structure. Indeed, a class of models that satisfy A1–A4 but not A5 is called a quasi-­mereology.38 But there are a few oddities about the substructure approach. Parts Twice Over?

Recall that substructures are identified up to isomorphism. This means that if a graph has two disparate parts which are isomorphic to one another, they are treated as the same part of the graph – the graph, in effect, has a single structural part twice over. In the case of powers, this can seem implausible. How could it be that simply because two parts of the network of powers, comprising very different simple powers, have the same overall pattern of manifestation relations, they are identical? Doesn’t this take structuralism too far? This raises an important question about which identity conditions on powers should apply to complex parts of the network. Should power structuralists extend their approach for individuating simple powers? Are complex powers structurally determined too? Or rather, is it that simple powers alone are identified by their place in the network, and then complex powers are ‘built up’ from the simple powers and their interrelations? Disconnected Wholes

This approach doesn’t solve the arbitrariness problems we encountered with the subset and subgraph approaches. We can find substructures where structural connections are thin. For example, we could choose a structure ⟨V, ∅ ⟩ where V has only three members. If f is a map to some other graph ⟨W, B⟩, it will be a monomorphism so long as f outputs three distinct members of W with no arcs between them in B. And worse, every three disconnected members of W will count as the same structural part of the graph! Generally, we can have substructures composed of many simple powers with no arcs between them, which appears to (wrongly) treat completely disconnected powers as unified wholes. Even if we restrict our complex powers to those substructures ⟨V′, A′⟩, where A′ is non-­empty, this still might be thought to be far too permissive. To sum up, Mormann’s (2009, 2010, 2012) approach finds a way of carving up the network into its substructures and, if he is right, delivers a fairly well-­behaved mereology. The approach adopts an extreme structuralist stance towards the identity conditions of those parts, however. Moreover, the approach is still too permissive in what it considers a part of the whole. It’s not obvious that arbitrary structuralist parts correspond to

Carving Up the Network of Powers  27 complex powers in a deep way. Perhaps a better approach is to look for real unities within parts of the network of powers. Clustering

Turning back to our main thread: Where can real unities be found in the network? Since the network of fundamental powers is highly interconnected by the manifestation relation, typically some of these powers are going to be found clustered together. What explains this clustering? One natural answer suggested by Williams (2019, 83): they are parts of the same power.39 The present idea is to find a way to carve up the network accordingly. We start with the notion of a partition, which we will use throughout the remainder of this chapter. A partition on a set V is a set of blocks V1, …, Vn s.t. (i) every member of V is in some block, that is, ⋃Vi = V, and (ii) the blocks are pairwise disjoint, that is, Vi ∩ Vj = ∅, for i ≠ j. A few further facts about partitions. Every equivalence relation ∼ gives rise to a partition by collecting together all the ∼-equivalent elements. Blocks are closed in the sense that, every member of block is ∼-equivalent to every other member of that block, and nothing outside the block is ∼-equivalent to anything inside it. Blocks are also maximal: no proper subset of a block is itself a block in the same partition. Let Π be the set of all partitions of the network ⟨V, Am, T⟩ – all possible ways of carving it up into blocks. We need a way to measure the naturalness of each of these partitions. For some partition π ∈ Π, let δ(π) be the set α of all arcs u → v ∈ Am such that u and v are in different blocks of π. These are the arcs that π ‘cuts across’. The unnaturalness of a given partition is the ratio between the cardinality of arcs cut across by the partition and the total number of arcs:

υ (π ) =

δ (π ) Am

The measure υ will output some fraction between 0 and 1. If your main concern is to identify the clusters of a graph, then a partition that cuts across fewer connections will, on the whole, be a better way to subdivide (relative to the number arcs total). Lower numbers are better – this is why the υ function measures the unnaturalness of a partition. (The function η(π) = 1 − υ(π) can be used to measure naturalness.) So, which partitions are good enough to warrant accepting the blocks as new complex powers? Consider the following carving policies.40 Min: Always accept partitions π with υ(π) = 0.

28  A. J. Cotnoir Decreasing: If you accept some partition π with υ(π) = x, then accept every partition π′ with υ(π) = y such that y ≤ x. Max: Never accept partitions π with υ(π) = 1. The first policy says you should make perfectly natural cuts, those guaranteed to cut across completely disconnected powers. There is of course always the trivial partition guaranteed to have the value 0: the coarsest-­ grained partition which doesn’t make any cuts at all but treats all vertices as a single block ⊤ = {V}. It follows that treating the entire network as a whole is always acceptable. Non-­trivial partitions with value 0 need not always exist; they won’t if the digraph is (weakly) connected, in the sense that for every pair of vertices x and y, either x is reachable from y or y is reachable from x.41 A slightly stronger policy would be to force us accept the minimum-­valued partition(s) which are guaranteed to exist. Min*: Always accept a partition π with = υ (π ) min{υ (π ′ ) | for all π ′ ≠}. This approach would force some split of the network along its weakest points of connection. The second policy doesn’t tell you which cuts you should make; rather it says that you shouldn’t make highly unified cuts if you are unwilling to make less-­unified cuts. The policy as written also requires you to make all cuts of a given naturalness value provided you are willing to make any cuts of that value.42 The third policy says not to make perfectly unnatural cuts, which would separate powers which are connected to the highest degree. The ‘highest degree’ in this case is equal to the total number of arcs. There’s always one partition guaranteed to have the highest degree: the finest-­ grained partition which carves the network up into singletons of vertices = ⊥ {{v} | for all v ∈ V }. Other partitions with unnaturalness value 1 will include any partition which only groups together vertices with no arcs between them. In formal terms, we say a block Vi is an independent set t whenever for any u and v in Vi and any t ∈ T, u → v does not exist. If all Vi ∈ π are independent, then δ(π) = Am and so υ(π) = 1.43 Mereology

Now we know how to assign values to partitions based on how separable or ‘disunified’ the entities are that we are cutting across. Our policies are somewhat weak, and so they do not completely determine which partitions we accept; they are compatible with a number of further constraints on how to carve the network. What the mereological structure will look like

Carving Up the Network of Powers  29 will be somewhat dependent on these decisions for carving, based on which partitions we accept. The basic mereological notion (parthood) will be as in the subsethood method but now relativised to acceptable partitions. Let X and Y be subsets of V. c-­Parthood: X is a c-­part of Y iff there are acceptable partitions π and π′ such that X ∈ π and Y ∈ π′ and X ⊆ Y. To see how this works, for example, you might choose to adopt a strategy to only to make value 0 cuts. (Or there might be no admissible cuts with value x such that 0 < x < 1, so we are only permitted to make the value-­0 set of cuts.) This would generate the set of partitions corresponding to υ=0 blocks and be a coarse-­grained way of carving the network. These partitions will include ⊤ which treats the web as one giant megapower and all partitions that separate the network into its disconnected components (as only perfectly separable powers may be separated). Indeed, if C is the set of disconnected components of the network, then the set of all blocks in any υ=0 partition will be the powerset of C. This means, we have a model of the axioms of classical mereology A1–A5 with the components serving as the base level of complex powers. But if, as seems likely, you want to adopt multiple admissible partitions with differing υ values, we end up with a multilayered model where the partitions are ordered by fineness of grain.44 It follows that when π is finer than π′ every block in π is the subset of some block in π′, and every block in π′ contains the union of some set of blocks from π. Now, this means that C-­parthood is a partial order on the set of all blocks of all admissible partitions satisfying A1–A3. Moreover, given that ⊤ is an acceptable partition always, we will be guaranteed that every collection of blocks with have an upper bound, satisfying the first conjunct of A4. But there is no guarantee that it will have a least upper bound, which is needed to satisfy the second conjunct of A4. Rather, this is a view according to which the complex powers satisfy restricted composition. Perhaps this is unsurprising since generally unrestricted composition leads to gerrymandered or disunified wholes, while we are attempting to avoid them.45 Weights

I now want to raise another choice point. The clustering approach outlined above treats all arcs as if they were equally important to carving. Cutting across any of them counts equally toward the unnaturalness value of a partition. But is that right? Are some fundamental connections between

30  A. J. Cotnoir powers more weighty than others? Here is one reason for thinking that they may be: some powers theorists deny that dispositions necessitate their manifestations.46 If not, then we need to assume that each fundamental power is connected up to another to a greater or lesser degree;47 in our system, this would mean that each manifestation link in Am comes with a weight. The network can now be modelled as a weighted digraph; indeed, we can use complete digraphs – in which every pair of distinct vertices is connected by a pair of unique edges, one in each direction – and treat previous no-­arc cases as arcs of degree 0. Given that fundamental powers are separable to specific degrees, we will want to assign a value to a specific partition based on the degrees of separability it cuts across; our old measure δ will no longer do. There are several options to explore along these lines, but I will leave that for another time.48 Losing Connections

Finally, I raise a philosophical consideration about the clustering approach. While the clustering view makes good sense for dividing up the network of powers into their most tightly clustered regions, ultimately the end result of the approach is to render the most complex powers relatively powerless.49 After all, a power’s being powerful is tied up with the fact that it can bring about manifestations (and perhaps even more so if it can manifest in many different triggering circumstances). By carving up the world according to more interconnected clusters, we are cutting across fewer arcs, leaving the blocks of powers with fewer connections to other blocks. By grouping powers together in this way, we create more independent clusters (not more powerful ones). In the most natural case – the coarsest partitions, we will be cutting across exactly 0 arcs – resulting in complex powers with no manifestations whatsoever (at least no complex manifestations in the same partition). Looking across partitions, we will find that even the fairly coarse-­grained powers can have manifestations existing as wholes in other partitions. In the typical case, they will count as C-­parts of the bigger power. I’m not entirely convinced this is a bad result. But it does give some reason to reconsider Williams’s (2019) suggestion that clustering is a mark of power-­composition. Coordinating The results of the last section ended with an observation that coarse-­ graining along clusters in the network yields less and less powerful powers. There are other approaches to measuring the naturalness of a partition. The core idea explored in our final section is the idea that grouping powers  together should coordinate manifestation links. To see what I mean,

Carving Up the Network of Powers  31 consider the following analogy: consider a chain of causally connected microphysical events. Now suppose I want to know how to partition this chain in order to get more complex causes and more complex effects? If the policy is ‘don’t cut across causal connections!’ the result will be simply longer and longer temporal events. To get complex causes and complex effects without skipping out causal steps, we want to make sure we cut things up in such a way that we group causes and effects such that casual connections are coordinated between them. The idea now is to do a similar thing with the network of powers. Preliminaries

I begin with two simplified examples using simple (unordered) graphs. Among other things, these graphs have (undirected) edges rather than directional arcs.50 For the first example, we use the method of quotienting. Let ⟨V, A⟩ be a graph and let π = {V1, …, Vk} be a partition of the vertex set V into non-­empty sets. The quotient of ⟨V, A⟩ by π is the graph whose vertices are the sets V/π = {V1, …, Vk} and whose arcs are the pairs ⟨Vi, Vj⟩ with i ≠ j such there is some vi ∈ Vi and some vj ∈ Vj where ⟨vi, vj⟩ ∈ A.51 Then the natural map pπ:V↦V/π defined by pπ(v) = Vi when v ∈ Vi, just maps each vertex to its corresponding block of the partition. (Hahn and Tardif 1997, 111) prove the following result. Natural Homomorphism: pπ is a homomorphism iff each Vi ∈ π is an independent set. (Recall that an independent set has no arcs between its members.) This result tells us that partitioning a graph’s vertices into independent sets gives rise to another coarser-­grained graph made up of the blocks of the partition and the arcs they inherit from their members. That graph preserves all the structure of the original graph exactly because the blocks group together disconnected vertices. This result probably isn’t much of a surprise; however, it does display the core idea of perfect coordination. Another similar result from Leach and Walsh (2007) displays the same point. We say a graph is multipartite iff V can be partitioned π = {V1, …, Vk} into independent sets. A multipartite graph is complete iff every pair of vertices from distinct blocks have an edge between them. In short no edges within a block; all possible edges across blocks. Leach and Walsh (2007, thm. 6) show that every complete multipartite graph is such that the set of all induced subgraphs forms a lattice. The upshot here is that, in the special case where perfect coordination is achieved – the graph is split into independent sets, all edges bridging between the sets exist – then the induced subgraphs have a natural mereological structure satisfying A1–A4.

32  A. J. Cotnoir These examples are instructive in that they suggest grouping relatively independent powers in a way that coordinates blocks yields more powerful complex powers. Now let’s turn again to LTSs and note an important caveat: some pairs of powers are mutual manifestation partners. This means there are arrows in both directions between them. (And more generally, larger reciprocal groups will be such that all their pairs have bidirectional arrows between them.) A natural philosophical suggestion is to group these powers together as joint powers all having the same manifestations. Weak and Strong Components

Following Knuth (2022, 4:11), I’ll write x ⇔ y to mean that x is reachable from y and y is reachable from x; the corresponding powers are manifestations of each other after some number of steps. I also write x ∥ y to mean that x is not reachable from y, nor is y reachable from x; not only is neither a manifestation of the other, but also neither is the manifestation of the other after any number of steps. Next, x ≈ y means that either x ⇔ y or x ∥ y; this rules out any one-­way manifestation links after any number of steps. Now we take the transitive closure of ≈, writing x ≍ y to mean that x and y are linked by an ≈-chain after some number of steps. Then, for any LTS ⟨V, Am, T⟩, ≍ is obviously an equivalence relation. This equivalence relation introduces a partition π≍ on V into its so-­called weak components {V1, …, Vk}.52 The important result for our purposes is the following coordination property53: Coordination: If Vi and Vj are distinct weak components of ⟨V, Am, T⟩, then either every x ∈ Vi is reachable from every y ∈ Vj or vice versa. This result shows that the weak components of a digraph are perfectly coordinated into blocks such that every member of a block is ≍-equivalent to every other member and that all arrows between blocks are asymmetrically coordinated by reachability. This is arguably a very natural partition, one that carves up the network in a coordinated way. But it’s only one way of dividing up the whole network, and there’s really not much interesting or complex about a three-­level mereology (whole network, weak components, simple powers) like this. We can make things slightly more interesting by considering that the mutual reachability relation ⇔ itself is an equivalence relation that gives a partition π⇔ of any LTS ⟨V, Am, T⟩ into its strong components.54 Every weak component of a digraph is a union of some of its (mutually unreachable) strong components. So, π⇔ is a finer partition than π≍.

Carving Up the Network of Powers  33 Mereology

This leaves us with a four-­layered mereology: (i) ⊤, (ii) π⇔, (iii) π≍ and (iv) and the simple powers.55 Each of these layers is a finer partition than the previous. The C-­parthood relation satisfies A1–A3. It also has the same restricted composition behaviour from the clustering approach. We do not have A5, but we can have another important decomposition principle which gives voice to a common ‘remainder’-like thought: if something has a proper part, then it ought to have another disjoint from the first. A6

∀x∀y(PPxy → ∃ z(Pzy ∧ ¬ Owx))

Weak Supplementation

A6 is perhaps the most common axiom in non-­classical mereological theories, and it is validated in the current models.56 So the mereology here has a parthood relation that is a partial order, weakly supplemented, with restricted composition. Bisimulation

I end this section with a final approach to the coordination of powers which borrows an idea that has seen widespread use in the computing sciences, modal logic, non-­ well-­ founded set theory. A binary relation R ⊆ V × V on a LTS ⟨V, Am, T⟩ is a strong bisimulation iff for all v, w ∈ V such that vRw, it follows that for all α ∈ T: α

α

1. v → v′ then there’s some w′ ∈ V such that w → w′ and v′Rw′ α α 2. w → w′ then there’s some v′ ∈ V such that v → v′ and v′Rw′ The idea here is that a bisumulation has two conditions required for two vertices v and w to be related. First, we require that for each manifestation of v in triggering circumstances α there’s a corresponding manifestation of w triggered in the same circumstances, and both of these manifestations are themselves related by R. This means that R simulates what is happening with the vs. The second condition is the same except it secures that R simulates what is happening with the ws. There is coordination between the arcs in both directions. Now, there may be many different bisimulations on the same graph, but there is always a biggest one. It’s defined as follows. Say that two vertices are bisimilar v ∼ w iff there is some bisimulation R on ⟨V, Am, T⟩ and vRw. It turns out that bisimilarity ∼ is itself a bisumulation relation, and indeed, it is the largest bisimulation relation on ⟨V, Am, T⟩ in the sense that it is the union of all bisimulations on ⟨V, Am, T⟩. More importantly, ∼ is reflexive,

34  A. J. Cotnoir symmetric, and transitive – an equivalence relation – and can be used to define a partition π∼ on V such that it groups all bisimilar vertices together. The philosophical idea behind this partition is to group together powers which involve the same patterns of manifestation in the same triggering circumstances. A complex power groups together fundamental powers and manifestations in such a way that the arrows are always synced up in the different blocks. It also means that the fundamental components of a complex power are all triggered in exactly the same circumstances; they are enabled for exactly the same triggers. In fact, this correlation is so strong, that it has led researchers in non-­ well-­founded set theory to impose a structuralist constraint on the identity of non-­well-­founded sets: bisimilarity is identity.57 I will not take powers that ∼-equivalent to be identical, as I don’t have any structuralist aims. I merely point to this relation, and its corresponding partition, as an important way of carving up the network in a highly coordinated fashion. Moving Forward I have tried to show how the carving approach to complex powers can be theoretically fruitful. I’ve given a number of options potentially of value to different researchers with differing philosophical commitments. The analysis I’ve given also reveals a deep distinction between the clustering and coordination approaches. There are philosophical questions to answer here: does the clustering vs coordinating distinction correspond to the static versus dynamic distinction? It would appear that arrows representing static connections motivate clustering, whereas arrows representing dynamic connections motivate coordinating.58 If powers themselves come in both sorts (Williams 2005; Nolan 2015), then perhaps we need both methods. To conclude, I want to gesture at my preferred views here. My sympathies lie with an underlying abundant ontology of properties, accepting all subregions of the network, which has the benefit of completely standard mereology. But this cannot be the entire story. We need a theory of sparse properties which underly causal roles and powerful qualities that play fundamental roles in characterising the world; in short, we want to identify natural parts of the network. But, in my view, this is a mutlifaceted phenomenon with complicated and competing considerations. What makes for real unities? Is it structural? Should we privilege interconnectedness? Should we try to coordinate the causal profiles in patterned ways? I have tried to show in the chapter that there are many choices along the way. Moreover, it’s important to recognise that the measures of naturalness I have often proposed are a matter of degree. Now this could be a problem without the background abundant ontology – the existence of a complex

Carving Up the Network of Powers  35 power can’t be a matter of degree. Maybe there’s isn’t just one way of carving up the world into its most natural portions of reality. Perhaps better to accept many kinds of unity, each tracking a different real phenomenon.59 Notes 1 See, for example, Jacobs (2017), Anjum and Mumford (2018), Marmodoro (2010), McKitrick (2018), Vetter (2015), and Williams (2019). 2 See Tahko (2018) for discussion. 3 Nor have I defended any particular view on Humeanism, although I’m inclined towards rejection. 4 The tools I use in this chapter are not available to carvers alone. I’ll generally assume (with others in the literature) that the network is characterised by fundamental powers, a building-­friendly assumption which permits them to take advantage of these tools as well. This is an assumption that carvers may wish to jettison. Along the way, I footnote how one might attempt modifications to accommodate. 5 Most commonly, the partial order axioms and Weak Supplementation have been put forward in this spirit (Simons 1987, 26, 116). 6 See, for example, the dispute over Weak Supplementation (Cotnoir 2019). 7 This goes back at least to Mumford (1999). 8 Bird himself follows a more general treatment of structure in Dipert (1997). See also Shackel (2011) for discussion. 9 Compare the fundamental qua minimal supervenience/grounding base for everything else vs. the fundamental as the underlying all objective similarities and differences. See Schaffer (2004) for discussion. Giannotti (2021) argues that powers theorists need their own unique conception of fundamentality. 10 Can mereologically simple powers be derivative in some other sense? According to the carving picture, at least, yes. For example, it might be the case that, say, a particle’s decay in highly specific circumstances α and a particle’s decay in other specific circumstances β are both determinates of the same determinable power. We might be convinced by Wilson (2012) that determinable powers are sometimes more fundamental than their determinates, although it would still be plausible to think determinates rather than determinables are the mereologically simple powers. Thanks to Alexander Roberts for raising the issue. 11 If one thinks that the trigger/power distinction plays no role (Vetter 2015) or that the distinction between triggers and powers is merely pragmatic (Mumford and Anjum 2011), then we can just do away with At. 12 Whether these different coloured edges are required depends crucially on whether each node has exactly one manifestation arc and triggering arcs incident from it; that is, it depends on the Single-­Track and Strong Triggering Constraints that follow. Since we will ultimately reject the Strong Triggering constraint, our system finds a different solution to association by using labels. 13 For a discussion, see Jenkins and Nolan (2012). For arguments against, see Vetter (2015, 257) and more discussion in Vetter (2016). 14 As do McKitrick (2003, 158) and Vetter (2015, ch. 1). 15 The distinction goes back to Ryle (1949, 43–45). 16 See, for example, Williams (2011) for discussion and references therein.

36  A. J. Cotnoir 17 For example, Williams (2011, fn. 10) writes, “Single-­tracker[s] … argue that we can treat any putative multi-­track power as a collection of single-­track powers. This is a point I gladly concede; it adds support to the claim that we are dealing with a decision not a discovery.” McKitrick (2018, 8) suggests that whether a disposition is single-­track or multi-­track might be relative to levels of generality. 18 One might rather drop the building-­friendly supposition that the network consists of simple powers, and simply allow digraphs which violate the Single-­ Track Constraint. One could then ‘carve up’ the multi-­track nodes into distinct single-­track nodes each with one of the manifestations of the original multitrack power. (It’s an interesting question how one should divide up the triggers.) This would result in a new, more complex graph. 19 Heil (2003, 198) also accepts them. Williams (2019, 51, 63) accepts triggerless powers for the same reasons as Molnar: he gives the decay of radium atoms and the gravitational force as examples. Manley and Wasserman (2008, 72f) contend that triggerless dispositional properties are perfectly plausible, although all their examples are non-­fundamental. See also Tugby (2013, sec. 6) and Hauska (2015) for a detailed discussion. 20 These symmetric edges aren’t actually part of his digraphs; they are merely ‘clarity enhancing features’ (Tugby 2013, 30). 21 One way of doing this would be to use a hypergraph which permits an edge to join any number of vertices. Another way that keeps Bird’s system using both Am and At is as follows: where u and v are reciprocal partners for a given manifestation w, we introduce symmetric pairwise arcs ⟨u, v⟩ and ⟨v, u⟩ into At, and we also ensure that ⟨u, w⟩ ∈ Am and ⟨v, w⟩ ∈ Am as well. (And similarly for groups of reciprocal partners larger than 2.) Where u and v are individually sufficient triggers for a power x to produce the same manifestation w, we represent them in the usual way, using asymmetric arcs ⟨x, u⟩ in At and ⟨x, v⟩ in At and ⟨x, w⟩ in Am. 22 Labelled Transition Systems were introduced in Keller (1976). This presentation is indebted to Groote and Mousavi (2014, ch. 2). 23 For example, Shoemaker (1980), Mumford (2004), Bird (2007b), and Tugby (2010). 24 This is the core suggestion of Dipert (1997) adopted by Bird (2007b). I’m ignoring the role of At in Bird’s system for simplicity. 25 Tugby (2013, 28) calls it the ‘Identity Constraint’. 26 Bird (2007b) and Tugby (2013) give some counter-­intuitive cases. 27 The usefulness point is noted by Tugby (2013, fn 2): “Property graphs could also serve a useful purpose for those who, while accepting that all properties have an irreducibly dispositional nature, deny that properties are purely dispositional.” He lists so-­called two-­sided theorists like Heil (2003) and Martin (2007) as potential beneficiaries, but I think the approach could be adopted widely. 28 See Cotnoir and Varzi (2021, ch. 5) for differences between rival definitions of sum and fusion. 29 This axiom set was identified by Cotnoir and Varzi (2019), who prove it equivalent to other known axiomatisations. 30 For a proof, see Cotnoir and Varzi (2021, ch. 2). 31 Compare the view of propositions as subsets of modal space. 32 Induced subgraphs contain all arcs from Am stemming members of V′. Note that this is not the same thing as a subgraph: ⟨V′, A′⟩ is a subgraph iff V′ ⊆ V and A′ ⊆ A. For example, it is compatible with the definition that a subgraph

Carving Up the Network of Powers  37 include all vertices from V but merely drops out some arcs. This is not the notion we want – we want to ensure that all the arcs present in Am between vertices in V′ are themselves in A′. 33 Strictly speaking, there will be multiple arcs with the same label stemming from V′ to V ′α→ , so it will not meet the Single-­Track constraint as defined, which wasn’t intended for complex powers like this. But any appropriate way of defining single-­versus multi-­tracking for complex powers will surely treat a case like this as single-­track. 34 Digraphs and their morphisms form a category. I leave labels behind for this approach. As we will see, the substructure approach is most well-­suited to hardcore structuralists about powers, exactly the folks who might be worried about independent identity conditions for triggers. 35 This is not the same idea as a subgraph (induced or otherwise). A homomorphism is called faithful if the homomorphic image of ⟨V, A⟩ in ⟨W, B⟩ is an induced subgraph of ⟨W, B⟩ (Hahn and Tardif 1997, 109). 36 Then the parthood relation is defined generally when there is a monomorphism between parts of the graph. See Mormann (2009, 332, 338) for details. 37 Mormann cites Lawvere and Rosebrugh (2003), but I can’t track down the relevant results, except for some exercises on p. 45ff. See also the same claims in Mormann (2010, 222). 38 See, for example, Sharvy (1980, 1983). 39 Compare the theory that treats natural kinds as a ‘homeostatic property clusters’; for a recent version of this view, see Slater (2015). 40 I am indebted to Caroline Touborg (2014), who first suggested these policies in her excellent talk, which started me thinking along these lines many years ago. 41 Reachability corresponds to the intuitive notion: x is reachable from y when α β γ ζ there’s a walk — a series of arcs x → v1 → v2 → v3 …vn → y — from x to y. 42 This latter constraint can be weakened by changing the ≤ for a t). A resultant state of an event is simply a state of the event having taken place. If Mary crosses the street, there is a state that obtains as a result: a state of Mary having crossed the street. So, an event in progress of Mary crossing the street is an event disposed to bring about a state of Mary having crossed the street. If such a state is brought about, then we have a manifestation of the disposition of the event. A simpler way of putting the proposal would be to say a ϕ event is progress is one disposed to become a ϕ event. So, an event in progress of Mary crossing the street is an event disposed to become one in which she crosses the street. I’m fine with this way of putting it. However, we need to be careful. To see why (and build to another argument for determinable dispositions), we need to say some words about the distinction between telic and atelic event types. A standard diagnostic for whether an event type is telic or atelic is the progressive-­to-­perfective test. Take a past progressive. If it entails its past-­ perfective correlate (assuming that the progressive is describing a sufficiently extended event in progress), then the uninflected verb phrase that combines with the progressive denotes an atelic event type. Otherwise, the event type denoted is telic. So, for example, ‘Zoltan was walking’ entails ‘Zoltan walked,’ so the uninflected verb phrase (‘Zoltan walk’) denotes the atelic event–type zoltan walk. However, ‘Mary was crossing the street’ doesn’t entail ‘Mary crossed the street’. So, its uninflected verb phrase denotes the telic event–type mary cross the street. One important difference between telic and atelic event types is exhaustibility. Suppose θ is a telic event type. Then any θ event in progress is exhausted if it becomes θ event. That is, the culmination of such an event in progress marks the limit or temporal bound of the event in progress. What it is to be such an event in progress requires the event to stop upon

Determinable Dispositions  105 culmination. However, this is not true for atelic event types. Suppose α is an atelic event type. Then no α event in progress is exhausted by it becoming an α event. A walk in progress can go on past t even if it is already composed of walk events at t.5 This leads to another difference between telic and atelic event types. Atelic event types are homogeneous in the following way. Suppose e is a sufficiently extended α event. Then, e is composed of smaller α events. For example, any sufficiently extended zoltan walk event is composed of smaller Zoltan walk events. This is not the case for telic event types. A mary cross the street event is not composed of smaller mary cross the street events. When she gets to the other side, the event is over or, as we put it earlier, exhausted. Now for why care is required for understanding the previous dispositional account of events in progress as saying that a ϕ event in progress is one disposed to become a ϕ event. Take a sufficiently extended α event in progress. For example, take a sufficiently extended atelic event in progress of Zoltan walking. The preceding proposal tells us that such an event is disposed to become a zoltan walk event. But that seems odd. After all, any sufficiently extended event in progress of Zoltan walking is already composed of a number of smaller zoltan walk events. So how can it be disposed to become one if it is composed of a bunch of them? Resultant states get around this issue. Each of the smaller zoltan walk events that are part of the event in progress of Zoltan walking has a corresponding resultant state. For example, suppose the event in progress starts when Zoltan is at point A and ends when he is at point C. Then there is, among many others, a zoltan walk event that begins at point A and stops at point B and another one that begins at point A and stops at point C. The one that stops at point C is temporally larger than the one that stops at B. So, the resultant state of the one that stops at point C is a resultant state of a zoltan walk event that is larger than the one that ends at point B. The upshot is that at any time during Zoltan’s walk in progress, the event is disposed to bring about a resultant state of a “larger” zoltan walk event. We could say, then, that such an event is disposed to become a “larger” zoltan walk event, which basically says that such an event is disposed to continue. Or we could be a little more formal and say a zoltan walk event in progress at t is an event disposed at t to bring about a resultant state of a zoltan walk event at some t′ > t, which is what the actual proposal says. Now what does this have to do with determinable dispositions? Well, similar to you wanting some but no particular cookie, an atelic event in progress at t is disposed to bring about a resultant state of an atelic event at some but no particular t′ > t. This is crucial for the non-­exhaustibility of atelic events in progress.

106  Nicky Kroll To see why, suppose we have an event e such that for some particular t′ > t, e is disposed to bring about a resultant state of a ϕ event at t′. We would then have an event in progress of ϕ-­ing until t. And this would be a telic event in progress. For example, take an event in progress of Zoltan walking until noon. Such an event in progress cannot continue past noon; it culminates “exhausted” when noon strikes. The upshot is that any α event in progress at any time is an event with a determinable disposition. In other words, any atelic happening is a happening with a determinable disposition. Telic events in progress also provide examples of determinable dispositions. The most obvious examples, however, involve agents with intentions. For example, Mirah can be baking some but no particular cake. Since we are interested in nonmental dispositions, we’ll put this aside and go back to our handy acorn. But this time, we’ll have it be the patient of an event in progress. Suppose there is an event in progress of the acorn becoming an oak tree at t. Such an event in progress is disposed to become one where the acorn becomes an oak tree. Suppose the event in progress culminates and so the acorn becomes an oak tree. In any such situation, there is a maximally specific way of becoming an oak tree such that the acorn became an oak tree in that way. However, it need not be the case the acorn was becoming an oak tree in that way at t. (Indeed, my hunch is that this is never the case. But I won’t argue for that here.) In such cases, we have a telic event in progress with a determinable disposition. We could continue with similar examples. Instead, we’ll just conclude that events, like objects, can have determinable dispositions. Lessons With determinable dispositions on the table, let’s close with some lessons they provide for understanding dispositonality. I’ll consider two. The first lesson is more of a reminder of three important points of the discussion so far: (i) determinable dispositions are distinct from multi-­track dispositions, (ii) standard alleged multitrack dispositions at the less fundamental level—for example, fragility, irascibility, knowing French—are really determinable dispositions, and (iii) the standard line of argument for a disposition being a multitrack disposition is invalid: a disposition can manifest in many different ways yet not be a multitrack disposition. The second lesson is concerned with the directedness of dispositions. Dispositions are directed at manifesting. For determinable dispositions, this

Determinable Dispositions  107 may seem a little peculiar. A determinable disposition is directed at a determinable state of affairs. But for any determinable state of affairs to obtain, it seems that a maximally specific determinate (of the determinable) state of affairs must obtain. Yet, the determinable disposition isn’t directed at any such maximally specific determinate state of affairs. Is there an account of the directedness of dispositions that could explain this? There is, and it just so happens to fall out of my preferred account of dispositions. According to my preferred account of dispositions, for something to be disposed to M is for it to be in a state directed at the end that it M.6 So, a vase disposed to break is in a state directed at the end that it break, and an event disposed to become a mirah bakes a cake event is in a state directed at the end that it becomes such an event. This directedness is teleological, and so the directedness of dispositions is a teleological directedness. Teleological directedness relates “subjects” (in the general sense) to “objects” (in the general sense). The objects are final causes, goals, aims, ends, purposes, and so on. What’s important for our purposes is that these objects can, very naturally, be determinable objects. Take a chair, an uncontroversial example of something with a purpose/end. It is for sitting. If you were to sit in it, there would be a maximally specific determinate sitting state of affairs that obtains. But the chair isn’t for such maximally specific sittings. Of course, what it is for does allow for such sittings. But what the chair is directed towards is the determinable state of affairs of (something) sitting (on it). In other words, the chair is for sitting. Hopefully, then, it is clear how a determinable disposition can be directed at a determinable state of affairs without being directed at any maximally specific determinate state of affairs. Just as a chair’s determinable end of sitting allows for maximally specific sittings, the teleological end of a determinable disposition to break allows for maximally specific breakings. But what it is for, what is directed at, is the determinable state of affairs of (something) breaking. In short, determinable dispositions find a natural home in a teleological account of dispositions. Indeed, I’m not sure they can find any other home. So, it seems to me that determinable dispositions provide further support a teleological account of dispositions, which is an important lesson for our understanding of dispositions. Notes 1 So, sometimes you can get what you want (an F) simply by getting something (a particular F) that you neither need nor want. 2 See Ellis and Lierse (1994) and Bird (2007) for such characterizations of multitrack dispositions. The single-­track versus multitrack distinction is often credited to Ryle (2009). But Ryle doesn’t even use the term multitrack. Interestingly, however, he does use the term determinable to characterize dispositions that are not single track. 3 Lowe (2010) is a notable exception.

108  Nicky Kroll 4 Bird (2007: 104) gives the following dispositional characterization of spin: “Spin is the property of a particle, which under the ‘stimulus’ of motion through a non-­uniform magnetic field, manifests itself as a force transverse to the direction of travel.” 5 We will continue to use θ as a variable for telic event types, α for atelic event types, and ϕ for either. 6 See Kroll (2017) for the details.

References Bird, A. (2007). Nature’s metaphysics: Laws and properties. OUP Oxford. Bokulich, A. (2014). Metaphysical indeterminacy, properties, and quantum theory. Res Philosophica 91(3), 449–475. Ellis, B. and C. Lierse (1994). Dispositional essentialism. Australasian Journal of Philosophy 72(1), 27–45. Kroll, N. (2017). Teleological dispositions. Oxford Studies in Metaphysics 10, 1–37. Kroll, N. (2018). Fully realizing partial realization. Glossa 3(1), 120. Lowe, E. J. (2010). On the individuation of powers. In The metaphysics of powers, pp. 16–34. Routledge. Molnar, G. (2003). Powers: A study in metaphysics. Clarendon Press. Quine, W. V. (1956). Quantifiers and propositional attitudes. Journal of Philosophy 53(5), 177–187. Ryle, G. (2009). The concept of mind. Routledge. Vetter, B. (2015). Potentiality: From dispositions to modality. OUP Oxford. Wilson, J. M. (2013). A determinable based account of metaphysical indeterminacy. Inquiry 56(4), 359–385.

Part II

Composition of Powers

6 What There Is and What There Could Be Mereology, Causality, and Possibility in an Ontology of Powers Sophie R. Allen Can powers be parts of powers? There are different strategies available to answer this question: one could take claims about powers being parts of powers (let us call these ‘powerful parthood claims’), test whether they match up to the central axioms of classical mereology, and then reject them as genuine mereological claims if they do not; or, one could take such powerful parthood claims at face value and work out what kind of an account of mereology would result. I pursue the latter strategy to find out what we are talking about when we talk about the composition of powers.1 Perhaps the analysis which I develop will ultimately not deserve the name mereology, but I hope it will tell us more about what is going on when we make powerful parthood claims. I distinguish powerful parthood claims into two kinds: cases of direct composition, in which the part and the whole are instantiated by the same individual (or are not instantiated), and indirect composition, in which they are instantiated by distinct individuals such that one individual is a proper part of another. I suggest that the most viable account of the direct composition of powers takes it to be brought about by their essentially causal or productive natures which also determine what a power can do in the future and, on some actualist accounts of modality, what is possible. When it comes to the composition of powers, composition goes hand in hand with causation. But should this count as mereology? I argue there are some important similarities between the part–whole relations which apparently hold between powers and those which hold between objects, events, and some abstract entities, although there are also some notable differences. After this, I turn to indirect composition and argue that this involves  a heterogeneous collection of metaphysical relations, with only some approximating part–whole relations between powers. My account will be defeasible, at risk from the appearance of counterexamples to what I have to say. Nevertheless, such counterexamples may not be fatal: there is room for flexibility about how classical mereology DOI: 10.4324/9781003298830-9

112  Sophie R. Allen should be formalised (Hovda 2009) and the axioms are controversial enough to be coherently denied (Simons 1987; Cotnoir 2013). Furthermore, one might treat alternative, non-classical mereological systems as a supplement to classical extensional mereology, rather than a replacement for it, especially if one thinks that the combination of different ontological categories may be characterised by different (but overlapping) sets of axioms. (See, for instance, Fine 2010: 561–65, Mellor 2006, Paul 2002, Simons 1987.) This position is strengthened if one is persuaded by Wallace’s (2021) argument that ‘part’ and ‘is a part of’ are polysemous expressions, with different meanings related by metaphorical extension associated with (for instance) concrete and abstract entities (2021: 4346). Such polysemy might be taken to further relax the requirement to adhere to a unique, universal account of mereology, and allow for pluralism about which systems apply. What are Powers? Questions about parthood and powers are complicated by there being different accounts of what powers are, both in the sense that there are alternative accounts of the ontological nature of powers, as universals or as tropes for instance, and because one might think that powers can be reduced, perhaps via a counterfactual analysis, to other non-powerful properties. For the purposes of this chapter, I ignore the latter, reductive accounts of powers for two reasons. First, I am interested here in whether powers can be parts of other powers qua powerful entities; that is, as property-like entities which have their causal powers essentially or necessarily and whose nature may or may not be exhausted by that causal power. (I aim to remain neutral about whether there is something more to powers than their causal power, so what I have to say will also include categories of entities which combine qualitativity and causal power, such as powerful qualities; Heil 2003, 2012; Strawson 2008; Taylor 2013, 2017, 2018.) Second, it seems reasonable to presume that if reductive accounts of powers are true, then the combination of powers will ultimately be accounted for by the combination of another category of entities and so lies outside the scope of this chapter. Moreover, if this is not the case, and powers do combine qua powers even though they are reducible, it seems likely that whatever I have to say about irreducible powers will apply to these entities as well. I will treat powers as being irreducible to non-powerful entities from now on. The differences between accounts of the ontological basis of powers are less easy to dismiss as inconsequential. Although it is not mandatory to give such an account, powers are variously regarded as transcendent or immanent universals, or as tropes. (I will not evaluate the arguments for these different views here.) The key differences between these categories from the

What There Is and What There Could Be  113 point of view of understanding parthood stem from whether they are abstract entities, whether they can exist uninstantiated,2 and whether they can tolerate differences in nature between instances (or between instances and the general case) such that they allow for inexact similarity. Given the concerns that a different account of part-whole relations may be required for abstract entities as opposed to spatio-temporally located ones (if the former is possible at all) (Mellor 2006, Simons 2021), one might worry that different accounts of the mereology of powers will be required. I will attempt to avoid these complications, although their consequences are not yet entirely clear. In this discussion, I will presume that most properties are powers but not require that all of them are. In part, this is an expedient move which allows me to talk about the spatio-temporal properties and part–whole relations of powers without requiring that these too are powers. I will leave questions about the reduction of such properties to powers (or something else) for another time. I will also restrict myself to examining part–whole relations between powers, avoiding the question of whether powers can combine with non-powerful properties, or enter into part–whole relations with them (or with other categories of entities). When are Powers Parts of Powers? Let us consider some putative examples of parthood relations between powers: ( a) The power to sprint is part of the power to jump 7.5 m. (b) The power to sprint is part of the power to beat the women’s 2022 long jump world record. (c) A salt molecule’s having polar charge is part of its power to dissolve in water. (d) The power to produce chlorophyll is part of the power (of the chloroplasts) to photosynthesise. (e) The power to play scales is part of the power to play a concerto. (f) The power to spot prey is part of the power to hunt antelope. (g) A salt molecule’s power to dissolve in water is part of the power of a grain of salt to dissolve in water. (h) The power (of the ovaries) to produce large gametes is part of the power (of female mammals) to reproduce. (i) The power (of the larynx) to produce sounds is part of the power to sing opera. (j) The power (of the chloroplasts) to produce chlorophyll is part of the power (of the plant) to photosynthesise. (k) The power of the heart to pump blood is part of the power to sprint.

114  Sophie R. Allen I have been careful to emphasise that these are putative examples. Just because we talk about powers being parts of powers does not imply that there are ever cases in which this is true. I will regard my project as successful if I can give an account which deals with only some of the cases listed. Moreover, as noted previously, the account proposed will be defeasible: if plausible examples surface which conflict with it, then I would have to admit either that what I have to say is not completely general or that it does not work at all. Perhaps of greater concern is the objection that none of these examples is genuine because we rarely talk about powers being parts of powers at all; even the fact we are talking about powers is only implicit in most ordinary cases. However, the same may be said when we talk about powers in other contexts and is not specific to mereology, so I will pass that problem by. Where are Powers and their Parts? On considering the examples in the previous section, a distinction suggests itself: in cases (a)–(f), the powers in question are instantiated by the same individual, whereas in (g)–(k), they are not. In these latter cases, the powerful part is instantiated by a proper part of the individual which instantiates the whole. Let us distinguish these cases as follows: (I) Direct part–whole relations, where P1 is part of P2 and P1 and P2 are instantiated by the same individual I (if they are instantiated at all); (II) Indirect part–whole relations, where P1 is part of P2 and P1 is instantiated by an individual I1 which is a proper part of the individual I2 which instantiates P2.3 I will also talk about direct and indirect composition respectively in relation to (I) and (II).4 This distinction hints at potential differences in the way in which parthood works for powers. For example, while powerful parthood claims could be of either type when we are considering powers instantiated in spatio-temporally located individuals, only the former make sense of part–whole relations of uninstantiated powers such as transcendent universals considered in the abstract.5 Moreover, when we focus on powers instantiated by material objects, the distinction marks a difference in the spatio-temporal properties of the parts and wholes involved. In (I), there is no interesting way in which P1 and P2 could be spatially related to each other – since the powers are instantiated by the same individual, they are co-located – and so, furthermore, there could therefore be no structural differences between individuals instantiating the same powers. However, in (II), P1 is located in a part of the spatio-temporal region in which P2 is instantiated, in virtue of belonging to a proper part of the individual I2

What There Is and What There Could Be  115 which occupies that region. In (II), differences in the spatio-temporal position of powerful parts relative to each other might make a difference to which whole they compose. The interest in the spatio-temporal properties of instantiated powers to better understand their mereology is not coincidental. One motivation is purely intuitive: pre-theoretically, we commonly think about things and their parts as having something to do with parts being spatio-temporal portions of a larger whole. This might just be pre-philosophical prejudice, arising from experience of ordinary objects, such as pizzas, houses, people and land, which should be laid aside once we develop a theory proper. Despite its intuitive underpinnings, the spatial understanding of mereology may not even work for ordinary material objects or not extend to powers. Nevertheless, there are well-developed accounts of material object mereology based on spatial relations (Markosian 2014) which provide a way of thinking about material objects and their parts with which powers can be compared. Third, theories based on the spatial properties of objects, such as Markosian’s, fit well with extensional accounts of mereology. Whether powers diverge from these, and how they do so, may give some indication about how a mereology of powers could be formulated. Direct Composition of Powers Powers standing in a specific direct parthood relation are by definition instantiated by the same individual if they are instantiated at all. As such, powers related in this way are colocated and are not spatially related to each other. What counts as a mereological sum of colocated powers? What kind of principle or principles govern the composition of powers which are instantiated by a single individual? I will restrict the discussion to the intrinsic powers6 of specific individuals; once we consider extrinsic powers, additional complications arise because extrinsic powers threaten to introduce an indirect element into the composition.7 What could determine the composition of the intrinsic powers of a single individual such as those in (a), (c), (d), (e) and (f)? Or the direct part– whole relations between these powers whether they are instantiated or not?8 While we could postulate the existence of sui generis composition relations,9 it would be expedient to consider features which are already thought to exist in an ontology of powerful properties before postulating new ones. Prima facie, this offers three choices, which are not mutually exclusive: direct part–whole relations arise due to logical or set-theoretic combination; they are something to do with the powers involved being co-located; or they occur due to the intrinsic causal or productive natures of powers. Neither logical combination nor co-location is a sufficient condition for  powers to combine: first, both produce ad hoc collections of powers,

116  Sophie R. Allen which we would not consider to be mereological sums, in addition to those which we would. Second, direct composition in virtue of co-location makes the parthood relation symmetric, rather than anti-symmetric (or more controversially non-symmetric; Cotnoir 2013: 837–9). I will suggest that these shortcomings are instructive and point towards the third option: that the direct combination of powers comes about in virtue of their productive natures and that we do not need to postulate sui generis composition principles. We can illustrate the problem of ad hoc collections by considering the intuitive cases of the direct composition of powers. For example, not all the powers which an individual has are relevant to the composition of a specific power, even though they are co-located or could be conjoined. In most specific cases of composition, some powers of the individual are irrelevant: if P1 is part of P2, other powers of the same individual I, such as P3 and P4, may play no role in the formation of P2. This is easiest to see in complex individual cases. Take Ceri the cellist whose power to play scales well is part of the power to play concertos. The fact that Ceri also has the powers to jump, to write bad poetry and to bake cakes is irrelevant to his having the power to play concertos while his power to play scales well is not. Given this, it also seems intuitively obvious that the Principle of Universal Composition does not hold for powers: any combination of an individual’s powers does not bring about a new power. Nor is the composition of powers simply additive: one does not get a non-trivial conjunctive power P1&P2&P3 on the composition of P1, P2 and P3 but a novel power Q of which P1, P2 and P3 are parts. (By ‘novel’, I do not mean ‘emergent’ or ‘novel fundamental power’ but simply one which the individual would not have had were it not for the instantiation of P1, P2 and P3 together.) One might trivially think of there being such a conjunction for every set of co-instantiated powers, but this does not tell an accurate metaphysical story and the powerful conjuncts are not part of the conjunction in anything more than a logical sense. To say that Ceri’s power to write bad poetry is part of his power to write bad poetry and play scales well and jump is true of the logic of the conjunction, but it has no metaphysical significance unless that conjunction of powers combines to produce a novel power. If it does not, one would be inclined to deny that composition of powers had taken place: there is no non-trivial whole power given that the individuation of powers is determined by their manifestations or causal role, and it is not obvious what makes this a mereological sum of powers rather than a logical construction.10 Another indication that colocation is insufficient to determine direct combination is that it conflicts with the formal properties expected of part–whole relations. Although colocation is transitive and reflexive, as usually required of proper parthood, it is also symmetric. Although some people allow that distinct entities can be parts of each other (for instance,

What There Is and What There Could Be  117 the statue and the piece of clay), this is usually restricted to the denial of anti-symmetry (such that parthood is non-symmetric); it is conceptually implausible to permit that parthood is symmetric. Being co-located in virtue of being instantiated by the same individual is not sufficient to explain what makes powers combine, nor is the settheoretic or logical combination of powers. We need another constraint to explain why the Principle of Universal Composition fails and why only some of the powers of an individual are relevant to the formation of a certain composite power. An obvious move here is to invoke the causal or productive natures of powers: not only do powers combine with each other to produce manifestations over time, but they also do so at a time; that is, the essentially productive nature of powers (which we usually think of as causal power which acts over time) works atemporally too, allowing powers to combine and form novel powers. This is not a metaphysically controversial move as the fact that powers have this atemporal productive capability is already implicit in many powers theories and explicit in some, especially those which deal specifically with atemporal relations between powers such as those between mental powers and physical ones (although I will consider some exceptions below).11 Notions such as realisation have been used to capture this atemporal determination relation between properties in the past, and also ontological dependence or grounding on some conceptions of grounding. I will not fix on a specific account of the phenomenon here, although I will stick to ‘realisation’ for the sake of giving it a name when required. It is, to use Karen Bennett’s terminology, one of a related family of building relations which are transitive, asymmetric and irreflexive and, as such, is consistent with the relation of proper parthood. (If realisation is the basis of the direct composition of powers, then the fundamental mereological notion in play will be that of proper parthood rather than parthood (on the assumption that powers do not cause or realise themselves12).) My suspicion is that we think of composition as being distinct from realisation, ontological dependence, grounding and the like because we usually think about composition as being about objects, events, sets, or sometimes non-powerful properties, rather than powers; that is, we usually conceptualise composition in terms of entities which are ontologically or causally inert in the sense that they do not necessarily interact to do or make something when they are contiguous or colocated.13 Powers are different, and their composition is different too. If the direct part–whole relation between powers is analogous to causation, then we can explain why the combination of a collection of powers (P1, P2 and P3) producing a novel power Q is defeasible by the presence of another power P4: P4 interferes with the mutual manifestation of P1, P2 and P3, and so Q is not produced. Like powerful causation (and unlike

118  Sophie R. Allen logical entailment or the composition of objects), the direct composition of powers is not monotonic as the addition of a novel power can change whether a particular power is produced. However, the addition of this interfering power P4 would not provide a counterexample to the extensionality of the direct composition of powers: given that powers have their productive roles necessarily, if Q and R both consist of parts P1, P2 and P3, then Q and R would be identical. No two distinct composite powers have all the same proper parts. The mereological sum of powers P1, P2, P3 and P4 (if there is one) would not count as having the same proper parts as Q and R. Treating the combination of powers as being analogous to causation allows us to explain: (1) which subsets of an individual’s powers are relevant to the production of a composite power (Q, in this case) and (2) the relevance of the wider context in which Q is produced and with it the defeasibility of combining powers. Moreover, the fact that powers have their causal or realisation roles as a matter of necessity explains why composite powers must have the parts which they do. Hence, apparent counterexamples to extensionality are explained away. (There may be a plausible conception of powerful composition in which extensionality does not hold, but it is notable that the direct composition of powers is extensional. As in the case of the mereology of objects (Varzi 2008, 2009; Rea 2010; Cotnoir 2016), opinions about extensionality might differ for powerful composition.) Realisation also explains why the direct composition of powers is not additive and why the Principle of Universal Composition does not hold: not every collection of powers produces another power because some collections of powers do not interact. Gerrymandered conjunctive collections are of logical interest only, and the powers involved are parts of the collection qua conjuncts rather than qua powerful entities. Because realisation explains why composition works selectively, it would also answer van Inwagen’s ‘Special Composition Question’ (1990): powers are, in virtue of their natures, constrained to interact with some powers and not others, so there is no metaphysical mystery about the range of composite entities which there are. One advantage of amalgamating the compositional capacities of powers with their productive capacities is, of course, parsimony: the direct composition of powers would be determined by the same phenomenon that drives the evolution of powers over time. There would be no need for the postulation of any combination principles different in kind to the causal capabilities which powers have by definition. Second, this move could also unify the direct composition of powers with the ontological basis of modality. In an actualist dispositionalist account of modality, such causal and productive capacities ground what is possible; for instance, by regarding powers as the truth-makers of modal claims (Borghini and Williams 2008; Jacobs 2010; Vetter 2011, 2015).

What There Is and What There Could Be  119 Objections to the Realisation Account of Direct Composition One might deny that there is an atemporal analogue of the causal power of powers to combine powers to produce new ones, of the kind I relied upon in the previous section. If this is right, the account I have given would fail. On some accounts of powers, such as those provided by John Heil (2003, 2012) or Neil Williams (2019), there are no ‘higher level’ or composite powers.14 The ‘real’ powers are the sparse, fundamental (probably physical) ones and all the other abundant powers we talk about, such as the power to dissolve salt, or to photosynthesise, or to play concertos, are simply rough and ready descriptions – what Williams (2019) calls ‘disposition ascriptions’ – which we predicate of what we take to be relevant features picked out from the buzzing confusion of the physical world. The productive capacity of powers on these views is restricted to what powers can cause. Accordingly, intuitive powerful parthood claims like those I  have relied on in this chapter would turn out to be mistaken, examples which should be rejected outright or explained away rather than given a firm ontological grounding. Heil’s or Williams’s views of powers are not only inconsistent with my account, there would also be no need for an account of the mereology of powers at all if they are correct. Their thesis that the only real powers are the sparse, fundamental ones amounts to a version of compositional nihilism about powers, since they rule out any atemporal way in which powers may combine to form other powers. I am sympathetic towards Williams’s concern that not all the power ascriptions we make are genuine and also towards his worry that trying to understand the nature of the world in terms of an abundant conception of powers is likely to compound this error (since the way we talk may not reflect the way which things are). Nevertheless, one could agree with Williams that a sparse conception of powerful properties is the most plausible way to explain the nature of the universe while also thinking that there appears to be – at least sometimes – a principled ontological relationship between the sparse powers and whatever we name with our abundant powerful predicates which demands an explanation, and it is this phenomenon which is under scrutiny in this discussion. However, I cannot do justice here to a full defence of composition or realisation, so Williams’s and Heil’s positions remain as general, viable threats to my project as a whole. If one is convinced there are only sparse, fundamental powers, then the ideas presented here are not for you. A second objection is that the examples of powers having parts are not really that at all: the parts belong to the manifestations of the power – the actions or the effects – and not the powers themselves. An unmanifesting power does not have parts, and the parts which a manifesting power appears to have are parts of its manifestation and not parts of the

120  Sophie R. Allen power itself.15 There are two points to make in response to this objection. First, although there are differing opinions about which category of entities the manifestations of powers belong to, they are usually thought to be, or to involve, powers and, if manifestations are powers, this objection would have no purchase because parts of manifestations would be parts of powers. Another, more general, response to this objection is that it is not clear why one should think that it interprets powerful parthood claims correctly instead of treating the powers themselves as having parts. For one, instantiated powers exist in a robust sense even when they are not manifesting, and the fact that the examples of direct composition between powers in (a)–(f) could also be interpreted as parthood relations between uninstantiated powers – transcendent universals, for instance – suggests that these are not claims about manifestations rather than about the powers themselves (if these are different). Moreover, the fact that actions have parts does not preclude the respective powers to perform those actions from having parts too. For example, the playing of the primary instrumental part in a concerto is an action which involves many different parts, usually producing complex movements involving both hands and significant cognition about pitch, melody, timing, timbre and so on, but this does not show that the power to do this is not also similarly complex (although its parts need not be isomorphic with the parts of the performance of the concerto qua action). Even so, the objector might respond, why should we think of this as parthood at all? This significant concern underlying the second objection becomes explicit in the third one: that the account which I have given of the direct composition of powers is not really an account of parthood at all. Rather, someone may argue, given its basis in the productive capacities of powers, the relation which has been accounted for is really a form of ontological dependence: instead of explaining the mereology of powers, the foregoing account simply changes the subject. I have some sympathy with the objector’s position: direct parthood between powers has been explained as an atemporal determination relation and what is, in fact, being said is that when P1 is directly part of P2, P2 (at least) partially depends for its existence upon P1. Someone could accept what I have said about how powers combine and reject my claim that this is an account of mereology. The responses available to this objection depend upon whether the objector thinks that there is an alternative account of the mereology of powers. If there is a competitor account which aligns more neatly with what we would expect of mereology, then that is the better candidate (although I am currently at loss to think what that is) and one could concede that what I have mistakenly talked about is simply ontological dependence. On the other hand, if there is no alternative account of mereology – and I am inclined to think that there may not be – then one can either say

What There Is and What There Could Be  121 (as Simons does) that there is no mereology of powers, or one can admit that part–whole relations in an ontology of powers are, or are very close to being, realisation or ontological dependence. How plausible is it to stubbornly align composition with realisation or ontological dependence in this way in order to defuse this objection? Karen Bennett (2017, chapter 4) suggests, when arguing that causation should be included as a building relation among a family of atemporal building relations including realisation, grounding and (notably for our purposes) composition, that composition especially can benefit from being understood in terms more familiar from the explanation of causation and causal role. Moreover, for this to work, she suggests that composition needs to be thought of as being strongly analogous to causation (2017: 77). Bennett is no powers theorist and the conception of causation and composition which she has in mind is based in an ontology of categorical properties, although she considers all building relations to involve necessitation (2017: 47). Nevertheless, I suggest that what she has to say applies just as much – if not more so – in an ontology of powers because of their essentially causal natures. To test this point, let us compare how closely the direct parthood relation outlined earlier aligns with classical mereology. If we consider proper parthood, the direct part–whole relation between powers is irreflexive, asymmetric and transitive, in keeping with the properties we would expect. If we allow that a power can realise itself, then we have a conception of parthood which is reflexive and anti-symmetric. However, reflexivity, transitivity and asymmetry are just definitive of partial ordering: lots of distinct metaphysical relations share these properties, and so the presence of these features does not pick out a relation as specifically compositional. We can add to this the foregoing observations that direct part–whole relations are extensional, and that there is a reason for the range of composition to be constrained and the Principle of Universal Composition to fail. A further key feature of composition is that parthood relations accord with one of the supplementation axioms: Strong Supplementation, Weak Supplementation, or the Complement Principle.16 Let us take the Weak Supplementation as a guide, since it is the weakest of these constraints and some mereologists consider it to be analytic of parthood (Simons 1987: 116; Varzi 2008: 110, 2009: 599).17 If they are right, then a relation which does not conform to the principle is not a mereological one. According to Weak Supplementation, if x is a proper part of y, then there is some z which is a part of y which is not part of x. Weak Supplementation conforms with our intuitions that if one thing x is part of another y, then there is some part of the whole y ‘left over’ (let us call that x*); nothing has just one proper part. Importantly, the relevant part z could itself be a part of that leftover x*, rather than being the whole of it,

122  Sophie R. Allen and there could be other parts of x* which are disjoint from each other and  x. (Unlike the Complement Principle, Weak Supplementation stops short of demanding that there is a part z* of y which includes every part of y which is disjoint from x, which would not be satisfied by the composition of powers.) This is fortunate, as it makes Weak Supplementation much more plausible in the case of powers, given that a power’s contribution to the whole might become causally entangled with other powers in various ways, such that one power might be a part of several others which themselves then form a whole. Take, for instance, the following case in which P1 is part of P3 and P1 is part of P4 (alongside other distinct powers in each case). When P3 and P4 combine together to make P5, then the remainder from P5 when P3 is ‘removed’ would be P4, but P4 overlaps P3 as they share a common part, P1. The Complement Principle does not hold in this case because P4 is not disjoint from P3, but Weak Supplementation would hold: there is still a part of P5 which is disjoint from P3 (the power or powers which compose P4 in addition to P1). If one looks at some of the examples which have appeared in this chapter, they satisfy the Weak Supplementation Principle. Aside from the power to sprint, the power to jump 7.5 m involves plenty of other powers, some of which might overlap with the power to sprint, but not all will. The power to photosynthesise involves powers other than the power to produce chlorophyll, and the power to hunt antelope likewise involves powers additional to those which permit an animal to spot prey. Let us consider another example: (I) The power to swim is part of the power to swim breaststroke. Simons18 rejects this example of parthood on the grounds that it fails the complement principle which I would agree that it does: what remains when one takes away the power to swim from the power to swim breaststroke is not itself a power. However, I think that he would be mistaken to think that it does not satisfy weak supplementation. The remainder of the power to swim breaststroke were one to ‘take away’ the power to swim would be a range of powers including the power to kick simultaneously with both feet parallel to the surface, the power to surface on each stroke, the power to move arms and legs in the correct rhythm which, although some of them may overlap with the power to swim, it is possible to lack and be a very proficient swimmer. Equally, as many beginners find, it is possible to have many of these powers and to still sink like a stone because one lacks the power to swim; that is, the power which itself is composed of the powers to (nearly) float and to propel oneself through water.19 (As in the example of the previous paragraph, it may be that all the complementary powers to being able to swim breaststroke overlap with being able to swim, but there

What There Is and What There Could Be  123 are some parts of those powers which do not.) Such examples do not all satisfy the Complement Principle, but we do not require such a strong constraint to hold in order to think of powers as being parts of powers. A second key principle associated with parthood is Idempotency: if x is part of y, the sum of x and y is y. Does this hold for the realisation account of parthood and powers? The result, if it does, would be the peculiarity that a power P is part of its manifestation (or the power it produces, if that is different) when P plays a role in realisation. The peculiarity stems, in part, from the fact that we wouldn’t say that a cause was part of its effect. One might allay this worry by saying that it relies on a conception of manifestation taken from temporally extended causation, one in which the cause is (usually) thought to be logically and spatio-temporally distinct from its effect and in which the power might cease to exist when its manifestation comes about. However, powers do not need to fit this conception, especially with respect to the logical or temporal separation of the cause and effect.20 Moreover, the simultaneous instantiation of realiser with realised power is much more coherent in the case of an atemporal determination than it is in the case of causation, so the objection loses its force. The satisfaction of Idempotence is not uncontroversial, but it is plausible in an ontology of powers. To summarise, although direct composition relations between powers are very similar to ontological dependence relations such as causation or realization and ontologically are brought about by the same mechanisms in the powers, they also have sufficiently many of the formal features of part–whole relations to count as mereological, they satisfy Weak Supplementation, Idempotency and are extensional. If one wanted to avoid calling such relations mereological, then I think that the debate would be one about terminology rather than a metaphysically substantial one. Indirect Part–whole Relations So far, I have concentrated on how we might think that powers are related as part to whole when they are instantiated by the same individual. Such relations are, I argued, a form of ontological dependence or atemporal determination analogous to causation. In addition to this, powers can also be thought of as standing in part–whole relations indirectly: (II) Indirect part–whole relations, where P1 is part of P2 and P1 is instantiated by an individual I1 which is part of the individual I2 which instantiates P2. For instance, a water molecule’s having polar charge is part of the power of water to dissolve salt, the power of the larynx to produce sound is part

124  Sophie R. Allen of the power to sing opera and the ovaries’ power to produce large gametes is part of the female mammal’s power to reproduce. To what extent is indirect composition a legitimate way to understand part–whole relations between powers rather than its simply being parasitic on part–whole relations between other entities? Indirect part–whole relations between powers hold in virtue of or in conjunction with part–whole relations between spatio-temporally extended concrete particulars such as objects or events and their parts, or (in the general case) between types of particulars and their parts. In contrast to direct composition, the powers involved in indirect part–whole relations stand in spatio-temporal relations to each other as well as in some cases being metaphysically involved in other ways. In fact, once we start trying to untangle the ways in which a power may be related to the powers of the parts of the thing which instantiates it, it turns out that indirect parthood is very heterogeneous. The task of understanding indirect composition is complicated further because of the lack of consensus about the best way to understand the mereology of material objects. Since I cannot examine these subtleties in detail here, I will confine myself to a few remarks about the way in which indirect composition might work. On a broadly Aristotelian model (Metaphysics Δ.26; Koslicki 2007), we can draw a distinction between composite entities in which the structure of their parts matters to which entity they are, and those for which the structure of parts is irrelevant. (This distinction was not possible when we considered the direct composition of powers, as there is no way to conceive of structural differences when powers are instantiated by the same individual.) Following Aristotle, we could call these Totals and Wholes, respectively, although the distinction as employed for powers will differ from its application to the composition of material objects and events. The powers of totals can appear to be parts of the whole in (roughly speaking21) two ways: (1) Trivial, additive cases such that P1 is indirectly part of P2, where the powers P1 and P2 are exactly similar tropes or instances of the same universal power; and (2) generative cases, where P1 and P2 are distinct powers. Examples of the former kind include the bundle of firewood which has the power to burn because each piece of wood in the bundle also has that power or the grain of salt which has the power to dissolve in water because each of its NaCl molecules has it too (or, more strictly, each pair of Na+ and Cl− ions has it too). The power to dissolve of a grain or a kilogram of salt is straightforwardly the result of each part having that power (at a certain level of division). In these cases, one might argue that the attribution of a power to the whole on the basis of the powers of the individual parts is really a convenient and fairly harmless shorthand, but it seems wrong to say that it marks any genuine part–whole relationship between the powers. In comparison, the generative cases of type (2) are not trivial because a novel power is produced as a result of the powers of the parts. Given that

What There Is and What There Could Be  125 powers are produced causally by other powers (or else they are atemporally determined), such generative cases must involve some causation or determination on the part of the powerful parts. In most such cases, a mixture of powers will be involved in the parts to generate the novel power P2, but this need not always be the case. There may be some examples in which the sheer number of instantiations of a power generate a different power in the whole. For instance, one piece of chocolate has the power to be a delicious snack, but one thousand such pieces together have the power to make someone sick. Or, one atom of uranium-235 has the power to produce neutrons by fission but it does not have the power to spontaneously start a chain reaction, whereas 52 kg of uranium-235 does have that power in virtue of the powers of its atoms. In these cases, it does seem plausible to say that the powers of the individuals are indirectly composing the power of the total. In Aristotelian wholes, in which the arrangement of parts matters (and a change in arrangement can change which whole there is), the situation is more complicated still. We might say, for instance, that the heart having the power to pump blood is part of the power to sprint, or the ovaries’ power to produce large gametes is part of the power of the female mammal to reproduce. In each case, it is claimed that a power of a part of an individual is part of a power of the whole individual. But should we accept such claims as mereological since, at the very least, their truth requires a complicated causal relationship, some facts about the structure of the individuals involved and perhaps some atemporal determination too? In general, we have P1 instantiated by I1 is part of P2 instantiated by I2. P1 clearly matters in some way to the existence of P2, but the relationship is not a straightforward one and it is not obvious that we should treat it as mereological. First, because of the importance of the structure of I2, extensionality fails for both the mereology of individuals, since an entity distinct from I2 could be composed of all the parts of I2 (I1 included), and their powers. Second, it is not obvious that the indirect part–whole relation is transitive. For instance, should we think of the power to pump blood as being part of the power to break the 2022 women’s long jump world record? The heart of the long jumper having this power is clearly a contributing factor of some kind, but parthood seems the wrong way to think about it. I suggest that instead of regarding indirect part–whole relations between powers as a genuine aspect of the mereology of powers, it would be clearer and more perspicuous to characterise any part–whole relations as being between whichever individual objects or events instantiate the powers. Ultimately, the individual parts may form into the whole that they do in virtue of their respective causal powers, and they may maintain their unity together as a whole because this whole has a novel power or powers which the parts did not have. Furthermore, the causal powers instantiated by parts might explain failures of extensionality for objects and events and

126  Sophie R. Allen hence explain the cases in which structure is important: the powers of the parts can only be causally active if they are in the vicinity of certain other powers. So, ultimately, the mereology of individuals might owe a lot to the behaviour of the powers those individuals have. But to characterise the complicated mixture of causal and spatio-temporal relationships involved (perhaps with some direct composition between powers as well) as being part–whole relations between powers is an overly simplified shorthand which misses the metaphysical action. To be sure, if we can class causation, composition and the like together as a family of building relations, the power P2 is built out of P1 (and more besides), but P1 is not part of P2 in any sense which fits with our usual understanding of parthood (even mereology of a non-classical sort). Conclusion I distinguished two ways in which a power can intuitively be a part of another: direct and indirect. The former, where part and whole are instantiated by the same individual, is best understood as a form of atemporal ontological determination analogous to causation, brought about by the same productive natures of powers which ground their causal roles and, if one is a supporter of modal dispositionalism, also grounds what is possibly the case. I have argued that this relation shares sufficiently many formal features with classical extensional mereology to justify our still thinking of it as a variety of composition or parthood. On the other hand, indirect composition is heterogeneous. When the structure of the whole is irrelevant, there are some cases in which we might consider the powers of parts to be part of powers of the whole and others in which the claim is one of linguistic convenience. Where the structure of the whole matters, we are better breaking down apparent powerful parthood claims into causation and realisation between powers and the composition relations of the individuals which instantiate the powers. Although powers may play a role in the how the entities which instantiate them combine, we should not characterise the relations between those powers and those of the whole as cases of composition, nor expect them to fit into a uniform mereological system.22 Notes 1 Peter Simons (2021) adopts the former strategy. 2 It is worth reiterating that powers can be instantiated without manifesting. A particular sugar cube has the power to dissolve even though it never does so because it is never located in the vicinity of other powers which would bring this about either by triggering the power to dissolve or by mutual manifestation with other powers. Exactly how one makes metaphysical sense of this need not concern us here.

What There Is and What There Could Be  127 3 If one would prefer an ontology in which individuals are derivative entities built from bundles of powers or power-tropes, one can reframe what I say here accordingly. If, like Paul (2002), one considers such bundling of powers into individual objects or events to be cross-categorial composition, it will have to be a different kind of composition from that between powers. 4 Paul (2002: 582) hints at this distinction while arguing that properties combine to form individual objects. 5 Indirect composition might make sense for powers qua abstract entities but only for the type of power which is instantiated by abstract objects, if we also have a robust account of parthood for abstract objects. This might include mathematical powers, but I can think of no plausible examples. 6 I am relying here on an intuitive understanding of intrinsicality and extrinsicality, but if one prefers a more precise formulation of the distinction, Langton and Lewis’s (1998) criterion of being independent of loneliness and accompaniment would fit the bill. Criteria in terms of grounding (e.g. Witmer et al. 2005) would be less suitable here both because of the threat of circularity and because grounding may turn out to be too close to other mechanisms which determine the composition of powers. 7 See for example (b) in the ‘When are powers parts of powers’ section. Prima facie, if an individual has the power to break the women’s 2022 long jump world record, her having this power arguably requires the existence of entities distinct from her and their powers. For reasons of space, I will not explore these complications here. 8 The latter would require powers to be able to exist uninstantiated. 9 As found, for example, for material objects in Fine 1999; see Koslicki 2007: 149–50 for discussion. 10 Simons (2021: 1) suggests that all collections of coinstantiated powers are like this: powers form countable pluralities rather than merging into wholes. My claim is that some coinstantiated powers do merge, although not all do. 11 For example, see Aranyosi 2010; Carruth 2016. 12 Those who maintain that a power can cause itself (Williams 2019) or that selfmanifestation of powers is trivially true, may prefer to take improper parthood as primitive. Since parthood and proper parthood are interdefinable, there are no significant grounds for disagreement here. 13 Powers will, of course, do nothing if there are no manifestation partners present and they are not spontaneously manifesting powers. If powers act with dispositional modality (Mumford and Anjum 2011a, 2011b, 2018), they will tend to interact, which is more than non-powerful properties do. 14 Williams (2019, chapter 3 and passim) endorses only a very sparse set of powers, including all and only fundamental properties of the universe. Other ascriptions of powerfulness are mere disposition ascriptions which should not be understood as picking out a real power. He argues that were there powers produced by realisation/composition as I have suggested, they would lack genuine causal power, which would reside in the fundamental powers. I will not address this challenge here. 15 This point is developed from one made by Simons (2021). 16 Weak Supplementation: If x is a proper part of y, then there is some z which is a part of y which is not part of x. Strong Supplementation: If y is not a part of x, then there exists z such that it is part of y but disjoint from x. Complement Principle: If y is not a part of x, then z exists which comprises all and only parts of y which are disjoint from x.

128  Sophie R. Allen 17 The analyticity of Weak Supplementation is a controversial claim which others reject (Cotnoir 2021). I will not consider this matter here as it turns out to be tangential to the discussion since Weak Supplementation seems to hold. 18 This example is taken from a presentation of his ‘Even if there are potentialities, they don’t have parts’ (2021). 19 What about the people who can only swim breaststroke? One might be concerned then that the power to swim just is the power to swim breaststroke and is not a proper part of it. I think this counterexample involves a lack of care about the individuation of powers since the powers have a different causal role. In such people, the power to swim is accidentally coextensive with the other powers needed to swim breaststroke, but the power to swim could be instantiated separately in conjunction with other powers (to swim butterfly, or doggy paddle, for instance). 20 See Mumford and Anjum (2011b). The problem of logical separation has long been abandoned in powers theory where the fact that the power to P causes P is seen as an artefact of the naming of powers and not of metaphysical interest. 21 A full consideration of the specific options would be too lengthy to include here. 22 I am grateful to Peter Simons and Neil Williams for clarifying their own positions in correspondence.

References Aranyosi, István (2010) Powers and the mind–body problem. International Journal of Philosophical Studies 18(1): 57–72. Aristotle (1984) The Complete Works of Aristotle (Vol. 1 & 2), J. Barnes (Trans.). Princeton University Press. doi: 10.2307/j.ctt5vjv4w (Vol. 1), doi: 10.2307/j. ctt6wq12z (Vol. 2). Bennett, Karen (2017) Making Things Up. Oxford University Press. Borghini, Andrea and Williams, Neil E. (2008) A dispositional theory of possibility. Dialectica 62: 21–41. Carruth, Alexander (2016) Powerful qualities, zombies and inconceivability. The Philosophical Quarterly, 66: 25–46. Cotnoir, Aaron (2013) Strange parts: The metaphysics of non-classical mereologies. Philosophy Compass 8(9): 834–845. Cotnoir, Aaron (2016) Does Universalism entail extensionalism? Noûs 50(1): 121–132. Cotnoir, Aaron (2021) Is weak supplementation analytic? Synthese 198(Suppl. 18): S4229–S4245. Fine, Kit (1999) Things and their parts. Midwest Studies in Philosophy 23(1): 61–74. Fine, Kit (2010) Towards a Theory of Part. Journal of Philosophy 107(11): 559–589. Heil, John (2003) From an Ontological Point of View. Oxford University Press. Heil, John (2012) The Universe as We Find It. Oxford University Press. Hovda, Paul (2009) What is classical mereology? Journal of Philosophical Logic 38(1): 55–82.

What There Is and What There Could Be  129 Jacobs, Jonathan D. (2010) A powers theory of modality: Or how I learned to stop worrying and reject possible worlds. Philosophical Studies 151: 227–248. Koslicki, Kathrin (2007) Towards a Neo-Aristotelian mereology. Dialectica 61(1): 127–159. Langton, Rae and David Lewis (1998) Defining ‘intrinsic’. Philosophy and Phenomenological Research 58: 333–345. Reprinted in David Lewis, Papers in Metaphysics and Epistemology, 1999 (Cambridge University Press): 116–132. Markosian, Ned (2014) A Spatial Approach to Mereology. In Shieva Kleinschmidt (ed.), Mereology and Location. Oxford University Press: 69–90. Mellor, D. H. (2006) Wholes and parts: The limits of composition. South African Journal of Philosophy 25 (2):138–145. Mumford, Stephen and Anjum, Rani Lill (2011a) Dispositional Modality. In C. F. Gethmann (ed.), Lebenswelt und Wissenschaft, Deutsches Jahrbuch Philosophy 2. Meiner Verlag: 380–394. Mumford, Stephen and Anjum, Rani Lill (2011b) Getting Causes from Powers. Oxford University Press. Mumford, Stephen and Anjum, Rani Lill (2018) What Tends to Be. Routledge. Paul, L. A. (2002) Logical parts. Noûs 36(4): 578–596. Rea, Michael C. (2010) Universalism and extensionalism: A reply to Varzi. Analysis 70(3): 490–496. Simons, Peter (1987) Parts: A Study in Ontology. Clarendon Press. Simons, Peter (2021) Even If There Are Potentialities, They Don’t Have Parts. Unpublished draft. Strawson, Galen (2008) The identity of the categorical and the dispositional. Analysis 68: 271–282. Taylor, John H. [Henry Taylor] (2013) In defence of powerful qualities. Metaphysica 14(1): 93–107. Taylor, Henry (2017) Powerful qualities, the conceivability argument and the nature of the physical. Philosophical Studies 174(8): 1895–1910. Taylor, Henry (2018) Powerful qualities and pure powers. Philosophical Studies 175(6): 1423–1440. Van Inwagen, Peter (1990) Material Beings. Cornell University Press. Varzi, Achille C. (2008) The extensionality of parthood and composition. Philosophical Quarterly 58(230): 108–133. Varzi, Achille C. (2009) Universalism entails extensionalism. Analysis 69(4): 599– 604. Vetter, Barbara (2011) Recent work: Modality without possible worlds. Analysis Reviews 71: 742–754. Vetter, Barbara (2015) Potentiality: From Dispositions to Modality. Oxford University Press. Wallace, Meg (2021) The polysemy of ‘part’. Synthese 198(18): S4331–S4354. Williams, Neil E. (2019) The Powers Metaphysic. Oxford University Press. Witmer, D. Gene, William Butchard, and Kelly Trogdon (2005) Intrinsicality without Naturalness. Philosophy and Phenomenological Research 70: 326–350.

7 What Can Causal Powers Do for Interventionism? The Problem of Logically Complex Causes Vera Hoffmann-Kolss Introduction Causal talk and causal reasoning are ubiquitous. In everyday reasoning, we take individual causal claims involving concrete individuals to be true, such as that Joanne’s being late caused her to miss an important meeting or that Jimmy’s leaving the cake in the oven too long caused Amy to be in a bad mood (because she does not like the taste of burnt cake). In scientific contexts, we often try to answer general questions about causal relations, such as whether COVID-19 infections cause heart problems or whether increased global temperatures cause forest fires. From a philosophical point of view, this raises the question of under what conditions we can say that certain causal claims are true. This question can be answered in several different ways. One option is to analyze causal relations in terms of recent interventionist theories of causation à la Woodward (Woodward 2003), which are based on the formalism of Bayesian causal models (Hitchcock 2007; Pearl 2000; Spirtes, Glymour and Scheines 2000). Another option is theories based on the assumptions that there are causal powers in the world and that these causal powers are the driving force that makes things happen. According to this picture, causal relations occur because things instantiate powers, and under certain triggering conditions, these powers produce changes in the world; proponents of powers theories include Bird (2007), Cartwright (1989), Molnar (2003), Shoemaker (1980), and Vetter (2015). These two approaches come from quite different philosophical camps. Interventionist theories of causation typically aim to be as ontologically undemanding as possible. They were originally designed to capture the way in which causal relations are discovered and described by practicing scientists, especially in fields that work with large data sets, such as econometrics, climate science, or neuroscience research using brain scan data. The general idea is that if the data under investigation show certain

DOI: 10.4324/9781003298830-10

What Can Causal Powers Do for Interventionism?  131 patterns (and if additional conditions are met), these patterns can be given a causal interpretation. This approach is typically neutral about the ontological question of whether there are fundamental powers in the world that give rise to causal necessitation relations. Powers theorists, in comparison, are by definition committed to the existence of causal powers, with the remaining question being what exactly is the connection between powers and causes or causal relations (see, e.g., Baltimore 2019; Mumford and Anjum 2011). Interestingly, however, at least certain parts of the debate on causal models have begun to increasingly incorporate metaphysical considerations and concepts. One example is the debate about the relationship between interventionism, Bayesian models, and the metaphysical causal exclusion problem in the philosophy of mind (see, e.g., Baumgartner 2009; Gebharter 2017; Kroedel and Schulz 2016; Woodward 2015). Another example is the thesis that the metaphysical grounding relation can be analyzed using the formal framework of causal models (Schaffer 2016; Wilson 2018). A topic that has not been explored in comparable detail, however, is the question of the metaphysical status of the relata of the causal relation. According to causal modeling approaches, causal relations can be described as dependence relations between variables. These variables assume at least two and possibly infinitely many mutually exclusive values, and these values represent the relata of the causal relation under consideration. This leaves open how logically complex the relata of the causal relation can be, that is, whether only fundamental or logically simple events or properties can be causally related to each other, or whether the values of the variables can also stand for logically complex entities. In this chapter, I argue that if arbitrary disjunctive variables can occur in causal structures, the interventionist criterion of causation becomes inadequate. I further argue that a possible solution to this problem is to exclude variables whose values represent disjunctions of overly disparate causal powers. I also suggest that this is an instance of a more general observation about interventionism, that is, the observation that interventionism needs at least some ‘metaphysical input’ in order to adequately represent causal structures in the world. I begin with an introduction to interventionism. I then argue that the interventionist criterion of causal relevance is problematic if the variables in the causal models under consideration can be disjunctive. I suggest that this problem can be solved on the basis of considerations about causal powers and conclude by briefly pointing out that interventionism in general must rest, at least to some extent, on substantial metaphysical assumptions.

132  Vera Hoffmann-Kolss The Interventionist Theory of Causation According to the interventionist account of causation, causal structures can be represented by directed causal graphs consisting of two elements: (a) a set V of vertices consisting of variables standing in causal relations to each other, and (b) a set of directed edges connecting these vertices. If a sequence of variables {X1, …, Xn} is such that for any i with 1 ≤ i < n, there is a directed edge from Xi to Xi+1, then the sequence is a directed path leading from X1 to Xn (Spirtes, Glymour and Scheines 2000; Woodward 2003). Directed paths between variables represent causal relevance relations. The standard locution in this context is that variables stand in causal relevance relations to each other. However, this should be understood as shorthand for the claim that the entities represented by the values of variables stand in causal relevance relations to each other. These entities may be properties or events. Accordingly, the interventionist criterion of causation as it is presented here can be applied either to so-called token causation, that is, causal relations between concrete events, or to so-called type causation, that is, causal relevance relations between properties. The relationship between these two kinds of causation is complicated (see, e.g., Hausman 2005). However, the details are not important for the purposes of the present argument. Therefore, for the sake of simplicity, I will simply follow the convention of talking about causal relevance relations between variables and leave open whether the values of these variables stand for events or properties. Against the background of a formal causal model, the interventionist criterion of causation classifies a variable X as causally relevant to a variable Y iff there is an intervention on the value of X that changes the value or the probability distribution of Y, provided that the values of all other variables that are not on the causal path between X and Y are held fixed by interventions (Woodward 2003; Hitchcock 2001, 2007). The notion of an intervention is an essential component of Woodward’s approach. Interventions are characterized by intervention variables, which are defined as follows: ‘I is an intervention variable for X, with respect to Y, if it meets the following conditions: (1) I is causally relevant to X. (2) I is not causally relevant to Y through a route that excludes X (3) I is not correlated with any variable Z that is causally relevant to Y through a route that excludes X, be the correlation due to I’s being causally relevant to Z, Z’s being causally relevant to I, I and Z sharing a common cause, or some other reason. (4) I acts as a switch for other variables that are causally relevant to X. That is, certain values of I are such that when I attains those

What Can Causal Powers Do for Interventionism?  133 values, X ceases to depend upon the values of other variables that are causally relevant to X.’ (Woodward and Hitchcock 2003: 12–13) The purpose of intervention variables is to do justice to the role of interventions in controlled experiments. To find out whether some variable X is causally relevant to some variable Y in an experimental situation, one must manipulate the value of X and hold all possible confounding factors fixed. Confounding can occur when the intervention is directly causally relevant to the effect under consideration. For example, if the effect of a painkiller on headaches is being studied, an intervention could be to offer a painkiller to a person with headaches. However, if the intervention consists of offering a painkiller together with a glass of water, the intervention itself might be directly causally relevant to the effect variable, since headaches can sometimes occur when a person is (mildly) dehydrated, and therefore, drinking water may also have a positive effect on headaches. Condition (2) is designed to eliminate this type of confounding. Sometimes confounding occurs because the intervention is correlated with some other cause of the effect variable. For example, if a person’s headache is due to too much exposure to the sun, and the intervention is to ask her to come into an air-conditioned room to take a painkiller, the intervention is interfering with a possible cause of the headache. Condition (3) is designed to rule out such confounding. In the next section, however, I argue that condition (3), and thus Woodward’s definition of an intervention, becomes problematic if the variable Z, that is, the variable describing possible alternative causes of Y, can be disjunctive. The Problem of Disjunctive Causes Consider a causal structure with two variables, one describing whether a person has a headache and one describing whether the person has an allergic rash. Suppose, somewhat simplistically, that the variables are binary and defined as follows: R:= 1 if Person P has allergic rash; 0 otherwise H:= 1 if Person P has a headache; 0 otherwise If an experimenter wants to find out whether H is causally relevant to R, the interventionist criterion requires that she carry out an intervention on the value of H and observe whether this intervention has an effect on the value of R. Suppose, in contrast to the experimental setup described in the previous section, where the goal was to investigate the effect of a painkiller

134  Vera Hoffmann-Kolss on headaches, the experimenter now has a painkiller that she knows to be very effective against headaches. Accordingly, if the initial value of H is H = 1, that is, if Person P has a headache, an obvious intervention is to administer this painkiller. Again, this intervention must satisfy the conditions of an intervention variable described in the second section. In particular, it must satisfy condition (2) and not be causally relevant to R via a causal path that excludes H. This condition would be violated, for example, if the painkiller also had an effect on allergic rashes. The intervention must also satisfy condition (3) and not be correlated with any other cause of R that is on a causal path that excludes H. For example, if Person P is allergic to apples and develops an allergic rash after eating apples or apple products, administering the painkiller with a glass of apple juice would not satisfy this condition. However, if administering the painkiller to Person P does satisfy the conditions of an intervention, and if it does indeed have an effect on the value of R, then the experimenter is justified in concluding that H is causally relevant to R. Note that the converse is not true. The interventionist causal criterion has the structure of an existential condition: if there is an intervention on X that changes the value of Y, then X is causally relevant to Y. If a particular intervention on X does not produce a change in Y, then it cannot be excluded that there is some other intervention on X that does change the value of Y. If, however, it can be plausibly concluded that no intervention on X changes the value of Y, then X is not causally relevant to Y. One of the strengths of the interventionist approach to causation is that it analyzes not only causal relations between two relata but also entire causal networks. Accordingly, interventionism is able to represent even complex causal structures with multiple interconnections. Taking into account the more complex causal structure is also crucial for the notion of intervention, since interventions must be independent of possible alternative causes of the effect in question. For example, as noted earlier, if Person P is allergic to apples and develops an allergic rash when consuming apples or apple products, then the intervention on Person P’s headache should not interact with the following variable: A:= 1 if Person P consumes apples or apple products; 0 otherwise. Moreover, as was also pointed out earlier, an intervention on H with respect to R should be independent not only of A but also of any other variable that is causally relevant to R on a causal path that does not include H. Interventionism per se does not rule out that the variables to be taken into account are logically disjunctive or otherwise logically complex. This is consistent with the pragmatic approach of interventionism, according to which the variables included in a causal structure should be chosen according to the purpose of the scientific inquiry (Woodward 2016). Variables

What Can Causal Powers Do for Interventionism?  135 assuming logically compound values should be taken into consideration if this is in accordance with the purpose of scientific inquiry. Considerations concerning the metaphysical structure of the properties represented by the values of a variable are at best of secondary importance. Variable A illustrates this consideration. The value A = 1 represents a disjunction of different properties, eating (pure) apples and eating (processed) apple products. In this context, it makes perfect sense to consider a disjunctive variable that refers to apples and all foods containing apples, since the relevant property is not how exactly the apples are prepared but whether the person somehow ingests substances contained in apples. Not all disjunctive variables are like this, however. Consider another disjunctive variable that is defined as follows: (A v not-I) := 1 if Person P consumes apples or apple products or does not take a pain killer; 0 otherwise The ‘or’-operator in (A v not-I) is to be understood as nonexclusive; that is, the variable assumes the value (A v not-I) = 1 if P consumes apples and an apple product and does not take a painkiller. Obviously, (A v not-I) is a rather artificial variable. But it does cause problems for the interventionist criterion of causation. To see this, first note that (A v not-I) is causally relevant to both R and H. To see that (A v not-I) is causally relevant to R, suppose that Person P does not have an allergic rash, that is, R = 0. Further suppose that she has not yet taken any painkillers and has not consumed any apples or apple products. Given the disjunctive structure of (A v not-I), this implies that (A v not-I) = 1. If P is now offered a glass of apple juice, which she is willing to drink, this is an intervention that changes the value of (A v not-I) to (A v not-I) = 1. But this intervention also changes the value of R: if Person P drinks the apple juice, she is likely to develop an allergic rash. Note that not every intervention that changes the value of (A v not-I) will have an effect on the value of R. If the value of (A v not-I) is manipulated by asking Person P to take a painkiller instead of drinking the apple juice, the value of R will remain unaffected. Here the fact that the interventionist causal criterion has the structure of an existential requirement becomes relevant again. There is an intervention on (A v not-I) that changes the value of R, and this is sufficient to conclude that (A v not-I) is causally relevant to R. Since it can be shown exactly analogously that (A v not-I) is also causally relevant to H, it follows that (A v not-I) is causally relevant to both R and H. This structure is illustrated in Figure 7.1. If (A v not-I) is causally relevant to R, then the interventionist criterion of causation becomes problematic. Recall that the original question was whether H is causally relevant to R. An intervention variable on H with respect to R must satisfy condition (3) of the definition of an intervention:

136  Vera Hoffmann-Kolss R (A v not-I) H

Figure 7.1 Causal structure in which the disjunctive variable (A v not-I) describing the use of painkillers (I) and the consumption of apples or apple products (A) is causally relevant to both allergic rash (R) and headaches (H).

it must not be correlated with any variable Z that is causally relevant to R through a route that excludes H, be the correlation due to the intervention’s being causally relevant to Z, Z’s being causally relevant to the intervention, the intervention and Z sharing a common cause or some other reason (Woodward and Hitchcock 2003). In the causal structure depicted in Figure 7.1, (A v not-I) is such a variable Z, since it is causally relevant to R through a route that excludes H. However, an intervention on H that consists of administering a painkiller to Person P is correlated with (A v not-I) for some other reason, the reason being that the intervention variable describing it is a logical component of (A v not-I). Therefore, administering a painkiller does not satisfy the conditions of an intervention on H with respect to R. And even worse, no other possible intervention satisfies this condition! The not-I component of (A v not-I) can be replaced by any possible intervention variable I. (A v not-I) will then still be causally relevant to R, and I will not satisfy condition (3). But then there is no variable I that can be an intervention variable on H with respect to R, and given the logical structure of the interventionist criterion of causation, this implies that H cannot be causally relevant to R on purely formal grounds – regardless of what the true causal structure is. Moreover, the problem does not depend on this particular example. It arises whenever one tries to investigate the causal influence of some variable X on some variable Y which has some other cause Z. Then any intervention variable I can be combined with Z to form a disjunctive variable (Z v not-I), and the situation has exactly the same structure as shown in Figure 7.1 (with X = H, Y = R, and (A v not-I) = (Z v not-I)). Accordingly, there is no variable I that satisfies the conditions of an intervention variable on X. One possible response is to argue that condition (3) should not be interpreted too strictly. Although the intervention of administering a painkiller is correlated with the disjunctive variable (A v not-I), the correlation is not due to any causal connection but arises only from the logical structure of (A v not-I), and such correlations should be exempted from the conditions that an intervention variable must satisfy.

What Can Causal Powers Do for Interventionism?  137 However, this would lead to even more problematic results. Suppose that H is in fact causally independent of R, that is, there is no causal relationship between Person P’s headache and her allergic rash. Suppose the initial value of H is H = 1, that is, Person P has a headache, and the initial value of R is R = 0, that is, Person P does not have an allergic rash. Further assume, as earlier, that she has not taken any painkillers and has not consumed any apples or apple products, that is, (A v not-I) = 1. Now suppose that P is given a painkiller that effectively cures her headache, so that the value of H changes to H = 0. The interventionist criterion of causation requires that an intervention on the cause variable under consideration must hold the values of all other variables not on a causal path between the cause and effect variables fixed. Accordingly, if Person P is given a painkiller, the value of (A v not-I) must be held fixed. Given that (A v not-I) = 1, this means that P must consume an apple or an apple product. But then she is likely to develop an allergic rash. It follows that if the value of H is changed by an intervention while the value of (A v not-I) is held fixed, the value of R will also change – even though H and R are causally unrelated. But this seems absurd. The real problem seems to arise from the assumption that artificial variables with the structure of (A v not-I) must be taken into account when carrying out interventions. How can this be avoided? In the next section, I argue that causal powers might prove helpful in this regard. Logically Complex Variables: A New Field of Work for Powers? As argued in the previous section, the interventionist criterion of causation is problematic when causal structures include logically complex variables that contain intervention variables as components. An immediate response might be to simply exclude disjunctive variables. It is well known in formally oriented metaphysics and philosophy of science that disjunctive entities cause problems here and there, and it may be a perfectly legitimate move, at least in some contexts, to simply ban them from theory. It is also well known that not everything that can be formally written as a disjunction is a disjunctive entity. The property of eating an apple is logically equivalent to the property of either eating an apple and eating a piece of chocolate or eating an apple and not eating a piece of chocolate (i.e., (eating an apple & eating chocolate) v (eating an apple & not eating chocolate)). However, this does not mean that it is a disjunctive property. Often, disjunctiveness is defined in terms of naturalness. The classical metaphysical view in this respect is that of Lewis, according to which there is a class of perfectly natural properties that are included in the fundamental laws of nature (Lewis 1983, 1986). Other properties can be constructed from perfectly natural properties by logical operations. The more logical

138  Vera Hoffmann-Kolss operations are required to construct a property from perfectly natural properties, the less natural it is. This means that properties can be ordered according to their degree of naturalness. A property is disjunctive if it is less natural than any of the disjuncts into which it can be decomposed (Langton and Lewis 1998). Would it help to exclude variables some of whose values represent disjunctive properties? Obviously, the problematic variable (A v not-I) would have to be excluded. One of its values represents the state that Person P consumes apples or apple products or does not take a painkiller, and this state is clearly constituted by a property that is disjunctive in Lewis’s sense. However, as noted previously, a strict prohibition on disjunctive variables in causal structures would be too strong a requirement. In investigating whether Person P’s headaches are causally related to her developing a rash, one must keep in mind other possible causes of her rash. And, given the context, the disjunctive variable A, representing whether she consumes apples or apple products, is one of those variables. One might object that instead of the disjunctive variable A, one could consider a variable representing whether Person P consumes apples and another variable representing whether she consumes apple products. However, it is plausible to assume that the property of consuming apple products is also disjunctive and consists of an infinite set of disjuncts representing the various apple products one might consume: apple juice, apple pie, apple ice cream, red cabbage with apples, and other possible apple dishes that have not even been invented. Given that causal structures are supposed to consist of a finite set of variables, one cannot include all these disjuncts into a causal structure. However, all these disjuncts are captured under the umbrella property of consuming apple products. The reason why it makes sense to use the disjunctive umbrella variable A is that all the disjuncts of consuming apples or apple products share a causal power that is relevant in the given context – the power to produce a rash in people with a certain condition. The crucial difference between variable A and variable (A v not-I) is not that the latter is even more disjunctive than the former but that the values of (A v not-I) represent even more diverse causal powers than the values of A. Here, then, is my hypothesis about how the interventionist framework can benefit from considerations about causal powers. The values of variables in a causal model represent properties or events that are constituted by properties. According to Shoemaker’s (1980) causal conception of properties, properties confer conditional causal powers on their bearers. For example, the property of being a painkiller, instantiated by a pill, gives the pill the causal power to relieve headaches on the condition that it is swallowed by a person who has headaches.

What Can Causal Powers Do for Interventionism?  139 Now consider condition (3) of Woodward’s definition of an intervention. According to this condition, an intervention variable I for X, with respect to Y, must not be correlated with any variable Z that is causally relevant to Y through a route that excludes X. Suppose that Z is disjunctive in the sense that at least one of its values has multiple disjuncts. According to Shoemaker, each of these disjuncts confers a set of conditional powers on its bearers. Consider the intersection S of all these sets. The intervention variable I should be required to be independent of Z iff S is not empty and at least some of the powers contained in S are relevant to Y. Otherwise, if S is empty or if all the powers contained in S are not relevant to Y, the intervention variable I need not be independent of Z. In our example scenario involving Person P, her headaches, and her allergic rash, an intervention on H should be independent of variable A. If A = 1, then the disjuncts of this value share a conditional causal power, the power to cause rashes in people who are allergic to one of the components of apples and who ingest apples. Moreover, this power is directly relevant to the effect variable R. In contrast, an intervention on H need not be independent of (A v not-I). It is plausible to assume that the intersection of the conditional causal powers of eating apples, eating apple products, and not taking a painkiller is empty. Therefore, (A v not-I) does not fall into the category of variables that need to be considered as possible confounders. If Z is non-disjunctive, then each of its values is non-disjunctive. Suppose that Zi is one of the values of Z. Then Zi confers a characteristic set of conditional causal powers on its bearers. Since Zi is non-disjunctive, it has only one disjunct, and the set S is identical to the conditional causal powers of Zi. It is plausible to assume that Z is causally relevant to Y if some of the conditional powers of any of its values are relevant to Y. Therefore, the limiting case in which Z is non-disjunctive collapses into the original definition of an intervention: an intervention variable I for X, with respect to Y, must not be correlated with any variable Z that is causally relevant to Y via a route that excludes X. This consideration is in accordance with a restriction on variables imposed by Woodward (2016), who argues that the variables appearing in a causal model should have unambiguous effects on the other variables in the model. One way to understand the notion that variables have ambiguous effects is to assume that the powers of their values are too diverse: if the value of (A v not-I) is manipulated by administering a painkiller to Person P, the possible effects of this manipulation will be very different from the possible effects of a manipulation that consists of feeding apples to P. The powers-based account proposed in this section provides a metaphysical explanation of what ambiguous manipulations might be and why they should be avoided.

140  Vera Hoffmann-Kolss Conclusion The aim of this argument was to show that supplementing the interventionist criterion of causation with a condition based on causal powers can solve a problem arising from logically complex variables. Of course, the argument does not show that powers ontology is the only way to solve the disjunctive variable problem described in the second section. Moreover, it leaves open the extent to which the interventionist criterion might benefit from considerations about causal powers. However, I have already argued elsewhere that the interventionist criterion of causation must rely on stronger metaphysical assumptions than is often assumed, and in particular must presuppose the distinction between metaphysical and nomological necessity (Hoffmann-Kolss 2022). The argument of this chapter can therefore be seen as an example of a more general claim: interventionist causation can only count as a fully-fledged philosophical theory of causation if it relies, at least to some extent, on substantive metaphysical claims about causation and causal relations – be they claims about necessity, causal powers, or something else. References Baltimore, J. (2019), ‘Expanding the Vector Model for Dispositionalist Approaches to Causation’, Synthese 196(12): 5083–5098. Baumgartner, M. (2009), ‘Interventionist Causal Exclusion and Non-reductive Physicalism’, International Studies in the Philosophy of Science 23(2): 161–178. Bird, A. (2007), Nature’s Metaphysics: Laws and Properties: Oxford University Press. Cartwright, N. (1989), Nature’s Capacities and Their Measurement, Oxford: Oxford University Press. Gebharter, A. (2017), ‘Causal Exclusion and Causal Bayes Nets’, Philosophy and Phenomenological Research 95(2): 353–375. Hausman, D.M. (2005), ‘Causal Relata: Tokens, Types, or Variables?’, Erkenntnis 63(1): 33–54. Hitchcock, C. (2001), ‘The Intransitivity of Causation Revealed in Equations and Graphs’, Journal of Philosophy 98(6): 273–299. Hitchcock, C. (2007), ‘Prevention, Preemption, and the Principle of Sufficient Reason’, Philosophical Review 116(4): 495–532. Hoffmann-Kolss, V. (2022), ‘Interventionism and Non-Causal Dependence Relations: New Work for a Theory of Supervenience’, Australasian Journal of Philosophy 100(4): 679–694. Kroedel, T. and Schulz, M. (2016), ‘Grounding Mental Causation’, Synthese 193(6): 1909–1923. Langton, R. and Lewis, D. (1998), ‘Defining “Intrinsic”’, Philosophy and Phenomenological Research 58(2): 333–345.

What Can Causal Powers Do for Interventionism?  141 Lewis, D. (1983), ‘New Work for a Theory of Universals’, Australasian Journal of Philosophy 61(4): 343–377. Lewis, D. (1986), On the Plurality of Worlds, Malden, MA: Blackwell Publishers. Molnar, G. (2003), Powers: A Study in Metaphysics, edited by S. Mumford, Oxford: Oxford University Press. Mumford, S. and Anjum, R.L. (2011), ‘Spoils to the Vector - How to Model Causes If You Are a Realist about Powers’, The Monist 94(1): 54–80. Pearl, J. (2000), Causality: Models, Reasoning, and Inference, Cambridge: Cambridge University Press. Schaffer, J. (2016), ‘Grounding in the Image of Causation’, Philosophical Studies 173(1): 49–100. Shoemaker, S. (1980), ‘Causality and Properties’, in P. Van Inwagen (ed.), Time and Cause. Essays Presented to Richard Taylor: Reidel: 109–136; quoted from: S. Shoemaker (1984), Identity, Cause, and Mind: Cambridge University Press: 206–233. Spirtes, P., Glymour, C. and Scheines, R. (2000), Causation, Prediction and Search, 2nd ed., Cambridge, MA: The MIT Press. Vetter, B. (2015), Potentiality: From Dispositions to Modality: Oxford University Press. Wilson, A. (2018), ‘Metaphysical Causation’, Nous 52(4): 723–751. Woodward, J. (2003), Making Things Happen: A Theory of Causal Explanation, New York: Oxford University Press. Woodward, J. (2015), ‘Interventionism and Causal Exclusion’, Philosophy and Phenomenological Research 91(2): 303–347. Woodward, J. (2016), ‘The Problem of Variable Choice’, Synthese 193(4): 1047–1072. Woodward, J. and Hitchcock, C. (2003), ‘Explanatory Generalizations, Part I: A Counterfactual Account’, Noûs 37(1): 1–24.

8 Collective Powers Xi-Yang Guo and Matthew Tugby

Some powers appear to be built out of others.1 There are higher-level powers, such as a screen’s powers to display various images, and lower-level powers, such as each pixel’s powers to display various colours. It is natural to think that higher-level powers are grounded in, or even composed by, lower-level powers. Thus, the relationship between higher- and lower-level powers might well be a prime example of a relationship of composition between properties. However, this appealing picture comes under pressure from three angles: (1) Is the very notion of a higher- and lower-level structure of powers coherent, or explanatorily useful? (2) What precisely is the relationship between higher- and lower-level powers? (3) What is it about the intrinsic natures of powers which make such structures possible? Our chapter addresses these questions by exploring a novel theory of higher-level powers, according to which such powers are collectively grounded by lower-level powers. Moreover, it is argued that in order to accommodate higher-level powers in a satisfactory way, we might have to accept that some powers are plurally instantiated. This theory can solve various puzzles about higher-level powers and their bearers. However, while there has been some focus on plural predication (e.g. Oliver and Smiley 2001), the topic of plural instantiation and collective properties has to a large extent been neglected by powers theorists and metaphysicians generally.2 We speculate that this is due in part to a widespread implicit commitment to an Aristotelian conception of instantiation, according to which a property can only be instantiated singularly by an individual.3 Our aim in this paper is to challenge this tradition and open up conceptual space for new ways of thinking about higher-level powers and their relationship to lower-level powers. Although it is too early to tell whether the DOI: 10.4324/9781003298830-11

Collective Powers  143 theory proposed is the best, it is certainly one which is parsimonious in various respects: First, since collective plural predication is not systematically construable as singular predication on aggregates or sums (Lewis 1991, Oliver and Smiley 2001) our account’s ideology does not imply a commitment to singular bearers of higher-level powers. Moreover, if we accept that higher-level powers are plurally instantiated by low-level entities, then there is no obvious ontological need to posit higher-level composite individuals as possessors of the higher-level powers. Thus, our account is able to bypass recent problems that Heil (2021) raises about composite substances. The paper is structured as follows: In the next section, we introduce powers-based theories of properties and the notion of higher-level powers. In the third section, we introduce puzzles that arise in connection with composite property-bearers and higher-level powers, drawing on recent work by John Heil. In the fourth section, we begin to respond to Heilean scepticism about higher-level powers by introducing the idea that higherlevel powers are genuine collective (non-distributive) properties which are plurally instantiated. We discuss preliminary arguments for thinking that some properties are irreducibly collective and plural. In the fifth section, we develop the idea further, focusing on the relationship between collective powers and the properties of the individuals which plurally instantiate those powers. We claim that this relationship is typically one of grounding and speculate that it is a species of composition. In the sixth section, we anticipate and address some objections that the proposal is likely to face. In the final section, we briefly address some remaining metaphysical questions about the causal efficacy of higher-level powers and the ultimate source of the grounding of higher-level powers. Powers and Higher-level Properties In this chapter we assume from the start that there is an intimate metaphysical connection between properties and powers. Consider a snooker ball. It has the property of being spherical, which means it has the power to roll down an incline. Many of us do not think it is a contingent fact that this property confers this power. Properties are not inert but rather confer causal power(s) on their bearers as a matter of metaphysical necessity. Moreover, we take it that this metaphysical necessity is not a brute feature of the world. There are at least three possible sources of the necessary connection between properties and powers. This necessary connection might be a consequence of the fact that properties are essentially powerful (the theory of dispositional essentialism), that properties are identical with powers (identity theory), or that properties metaphysically ground powers (the grounding theory of powers). For the purposes of this chapter,

144  Xi-Yang Guo and Matthew Tugby we remain neutral about which of these three theories is correct.4 We take this issue to be a matter for in-house dispute between those who, unlike neo-Humean philosophers, take causal powers metaphysically seriously. What advocates of all these anti-Humean theories can agree on is that properties are not merely categorical: they confer genuine powers by their very natures. If we follow powers theorists and accept that powers are part of the world’s ontological furniture, questions quickly arise about how many or which types of power there are. All powers theorists can probably agree that the fundamental properties figuring in our best physics are genuine, such as charge and spin (indeed, an influential argument for the powers metaphysics is precisely that the theoretical properties of physics appear to be defined in exclusively dispositional terms). But beyond that, there is room for disagreement. For example, Mumford and Anjum (2011: 17) appear to take a liberal stance, accepting that there might be what Bird (2016: 342) calls ‘macro-powers’, which exist at higher (non-microscopic) levels of nature (see also McKitrick (2018), who proposes a particularly abundant conception of powers). Recently, however, Bird (2016, 2018) has questioned whether the powers theory should be extended beyond physics and certain parts of biology. Heil (2003, 2012) takes an even more sceptical line against higher-level powers and argues that there is no room in our ontology for properties of composite objects, even though it is often useful to employ higher-level predicates for various purposes. We are attracted to the idea that the world exhibits causally powerful properties other than those found in fundamental physical theory. As the world takes more complex forms, in the special sciences and everyday life, an array of further powers appears to play an ineliminable role in how we view, and theorise about, the world. These are what we are calling the ‘higher-level’ powers.5 For example, at the molecular level, we find chemical properties with distinctive dispositional profiles, which allow them to play important predictive and explanatory roles in chemical theory. The same could be said of biological properties, geological properties, economic properties, and so on. Our everyday dealings with medium-sized dry goods also seem to reveal a wide range of higher-level causally powerful properties. I miss my alarm in the morning. (Damn.) If I drive really fast, can I still get to work on time? The concern here is with what is possible. On the powers ontology that we are assuming, it is a concern with what powers there are – specifically (albeit colloquially), what powers my car has. But it is not, directly, a concern about the powers that the parts of my car each have (the wheels can go round), nor is it a concern about any mere conjunction of those powers (the wheels can go round and the fuel can combust). The concern

Collective Powers  145 is only with what these lower-level powers jointly contribute to – namely the power to be driven at high speeds. Note also that the power to be driven at high speeds is not the kind of property that a quark can have. It is a property that can only arise at a certain level of complexity. However, that is not to say that higher-level powers are metaphysically emergent. ‘Emergent property’ is a slippery term – even within academic philosophy – but the term is usually used to get at the idea that a property is basic and not fully explicable, even though it depends in some way on other properties. However, the power that a car has to be driven is surely not inexplicable in that way: we can explain why the car has this power with reference to the powers had by the car engine, the gearbox, the wheels, and so on. This point will be of importance later on. Unfortunately, this very natural picture of higher-level powers raises some difficult philosophical questions. For example: What are the bearers of higher-level powers? What is the relationship between higher-level powers and the low-level powers on which they apparently depend? If higherlevel powers are dependent entities, do we really need them in our ontology? Is there not a danger that the alleged causal efficacy of higher-level powers is undermined by the low-level powers on which they depend? In the discussion that follows, we shall use John Heil’s work on substance and properties as a point of departure for thinking about some of these questions. This is a useful starting point insofar as Heil’s work suggests reasons to be sceptical about the existence of higher-level powers. While we agree with some aspects of Heil’s picture, it will become clear that we are more optimistic than him about the prospects of accommodating higher-level powers as genuine elements of ontology. More precisely, our speculative proposal is that paradigmatic higher-level powers can be regarded as genuine collective, or non-distributive,6 properties. A collective property is one which is jointly instantiated by some things, plural, rather than a singular thing. Our proposal thus clashes with the broadly Aristotelian tradition mentioned earlier, according to which a property is always instantiated by an individual. Importantly, in the fourth section, we shall see that it is far from clear that collective properties can be explained away. Scepticism about Composite Substances and Higher-level Powers Suppose you thought that only substances are the bearers of properties. Then, it would seem plausible that if there are higher-level properties, they are instantiated by mereologically complex substances. The idea would be that a property is a higher-level one precisely because it is instantiated by a complex particular rather than a simple one. Such complex particulars are

146  Xi-Yang Guo and Matthew Tugby what Lowe calls ‘composite substances’ (1998: 190).7 Aristotelians typically accept that there are composite substances but disagree on precisely which objects count as composite substances. This disagreement largely turns on what one thinks it takes for a bunch of parts to compose a substance, as opposed to a mere aggregate or collective such as a pile of stones (Lowe, 1998: 162). According to some Aristotelian hylomorphists (e.g. Koslicki 2008, 2018), a composite substance must be composed of parts of a certain kind and have an organisational or functional unity that is imposed by the natural kind (substantial form) that the substance exemplifies. Complex organisms are often given as paradigmatic examples of composite substances, but artefacts such as clocks (Lowe 1998: 164) or motorcycles (Koslicki 2018: 27) could also be examples. Details aside, the important point for current purposes is that once we have Aristotelian composite substances in play, it is entirely natural to ascribe higher-level powers to them – powers which are not had by any of the composite substance’s proper parts. For example, a clock as a unified whole has the power to convey time even though none of its simple parts has that power. This picture of complex particulars and higher-level powers is a very natural one and probably accords well with what Heil and others call the manifest image of the world. But unfortunately, this natural metaphysical picture is not without its problems. Heil (2012, 2021), for one, has recently reiterated his scepticism about composite substances and their alleged properties. Heil (2003: Ch. 11) certainly embraces the notion of substance and accepts that only substances are the bearers of properties. And properties, for Heil, are identical with powers. However, Heil is sceptical of the notion of a composite substance, favouring a view on which all genuine substances – that is, property bearers – are simple. Simple substances, on Heil’s definition, are substances which have no further substantial parts: they are mereologically simple (although they might nevertheless have a spatial or temporal extension). Obvious candidates for the simple substances are the subatomic particles (or perhaps fields) of physics. Heil (2021: 58) argues that the postulation of complex substances and the higher-level powers they allegedly bear is unnecessary and implausible, involving a sort of metaphysical double-counting. For Heil, accepting composite substances (and their properties) is a bit like saying someone has three objects in their pocket because they possess two coins plus the sum of the two coins. The sum exists (in some sense), but one should not regard it as a third object that is additional to the two coins (ibid.:58). The same goes for a tomato. For Heil, a tomato might appear to be a complex substance bearing higher-level powers like redness or sphericality, but on closer metaphysical and scientific inspection, this appearance is deceptive. The tomato is nothing over and above simple substances dynamically arranged in a certain way. One does not need to accept that, in addition,

Collective Powers  147 there is a tomato or a property of redness. However, to be clear, Heil (2021: 45; 52) claims not to be an anti-realist, reductionist or eliminativist about tomatoes or their redness. On Heil’s picture, we can truly say that there are tomatoes and that such things are red. The point is just that the deep truthmaking story about tomatoes need not involve complex substances bearing ontic macro-properties like redness. Tomatoes exist, then, but are not what they appear to be. If the simple substances are atomic then the truth that tomatoes are red is likely to be made true by a fleeting, dynamic arrangement of particles, none of which is itself red. We see the attraction of Heil’s rejection of complex substances. If we can do without them, and let the simple substances (or a monistic substance) do the truthmaking work, then we are left with a more parsimonious metaphysical picture.8 However, what is of interest for current purposes is the question of whether we should also jettison higher-level powers along with composite substances. Heil appears to infer that if there are no composite substances, then there can be no higher-level powers (ontologically speaking) such as redness or sphericality, mental properties, or the sorts of properties posited in the special sciences. Thus, Heil’s picture jettisons a vast array of powers from our metaphysics. Heil’s theory still permits us to speak truly of higher-level powers, but metaphysically speaking, such powers are redundant: the ontology of higher-level powers is just an ontology of low-level powers and nothing more. Insofar as we speak of higher-level properties, they are merely properties by courtesy, quasi-properties (Heil 2021: 58), or ‘Episcopalian’ properties (Heil 2012: 152). Higher-level Powers as Collective Properties: the Case for Plural Instantiation One of the aims of this chapter is to question Heil’s sceptical conclusion regarding higher-level powers. We suggest that even if it is only simple substances that are the bearers of properties, there might still be metaphysical room for so-called higher-level powers. In particular, we explore the idea that higher-level powers like redness are irreducibly collective properties which are plurally instantiated by simple substances. This idea is compatible with Heil’s rejection of complex substances. It merely requires us to be open-minded about the kinds of properties that simple substances instantiate. While a simple substance can instantiate a property on its own as the standard Aristotelian picture suggests, simple substances can also work together to instantiate certain properties collectively. What we call higher-level powers would be properties of this latter sort. Such powers – and their associated properties – would be plurally instantiated. Why think that collective properties are needed in the metaphysical inventory? Presumably, those sympathetic with Heil’s picture will say that even if there are predicates which truly apply to pluralities rather than

148  Xi-Yang Guo and Matthew Tugby singular subjects, the deep truthmaking story is not one that requires us to posit genuine collective properties – namely properties which are plurally rather than singularly instantiated. Against this view, we now present an argument in favour of collective properties. While we do not intend our argument to settle every question, we do mean to put collective powers on the table as a live option. To this end, we first marshal some considerations in favour of irreducibly plural predication, before turning to plural instantiation. Consider the wheels on a bus. For the wheels to go round and round is – all being well – nothing more or less than for each wheel to go round and round. The predicate goes round and round can apply to the wheels plurally, but its doing so is equivalent to its applying to each wheel individually. In such cases, where the Fs are G is equivalent to each F is G, we say that G occurs distributively. We describe any predicate that is not distributive as collective or nondistributive. Consider the seats on a bus. The seats are arranged in rows. On pain of nonsense, this is not equivalent to their each being arranged in rows. The predicate arranged in rows applies to the seats (plural) but not to each seat; a fortiori, its applying to the seats (plural) cannot be equivalent to its applying to each seat.9 To attempt to reduce all apparently collective predicates to distributive ones is tempting. For logics admitting only singular predication are familiar, while plural logics have – until recently – remained little explored. However, a solid case has been made in the literature for the existence of irreducibly collective plural predicates (see e.g. Lewis 1991, Oliver and Smiley 2001, Yi 2002). Two salient reduction strategies (Oliver and Smiley 2001) are Changing the Predicate (CTP) and Changing the Subject (CTS). Each strategy attempts to fully replace apparently plural apparatus with familiar, singular constructions: in the predicate place and the subject place, respectively. Consider the collective statement the premises entail the conclusion. CTP proposes reducing this to: each premise co-entails the conclusion. But co-entails and entails are simply different predicates. What we have shown is that the premises co-entail the conclusion is distributive, but not that the premises entail the conclusion is. Adding that the premises entail the conclusion iff each premise co-entails the conclusion merely shows the premises entail the conclusion to be equivalent to a statement that is distributive – not that it is itself distributive. (Nor does this equivalence make any reductive moves available for CTP – for each premise co-entails the conclusion only because the premises entail the conclusion.) So as a strategy for showing that collective predicates are reducible to distributive ones, CTP falls flat.10 CTS offers a more sophisticated approach: replace the plural subject the premises with a singular aggregate such as the set of premises. Against this

Collective Powers  149 view, Oliver and Smiley (2001: 292f.) offer two lines of reply. The first is that replacing plural things with singular sets of things does not eliminate the collectivity of the example but merely buries it a little deeper. Since entailment is a matter of truth-preservation and sets are not truth-apt, no set can entail a conclusion. Rather, it is the members of a set of premises which entail a conclusion. But making this explicit shows up the set itself as redundant: the members of the set entail the conclusion collectively. Oliver and Smiley offer a further, general argument against CTS which is schematic and aims to take down any version of CTS. (Lewis 1991: 68 makes the same case). Considered schematically, CTS licenses the replacement of the Fs are G with the H of Fs is G for some value of H, where H is some term standing for an aggregate of Fs. CTS will not work without committing, in each case, to some particular instance of the schema and, hence, some specific aggregate kind as a value of H. But problems arise when we consider any such instance. Consider the example: the forces are in equilibrium. Waiving the previous argument, CTS recommends substituting: the set {F} is in equilibrium.11 But once we are in the business of replacing plural talk with talk of sets, CTS forces us to be all in: plural talk is replaceable by set-talk in general. In particular, then, plural statements about sets12 should be treatable by the same strategy. From here it is a short step to a Russellian paradox: there are plural truths about the nonselfmembered sets,13 and CTS forces us to treat these as singular truths about a set of the nonselfmembered sets. We consider these arguments against CTP and CTS to be persuasive: some plural predicates are irreducibly collective. It does not automatically follow from this, however, that any properties are irreducibly collectively instantiated. The remainder of this section considers ways to bridge this gap. We assume that the existence of irreducibly collective predicates gives pro tanto reason to hold that there are corresponding collective properties, and consider strategies for blocking this move.14 In shifting focus from predicates to properties, the situation with CTP and CTS reverses.15 CTS becomes a straightforward non-starter, given that we are joining Heil in rejecting composite or higher-level substances: there is simply no room for apparently plural properties to be instantiated by singular but composite substances. CTP, however, becomes a live option. Since properties need not correspond with predicates, giving an account of an apparently plural property in terms of different singularly instantiated properties is not – at least on the surface – a misguided idea. To illustrate CTP for properties, consider two examples: the lights make a pattern, and the jury members are unanimous. In the first case, CTP substitutes a reduction base involving each light and its location.16 In the second case, the base includes each jury member and their respective belief. The objection will then be that our commitment to collective power

150  Xi-Yang Guo and Matthew Tugby properties is superfluous: given each light and its location (each jury member and their belief), the facts about patterns and unanimity are fixed: for the lights to make this pattern just is nothing more than for each light to be located thus-and-so (mutatis mutandis each jury member). To this line of objection, we reply that CTP’s attempt to reduce away the apparent collectivity of our examples simply fails. Recall that our proposal here includes three claims: an existence claim (there are higher-level powers), a grounding claim (higher-level powers are grounded collectively by low-level ones), and an explanatory claim (higher-level powers do distinctive explanatory work). CTP attempts to undermine this picture by arguing that the explanatory claim is false because the higher-level powers can be reduced to low-level properties. In order for CTP’s reductive move to work, it must be the case that our examples of apparent collectivity are fully explainable in terms of reductive bases that do not themselves contain irreducible collectivity which plays the same explanatory role as the collectivity in our examples themselves. Indeed, on the face of it, offering each light and its location as a reduction base for the lights form a pattern appears to do exactly this. But there is a problem here which parallels Oliver and Smiley’s reply to CTS in the case of predicates. For each light and its location, taken singly, does not suffice for the lights to form a pattern. Rather, it is the aggregate which aggregates all of the lights and their respective locations which does so. For illustration, consider each light and its location as forming a fact that light l is at place p. Then the relevant aggregate will be the conjunctive fact: that l1 is at p1, that l2 is at p2, and so on. Now, recall that we are continuing to reject composite or higher-level entities, but this conjunctive fact is precisely such an entity. So, we cannot offer the conjunction itself as a reductive base for the fact that the lights form a pattern.17 This leaves us with only the conjuncts themselves. But the conjuncts – that l1 is at p1, that l2 is at p2, and so on – only collectively make it the case that the lights form a pattern.18 One may object here that if this line of argument is correct, then it proves too much: all plurals will turn out to be collective plurals. For suppose that the Fs are G is distributive. Then it is equivalent to each F is G. This, in turn, is equivalent to a conjunction of facts that Fn is G. But that conjunction will be true in virtue of the collective truth of its conjuncts. So goes the objection. But the objection fails to note a key feature of distributive plurals, whether involving properties or predicates: for a plural to be distributive, the Fs are G must be equivalent to each F is G where the occurrences of G on each side of the equivalence stand for the same thing. For example, the philosophers are in the pub is distributive because it is equivalent to each philosopher is in the pub. The conjuncts philosopher A is in the pub, philosopher B is in the pub … need only explain the emergence of the

Collective Powers  151 conjunction philosopher A is in the pub and philosopher B is in the pub. By contrast, in the example the lights make a pattern, the conjuncts that l1 is at p1, that l2 is at p2, and so on are jointly responsible for explaining not only the emergence of the conjunction but also the emergence of a pattern made by the lights. CTP fails in the case of the lights make a pattern because the reduction base that it offers does not do away with this collective element. We close this section with some clarifications. Just because plural collective powers cannot be eliminated in favour of logical constructions of singular properties, this does not mean that collective powers are somehow strongly emergent properties which are not explicable or predictable in terms of the various non-relational and/or relational properties of the individuals which collectively instantiate those powers. On the contrary, we take it that plurally instantiated collective powers are typically grounded in various properties of the individuals which make up the plurality (see the next section). Indeed, we take this to be the right lesson to draw from the CTP strategy discussed earlier. The character of a collective power will typically depend on the characters of the individuals that plurally instantiate the collective power. However, note that in our view, grounding does not entail ontological reduction. As should be clear already, the prospects for reducing collective (non-distributive) properties to collections of singular properties are dim. As we conceive it, grounding implies the opposite status of reduction. Reduction trades on identity: if one thing is ontologically reducible to another, that is because the one just is the other. However, metaphysical grounding is not compatible with identity. For one thing, grounding is an asymmetric and metaphysically generative relation while identity is not (see e.g. Audi 2012; Tugby 2022a: Ch. 6.2).19 Before proceeding, we must also acknowledge the possibility that not all the higher-level powers that philosophers speak of will turn out to be collective, non-distributive properties. For example, macroscopic things have mass and this might well be a distributive property.20 Heil may well be right that it is unnecessary to countenance higher-level powers like these in our ontology. To be clear, our endorsement of higher-level powers is restricted to the non-distributive collective properties. However, this will still capture many of the cases that are regarded as higher-level powers. Again, redness is likely to count as non-distributive because redness (or the light-reflectance disposition associated with redness) is arguably not a property had by any individuals in the relevant plurality. Collective Powers and their Grounding In everyday contexts, we freely ascribe higher-level powers, such as the power of a car to be driven at 70 miles per hour. As noted earlier, such talk

152  Xi-Yang Guo and Matthew Tugby seems to be justified by the fact that higher-level powers do important explanatory work, especially in the special sciences. On the account we are proposing, many of the so-called higher-level powers are indeed genuine ontic properties. More precisely, we have argued that some properties are irreducibly collective and cannot be explained away in terms of logical constructions of non-plural properties. In truthmaking parlance, it is difficult to see how truthmakers can be given for non-distributive plural truths which appeal only to non-plural properties. So, it seems the truthmakers for such truths must inevitably appeal to collective properties. As we have seen, this opens the ontological door for those so-called higher-level powers which can be interpreted as collective properties. We provide further examples in this section and consider the important question of how collective powers relate to the individual properties of the substances which plurally instantiate those powers. To continue first with the car example, we might say that its power to be driven at 70mph is plurally instantiated by the engine, the wheels, the gearbox and so on. Neither the engine, the wheels nor the gearbox individually has the power to be driven at 70mph, but collectively, they do. Notice, however, that this still cannot be the ultimate metaphysical story, since wheels and engines are arguably not themselves simple substances and (if we agree with Heil) therefore not really the kinds of things that can instantiate properties – plural or otherwise. Whilst it is often perfectly fine for explanatory purposes to speak of non-fundamental pluralities as instantiating higher-level collective powers (such as the power to be driven), the ultimate metaphysical explanation will be one which appeals only to pluralities of simple substances (whatever they may be). Thus, if an atomistic theory of substance is correct, the collective power to be driven is one that is collectively instantiated by a certain (large) plurality of particles.21 We can expect that different special sciences will also posit collective powers of varying complexity. Consider the following example from elementary chemistry: the dissolution of a portion of salt in water. H2O molecules surround the dissolved Na+ and Cl− ions. And if enough salt is present, the dissolved ions may saturate the water. However, no individual water molecule surrounds a dissolved ion, and no individual ion saturates the water: they instantiate these properties collectively. Let us now start to address in more detail an important question that this picture raises: How do collective powers relate to the individual lowerlevel properties (non-relational and relational) of the substances which plurally instantiate those collective powers? The first thing to note is that in the examples discussed, it is plausible that the collective powers are metaphysically determined by the properties of the individuals that plurally instantiate the powers. So, to repeat, we do not regard collective properties like the power to be driven as being metaphysically emergent.22

Collective Powers  153 In the cases discussed in this chapter, we take it that the relationship between higher-level collective powers and low-level powers is best thought of as involving some form of metaphysical grounding. We employ the term ‘grounding’ in much the same way as Bennett (2017) employs ‘building’. Grounding picks out a family of relations which each have three metaphysical features in common: they are asymmetric, necessitating, and generative. In the case of collective powers, the idea is that (i) they are grounded in the properties (non-relational and/or relational) of the individuals that plurally instantiate them, rather than vice versa; (ii) the instantiation of a collective power is necessitated by the properties (non-relational and/or relational) of the individuals that plurally instantiate that power; and (iii) the instantiation of a collective power is metaphysically generated by the properties (non-relational and/or relational) of the individuals that plurally instantiate that power. Again, in the cases we have examined, it seems overwhelmingly plausible that grounding is at work. The power of a car to be driven is collectively grounded by the powers instantiated by the engine, the gearbox, the wheels and so on. The power of some H2O molecules to form solvation shells around Na+ ions is collectively grounded by – inter alia – the power of each (electronegative) oxygen component to attract an (electropositive) Na+ ion. We said that talk of grounding refers to a family of finer-grained relations. These include relations such as composition, constitution, realization, set formation, and the relation of determination between determinate and determinable properties. Which of these specific relations might apply in the case of collective powers and the properties of the individuals on which those powers depend? We are open-minded, but if we take a suitably liberal stance towards what can compose what, and allow that some property instances might compose others, then it seems to us that the notion of composition might fit the bill here. Composition occurs when an entity is ‘made up’ of several others and it is typically a many–one relation. In contrast, many other common determination relations, such as constitution and realization, are typically a one–one affair, and therefore it is not plausible that these other relations apply in the cases we have discussed. Some philosophers reserve the term ‘composition’ for the category of objects, but it is also fairly common for philosophers to apply the concept of composition to entities in other ontological categories, such as events (Fine 2010), states of affairs and properties (Armstrong 1997 and McDaniel 2009), and, importantly for us, power instances (Marmodoro 2017). We propose to take a similarly liberal view of composition and follow pluralists in thinking there are different forms of composition (e.g. Fine 2010) which apply to different kinds of relata (e.g. McDaniel 2009). What emerges, then, is the following picture of so-called higher-level powers. Such powers are irreducibly plural properties, which means

154  Xi-Yang Guo and Matthew Tugby they are collectively instantiated by a plurality of individuals (simple substances). Our second, supplementary claim is that collective powers are grounded in the low-level properties (non-relational and relational) of the individuals that plurally instantiate those powers. To be more specific, higher-level (collective) powers are composed of low-level property instances. However, to be clear again, none of this means that collective powers are reducible. As we understand it, grounding relations do not entail reduction, and for reasons discussed, it is highly unlikely that collective properties can be reduced to properties of individuals or logical constructions thereof. Three further features of this grounding theory are well worth noting. First, we avoid exacerbating the problems of tractability that afflict views  on which powers are treated as merely functional ‘black boxes’ (Marmodoro 2022). Such views individuate powers by their manifestations – such as a power to roll downhill – but say little about what it is about the natures of powers in virtue of which they have these manifestations. Such ontologies of powers merely parcel up and label, rather than illuminate, the phenomena that powers are invoked to explain. We do not claim that our proposal completely clears up this mystery about the nature of powers. However, we do claim that the ingredients of our proposal – collective plural instantiation, grounding, and so on – are as tractable and transparent as any in metaphysics and hence do not compound or add to any ‘black box’ mysteries in explaining composition for powers. In particular, we avoid positing sui generis or otherwise mysterious composition relations to explain the part–whole structure of powers: powers composed by powers are simply collective powers. Second, our account, if correct, introduces a corresponding grounding constraint on what higher-level powers are ontologically admissible. Admissible higher-level powers are those that can be accounted for as collective powers. Third, our proposal is testable by counterexample: it fails if there are compelling reasons to accept a higher-level power which violates the grounding constraint. With our picture of collective powers now in place, we shall consider some immediate lines of resistance that the theory is likely to face. By offering replies to these objections, we shall hopefully shed further light on the theory. Some Objections and Replies In this section, we anticipate, and reply to, six objections to the theory sketched thus far. In what follows we convey the objections and replies through a discussion with an imaginary interlocutor.

Collective Powers  155 Objection 1 It is absurd to suggest that, for example, a bunch of particles can plurally instantiate the power to be driven at 70mph. Particles are just not the kinds of things that can be driven – collectively or otherwise. Only cars and other medium-sized vehicles can instantiate the power to be driven at 70mph. So, the theory is clearly wrong. We suspect that this kind of objection rests on an implicit commitment to the Aristotelian tradition in which a power has to be instantiated by a single individual.23 Of course, if one accepts this Aristotelian assumption, then a car – qua composite substance – will be the obvious candidate as the possessor of the power to be driven. However, once we leave such Aristotelian assumptions behind, a new possibility opens up: the power to be driven is collectively instantiated by substances at a more fundamental level.24 If we accept Heil’s arguments against composite substances, then the individuals in question might be simple substances such as the fundamental particles of physics. We do not deny that the so-called manifest image presents the world as one in which cars are composite objects that instantiate various higher-level powers. We also do not deny that it’s true to say that a car has such powers. The crucial point is just that the deeper truthmaking story behind such truths is that these higher-level powers are collectively instantiated by pluralities of fundamental entities. Like Heil’s (2021) theory, the view we have proposed about higher-level powers can be seen as an attempt to shed light on the relationship between the scientific and manifest images of the world. Objection 2 I’m still not convinced that you need irreducible collective powers in order to tell a plausible truthmaking story here. In the Aristotelian tradition, a property is said to be instantiated singularly by an individual. However, no sensible Aristotelian would deny that relations are instantiated by more than one thing. Can’t your so-called collective properties simply be analysed in terms of relations? Once the individuals in a plurality are relationally arranged in a certain way, do you not get the collective properties for free? If that’s the case, then ontologically speaking there is no need to accept collective powers in addition to relations.

156  Xi-Yang Guo and Matthew Tugby We think this suggestion paints a misleading picture of collective properties. Many collective properties are grounded not only in the relational features of a plurality but also specific non-relational properties of the relevant individuals involved. As we saw earlier, the power of some H2O molecules to form solvation shells around Na+ ions is collectively grounded in the power of each (electronegative) oxygen component to attract an (electropositive) Na+ ion. We take it that this power of each oxygen component is non-relational. So, to ascribe a collective property to a plurality is to do more than ascribe relations among the substances in that plurality. Objection 3 If your truthmaking story were the only plausible truthmaking candidate, then perhaps I would be convinced by your account of higherlevel powers. However, I worry that you are failing to distinguish propertyhood and composition. I also detect this kind of worry in Heil’s (2021: 46) discussion of shape. A complex, such as a ship, is composed of its parts organized in a certain way, and the ship’s shape is just a matter of how the complex is composed. Similarly, couldn’t we also say that a tomato’s being red is just a matter of how it is composed? This compositional analysis may not be a live option – at least not for us. Indeed, we have tried to move away from the idea that complexes like ships are composite substances or particulars. So, it would be implausible to think that we are conflating propertyhood and composition. On our account, collective powers are plurally instantiated and do not require mereological wholes to bear them. That is, we are not treating an arrangement of individuals as some further thing to which higher-level properties are being ascribed. It is true that we employ compositional language when theorising about the properties themselves: we are happy to say that collective powers are composed or ‘made up’ of various properties of the individuals which collectively instantiate those powers. However, this idea must not be confused with the further idea, which we do not endorse, that such powers involve a composite particular. Objection 4 Your response to objection three shows that your theory of higherlevel properties pushes you towards a nihilistic picture on which there are no composite objects (e.g. van Inwagen 1990). But such a view is implausibly radical and counterintuitive.

Collective Powers  157 Here we believe we may make the same sorts of moves as Heil when he is accused of being an anti-realist or eliminativist about higher-level entities such as tomatoes. We maintain, for example, that it is true that tomatoes exist and are red. The point is just that the truthmakers for such claims involve a plurality of simple substances collectively instantiating various powers. Like Heil’s (2021: 45; 52) view, we do not regard this as leaving us with an anti-realist or eliminativist position about ordinary things. Tomatoes exist, it’s just that, according to the view we are proposing, the deep metaphysical story about tomatoes is that they are pluralities of simple substances arranged in a certain way and collectively instantiating various powers. Note also that, like Heil (2012: 25), we do not endorse the idea that talk of tomatoes can be conceptually reduced to talk of simple substances having various properties. Objection 5 Your response to the previous objection suggests that there is not a great deal of divergence between your view and Heil’s. Indeed, although Heil does not explicitly discuss collective powers, we see no obvious reason why his picture cannot accommodate them. Sure, Heil is sceptical of ‘higher-level’ properties. However, if there are collective properties which are instantiated by pluralities of simple substances, then such properties seem not to be higher-level after all. We do not need a ‘levels’ conception of reality here, given that it is always the fundamental, simple substances which are instantiating the properties. We concede that we are not entirely comfortable with the terminology of ‘higher-level’ powers. However, the important point is that our theory lets in more powers than Heil’s does, since Heil denies that powers such as sphericality or redness are genuine (ontologically speaking). According to the theory we have proposed, such powers are genuine but collectively instantiated by various pluralities of simple substances. Maybe the upshot of all this is that when endorsing such powers we should simply replace talk of higher-level powers with talk of collective powers. In that case, the ‘higher-level’ terminology can be regarded as a ladder that we have used in a helpful way before kicking it away. Objection 6 Okay, but there remains a possible way of accommodating ‘higherlevel’ powers like sphericality or redness that you have overlooked.

158  Xi-Yang Guo and Matthew Tugby Like your theory and Heil’s, this alternative does not need to posit high-level composite substances. It also beats your theory on parsimony because it respects the collectivity of at least some powers, while doing away with collective instantiation. On this view, while all powers are instantiated by substances individually, it is open to some powers to have joint, or collective, manifestations. Although a plurality of substances may be needed for such collective manifestations to occur, the manifestations in question are nevertheless collective manifestations of singularly instantiated powers - not singular manifestations of collectively instantiated powers. This suggests that your theory might rest on a confusion between power instantiation and the conditions of a power’s manifestation.

In a recent discussion about collective powers, Williams (2019: 72ff.) develops precisely this kind of argument. According to Williams, all powers are intrinsic powers. Hence, putatively collectively instantiated powers must be accounted for in terms of non-collectively instantiated, intrinsic powers. A concrete case will help us to grasp Williams’ idea. To use Williams’ own example, consider the power that a rugby team has to lift a 1,200 lb grand piano. Prima facie, this looks like an example of a power that is non-distributive and plurally instantiated by members of the team. However, as we interpret Williams, his view is that while the rugby team plainly can lift the piano, they do not instantiate any power to do so, either individually or collectively. Each individual may have an intrinsic power to lift, say, 200 lbs, but it is a mistake to account for the team’s ability to lift the piano by ascribing to its members, collectively, a power whose manifestation is in some sense the sum of the manifestations of their intrinsic powers (2019: 75). Instead, according to Williams, each individual has a power to lift 200 lbs, and these intrinsic powers themselves have a further joint, or collective, manifestation – namely lifting a 1,200 lb grand piano. Hence, for Williams, while pluralities of intrinsic powers can have collective manifestations, there are no collectively instantiated powers. Why think that all powers must be intrinsic? For Williams, the central answer is parsimony (2019: 69). Since at least some powers are intrinsic, any powers ontology should admit intrinsic powers. Then collectively instantiated powers are rejected in the following way. If there were any collectively instantiated powers, then the only manifestations that they could have would be such manifestations as could equally arise, in the same circumstances, as collective manifestations of intrinsic powers. Hence, collectively instantiated powers fail Williams’ novelty condition (2019: 70) and should not be admitted.

Collective Powers  159 Williams offers an interesting alternative here, and it is one that deserves more attention than we are able to offer.25 Nonetheless, our position is that of the two theories (collective instantiation versus individual instantiation with collective manifestation), the collective instantiation theory has greater theoretical virtue overall, all else being equal.26 In particular, Williams writes that ‘It is a brute fact about any [type plurality of powers] that it produces the manifestation type that it does, and that is the end of the story’ (2019: 75). That this is a theoretical cost appears not to be in doubt: ‘If we take things down to the fundamental level, the brutality might be easier to swallow’ (2019: 75). In the next section, we briefly discuss some grounding-based alternatives to the brute fact approach to collectivity. We leave it open whether Williams’ collective manifestation account is compatible with these alternatives. Moreover, considerations of parsimony work in favour of collective manifestation here only if we assume that there are no other grounds to accept collective instantiation. Yet our arguments above attempt to provide precisely such grounds. If collective instantiation is accepted on other grounds, then accepting collectively instantiated powers will do no harm to the parsimony of our ontology overall. Some Remaining Issues: Causal Exclusion and the Metaphysical Source of Grounding In this final section, we briefly address some outstanding issues. First, we discuss a so-called exclusion problem which Heil and others have raised against higher-level properties. We argue that advocates of our collective powers theory need not be worried by this alleged problem. Finally, we end with some speculations about the ultimate source of the compositional grounding principles governing collective powers. The first important problem to address – the exclusion problem – is one that first came to prominence in critiques of non-reductive theories in the philosophy of mind (e.g. Kim 2005). The same sort of worry has been applied more generally by Heil (2003) and others to theories which accept higher-level properties. The problem can be expressed in terms of the issue of causal overdetermination: If higher-level collective powers are part of ontological furniture, then surely they should make their own causal contributions to the world. However, the worry is that such causal work is already carried out by the properties of the individuals that allegedly collectively instantiate those higher-level powers. Hence, it starts to look as if higher-level powers are theoretically redundant. If, however, we are to insist that collective powers and their low-level grounds both carry out the relevant causal work, then we seem to be committing to widespread causal overdetermination in the world. This leaves us with an inelegant, cluttered

160  Xi-Yang Guo and Matthew Tugby theory on which the same causal work is being carried out by both the properties of individuals and their collective properties. In the interests of economy, then, it would be better to say that only the low-level properties of individual substances are genuine.27 Fortunately for us, work has already been undertaken by non-reductionists in the philosophy of mind on how to blunt the force of this kind of overdetermination worry (see e.g. Kroedel and Schulz 2016; for earlier discussions see Yablo 1992, Bennett 2003 and Stoljar 2008).28 A common theme in these responses is to emphasise that higher-level properties (such as mental properties) are not metaphysically independent of the low-level properties (such as physical properties of the brain) with which they are supposedly in causal competition. So it is urged that this kind of overdetermination is crucially different to that which we find in the common examples of causal overdetermination, such as when a person is simultaneously shot with lethal bullets from different guns. In that example, the different bullets come from independent sources. If this example is used as a model for overdetermination, and overdetermination is thus defined in such a way that overdetermining causes are independent, then higher-level and low-level properties do not overdetermine their effects after all. Note that this argumentative move is also available within our collective powers theory given that we develop it as a grounding theory. Given that collective powers are grounded in low-level property instances, the former are metaphysically dependent on the latter. At this point, the opponent might try to weaken the notion of overdetermination so that it applies in cases where the overdetermining causes are not metaphysically independent. However, it is not at all clear why this kind of overdetermination is problematic. If the relevant causes are not metaphysically independent, then it is far from clear that they are in causal competition. Indeed, the fact that a higher-level collective power is causing the relevant effect is simply a reflection of the fact that the relevant lowlevel properties are operative. The higher-level power inherits its causal profile from its grounds, ensuring that they work in harmony. Notice also that as soon as we take the special sciences metaphysically seriously, it looks inevitable that this weak form of overdetermination is widespread. For example, biological and chemical properties appear to play important explanatory roles. Indeed, our earlier chemical example of dissolution illustrates this. However, we take it that few chemists would deny that chemical powers are dependent for their existence on various properties in physics, which themselves make sufficient causal contributions to chemical processes such as dissolution. Our theory accepts this and, importantly, provides an account of how such dependence arises: it arises because higher-level powers are collectively grounded in the relevant properties at the lower level.

Collective Powers  161 Setting the exclusion worry aside, let us finally address an important lingering question about the source of the dependence between higher-level and low-level powers. In particular, one might wonder why collective powers are grounded in just the way(s) that they are, rather than some other way(s). Is it a brute fact that a collective power is grounded in one way rather than another, or is there a deeper metaphysical story to be told about the grounding profiles of collective powers? These questions take us into interesting territory in the so-called meta-grounding literature. The same sort of question also arises if we replace talk of grounding with the more specific notion of composition. There are arguably numerous metaphysical principles at work in determining what composes what. For example, according to Fine’s (2010) operational account of composition, different forms of composition are defined by the various formal and material principles that they obey. In the case of power composition, so-called ‘characterization conditions’ (Fine 2010: 571) will be particularly important since the character of a higher-level power is presumably a function of the characters of the low-level property instances out of which it is built. To return to our toy example, the power of H2O molecules to form solvation shells is plausibly a function of the character of the (electronegative) oxygen components, particularly their power to attract an (electropositive) Na+ ion. What, then, is the metaphysical source of such compositional characterization conditions? In response, we could adopt a primitivist stance and just accept it is a brute fact that collective properties are grounded in the way that they are. However, there are two other main options, which elsewhere Tugby has called the ‘bottom-up’ and ‘top-down’ strategies for explaining grounding (2022a: 146).29 According to the bottom-up approach, it is the low-level grounding entities themselves which explain why the grounding or composition occurs. On an essentialist reading of this approach, it is part of the essences of the grounding entities that they help to ground or compose the things that they do. Focusing on the compositional characterization conditions introduced earlier, the idea would be that it is part of the essential character of the composing properties that they collectively compose a higher-level power with a certain character. In contrast, in a top-down essentialist approach, the direction of explanation would run in the opposite direction, from the composed entity to its compositional grounds. The top-down idea would be that it is part of the essence of the collective power itself that it is collectively grounded or composed by low-level property instances with a certain character (or, perhaps, a certain disjunction of such properties). So which of these options is to be preferred? We do not have any conclusive arguments to offer here but it seems to us that of the non-primitivist options, the top-down explanation is more plausible. The main problem with the bottom-up approach is that it seems rather extreme to require that in order to grasp the essence of, say, a

162  Xi-Yang Guo and Matthew Tugby fundamental physical property, we must grasp all the grounding or compositional contributions that it could make towards a vast array of higherlevel powers. Such a view would make the essences of fundamental low-level properties incredibly complex. What we tentatively suggest, then, is that if there is a deep explanation for the way in which certain low-level property instances collectively ground or compose certain higher-level powers, this explanation is more likely to come from a top-down direction. And indeed, in recent grounding literature, the top-down approach has attracted a good deal of attention, having been endorsed in varying degrees by, for example, Rosen (2010), Fine (2012, 2015) and Dasgupta (2014). Again, if this view is carried over to the composition of collective powers, we are left with a picture in which it is part of the essential character of a collective power that it is composed in just the way it is by certain kinds of low-level property (or a disjunction of such properties, if the same higher-level power can be composed in more than one way). The upshot of all this would be that the characterization conditions mentioned earlier are determined by the essences of the higherlevel powers themselves. This suggests that collective powers have a complex essence, which is perhaps unsurprising given that such powers require a plurality of instantiators. By accepting this view rather than the bottomup theory, we can accommodate the compelling idea that low-level, noncollective properties have a simpler essence. Notes 1 The authors have made an equal contribution to this chapter. 2 Florio and Linnebo (2021) are a notable exception. Previously, metaphysical literature on collective properties has tended to focus more on topics such as emergence and monism rather than powers (e.g. Bohn 2012, Caves 2018). However, in recent powers literature, a more abundant conception of powers  has started to become popular, as in work by Vetter (2015: Ch. 3) and McKitrick (2018: Ch. 8), who both argue that some powers are extrinsic. So, perhaps the tide is beginning to turn. 3 A certain pragmatic neutrality may also be in play: constructing a theory of predication might not require a commitment to any metaphysics of properties (although see Lowe 2013: 55). Fair play, say we. But we are after such a theory here. 4 For what it’s worth, at least one of the authors leans towards the grounding theory; see Tugby (2021, 2022a). Prominent advocates of dispositional essentialism include Ellis (2001) and Bird (2007), and well-known proponents of the identity theory include Heil (2003) and Martin (2008). It is a matter of dispute as to whether there is a substantial difference between dispositional essentialism and identity theory; see Taylor (2018). 5 We are not entirely comfortable with this terminology and later shall recommend simply replacing talk of higher-level powers with talk of collective powers. Bird’s terminology of macro-powers is also not ideal, as we want to discuss an example involving powers in chemistry which are arguably not macroscopic.

Collective Powers  163 6 We use these terms interchangeably. 7 The idea has its roots in Aristotle. In the Categories (Ackrill 1963), Aristotle appears to allow that both composite substances and their substantial parts are primary substances. 8 Heil also provides further reasons for doubting the coherence of the notion of a composite substance. For instance, according to the traditional definition of substance, substances are non-dependent entities. Yet, prima facie, composite objects are always dependent in some way on their substantial parts. For details see Heil (2021: 45). 9 Note that a predicate may appear to be both collective and distributive at the same time, for example the families gathered in the courtyard. In such cases— which resemble cases of syllepsis—it suffices for our purposes that the distributive element does not undermine the collective one. A similar thing occurs in the subject place with ‘Tim and Alex met in the pub and had a pint’ (Oliver and Smiley 2001: 294). 10 We will, however, return to CTP in the case of properties. 11 We use ‘set’ for illustration, but the point applies mutatis mutandis to ‘fusion’, ‘whole’, ‘sum’, ‘bunch’, or any other aggregate kind. 12 Again, mutatis mutandis whatever aggregate kind one prefers. 13 Note that the target plural statements involve no antecedent or purely settheoretic commitment to a set of all sets, or anything like a separation axiom. It is CTS which supplies these ingredients of the paradox. 14 The move will be automatic, of course, if every predicate corresponds with some property. But we assume that the task should not be so easy. 15 We trust it to cause no confusion that we are, of course, now changing the property and the substance(s) rather than the predicate and the subject. 16 It should not matter whether we treat locations as monadic properties or relations. The point is that a location is something that each light has. 17 Not that it would help if we helped ourselves to conjunctions: the conjuncts form a conjunction is still irreducibly collective and brings us back to the main point of our reply. 18 Parallel reasoning applies with the jury members are unanimous. The availability of a prefabricated kind-term jury may tempt one to blend CTP with CTS, offering a two-step reduction in which the jury members are unanimous reduces to the jury is unanimous, which reduces in turn to facts about each jury member and their respective belief. But the second step fails for the reasons already given: the jury is unanimous is true only in virtue of the members being collectively of the same view. 19 For similar reasons, we reject the thesis of composition as identity. This will be of relevance in the next section. 20 Of course, if there are no such cases, then our account simply needs no such caveat. 21 We maintain this grammatically singular way of talking about a ‘plurality’ as a convenience. Strictly (or rather, metaphysically) speaking, of course, there are no such singular things - on pain of the Russellian paradox presented earlier. Where we use ‘a plurality’, what we mean can always be paraphrased more plurally, correctly, and circuitously in terms of ‘some things’. 22 The precise definition of metaphysical emergence is a matter of dispute but a common idea is that emergents bring with them novel powers which are not fully accounted for in terms of the powers on which they depend. For discussion, see Wilson (2021).

164  Xi-Yang Guo and Matthew Tugby 23 Ironically, for this reason, the objection risks overgenerating gerrymandered substances. For suppose that some things have a collective power. Then on the Aristotelian view, those things must compose a substance which is the bearer of that power. But there is no clear in-principle constraint on what things may have a collective power — not, at least, without dogmatically taking the Aristotelian view as an assumption. 24 This is not at all to say that it should not matter to which more fundamental substances the relevant collective powers are attributed. Compare Oliver and Smiley (2001: 293) on this point. 25 Williams’ view relies in part on his mutual manifestation model of powers. A thorough critical discussion of that model would require a separate paper. 26 Our theory must be able to respond to the exclusion-type worry that Williams himself raises (2019: 69–70). See the next section. 27 Another alternative, which is not attractive, is to say that collective powers exist but are causally redundant. But this seems to clash with the very idea that they are powers. 28 Here we provide only a brief sketch of how to blunt the force of the exclusion worry. For more details of this strategy, see Kroedel and Schulz’s (2016) defence of grounding physicalism. See also McKitrick’s (2018: Ch. 9) and Tugby’s (2022a: 151–154) recent defences of the causal efficacy of dispositions. 29 We do not claim that our discussion of the possibilities is exhaustive. For example, another option is to say that the grounding profiles of low-level properties are determined or governed by so-called laws of metaphysics. However, we think that this option raises further difficult questions about the nature and source of such laws. For discussion, see Wilsch (2015), Schaffer (2017), Rosen (2017), and Tugby (2022b).

References Ackrill, J. L. (1963) Aristotle: Categories and De Interpretatione. Oxford: Clarendon Press. Armstrong, D. M. (1997) A World of States of Affairs. Cambridge: Cambridge University Press. Audi, P. (2012) ‘A Clarification and Defense of the Notion of Grounding’. In F. Correia & B. Schnieder (Eds.), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press, 101–121. Bennett, K. (2003) ‘Why the Exclusion Problem Seems Intractable, and How, Just Maybe, to Tract It’. Noûs 37, 471–497. Bennett, K. (2017) Making Things Up. Oxford: Oxford University Press. Bird, A. (2007) Nature’s Metaphysics: Properties and Laws. Oxford: Oxford University Press. Bird, A. (2016) ‘Overpowering: How the Powers Ontology has Overreached Itself’. Mind 125, 341–383. Bird, A. (2018) ‘Fundamental Powers, Evolved Powers, and Mental Powers’. Aristotelian Society Supplementary Volume 92, 247–275. Bohn, E. D. (2012) ‘Monism, Emergence, and Plural Logic’. Erkenntnis 76, 211–223. Caves, R. L. J. (2018) ‘Emergence for Nihilists’. Pacific Philosophical Quarterly 99, 2–28.

Collective Powers  165 Dasgupta, S. (2014) ‘The Possibility of Physicalism’. The Journal of Philosophy 111, 557–592. Ellis, B. (2001) Scientific Essentialism. Cambridge: Cambridge University Press. Fine, K. (2010) ‘Towards a Theory of Part’. The Journal of Philosophy 107, 559–589. Fine, K. (2012) ‘Guide to Ground’. In F. Correia & B. Schnieder (Eds.), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press, 37–80. Fine, K. (2015) ‘Unified Foundations for Essence and Ground’. Journal of the American Philosophical Association 1, 296–311. Florio, S., & Linnebo, Ø. (2021) The Many and the One. A Philosophical Study of Plural Logic. Oxford: Oxford University Press. Heil, J. (2003) From an Ontological Point of View. Oxford: Oxford University Press. Heil, J. (2012) The Universe As We Find It. Oxford: Oxford University Press. Heil, J. (2021) Appearance in Reality. Oxford: Oxford University Press. Kim, J. (2005) Physicalism or Something Near Enough. Princeton: Princeton University Press. Koslicki, K. (2008) The Structure of Objects. Oxford: Oxford University Press. Koslicki, K, (2018) Form, Matter, Substance. Oxford: Oxford University Press. Kroedel, T., & Schulz, M. (2016) ‘Grounding Mental Causation’. Synthese 193, 1909–1923. Lewis, D. K. (1991) Parts of Classes. Oxford: Blackwell. Lowe, E. J. (1998) The Possibility of Metaphysics: Substance, Identity, and Time. Oxford: Clarendon Press. Lowe, E. J. (2013) Forms of Thought: A Study in Philosophical Logic. Cambridge: Cambridge University Press. Marmodoro, A. (2017) ‘Power Mereology: Structural Powers versus Substantial Powers’. In M. P. Paoletti & F. Orilia (Eds.), Philosophical and Scientific Perspectives on Downward Causation. Abingdon, Oxon: Routledge, 110–127. Marmodoro, A. (2022) ‘What’s Dynamic about Causal Powers? A Black Box!’ In C. J. Austin, A. Marmodoro, & A. Roselli (Eds.), Powers, Time and Free Will. Synthese Library 451. Cham: Springer, 1–15. Martin, C. B. (2008) The Mind in Nature. Oxford: Oxford University Press. McDaniel, K. (2009) ‘Structure-Making’. Australasian Journal of Philosophy 87, 251–274. McKitrick, J. (2018) Dispositional Pluralism. Oxford: Oxford University Press. Mumford, S., & Anjum, R. L. (2011) Getting Causes from Powers. Oxford: Oxford University Press. Oliver, A., & Smiley, T. (2001) ‘Strategies for a Logic of Plurals’. The Philosophical Quarterly 51, 289–306. Rosen, G. (2010) ‘Metaphysical Dependence: Grounding and Reduction’. In B. Hale & A. Hoffman (Eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press, 109–136. Rosen, G. (2017) ‘Ground by Law’. Philosophical Issues 27, 279–301. Schaffer, J. (2017) ‘Laws for Metaphysical Explanation’. Philosophical Issues 27, 302–321.

166  Xi-Yang Guo and Matthew Tugby Stoljar, D. (2008) ‘Distinctions in Distinction’. In J. Kallestrup & J. Hohwy (Eds.), Being Reduced: New Essays on Reduction, Explanation, and Causation. New York: Oxford University Press, 263–279. Taylor, H. (2018) ‘Powerful Qualities and Pure Powers’. Philosophical Studies 185, 1423–1440. Tugby, M. (2021) ‘Grounding Theories of Powers’. Synthese 198, 11187–11216. Tugby, M. (2022a) Putting Properties First: A Platonic Metaphysics for Natural Modality. Oxford: Oxford University Press. Tugby, M. (2022b) ‘The Laws of Modality’. Philosophical Studies 179, 2597–2618. van Inwagen, P. (1990) Material Beings. Ithaca, NY: Cornell University Press. Vetter, B. (2015) Potentiality: From Dispositions to Modality. Oxford: Oxford University Press. Williams, N. E. (2019) The Powers Metaphysic. Oxford: Oxford University Press. Wilsch, T. (2015) ‘The Nomological Account of Ground’. Philosophical Studies 172, 3293–3312. Wilson, J. M. (2021) Metaphysical Emergence. Oxford: Oxford University Press. Yablo, S. (1992) ‘Mental Causation’. Philosophical Review 101, 245–280. Yi, B. (2002) Understanding the Many. New York: Routledge.

9 The Special Power-Composition Question and the Powerful Cosmos Joaquim Giannotti

The Special Power-Composition Question Any account holding that ‘objects are built out of powers’ (Marmodoro 2017: 110) faces an immediate question: In what circumstances do some powers compose an object? This question is structurally analogous to the more familiar mereological question: In what circumstances do some parts compose an object? (e.g., Van Inwagen 1990: 29). The similarity between the two questions licenses a convenient label for our topic. Let us call it the special power-composition question.1 To assess the tenability of any power mereology view, namely any theory claiming that objects are composed of powers, we must consider how it answers the special power-composition question. In the mereological case, we find two main types of approaches: radical (or ‘extreme’) and moderate (or ‘restricted’). In turn, radical views are divided into ‘mereological nihilism’ and ‘mereological universalism’.2 Schematically, we can say that mereological nihilism is the view that it is never the case that some parts (when they are two or more) xs compose an object y because, necessarily, nothing is such that the xs compose it. Mereological nihilism entails that there are no composite objects. The only existing objects are mereological atoms lacking any proper parts. Mereological universalism is the converse of nihilism. This view holds that it is always the case that the xs compose some y because, necessarily, something is such that the xs compose it. Moderate approaches deny both mereological nihilism and universalism. On these views, sometimes but not always, the xs compose y. For example, Van Inwagen defends the idea that there is something composed by the xs when the ‘activities of the xs constitute a life (or there is only one of the xs)’ (1990: 82). Here I do not aim to discuss Van Inwagen’s view. I offer it as an example of a moderate answer to the special composition question. Since it is not always the case that the xs constitute a life, composition is restricted.

DOI: 10.4324/9781003298830-12

168  Joaquim Giannotti The preceding approaches to the special composition question have counterparts in the mereology of powers. We can schematically formulate them as follows. ‘Power-nihilism’ is the view that it is never the case that there is some y composed by a plurality of powers Ps because, necessarily, nothing is such that the Ps compose it. ‘Power-universalism’ is the converse of power-nihilism. It is the view that it is always the case that the Ps compose some y because, necessarily, something is such that the Ps compose it. Moderate answers to the special power-composition question deny both power-nihilism and power-universalism. Moderate approaches hold that sometimes but not always, there is some y that is composed of the Ps. In the next section, I illustrate some reasons why a power mereologist should favour a moderate approach. But first, I clarify the chapter’s aims. Here I explore an application of Anna Marmodoro’s (2017) moderate approach to the special power-composition question. On the Marmodorean view, which I unpack in due course, an object is composed by a plurality of powers when they form a structure that is both physically united and metaphysically unified. I argue that this two-fold condition, which I name the ‘Marmodoro Condition’, rules out some implausible consequences that radical answers to the special power-composition face. However, the  main goal of the chapter is different. I endeavour to show that the Marmodoro condition, coupled with plausible considerations from quantum theory, entails the existence of the powerful cosmos – an object composed of all the compossible fundamental powers instantiated across the universe. Advocates of the Marmoderan view and other similar moderate approaches might experience an intuitive resistance to the powerful cosmos on the grounds of its apparent implausibility. In this chapter, I defend the opposite view: we should embrace the powerful cosmos. I make my case by arguing that there are three considerations, which I indicate in the following, for thinking that a moderate power mereology view accepting the existence of the powerful cosmos is preferable to one that rejects it. My conclusion is that the existence of such an object is a beneficial consequence of the Marmodorean view. Here is the plan. In the remainder of this section, I clarify how I understand powers. I also elucidate some important differences between power mereology and the mereology of parts. In the next section, I offer two considerations for preferring a moderate approach to the special powercomposition questions over the more radical power-nihilism and poweruniversalism, respectively. In the third section, I illustrate Marmodoro’s moderate approach to power composition. I turn my attention to the powerful cosmos in the fourth section. There I discuss an argument for the existence of such an object, drawing from plausible considerations about the metaphysics of quantum entanglement. In the final section, I argue that proponents of the Marmodorean view and similar approaches should

The Special Power-Composition Question and the Powerful Cosmos  169 welcome the powerful cosmos. In that section, I offer three reasons – one metaphysical, another empirical, and a further other methodological – for thinking that a moderate approach that embraces the powerful cosmos is preferable to one that does not. I close by pointing out an interesting yet unexplored connection between the emerging power mereology view and priority monism, namely the view that the cosmos is a fundamental whole prior to its parts. Before we proceed any further, two issues must be clarified. The first one concerns the metaphysics of powers. In what follows, I will remain neutral on the nitty-gritty details of the operative conception of powers. Diversity abounds among theories of powers (for a recent overview, see Tugby 2020). But here I am concerned with a more general discussion of the special power-composition question. This task does not require us to adopt a specific conception. My arguments can be reframed for more specific views if one wishes. I shall take powers to be actual properties whose nature or essence is to be directed toward certain effects that are manifested in distinctive circumstances. These effects may involve the instantiation of other powers. Powers thus have a fixed modal profile, but they need not be constantly manifested. My focus will be on fundamental powers, but I will omit the qualifier for the sake of brevity. Putative examples of fundamental powers are charge, mass, and spin. Following the orthodox view amongst theorists of powers, I shall take powers to essentially contribute to the causal or dispositional profile of their bearers. As Chakravvartty puts it, powers ‘are quintessentially causally relevant properties – they empower things that have them to behave in certain ways in certain circumstances’ (2017: 107). One might say, for example, that a charged particle produces an electromagnetic force when in motion by virtue of instantiating the powerful property of having a determinate charge. The second clarification is about the difference between the mereology of powers and that of parts. One might expect that the mereological principles that govern parthood relationships of the form ‘the xs are part of y’ extends to power-parthood relationships of the form ‘the Ps are part of y’. But such an expectation might be misplaced. To start, we should note that the power mereology view under scrutiny is not explicitly committed to the axioms of classical mereology (the theory stemming from the work of Leśniewski [1916, 1927–1931], and Leonard and Goodman [1940]). Nor does the viability of the power mereology view demand them. Here are the axioms: Reflexivity: for every x, x is part of x. Antisymmetry: for every x and for every y, if (x is a part of y and y is a part of x), then x is identical with y. Transitivity: for every x, for every y and for every z, if (x is a part of y and y is a part of z), then x is a part of z.

170  Joaquim Giannotti These structural principles may fit the mereology of powers. But they appear to be negotiable. The discussion of the Marmodorean view and the powerful cosmos does not force us to embrace them. As such, I will leave these matters open. A related elucidation concerns the difference between composition and power-composition (i.e. composition of powers). It is unclear how deep the similarities between these two notions run. A typical formulation of mereological composition is this: the xs compose y just in case ‘the xs are all part of y and no two xs overlap and every part of y overlaps at least one of the xs’ (Van Inwagen 1990: 29; the xs overlap is they have a common part). It is far from obvious whether we should impose some constraint about overlap on the powers composing an object. Unfortunately, things get messy. Presumably, an answer to the overlap constraint for  powers implies an answer the general power-composition question, namely the question of what power-composition is. Regrettably, I have no insightful proposal to offer (recall that my focus is on the special powercomposition question). But here is the important bit. It might be that power-composition is a sui generis relation, one which bears some similarities to parthood composition but is metaphysically distinct from it. Accordingly, we should be more cautious in distinguishing between these two forms of composition. For the sake of readability, however, I use ‘composition’ instead of ‘power-composition’ when it is evident that I refer to the composition of powers. Finally, I shall assume that powercomposition is not identity. Why Adopt a Moderate Approach to the Special Power-Composition Question? A power mereologist has compelling reasons for rejecting both powernihilism and power-universalism. I outline these views in this section, starting with the former. Power-nihilism denies the existence of objects composed of powers. This approach is in tension with the very reason for  adopting a mereology of powers in the first place. Arguably, a chief motivation for embracing this view is the desire to offer a metaphysical account of composite objects in terms of their powerful parts. This project presupposes that at least some objects can be composed of powers. But  power-nihilism rejects this very claim. It would be uncharitable to regard power  mereologists as engaged in a self-defeating project. Therefore, power-nihilism is not a plausible option for them. Power-universalism does not evidently clash with the prospects of the power mereology view. But a different consideration gives power mereologists reasons to favour an alternative approach. Power-universalism does not harmonise with the commitment to the so-called Eleatic Principle.

The Special Power-Composition Question and the Powerful Cosmos  171 This tenet expresses the idea that the mark of being of a thing is its power to affect and be affected by other things. Here is a passage illustrating the thought: I suggest that anything has real being that is so constituted as to possess any sort of power either to affect anything else or to be affected, in however small a degree, by the most insignificant agent, though it be only once. I am proposing as a mark to distinguish real things that they are nothing but power. (Sophist 247d–e; from Heil 2003: 75) All or many theories of powers subscribe to the Eleatic Principle or something in the vicinity. Since it is a theory of powers, the power mereology view should presumably do the same. The problem with power-universalism is that it entails the existence of composite objects that pass the Eleatic test suspiciously. As I explain in the following, this form of ‘ontological cheating’ calls into question whether such objects deserve genuine being. An example will illustrate. Let us suppose that instances of charge are fundamental powers. Now consider an instance of charge in Birmingham and another in Glasgow. Power-universalism entails that there is an object, say o, these powers compose. Does o pass the Eleatic test? In a sense, it does. The parts of o are instances of charge, and these indeed have the power to affect or be affected by other things, such as other instances of charge. But does o deserve to be considered a ‘real thing’ on these grounds? Two closely related considerations suggest we favour a negative answer. First, objects like o, which come into existence because of the truth of power-universalism, may lack physical unity. Second, they are also disunified in a metaphysically relevant sense. An object like o lacks unity because power-universalism, on its own, does not ensure that its parts – namely the Birmingham charge and the Glasgow charge – are physically ‘glued’ together. On power-universalism, composition is cheap. There is always something that a plurality of powers Ps composes. But this view cannot guarantee that the Ps stand in some physical relationship that would ground their unity in every case. For a kindred reason, power-universalism does not guarantee that objects such as o display unification. Cheap composition of the sort licensed by power-universalism does not warrant that the parts that compose an object form a unified whole. For example, the fact that o has the parts it has does not depend on its nature. Nor does it seem that it lies in the natures of the Birmingham charge and the Glasgow charge, respectively, that they compose o. The existence of o is nothing but a consequence of an unrestricted principle of power-composition.

172  Joaquim Giannotti To drive the point home, I suggest we compare o with an object that displays both unity and unification. Think of an electron. Its determinate charge, mass, and spin are plausible fundamental powers. On the power mereology view, we could argue that these powers compose the electron. Unlike o, the electron displays a structural cohesion among its parts. Science, for all we know, tells us that electrons and their specific determinate properties come into and go out of existence altogether. By contrast, no similar considerations apply to o. Moreover, the possession of determinate powers seems to be constitutive of the nature of an electron. That is, it appears to be lying in the essence of electrons that they possess such specific powers. An analogous a link is hard to justify for o. To be clear, I do not wish to suggest that the preceding considerations render both power-nihilism and power-universalism hopeless. There might be ways to salvage these views. But until these strategies are proved successful, the power mereologist should regard the adoption of a moderate answer to the special power-composition question as a more promising way to evade the previously mentioned issues. By admitting that sometimes, but not always, powers compose objects, a moderate approach does not generate a methodological tension with the goals of the power mereology view. And a moderate approach is not forced to admit the existence of composite objects such as o that lack cohesion and integration. However, the challenge for this approach is to specify under what circumstance a plurality of powers composes an object in a way that displays both physical unity and metaphysical unification. Lucky us: Marmodoro (2017) offers a theory that does just that. Marmodoro’s Moderate Approach On Marmodoro’s view, power composition occurs when a certain condition is satisfied (Marmodoro 2017: 118–119; note that Marmodoro’s presentation of the condition is slightly different). We can formulate it as follows: Marmodoro Condition (basic): there is something a plurality of powers Ps compose if and only if the Ps are (1) physically united and (2) metaphysically unified. The Marmodoro Condition can be further sharpened, depending on one specific view of powers. Here this generic formulation will suffice for illustrating Marmodoro’s account. Accordingly, for example, an electron is composed by its determinate charge, mass, and spin (assuming that these are powers) when these both are physically united and metaphysically unified. On Marmodoro’s view, when a structure of powers is metaphysically unified (and not just physically united), the composite object emerges as a

The Special Power-Composition Question and the Powerful Cosmos  173 powerfully unified individual: a ‘substantial power’ (in Marmodoro’s terminology; 2017: 120). To use the previous example, we could say that the electron is the substantial power constituted by (but not reducible to) and emerging from its structure of powers (namely charge, mass, and spin). There are some interesting and intriguing issues concerning the notion of emergence at play in Marmodoro’s view. But in what follows, my focus is on the conditions a structure of powers must satisfy to yield a substantial power. To avoid confusion, however, I will keep using the more familiar ‘composite object’ to refer to a substantial power. The adoption of the Marmodoro Condition yields a moderate answer to the special power-composition question. According to Marmodoro, not all pluralities of powers satisfy it. This amounts to a rejection of poweruniversalism. But since some pluralities do form physically united and metaphysically unified structures, this approach also denies power-nihilism. Now I turn to illustrate clauses (1) and (2) encoded in the Marmodoro Condition, starting with the idea of physical unity. As I understand it, a physically united structure of powers displays various ontological dependency relations among its constituent powers (Marmodoro 2017: 119). There is a staggering abundance of more specific ontological dependencies (see Lowe [1994] and Correia [2005] for an overview). The Marmodorean account is sufficiently flexible to accommodate various options. Here we can liberally use ‘ontological dependence’ as a placeholder for whatever more specific ‘small-d’ dependence relation one might have in mind. Such ontological dependencies can be both causal and metaphysical. What matters is they impose ‘physical continuity and connectedness, synchronically and often diachronically’ (Marmodoro 2017: 119) among the powers in the plurality. An important specification of Marmodoro’s account is that the relevant ontological dependencies stem from the nature of powers, namely from their directedness. Accordingly, it is the nature of powers that determines how they become physically united. Fortunately for us, Marmodoro suggests that some familiar objects display physical unity among their powers. Functionally organised artefacts such as laptops and living organisms, like you and me, are plausible examples of entities constituted by physically united structures of powers. The difficult question is, of course, whether these objects are also metaphysically unified. Here we should expect disagreement. The examples are, here and in Marmodoro (2017), best regarded as merely illustrative. Now let us turn to metaphysical unification. Under what circumstances is a plurality of physically united powers metaphysically unified? This passage answers the question: My claim is that the difference between a structured plurality and a single individual it may constitute lies in the ontological dependencies that develop between the components of the structure. Unification of

174  Joaquim Giannotti the structured components into a single individual ‘interferes’ with the components that are unified into one. The structured components become unified into one individual by being re-individuated in terms of the whole. This involves more than ontological dependence; it involves holistic dependence. (Marmodoro 2017: 120) We can extrapolate two components of the mechanism of metaphysical unification. First, a plurality of physically united powers becomes unified when it displays holistic dependencies. Second, the process of metaphysical unification amounts to the re-individuation of the powers as qualifications or ways of being of the whole. Once unified, the powers ‘cease being discrete entities in the structure and become qualification of the individual’ (Marmodoro 2017: 120). When the mass, charge, and spin of an electron become unified, assuming that these are its constituent powers, they are re-individuated as ways of being of the electron (for more on a conception of properties as ways of being, see Levinson [1978] and Heil [2003]). Putting these pieces together, we can refine the initial formulation of the Marmodoro Condition as follows. Since my focus for the remainder of the chapter is on the refined version, I will omit the qualifier. Marmodoro Condition (refined): there is something y a plurality of powers Ps compose if and only if the Ps and y (1) display some holistic dependencies and (2) the Ps are re-individuated in terms of y. There are various ways in which the notions of holistic dependence and re-individuation can be unpacked, depending on one’s favourite view. Here I will employ a relatively neutral conception, which I discuss further in the next section. Minimally, I regard holistic dependence as schematically formulated along these lines: the Ps and y are holistically dependent just in case the Ps both depend on each other and on y. And I shall take, again minimally, that re-individuation of Ps in terms of y entails that the Ps cannot be removed from y or re-arranged without destroying y. An analogy will illustrate. We might think of a plurality of physically united powers as something like a Lego construction where the bricks are physically connected yet discrete entities that can be freely re-arranged. A plurality of metaphysically unified powers is something like a Lego construction whose parts are no longer identifiable as discrete bricks; they cannot be picked and moved around. My aim is not to defend the correctness of the Marmodoro Condition. As such, I will not attempt to make it more precise. To repeat the goal of this section, I presented Marmodoro’s account as an illustration of a wellmotivated moderate approach to the special power-composition question.

The Special Power-Composition Question and the Powerful Cosmos  175 Things like dogs, electrons, and trees are plausible candidate entities satisfying the Marmodoro Condition. Things like the object o or the sum of my hand, your copy of On the Plurality of Worlds, and a tea leaf in Jiangnan intuitively fail to satisfy it. Unsurprisingly, controversy over specific cases is inevitable and predictable. I will not attempt to settle the question of whether a specific item, say, a neuron, is really a unified whole composed of powers. Instead, I wish to explore a prima facie surprising and more philosophically interesting consequence of Marmodoro’s moderate approach. Coupled with plausible considerations from quantum theory, the Marmodoro Condition entails the existence of an object composed by all the compossible fundamental powers instantiated across the universe. I call this object the powerful cosmos. The Argument for the Powerful Cosmos In this section, I discuss an argument for the existence of the powerful cosmos. In its simplest form, we can build it like this. 1) Cosmic Entanglement. Some considerations from quantum theory suggest that the universe as a whole is a vast entangled system. 2) Holistic Dependence. Entangled systems display holistic dependencies among their components. 3) Power Mereology View. The components of the entangled universe are all the compossible fundamental physical powers instantiated across the cosmos. 4) Marmodorean Link. If we adopt the Marmodoro Condition, then there is a metaphysically unified object composed by all the compossible fundamental physical powers instantiated across the cosmos. Assuming the Marmodoro Condition for the sake of the discussion, we reach the following: 5) Powerful Cosmos. There is a metaphysically unified object composed by all the compossible fundamental physical powers instantiated across the cosmos. This argument is admittedly speculative. But I offer it in an exploratory spirit. Recall that my overall goal, which I establish in the next section, is to argue that the existence of the powerful cosmos is a beneficial consequence of the Marmodorean moderate approach and similar accounts. I shall not attempt to settle difficult questions concerning the correct interpretation of the formalism of quantum mechanics. Similarly, I will refrain from diving into complicated technical matters that will confuse the discussion unnecessarily. Instead, I wish to discuss the argument for the powerful cosmos in its full generality, leaving open insofar as possible certain

176  Joaquim Giannotti details concerning its implementation into physical theory. Having clarified the scope of the argument, I turn to explain each premise. Let us start with Cosmic Entanglement. An entangled system is one whose wave function cannot be reduced to the wave functions of its components. The probabilities of joint outcomes of measurements carried over the entangled components are not the product or combination of the outcome probabilities of each separate component. In a more informal way, as Ismael and Schaffer put it, we can say that the components of an entangled system behave in ways that are ‘individually unpredictable but jointly constrained so that it is possible to forecast with certainty how one component will behave, given information about the measurements carried out on the other(s)’ (2020: 4141). Suppose, for example, that particles Amira and Beke are entangled with respect to their x-spin such that their joint state has total x-spin 0. The quantum formalism predicts systematic anti-correlations: if Amira measures x-spin up, then Beke measures x-spin down, and vice versa. The Cosmic Entanglement premise expresses the idea that the universe as a whole can form a vast entangled system. This premise might well be the most controversial of the entire argument. I discuss some objections against it in the next section. Here I outline two ways, defended by Schaffer (2010: 52) and Ismael and Schaffer (2020: 4150), the idea of an entangled universe can be made more plausible. The first way is physical. If we assume that the Big Bang is the starting point of the universe at which everything interacts, we obtain an initial entangled state. If we also assume that the world evolves in accordance with Schrödinger’s equation, then the initial entanglement is preserved. It is worth noting that even without the initial entanglement, assuming that the world evolves in accordance with Schrödinger’s equation, we may reach the entangled universe as its evolution tends to spread entanglement. The second way is mathematical. If there is a wave function of the whole universe, it is ‘almost certainly entangled’ (Ismael and Schaffer 2020, p. 4150) as it should measure 1. All wave functions measuring 1 are entangled. In the absence of a wave function collapse, one should ‘expect universal entanglement’ (Schaffer 2010: 52).3 The Cosmic Entanglement premise has wider implications that go beyond what I want to achieve in this chapter. For example, we might wonder what reality is fundamentally like if we embrace this premise (for more on this, see Ismael and Schaffer 2020: 4151–4154). Discussing such a topic would leave us far astray from the different and more modest goals of the chapter, namely defending the fruitfulness of the powerful cosmos. Here we should note two things. First, my claim is not that all physical interpretations support Cosmic Entanglement. Second, our focus should be on the conjunction between Cosmic Entanglement and the other premises, which yields the conclusion that the powerful cosmos exists.

The Special Power-Composition Question and the Powerful Cosmos  177 Now let us consider the Holistic Dependence premise. As with the Marmodoro Condition, there are various ways to precisify the notion of holistic dependence. On the minimalist conception adopted earlier, a plurality of powers is holistically dependent just in case they depend on each other and on the whole they compose. It seems to me that this interpretation is naturally suited to making sense of the holistic dependence displayed by entangled systems. For example, Schaffer (2010, 2013) and Ismael and Schaffer (2020) take entangled components to be dependent not only on each other but also on the entangled system as a whole. Consider the example of Amira and Beke, the two entangled particles. Call Amira+Beke their entangled system. The wave function of Amira+Beke is not the product of the wave functions of Amira and Beke. However, because they are entangled, we know that the measurement outcomes of Amira and Beke are jointly constrained in an anti-correlated fashion that strongly suggested a mutual dependence between them. But assuming that it is not brute, what explains the mutual dependence between Amira and Beke? Holistic approaches to entanglement would argue that Amira and Beke are dependent on the composite system Amira+Beke. On these views, it is the quantum entangled system as a whole that contains more information about the observable behaviour of its modally correlated components – rather than the other way around. As such, the components of an entangled system do not just depend on each other. They also depend on the whole entangled system. We should note, and this is crucial for the discussion of the argument for the powerful cosmos, that Holistic Dependence is not confined to systems of two particles (such as Amira+Beke). It extends to systems as vast as the universe. Given the Cosmic Entanglement premise, Holistic Dependence implies that the universe displays holistic dependencies among its parts. Schaffer would make a further claim (2010: 45–50): because the entangled components are dependent on the whole entangled system, the whole is prior to its parts.4 Here we do not need to follow this approach. For example, the power mereologist is not forced to accept that the holistic dependency exhibited by the universe and its parts yields a priority claim. Thus, we should distinguish between a priority version of the argument, leading to the conclusion that the powerful cosmos exists and is more fundamental than its powerful parts, and a non-priority version committed solely to the existence claim. Here I am discussing the latter. I will therefore remain neutral on whether the Holistic Dependence premise should nudge power mereologists to follow Schaffer in defending the priority of the cosmos over its parts. But I will return to this view at the end of this chapter. Concluding this digression, I stress that the point of the discussion is that we can defend the Holistic Dependence premise by endorsing a holistic approach to entanglement.

178  Joaquim Giannotti As for the Cosmic Entanglement premise, also Holistic Dependence raises critical technical questions about the physical interpretation of quantum formalism. Here I wish to stress, once again, that my interest is in exploring the argument for the powerful cosmos inasmuch as it is a philosophically surprising consequence of the power mereology view (in conjunction with certain physical considerations). Such an intellectual exercise retains its value even if we do not dive into the nitty gritty of physics. Given this goal, I focus the discussion on the motivations for endorsing Holistic Dependence and then discuss the argument’s implications for the metaphysics of powers. Why would a power mereologist endorse Holistic Dependence? Arguably, the main reason concerns the general appeal of this interpretation for making sense of the modal connectedness of entangled components. For example, the power mereologist could agree with Ismael and Schaffer (2020: 4142–4144). They argue that accepting a holistic dependence view of entangled wholes is preferable to both hidden variable approaches and interpretations that embrace nonlocality (and, consequently, superluminal influence). In short, Ismael and Schaffer argue that [t]here is a deeper implausibility to both incompleteness and nonlocality: both are ways of denying that the quantum state provides a complete description of systems, differing only in whether the additional “hidden variables” posited operate locally or not. (2020: 4144) On their preferred interpretation, what explains the systematic anticorrelations among the individual entangled components is the fact that their respective intrinsic states are determined by the state of the entangled system as a whole. The underlying idea is that the entangled composite system contains more information, encoded by the formalism of the wave function, than the individual entangled components (Ismael and Schaffer 2020: 4145–4147). The claim here is not that hidden variable approaches and interpretations embracing nonlocality are hopeless. In fact, I shall suspend judgment on Ismael’s and Schaffer’s assessment of the prospects of these views. Instead, the point is that the power mereologist can appeal to similar considerations for supporting Holistic Dependence. The third premise expresses a consequence of the power mereology view. Recall that the latter view endorses a conjunction of two claims. The first is that all fundamental physical properties are powers. The second is that fundamental powers compose objects when the Marmodoro Condition, as I called it, is satisfied. Accordingly, for the power mereologist, the entangled components of the universe (construed as a vast entangled system) are fundamental powers or objects composed of fundamental powers. It is

The Special Power-Composition Question and the Powerful Cosmos  179 important to recall that objects built of powers are also powers (see the section “Marmodoro’s Moderate Approach”; Marmodoro (2017: 121– 122) calls them ‘substantial powers’). To be more precise, we should think of the third premise as including a disjunctive clause. We could reformulate it like this: (3*) The components of the entangled universe are all the compossible fundamental physical powers instantiated across the cosmos or powers constituted by all the compossible fundamental physical powers instantiated across the cosmos. The choice between the two disjuncts depends on how one understands the entanglement relation. Textbook descriptions of the phenomenon are naturally read as suggesting that the entangled components are physical objects such as particles. But the distinctive modal connectedness displayed by entanglement components links physical properties, such as spin and momentum. Either way, since we are discussing a surprising implication of the power mereology view, the entangled entities should be taken to be fundamental powers or composite objects they build, which are themselves powers. The last piece of the argument for the powerful cosmos, namely the Marmodorean Link, bridges the Marmodoro Condition to the other premises. The tricky part is establishing that the entangled universe displays the right sort of holistic dependence and re-individuation of parts satisfying the Marmodoro Condition. The defender of the argument could perform an evading strategy. They could claim that the argumentative burden of showing that the holistic dependence exhibited in entanglement does not suit the Marmodoro Condition lies on the shoulder of the opponent. While it would be preferable to avoid it, this move is consistent with Marmodoro’s version of the power mereology view. And it is a more economical approach since it does not require us to adopt a disunified account of holistic dependence. The re-individuation condition is more challenging to assess. Under the  Marmodoro Condition, the parts of a metaphysically unified whole ceased to be discrete entities (see see the section “Marmodoro’s Moderate Approach”; Marmodoro 2017: 120). In the context of this argument, this requirement implies that the entangled parts of the universe are not discrete items. Perhaps, it is intuitively easier to accept that the physical powers of a unified electron are re-individuated as its ways of being rather than to buy the same claim for the entangled particles of the universe. But such an intuitive resistance does not count against the possibility that the same sort of re-individuation extends to the physical powers of the universe, where the former are re-individuates as ways of being of the latter.5

180  Joaquim Giannotti So far, I have outlined the four premises of the argument for the powerful cosmos. Then, I have offered considerations in favour of their initial plausibility within the perspective of the power mereology view under study. Informally, we can state the argument like this. If we adopt the Mamorodoro Condition, and if we accept Cosmic Entanglement, Holistic Dependence, the Power Mereology View, and the Marmodorean Link, we reach the prima facie surprising conclusion that there is an object which is constituted by all the entangled powers instantiated across the universe: the powerful cosmos. The existence of such an object will strike many supporters of a moderate answer to the special power composition question as sur­ prising and potentially distasteful. Recall that one of the motivations to embrace a moderate answer to the special power composition question is to rule out intuitively strange objects like o (namely, the object composed by the Glasgow charge and the Birmingham charge; see the section “Why Adopt a Moderate Approach to the Special Power-Composition Question?”). In a superficial sense, the powerful cosmos is a vastly bigger version of o. Contrary to this reaction, I end this chapter by arguing for the acceptance of the powerful cosmos as an unexpected yet beneficial consequence of Marmodoro’s approach. Why Embrace the Powerful Cosmos? To begin with, I assure the reader of two important things. First, I do not claim that the power mereology view, on its own, entails the existence of the powerful cosmos. Second, the argument discussed in the previous section is openly controversial and apt to be the target of all sorts of responses. The power mereologist who wishes to preserve this view but block the powerful cosmos has three main options, which I sketch next. First, against Cosmic Entanglement, someone could invoke physical considerations that cast doubts on the possibility of the universe forming a vast entangled system. For example, one could deny the existence of a wave function describing the entire quantum state of the universe. Alternatively, one could argue that collapse theories (encoding processes of entanglement) are inconsistent with Cosmic Entanglement.6 Second, against Holistic Dependence, someone could argue for adopting a different interpretation of the metaphysics of quantum entanglement relations. For instance, there are structuralist (e.g., McKenzie 2014) and coherentist views (e.g., Calosi and Morganti 2018) available on the market. On these approaches, as I understand them, the entangled components do not display the kind of holistic dependence that would satisfy the Marmodoro Condition. On structuralist views, the entangled components are asymmetrically dependent on the entanglement relation rather than the composite system. On coherentist approaches, there is a mutual dependency

The Special Power-Composition Question and the Powerful Cosmos  181 between parts and whole. By contrast, holistic dependence demands mutual dependency between the parts, but these are asymmetrically dependent upon the whole. Third, against the Marmodorean Link, one could design an objection undermining the re-individuation part of the Marmodoro Condition, showing that it is not satisfied by the universe and its entangled components. Suppose, however, that you are on board with the power mereology view. Should you look for alternative ways to deny the ontological privilege of existence to the powerful cosmos? I do not think so. There are three main advantages you could claim over a power mereology view that does not embrace the powerful cosmos: one is metaphysical, another is empirical, and a further other is methodological. Let us start with the metaphysical advantage. It seems to me that the acceptance of the powerful cosmos is preferable to the imposition of an arbitrary restriction on the kinds of objects the Marmodoro Condition can yield. The argument for the powerful cosmos does not rely on tweaking the idea that power composition occurs when collections of powers are holistically dependent and re-individuated in terms of the whole. The existence of the powerful cosmos is a metaphysical possibility consistent with the Marmodoro Condition as is, for nothing in its proposed formulation rules it out from the armchair. I argued that the actualisation of such a possibility follows from its conjunction with certain considerations from physical theory. We need some non-arbitrary justification for believing that a collection of powers satisfying the clauses of the Marmodoro Condition does not compose an object. As I suggested earlier, the power mereologist who endorses the Marmodoro Condition but wants to dodge the powerful cosmos has a better chance by targeting the peculiar interpretation of quantum mechanics and the metaphysics of the entanglement required by the other premises. The second advantage is empirical. A view accepting the existence of the powerful cosmos is preferable to one facing the challenge of showing that the relevant scientific evidence is incorrect. Albeit I noted that rejecting the Cosmic Entanglement premise is a promising way to resist the argument, it should be stressed that empirical considerations support its truth. For example, the formalism of quantum theory appears to entail that the systems that evolve out of entanglement will become entangled again (Ney 2010: 229–230; Ismael and Schaffer 2020: 4150). Even on collapse approaches, systems do not completely evolve out of entanglement (this is sometimes called the ‘problem of the tails of the wave function’). If it satisfies the Marmodoro Condition, the fleeting residual entanglement suffices for composing the powerful cosmos. Note that the argument discussed in the previous section can be temporally indexed. The existence of the powerful cosmos need not be a long-lasting affair. Consistently with the argument, it can occur and be confined to specific moments (namely all and

182  Joaquim Giannotti only those times in which all the compossible fundamental powers instantiated across the universe are entangled). That is, the powerful cosmos may have a short life span. Recall that what we are scrutinising here is its existence, not its persistence. The last advantage is methodological. A view that welcomes the powerful cosmos need not impose further conditions on power-composition. It can happily maintain that the Marmodoro Condition answers the special power-composition question in a suitable way. By contrast, a view that rejects the powerful cosmos on the grounds of it being an unacceptable consequence of moderate power-composition implies that either some further requirement must be included in the Marmodoro Condition or that the circumstances under which power-composition occurs are completely different. Either option is problematic. Each of them leaves us with the task of identifying what these more appropriate conditions are. Of course, there may be independent reasons for rejecting or revising the Marmodoro Condition. Here my claim is that it is methodologically problematic to give up the Marmodoro Condition because its conjunction with some views about entanglement yields the existence of the powerful cosmos. The advantages I outlined earlier are not conclusive and remain defeasible. However, they represent prima facie compelling reasons for believing that a Marmodorean view embracing the powerful cosmos is superior to one that does not. Therefore, moderate power mereologists who feel an intuitive resistance to the powerful cosmos should consider these benefits and go beyond the incredulous stare. I conclude by paving the way for future work in this area. The Cosmic Entanglement premise is shared with priority monism – the view that the cosmos is an integrated whole which is prior to its parts (e.g., Schaffer 2010; Ismael and Schaffer 2020). This view has generated extensive literature (see Trogdon [2017] for a survey article on this topic, including useful references for objections and replies). The argument for the powerful cosmos does not commit the power mereologist to take it as the sole fundamental object, which is the distinctive claim of priority monism. Nor does the holistic dependence embedded in the Marmodoro Condition force us  to think that the whole cosmos is prior its constituting powers. For instance, someone might argue that the relation of holistic dependence between the powerful parts and the whole they compose is naturally interpreted as these being equally fundamental. Yet we may wonder whether there are fruitful ways of combining priority monism and the mereology of  powers. For example, we could investigate whether a powers-based approach to priority monism can claim some major advantages over its standard formulation. I cannot advance this project here. But I wish to end this chapter by stressing that priority monism and the discussed moderate answer to the special power-composition question share the idea that the

The Special Power-Composition Question and the Powerful Cosmos  183 cosmos is a unified whole. With respect to this claim, such views are unexpected allies.7 Notes 1 One might ask a closely related question that could deserve the same name: In what circumstances do some powers compose some other power? I shall not discuss this question. See Mumford and Anjum (2011) for a compositional account of powers. See Bird (2016) and Pechlivanidi and Psillos (2020) for an assessment. 2 For an overview of these answers in the mereological case, see Van Inwagen (1990) – a locus classicus on this topic. 3 Even collapse views may recover something like the Cosmic Entanglement premise. For example, on Bohmian mechanics, the universal wave function encodes ways the universe could evolve including different sets of trajectories in  which its particles can be guided. In Bohmiam mechanics, the universal wave functions representing the universe are not reducible to the states of its particles. 4 Other interpretations might support a similar claim. For instance, Ney (2021: 238–241) suggests that wave function realism ought to be committed to an analogous view. 5 Interestingly, the supporter of the argument for the powerful cosmos could draw from Ismael and Schaffer (2020) again. They take that the entangled parts are ‘derivative aspects or fragments abstracted from a more fundamental whole’ (2020: 4149). It seems to me that such a remark about abstraction fits nicely the idea of ways of being (cf. Levinson 1978). 6 For more details on how to develop these objections, see Calosi (2014), who argues that Schaffer’s considerations in favour of the universe as a whole are not as straightforward as a first impression might suggest. See also Calosi (2018) for the connection between collapse theories and the universe as a vast entangled system. 7 I am grateful to Anna Marmodoro, Christopher J. Austin, Andrea Roselli, the members of the ‘Mereology of Potentiality’ seminar, Noelia Iranzo-Ribera, Katie Robertson, Nicholas Emmerson, Michael Townsen Hicks, Al Wilson, and the members of the FraMEPhys project for helpful comments on an earlier draft. This chapter’s research was funded by the FONDECYT de Iniciación No. 11220030 ‘Dual Aspect Essentialism: A Scientifically Responsible Metaphysics of Fundamental Properties’. I wish to thank María Pía Méndez Mateluna for her unwavering support.

References Bird, A. (2016) Overpowering: How the powers ontology has overreached itself. Overpowering: How the powers ontology has overreached itself. Mind 125(498):341–383. Calosi, C. (2014) Quantum mechanics and priority monism. Synthese 191(5): 915–928. Calosi, C. (2018) Quantum monism: An assessment. Philosophical Studies 175(12):3217–3236.

184  Joaquim Giannotti Calosi, C. and Morganti, M. (2018) Interpreting quantum entanglement: steps towards coherentist quantum mechanics. The British Journal for the Philosophy of Science 72(3):1–51. Chakravartty, A. (2017) Scientific ontology: integrating naturalized metaphysics and voluntarist epistemology. New York: Oxford University Press. Correia, F. (2005) Existential dependence and cognate notions. Munich: Philososia Verlag. Leonard, H. S. and Goodman, N. (1940) The calculus of individuals and its uses. The Journal of Symbolic Logic 5:45–55. Leśniewski, S. (1916) Podstawy ogólnej teoryi mnogości. In Collected works (Leśniewski 1992), eds. S. J. Surma, J. T. Srzednicki, D. I. Barnett, and F. V. Rickey, pp. 129–173. Kluwer: Dordrecht. Leśniewski, S. (1927–1931) O podstawach matematyki. In Collected works (Leśniewski 1992), eds. S. J. Surma, J. T. Srzednicki, D. I. Barnett, and F. V. Rickey, pp. 174–382. Kluwer: Dordrecht. Levinson, J. (1978) Properties and related entities. Philosophy and Phenomenological Research 39(1):1–22. Lowe, E. J. (1994) Ontological dependency. Philosophical Papers 23(1):31–48. Heil, J. (2003) From an ontological point of view. Oxford: Oxford University Press. Ismael, J. and Schaffer, J. (2020) Quantum holism: Nonseparability as common ground. Synthese 197(10):4131–4160. Marmodoro, A. (2017) Power mereology: Structural powers versus substantial powers. In Philosophical and scientific perspectives on downward causation, eds. M. Paolini Paoletti, and F. Orilia, pp. 110–129. New York: Routledge. McKenzie, K. (2014) Priority and particle physics: Ontic structural realism as a  fundamentality thesis. British Journal for the Philosophy of Science 65(2): 353–380. Mumford, S. and Anjum, R. L. (2011) Getting causes from powers. New York: Oxford University Press. Ney, A. (2010) Are there fundamental intrinsic properties? In New waves in metaphysics, ed. A. Hazlett, pp. 219–239. New York: Palgrave-Macmillan. Ney, A. (2021) The world in the wave function: A metaphysics for quantum physics. New York: Oxford University Press. Pechlivanidi, E. and Psillos, S. (2020) What powers are not. In Dispositionalism: Perspectives from metaphysics and the philosophy of science, ed. A. S. Meincke, pp. 131–149. Dordrecth: Springer. Schaffer, J. (2010) Monism: The priority of the whole. Philosophical Review 119(1):31–76. Schaffer, J. (2013) The action of the whole. Aristotelian Society Supplementary 87(1):67–87. Tugby, M. (2020) Grounding theories of powers. Synthese 198(12):11187–11216. Trogdon, K. (2017) Priority monism. Philosophy Compass 12(11):1–10. van Inwagen, P. (1990) Material beings. Ithaca: Cornell University Press.

10 The Composition of Naïve Powers Michele Paolini Paoletti

Causal powers – or powers, in short1 – are strictly connected to causation and causal processes. Indeed, most – if not all – power theorists hold that causation and causal processes can be accounted for in terms of powers.2 This need not imply that powers themselves may count as causes.3 Yet, the intuition is that there is at least something about/within powers that is crucially involved in causation and causal processes. If powers and causation are strictly connected, one natural view suggests itself. This is the view I shall call here “the naïve view of powers”. According to the naïve view of powers, there is a strict, one-to-one correspondence between powers, their bearers, and their manifestations and activations, on one hand, and the causes, effects, and causal processes, on the other hand. The naïve view of powers has one clear advantage: it makes it easy to single out powers and their features by taking into account which causal processes take place and the entities involved in them. For single and specific causal processes are accounted for by single and specific powers. For example, if there is a single and specific causal process such as Winston’s raising his arm, then there is a single and specific causal power that accounts for that process, that is, Winston’s power to raise his arm. By studying the features of the former (e.g., its cause and its effect), we may also single out the features of the latter (e.g., its bearer and its manifestation). This does not rule out that the relevant causal process may also involve further causal processes and somehow depend on the latter (e.g., processes taking place in Winston’s brain, nerves and muscles). Subsequently, this does not rule out that the corresponding power borne by Winston, in order to be activated, may also involve the activation of further powers and somehow depend on the latter (e.g., powers borne by Winston’s brain, nerves and muscles). However, also in this case, the additional causal processes are accounted for by the additional powers. Therefore, one may establish a one-to-one correspondence between the additional causal processes and the additional powers. At least prima facie, this does not DOI: 10.4324/9781003298830-13

186  Michele Paolini Paoletti endanger the one-to-one correspondence between Winston’s original causal process and his original power to raise his arm. Unfortunately, almost no one accepts the naïve view of powers. There are two main problems with it. First, there is the idea that not all powers are causal.4 I shall not evaluate this idea here. Second and more important, there is the idea that, if we accept the possibility that powers compose so as to give rise to composite phenomena, we need to dismiss at least some relevant parts of the naïve view of powers. In this article, I shall defend the naïve view of powers against this latter threat. I shall argue that it is possible to preserve the naïve view of powers and to allow for the possibility that powers compose. In the next section, I articulate the naïve view of powers in more detail. Then I introduce five cases of composition and show how power theorists were led to reject the naïve view in order to account for such cases. In the third section, I cope with such cases in a way that actually preserves the naïve view. Finally, in the fourth section, I anticipate some objections and provide my replies. Naïve Powers Before introducing the naïve view of powers, let me state some assumptions. By “powers”, I shall point to property-like entities such as Winston’s power to raise his arm. Powers are typically attributed to ordinary, commonsensical entities such as mesoscopic inanimate objects, organisms, persons, and so on. Additionally (or alternatively), they are attributed to certain scientifically respectable entities, that is, to the entities that are the basic constituents of the best current scientific theories (e.g., fields, particles, and so on). Be that as it may, the bearer of a power is the entity that is supposed to possess that power and that is able to exercise (i.e., activate) it. Powers get activated and they manifest themselves. I shall assume here that the activation of a power is a process, whereas its manifestation is the end result of that process.5 The manifestation of a power seems to be essential to that power. Namely, if a power has a certain manifestation M, it is essential to that power that it has M as its manifestation.6 Finally, at least some powers have activation conditions, that is, conditions that, by obtaining, guarantee the activation of that power.7 The activation conditions may be the activation of further powers and/or the obtaining of specific states in the universe. I have argued in Paolini Paoletti (2021) that, if a power has specific activation conditions, then the latter are essential to it. This thesis will be useful later. Take Winston’s power to raise his arm. Winston is the bearer of such a  power. Winston’s raising his arm is its activation-process, whereas Winston’s arm being raised is its essential manifestation. Finally, assume

The Composition of Naïve Powers  187 that such a power has essential activation conditions, for example, that it gets activated by virtue of Winston deciding to raise his arm. In this case, Winston’s power turns out to be the following power: Winston’s power to raise his arm in virtue of deciding it.8 The naïve view of powers may be articulated as follows: (naïve) as a matter of metaphysical necessity, P is a power if and only if (a) there is at least and at most one entity that bears P; (b) such an entity is an ordinary entity and/or a scientifically respectable one; (c) each power has at least and at most one manifestation; (d) every manifestation of a power is an effect; (e) each power has at least and at most one activation-process; (f) every activation-process of a power is a causal process; (g) every activation-causal-process includes at least and at most one cause; (h) the cause included in an activation-causal-process is the activated causal power or the bearer of the latter. Conditions (a) and (b) are clear enough. Each power has at least and at most one bearer. Of course, if powers are universals, they may be borne by multiple entities at one and the same time. Yet, in this case, (a) should be rephrased so as to rule out that one and the same instance of a power may have multiple bearers. By (b), the bearers of powers are ordinary and/or scientifically respectable entities. This seems to rule out that bearers may be entities existing by fiat, so to say, that is, entities whose existence is only introduced for the sake of having bearers for the relevant powers, even if such entities do not resemble ordinary and/or scientifically respectable entities. I shall give an example in the next section. Conditions (c) and (d) concern the manifestations of powers. I allow for the possibility that one and the same manifestation may occur at distinct times and in distinct circumstances. Namely, that manifestations are not “fragile”. Otherwise, given (naïve), one would have too many powers: one power P1 when a certain type of manifestation M occurs at t1, another power P2 when the same type of manifestation occurs at t2, and so on. However, one is also free to reject this possibility and hold that manifestations – and the corresponding powers – are “fragile”. This is still compatible with (c). By (d), if manifestations are effects, the former possibility entails that the same effect may occur at distinct times and in distinct circumstances. Again, one is free to reject this possibility and introduce “fragile” effects, together with “fragile” manifestations and powers. Condition (e) states that each power is only characterised by one activationprocess. Namely, that a power cannot be activated in multiple ways, thus giving rise to distinct activation-processes. And, by (f), the activationprocess of a power is a causal process. Also activation-causal-processes are

188  Michele Paolini Paoletti taken here to be non-“fragile”, that is, as possibly taking place at distinct times and in distinct circumstances. However, one is free to reject this view and only allow for “fragile” activation-causal-processes. By (g), every activation-causal-process is taken to include at least and at most one cause. There is no activation-causal-process that includes multiple causes. At best, multiple activation-causal-processes such as CP1 and CP2, involving distinct causes, may somehow compose. Yet, this need not entail that a composite activation-causal-process CP3 – composed of both CP1 and CP2 – comes into existence. Nor that CP3 has as its causes two distinct entities, that is, the cause involved in CP1 and the cause involved in CP2. Condition (h) allows for causes to be either the activated causal powers, or their bearers. Yet, what about activation conditions? Cannot they also count as bona fide causes involved in the activation-causal-processes of the powers characterised by them? Namely, cannot Winston’s decision to raise his arm count as the cause of the activation-causal-process connected with Winston’s power to raise his arm in virtue of deciding it? I maintain that we should dismiss this option. What causes Winston to raise his arm is Winston himself – or his activated power to raise his arm in virtue of deciding it. It is true that the latter gets in turn activated in virtue of Winston’s decision. Thus, Winston’s decision may at least count as an indirect cause of Winston raising his arm. However, by (g), the activationcausal-process of Winston’s power to raise his arm in virtue of deciding it can only include one cause. And the best candidate cause to be included is the immediate cause, that is, Winston himself or the self-same power that gets activated.9 Therefore, by (naïve), Winston’s power to raise his arm in virtue of deciding it has at least and at most one bearer, which is an ordinary entity such as Winston. It has at least and at most one manifestation, which is an effect, that is, Winston’s raising his arm. It has at least and at most one activation process, which is a causal one, that is, Winston’s raising his arm in virtue of deciding it. Finally, the latter activation-causal-process has at least and at most one cause included in it, that is, Winston himself or the self-same activated power. Composition In this section, I introduce five cases that seem to put in question (naïve). More precisely, such cases lead to the rejection of at least one thesis among (a)–(h). I then briefly examine six strategies to cope with these cases. All such strategies reject at least one thesis among (a)–(h). In the next section, I develop my positive proposal, which preserves all of (a)–(h) and the naïve view of powers.

The Composition of Naïve Powers  189 The first case does not concern the composition of powers. Therefore, I shall call it “Case 0”. Jim has to move Ball1. Ball1 has a 1-kg mass. Jim imparts on Ball1 a 1N force in a certain direction d1 for a certain amount of time t1. As a result, there is a 1-m movement of Ball1 in direction d1.10 Recall (naïve) as a matter of metaphysical necessity, P is a power if and only if (a) there is at least and at most one entity that bears P; (b) such an entity is an ordinary entity and/or a scientifically respectable one; (c) each power has at least and at most one manifestation; (d) every manifestation of a power is an effect; (e) each power has at least and at most one activation-process; (f) every activation-process of a power is a causal process; (g) every activation-causal-process includes at least and at most one cause; (h) the cause included in an activation-causal-process is the activated causal power or the bearer of the latter. If we stick to the idea that there is only one power at work in Case 0, we have two possibilities. First possibility: this power has two distinct manifestations, that is, the 1N force on Ball1 in direction d1 for t1 and the 1-m movement of Ball1 in direction d1. This violates (c). And it may also violate (e), insofar as two distinct activation-processes seem to be at stake, leading to two distinct manifestations. Second possibility: the relevant power actually has only one manifestation, which may well be an effect, i.e., the 1-m movement of Ball1 in direction d1. However, what about the 1N force? If it is not an effect but a manifestation of the power, this violates (d). And, at any rate, (c) and possibly also (e) are still violated. For one and the same power still has two distinct manifestations. On the contrary, if the 1N force is not an effect and it is not a manifestation either, what is it? Let me now turn to Case 1. There is another ball: Ball2. Ball2 has a 2-kg mass. Jim asks for John’s help. Jim imparts a 1N force in direction d1 for t1 on Ball2. John does the same. As a result, there is a 1-m movement of Ball2 in direction d1. Consider now Case 2. Now we have Ball1, which has a 1-kg mass. Both Jim and John impart on it a 1N force in direction d1 for t1. The result is that there is a 2-m movement of Ball1 in direction d1. In Case 1 and Case 2, as it happened in Case 0, (c) and possibly (e) get violated. The reason why they get violated is even more apparent. There is a power exercised by Jim, which seems to have two distinct manifestations: one by itself (i.e., the 1N force) and one together with another power exercised by John (i.e., the overall movement of the balls). And something analogous happens from the side of John. Namely, John has a similar power with two distinct manifestations.

190  Michele Paolini Paoletti Moreover, (d) may get violated as well, insofar as the imparted 1N force is not taken to be a bona fide effect. Alternatively, we may assume that, in Case 1, there is only one composite power at work, that is, the power leading to the 1-m movement. And that, mutatis mutandis, something analogous happens in Case 2. However, by (e), we also hold that that composite power has at least and at most one activation process, which includes, by (g), at least and at most one cause. Moreover, by (h), the cause included in the activation-causal-process is the activated causal power or the bearer of the latter. This implies that the cause/bearer cannot be Jim. Nor can it be John. It must be some novel entity, made up of both Jim and John. But this may run into the risk of violating (b). For the novel entity (e.g., the plurality made up of Jim and John) may not be an ordinary or a scientifically respectable entity. To be clear: I do not rule out that apparently “composite” powers may sometimes come together with ontologically novel bearers. On the contrary, I have defended a view according to which this often happens, that is, when emergent powers are in place.11 What I find troublesome is that this must always be the case. That is, I deny that, whenever we have a “composite” power or some apparent case of composition of powers, we must also postulate the existence of an ontologically novel bearer. Alternatively, one may hold that the “composite” power has two bearers, that is, Jim and John, which are both causes of the relevant, overall effect. However, this violates (a) and (g): there are two distinct bearers and two distinct causes. Consider now Case 3. Here we have Ball3, which has a 1,000-kg mass. Jim imparts a 1N force in direction d1 for t1. But Ball3 stands still, that is, it does not move. In Case 3, there is no manifestation and/or no overall effect, at least if we only focus on the overall movement of the ball. True: there is the imparted force. But the imparted force does not result in anything. Thus, can the imparted force be taken as a bona fide manifestation/effect, in this case? If there is no manifestation here, (c) is violated. Or, if the imparted force counts as a manifestation, there is no apparent effect produced by it, contra (d). Finally, in Case 4, we have our old friend, that is, Ball1, which has a 1-kg mass. Jim now imparts on it a 1N force in direction d1 for t1. However, John now imparts on Ball1 a 1N force for t1 in the opposite direction d2. As a result, Ball1 stands still. Even in this case, (c) seems to be violated. Or, if (c) is not violated, at least (d) gets violated. I shall now briefly introduce six strategies to cope with Cases 0–4. I shall not examine in detail how all of such strategies cope with the Cases. What I shall point out is that each strategy rebuts at least one among (a)–(h), thus rejecting the naïve view of powers.

The Composition of Naïve Powers  191 Radical pandispositionalism holds that only powers exist – or that they are the only ontologically fundamental entities.12 This results in there being no bearers for powers, contra (a). Other authors suggest that at least some powers are multi-track, that is, that they have multiple manifestations in multiple circumstances – possibly together with multiple activation conditions.13 When composition occurs – or when multiple manifestations/effects occur – one and the same power may get involved, thus giving rise to distinct manifestations/effects in distinct circumstances – or even in the same circumstances. Yet, this obviously violates (c), that is, that each power has at least and at most one manifestation. It may also violate (e), insofar as distinct manifestations are connected with distinct activation-processes.14 According to some philosophers, powers are only exercised when they meet their mutual manifestation partners.15 For example, salt exercises its power to dissolve in water only if and when it meets the water’s power to dissolve salt and vice versa. We may well hold that, in this case, there is only one activation-causal-process. However, either (g) or (h) gets violated; that is, either this process has two distinct causes (i.e., salt and water or their activated powers) or it has only one cause, which does not correspond to the bearers of powers (i.e., salt and water) or to self-same activated powers.16 On the vector model defended by Anjum and Mumford (2011) and on the constellation model defended by Williams (2019), effects are only reached through the exercise of multiple powers. Therefore, one effect (and possibly one causal process) always corresponds to the exercise of multiple powers. This violates (d), that is, that every manifestation of a power is an effect. Moreover, it also violates the conjunction of (e) (each power has at least and at most one activation-process) and (f) (every activation-process of a power is a causal process). For either multiple powers get activated in distinct activation-processes but there is only one causal process leading to the overall effect or one and the same power has two distinct activationcausal-processes, that is, the one leading to its contribution to the overall effect and the one leading to the overall effect. In a similar vein, some authors argue that the manifestations of powers are not effects but contributions/influences/wirkungen.17 This clearly violates (d). Finally, Vetter (2015) suggests that there are joint potentialities, i.e., powers exercised by pluralities of entities. Joint potentialities may be at work in Cases 1, 2 and 4 – though in Case 4 there is no overall effect. Yet, at any rate, joint potentialities seem to violate (b). For their bearers, i.e., pluralities of entities, are not ordinary, nor scientifically respectable entities. They are put together just in order to find out suitable bearers for the relevant joint potentialities.

192  Michele Paolini Paoletti Naïve Powers Preserved To preserve (naïve) and account for Cases 0–4, I shall distinguish between two kinds of powers: component powers and derivative powers. Component powers are powers that have forces as their manifestations – or, more precisely, forces with specific magnitudes imparted on specific entities in specific directions for specific amounts of time. Derivative powers are powers that have movements (or other phenomena “deriving” from forces) as their manifestations – or, more precisely, movements of specific entities in specific directions for specific lengths. As we shall see, derivative powers entirely depend on component powers (and possibly on further conditions) for their activation and possession. Moreover, both component and derivative powers fit well with (naïve). From now onwards, I shall use a “C” subscript for component powers and a “D” subscript for derivative ones. There is one component power I shall be first interested in. This is Jim’s power to impart on Ball1 a 1N force in direction d1 for t1. I shall call it “PC1”. The manifestation of PC1 is a force imparted with a certain magnitude (i.e., 1N) on a specific object (i.e., Ball1) in a specific direction (i.e., d1) for a specific amount of time (i.e., t1). Some clarifications are in order. First of all, I am neutral here on the ontology of forces. I am inclined to take forces as relations, partly in the footsteps of Massin (2009). However, nothing crucial hinges here on the ontological interpretation of forces. Second, the manifestation of PC1 is not just a force but also a force endowed with specific features. Again, I am neutral here on the ontology of the relevant manifestation. Maybe it is a complex relational entity, for example, a fact or a fact-like entity. But nothing crucial is at stake here. Third, the specific amount of time included in the manifestation of PC1 (i.e., t1) is not the amount of time required for Jim to activate PC1. Namely, t1 is not the specific amount of time that goes from Jim starting to exercise PC1 to the appearance of the end result, that is, of the manifestation. On the contrary, t1 is the duration of the end result, that is, of the manifestation. Namely, the 1N force imparted on Ball1 in direction d1 lasts t1. Fourth, Jim is the bearer of the power. But the power need not be a particular property, that is, a trope or a mode. Maybe Jim is nothing but one of the possible entities that instantiate the universal power at stake. But, again, nothing crucial hinges on taking powers such as PC1 as universal or as particular properties. Yet, fifth, it is crucial that Ball1 (i.e., that specific ball with its specific features) is included in the manifestation of PC1. For otherwise, PC1 could not be the very power at work in those very cases that involve Ball1 – and no other specific ball with other features.18

The Composition of Naïve Powers  193 Sixth and finally, for the sake of simplicity, I presented PC1 as a basic power, that is, as a power not endowed with activation conditions. However, I do not rule that component powers may actually have essential activation conditions. Of course, in this case, PC1 should be replaced with some non-basic counterpart PC1* endowed with essential activation conditions. Moreover, both basic component powers and their non-basic counterparts could have background conditions for their activation, that is, conditions that must be met in order for them to be activated, though they do not guarantee the activation.19 For example, a certain spatial relation between Jim and Ball1. In addition to component powers, there are also derivative powers. Derivative powers are non-basic powers that are activated (also or only) in virtue of the activation of component powers. Here is the first derivative power we shall meet: Jim’s power to move Ball1 by 1 m in direction d1 in virtue of Jim’s exercising PC1. I shall call such a derivative power “PD1”. Again, I am neutral here on the ontology of movements and on the ontological interpretation of the manifestation of PD1. Moreover, I am also neutral on its being a universal or a particular property, though I maintain that Ball1 is crucially involved in its manifestation. Finally, I do not rule out that the derivative power at stake may also include further essential activation conditions (thus turning out to be another, more complex derivative power PD1*). And I do not rule out that derivative powers may also have specific background conditions. However, for the sake of simplicity, I shall not dwell here on these issues. There are two further clarifications to be made about derivative powers such as PD1. First, one could ask why the activation conditions of PD1 must consist in Jim’s exercising PC1, rather than in the manifestation/end result of the activation of PC1 – regardless of its being produced by Jim (i.e., the 1N force imparted on Ball1 in direction d1 for t1). I reply that what is crucial in order for PD1 to be exercised by Jim (i.e., by its bearer) is that Jim himself exercises PC1 and that, in virtue of Jim’s exercising PC1, he also exercises PD1. Thus, it is not enough that there is some 1N force imparted by someone or something on Ball1 in direction d1 for t1. It is not enough that there is the relevant manifestation. The presence of the relevant manifestation would not be enough to make it the case that PD1 is activated by Jim, and by nothing/no one else in the relevant circumstances. Thus, the activation conditions of PD1 should consist in Jim’s exercising PC1. Second, it is important to point out that PD1 depends on PC1 both for its activation and its possession. More precisely, PD1 depends on PC1 for its activation, insofar as the activation of PC1 (by Jim) guarantees the activation of PD1 (by Jim). Moreover, PD1 depends on PC1 for its possession by Jim, insofar as Jim possesses PD1 in virtue of possessing PC1. Namely, Jim

194  Michele Paolini Paoletti can produce the relevant movement of Ball1 in virtue of being able to produce the relevant force on Ball1. Of course, as I have already conceded, the derivative power PD1 may also depend on something else besides PC1 for its activation and/or for its possession. Namely, it is not necessary that PD1 entirely depends for its activation and/or for its possession on PC1. But I shall assume here that this is the case for the sake of simplicity. Namely, I shall assume here that PD1 entirely depends for its activation and its possession (only) on PC1. The (partial or entire) dependence of PD1 on PC1 makes the former a derivative power. We are now equipped with all the tools to deal with Cases 0–4. In Case 0, Jim has to move Ball1. Ball1 has a 1-kg mass. Jim imparts on Ball1 a 1N force in a certain direction d1 for a certain amount of time t1. As a result, there is a 1-m movement of Ball1 in direction d1. What happens here is that Jim activates PC1, that is, his power to impart on Ball1 a 1N force in direction d1 for t1. In virtue of activating PC1, Jim also activates PD1, that is, his power to move Ball1 by 1 m in direction d1 in virtue of Jim’s exercising PC1. And the ball moves. In Case 1, there is another ball: Ball2. Ball2 has a 2-kg mass. Jim asks for John’s help. Jim imparts a 1N force in direction d1 for t1 on Ball2. John does the same. As a result, there is a 1-m movement of Ball2 in direction d1. Here Jim has a certain component power PC2, that is, his power to impart a 1N force in direction d1 for t1 on Ball2. John has another component power PC3, that is, his power to impart a 1N force in direction d1 for t1 on Ball2. Of course, if powers are universals, PC2 and PC3 (and all the derivative powers below) actually are two instances of one and the same power. But I shall set this complication aside. Jim activates PC2. John activates PC3. Moreover, Jim possesses a certain derivative power PD2, that is, his power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3. And John possesses a certain derivative power PD3, that is, his power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3. Derivative powers PD2 and PD3 have two activation conditions, that is, Jim’s exercising PC2 and John’s exercising PC3. Therefore, each of such derivative powers gets activated in virtue of the obtaining of both conditions. Namely, it is not the case that PD2 gets activated by Jim only by virtue of Jim’s exercising PC2. Nor is it the case that PD3 gets activated by John only in virtue of John’s exercising PC3. Jim activates PD2 in virtue of his exercising PC2 and of John’s exercising PC3. Likewise, John activates PD3 in virtue of Jim’s exercising PC2 and of his exercising PC3. PD2 and PD3 entirely depend for their activation and possession (by Jim and John) on both PC2 and PC3.20 In Case 1, since Jim activates PC2 and John activates PC3, Jim also activates PD2 and John also activates PD3. As a result, Ball2 moves. And the

The Composition of Naïve Powers  195 movement is caused by both Jim and John through distinct activationcausal-processes. In the next section, I try to dissipate some concerns about this account. In Case 2, we have Ball1, which has a 1-kg mass. Both Jim and John impart on it a 1N force in direction d1 for t1. The result is that there is a 2-m movement of Ball1 in direction d1. In this case, there are two component powers at work. Jim exercises PC1, that is, his power to impart on Ball1 a 1N force in direction d1 for t1. John exercises PC4, that is, his power to impart on Ball1 a 1N force in direction d1 for t1. Additionally, there are two derivative powers. These are PD4 and PD5. PD4 is Jim’s power to move Ball1 by 2 m in direction d1 in virtue of Jim’s exercising PC1 and of John’s exercising PC4. PD5 is John’s power to move Ball1 by 2 m in direction d1 in virtue of Jim’s exercising PC1 and of John’s exercising PC4. It goes without saying that each of PD4 and PD5 entirely depends for its possession and activation on PC1 and on PC4. Since PC1 and PC4 are activated, PD4 and PD5 get activated as well. As a result, Ball1 moves. In Case 3, we have Ball3, which has a 1,000-kg mass. Jim imparts a 1N force in direction d1 for t1. But Ball3 stands still; that is, it does not move. What happens here is that Jim possesses and exercises his component power PC5, that is, his power to impart on Ball3 a 1N force in direction d1 for t1. However, Jim does not possess the derivative power PD6, that is, the power to move Ball3 by 1 m in direction d1 in virtue of Jim’s exercising PC5. Nor does he possess similar powers with other lengths and directions. Therefore, Ball3 stands still. Finally, in Case 4, we have Ball1, which has a 1-kg mass. Jim imparts on it a 1N force in direction d1 for t1. However, John imparts on Ball1 a 1N force for t1 in the opposite direction d2. As a result, Ball1 stands still. Also in this case, Jim and John possess and activate two distinct component powers. Jim possesses and activates PC1, that is, his power to impart a 1N force in direction d1 for t1 on Ball1. John possesses and activates some further component power PC6, that is, his power to impart a 1N force in direction d2 for t1 on Ball1. Crucially, d1 and d2 are in opposite directions. What happens in this case is that the activation of PC1 by Jim prevents the activation of some further derivative power(s) possessed by John. For example, the activation of PC1 by Jim prevents the activation of John’s derivative power PD7, that is, his power to move Ball1 by 1 m in direction d1 in virtue of John’s exercising PC6. John may still possess PD7. But the activation of PD7 is prevented by Jim’s exercising PC1. Likewise, the activation of PC6 by John prevents the activation of Jim’s derivative power PD1, that is, his power to move Ball1 by 1 m in direction d1 in virtue of Jim’s exercising PC1. Jim may still possess PD1. But the activation of PD1 is prevented by John’s exercising PC6. In sum, as a result, Ball1 stands still.

196  Michele Paolini Paoletti I shall not provide here an ontological interpretation of prevention. Maybe the non-activation of PC1 by Jim is among the background conditions for the activation of PD7 by John. And the non-activation of PC6 by John is among the background conditions for the activation of PD1 by Jim.21 At any rate, we can make sense of Case 4 by invoking the possibility that the activation of certain powers can be prevented by the activation of other powers. It is now easy to show that both component and derivative powers fit well with (naïve) as a matter of metaphysical necessity, P is a power if and only if (a) there is at least and at most one entity that bears P; (b) such an entity is an ordinary entity and/or a scientifically respectable one; (c) each power has at least and at most one manifestation; (d) every manifestation of a power is an effect; (e) each power has at least and at most one activation-process; (f) every activation-process of a power is a causal process; (g) every activation-causal-process includes at least and at most one cause; (h) the cause included in an activation-causal-process is the activated causal power or the bearer of the latter. Component and derivative powers have single bearers such as Jim and John (a), which are ordinary entities (b) – and, possibly, scientifically respectable ones. They have single manifestations (c), which are bona fide effects (d). They have single activation-processes (e), which are causal (f). Finally, they have single causes included in them (g), which coincide with their bearers or with those self-same, activated powers (h). True: derivative powers such as PD2 (i.e., Jim’s power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3) and PD3 (i.e., John’s power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3) include further entities distinct from their bearers in their activation conditions. For PD2 also includes John in its activation conditions, and PD3 also includes Jim in its activation conditions. However, this does not make John one of the causes involved in the activation-causal-process of PD2. Nor does it make Jim one of the causes involved in the activation-causal-process of PD3. For only Jim activates PD2 – even if he also requires John’s ‘participation’ in the activation conditions, so to say. And only John activates PD3 – even if he also requires Jim’s ‘participation’ in the activation conditions. Therefore, PD2 includes no further cause besides Jim – or besides PD2 itself. And PD3 includes no further cause besides John – or besides PD3 itself.22

The Composition of Naïve Powers  197 Additionally, PD2 and PD3 share the same manifestation – and the same activation conditions. Yet, they still give rise to two distinct activationcausal-processes. This implies that two distinct activation-causal-processes may result in one and the same manifestation (in the same circumstances). But this consequence is fully compatible with (naïve).23 Objections and Replies In this final section, I shall anticipate some objections and replies, that mainly concern my treatment of Cases 1 and 2. For the sake of brevity, I  focus on Case 1. However, what I claim may be also applied, mutatis mutandis, to Case 2 and to similar cases of composition. I have suggested that, in Case 1, Jim has a certain component power PC2, that is, his power to impart a 1N force in direction d1 for t1 on Ball2. John has another component power PC3, that is, his power to impart a 1N force in direction d1 for t1 on Ball2. Jim and John activate such powers. Moreover, Jim possesses a certain derivative power PD2, that is, his power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3. And John possesses a certain derivative power PD3, that is, his power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3. The latter derivative powers get activated in virtue of the activation of both PC2 and PC3. Ball2 moves by 1 m in direction d1. It is worth reminding here that derivative powers such as PD2 and PD3 entirely depend for their possession and activation on component powers such as PC2 and PC3. Moreover, they necessarily coexist and they are necessarily coactivated, since they have the same possession conditions and the same activation conditions (i.e., PC2 and PC3). They enjoy derivative ontological status with respect to component powers such as PC2 and PC3. Finally, they do not depend on one another for their possession or for their activation. There are two sets of objections against this view. First, there are some objections against the ontological status of derivative powers PD2 and PD3. Second, there are some objections that may arise when one connects my  account of component and derivative powers with the metaphysical debates on component and resultant forces. Let me address the first set of objections. One may claim that PD2 and PD3 give rise to some sort of causal overdetermination. For the activation of one among PD2 and PD3 is sufficient to bring about the relevant manifestation/effect, that is, the movement of Ball2 by 1 m in direction d1. Therefore, PD2 and PD3 causally overdetermine the manifestation.

198  Michele Paolini Paoletti I reply, first, that it is not legitimate to get rid of either PD2, or PD3. For PD2 and PD3 – through their activation – constitute the ineliminable causal contributions, respectively, given by Jim and John to the manifestation at stake. In other terms, if it is true that both Jim and John causally contribute to the manifestation, then it is also true that PD2 and PD3 – through their activation – constitute the relevant causal contributions. Thus, none of them can be eliminated. Second and more important, as Bennett (2007) points out, there is genuine causal overdetermination only if the candidate overdeterminers are somehow independent and when there is no metaphysically necessitating relation between them. On the contrary, it is questionable that causal overdetermination is in place when the candidate overdeterminers enjoy dependence and/or some intimate and strong relation of metaphysical necessitation. PD2 and PD3 do not depend on one another. However, they necessarily coexist and they are necessarily coactivated, since they have the same dependees (i.e., PC2 and PC3). Therefore, there is some intimate and strong relation of metaphysical co-necessitation between PD2 and PD3 so that they cannot count as candidate overdeterminers. A related worry is that my view is not ontologically parsimonious. For it admits two derivative powers (i.e., PD2 and PD3) rather than one and two activation-causal-processes (i.e., that of PD2 and that of PD3) rather than one. However, first, there is no ontological profligacy in types. For both my account and some rival account on which there is only one derivative power and only one activation process admit of two distinct types of entities: derivative powers and activation-causal processes. Type-parsimony is generally taken to be far more important than token-parsimony.24 Second, PD2 and PD3 are derivative powers so that they only count as derivative entities. But if what counts is only parsimony in the number of fundamental entities (or of fundamental types of entities),25 then the existence of both PD2 and PD3 is not troublesome from the standpoint of parsimony. Third, consider the rival view, on which there is only one derivative power and only one activation-causal-process. The relevant power and the relevant process should be composite. Recall (naïve). If we keep both (a) (i.e., there is at least and at most one entity that bears P) and (g) (i.e., every activation-causal-process includes at least and at most one cause), the rival view leads us to postulating the existence of a new entity as the bearer of the composite power and as the cause in the causal process. Such an entity cannot be identical with Jim or with John. For the composite power – and the composite process – is had by/involves both Jim and John taken together and none of them taken in isolation. Therefore, there should be a new entity somehow composed of both Jim and John that bears the relevant

The Composition of Naïve Powers  199 composite power and that is involved as the single cause in the relevant process. Such an entity may be a non-ordinary and non-scientifically respectable one, thus violating (b). It may also belong to a new type of entities, thus endangering type parsimony. And the existence of this new entity also turns out to endanger token parsimony. For we now have two entities that are introduced for the sake of making sense of the composition of powers, that is, the composite power and its new bearer. On the original view, we already had two entities that made sense of the composition of powers, that is, two derivative powers. However, the bearers of such powers (i.e., Jim and John) were not introduced in our original scenario just for the sake of making sense of the composition of powers. On the contrary, in the new scenario, the bearer of the composite power is introduced just for the sake of making sense of the latter phenomenon.26 Thus, there is no gain in token parsimony on the new alternative. Another objection is that the activations of PD2 and PD3 lead to a double effect. Namely, that the activation of PD2 leads to a 1-m movement of Ball2 in direction d1 and the activation of PD3 leads to another 1-m movement of Ball2 in direction d1. As a result, Ball2 moves by 2 m in direction d1, rather than by 1 m, as it does. But this phenomenon would only follow if we were committed to the following clause: (i) a certain manifestation/effect is due to one and only one activated power through one and only one activation-causal-process. Following (i), there must be a one-one correspondence between manifestations/effects and activated powers (and their activation-causal-processes). Thus, whenever there are two activated powers (and the corresponding processes), there must also be two distinct manifestations/effects. And this results, for example, in there being two distinct 1-m movements of Ball2 in direction d1, thus leading to an overall 2-m movement in direction d1. But I am not committed to (i). Nor do I think that the naïve view of powers should include (i). For (i) rules out the possibility that powers compose so as to give rise to composite processes and effects. Therefore, I grant that multiple powers (and processes) may be involved in giving rise to single manifestations/effects. The manifestations/effects at stake (e.g., the 1-m movement of Ball2 in direction d1) are not multiplied by virtue of their being connected with multiple powers (and processes). I suspect that there is one fundamental problem lurking behind the interpretation of PD2 and PD3 – and of all derivative and non-derivative powers in general. Take PD2, that is, Jim’s power to move Ball2 by 1 m in direction d1 in virtue of Jim’s exercising PC2 and of John’s exercising PC3. If Jim

200  Michele Paolini Paoletti possesses this power, he is obviously able to bring about the relevant manifestation/effect. However, this does not necessarily nor always imply that Jim is able to bring about the relevant manifestation/effect by himself, that is, without the contribution of no one and nothing else. That is, whenever we attribute a certain power to something, we obviously imply that the latter is able to bring about the manifestation/effect of the former. Yet, we do not necessarily nor always imply that the bearer is able to bring about the manifestation/effect of the power by itself, without the contribution of nothing else. It is only if we think that Jim, by possessing PD2, is able to bring about the manifestation by himself and that John, by possessing PD3, is also able to bring about the same manifestation by himself that we run into the risk of seeing two independent and non-necessarily-coexisting processes and two distinct effects brought about through the latter. It is now time to briefly connect my account of composition with the debate on the metaphysical status of component and resultant forces. Component forces are those forces that are at work in complex systems. Resultant forces result from the vector sum of component forces. According to some authors, only component forces exist.27 For resultant forces just derive from the latter and/or they may be seen as abstractions from the latter. According to other authors, only resultant forces exist.28 For only resultant forces have their manifestations displayed (or fully displayed) in complex systems (e.g., resultant movements with specific magnitudes in specific directions). Finally, still other authors are more ecumenical, and they accept both component and resultant forces.29 I admit that both component and derivative powers are real. However, the latter derive from the former: they owe their existence and activation to the former. Therefore, derivative powers enjoy a derivative metaphysical status in comparison with component ones. Within this perspective, the problem of determining the status of component and resultant forces is partly orthogonal to my project. First of all, it is far from clear that forces are powers.30 And, at any rate, I am not committed to this view here. Second and more important, component powers are not component forces. Nor do they correspond to component forces. And derivative powers are not resultant forces. Nor do they correspond to resultant forces. At best, component powers have component forces ‘involved’ in their manifestations. For the manifestations of component powers are forces with specific magnitudes and directions imparted on specific entities for specific amounts of time. However, derivative powers do not have resultant forces (nor component forces) in their manifestations. Their manifestations consist in specific movements of entities in specific directions – at least in all the cases examined here.

The Composition of Naïve Powers  201 But I recognize that, if I were to take sides, I would be nearer to those who claim that only component forces are real. For I only invoke component forces when dealing with the composition of powers. At any rate, my model of the composition of powers can also be extended to cases in which forces are not the manifestations of component powers, that is, to cases in which component powers have manifestations different from forces. Forces have been examined in this contribution only because they are the most debated and most controversial manifestations when it comes to the composition of powers. But let me stick to the case of forces. One could ask the following question: Is there also a place for resultant forces in my account? I can only give a tentative answer here. Yes, I am eager to admit resultant forces. They may well exist. Yet, resultant forces entirely depend for their existence and for what they are (including their magnitudes and directions) on component forces. Indeed, one may think of resultant forces as relational facts or fact-like entities, consisting in component forces standing in some functional relation (e.g., vector sum or its ontological counterpart). Such relational facts or fact-like entities entirely depend for their existence and identity on the relevant relata, that is, on the relevant component forces. Moreover, by virtue of such dependence, resultant forces qua relational facts or fact-like entities also possess specific magnitudes and directions. Thus, there is no parthood relation between resultant forces and component ones, if not figuratively. The only relation at stake is dependence – for existence and identity. Nor is there any parthood relation between the magnitudes and directions of resultant forces and those of component forces. Again, the only relation at stake is dependence.31 It may look strange to attribute magnitudes and directions to relational facts or fact-like entities. And to treat component and resultant forces in different ways: the former are relational facts or fact-like entities, whereas the latter need not be relational facts or fact-like entities. However, the first objection is not well motivated. Facts and fact-like entities may well possess properties and stand-in relations, for example, when there are causal relations between them. Therefore, among their properties, one may well include magnitudes and directions. The second objection can be dealt with by claiming that the ontological dissimilarity between component and resultant forces may justify their distinction and their different ontological status. In sum, having ontological dissimilarity between the former and the latter may actually turn out to be an advantage. And, at any rate, also component forces may be seen as relational facts or fact-like entities. I do not wish to rule out this option here and – as I anticipated – I am actually eager to embrace it.32 In this way, there is no threat of causal overdetermination when it comes to resultant and component forces. For resultant forces depend on

202  Michele Paolini Paoletti component ones so that they do not qualify as independent candidate overdeterminers.33 Notes 1 Or dispositions, as I shall use here “power”, “causal power” and “disposition” as having the same meaning. 2 For a recent example, see Anjum, Mumford (2018). 3 For an overview of some problems concerning the causal efficacy of powers, see Choi, Fara (2018). 4 See for example Nolan (2015). 5 Other authors argue that the manifestation of a power coincides with its activation, for example, Lowe (2011) and Vetter (2014, 2015). If one accepts this view, what we will claim here with respect to manifestations will also hold for activation-processes. What I claim here is also compatible with manifestations’ being internal states of powers (Marmodoro 2017a). 6 See for example Molnar (2003) and Lowe (2010). 7 In Paolini Paoletti (2021) I also distinguish between the activation conditions of a power, its background conditions and its possession conditions. The background conditions of a power are those conditions that have to be met in order for that power to be activated, although they do not guarantee its activation. The possession conditions of a power are those conditions that have to be met in order for something to bear that power. 8 Please note that Winston may raise his arm even without deciding it, for example, by reflex. In this case, another power possessed by Winston would get exercised, that is, Winston’s power to raise his arm in virtue of a reflex. 9 I am inclined to count only Winston as a cause, as I hold that substances are the only causes in the universe (see Paolini Paoletti 2018). 10 Even if imparting the force actually results in accelerating the movement of the object, I simplify the framework here and only consider the overall effect, that is, the 1-m movement in direction d1. 11 See for example Paolini Paoletti (2017, 2020). 12 See for example Marmodoro (2017a, 2017b). 13 See for example Martin (2008), Kistler (2012), Vetter (2015), Corry (2019), Williams (2019), Hüttemann (2021). 14 For some criticisms, see for example Cartwright, Pemberton (2013) and Austin (2016). 15 See for example Martin, Heil (1998, 1999); Martin (2008); Marmodoro (2017a); and Ingthorsson (2021). 16 For some criticisms, see for example Austin (2016) and Anjum, Mumford (2017). 17 See Molnar (2003); Anjum, Mumford (2011); Fischer (2018); Corry (2019); and Williams (2019). In a similar fashion, Hüttemann (2013, 2021) holds that powers do not fully manifest when they compose with other powers. For some criticisms of these views, see McKitrick (2018). 18 In principle, one could also replace PC1 with another power with a more generic manifestation, for example, imparting a 1N force on a 1-kg ball (with other relevant features) in direction d1 for t1. But, in this case, what would matter would not be the generic manifestation as such, but its specific instantiation by one specific ball, that is, by Ball1. Another point: directions and magnitudes may also be taken to be essential to forces. In this case, PC1 would be the power

The Composition of Naïve Powers  203 to impart force f1 on Ball1 for t1 – where it is assumed that f1 essentially has direction d1 and 1N magnitude. 19 See note 7 and Paolini Paoletti (2021). 20 More precisely, in this case and in all analogous cases, (i) the possession of PD2 by Jim entirely depends on the possession of PC2 by Jim and on the possession of PC3 by John; (ii) the possession of PD3 by John entirely depends on the possession of PC2 by Jim and on the possession of PC3 by John; (iii) the activation of PD2 by Jim entirely depends on the activation of PC2 by Jim and on the activation of PC3 by John; (iv) the activation of PD3 by John entirely depends on the activation of PC2 by Jim and on the activation of PC3 by John. 21 More on this in Paolini Paoletti (2021). 22 At best, the entities that ‘participate’ in the activation conditions may only count as indirect causes. In this case, (g) and (h) should be reformulated, so as to only concern direct causes. 23 Baltimore (2022) argues that, when accounting for the composition of powers, it is necessary to explain how powers can interact with one another and why they produce certain overall results (and not others) when they interact in specific ways. My model can satisfy both desiderata by appealing to the essence of derivative powers, including their activation conditions and their manifestations: multiple powers interact in specific ways so as to produce specific results insofar as this is part of the essence of specific derivative powers. Moreover, when non-linear modes of combining powers are involved, the relevant modes of combination may be included in the activation conditions of the relevant derivative powers. Pace Baltimore, neither does this result in accepting any sort of mutual manifestation model, nor in holding that powers are multi-track. 24 See for example Lewis (1973). 25 See for example Schaffer (2015). 26 And true: in the original view, there are two activation-causal-processes (i.e., those of component powers), rather than one. But activation-causal-processes are ontologically derivative and parasitic upon powers, at least on most powers theories, so that they do not profligate the number of fundamental entities. 27 See Creary (1981) and Spurrett (2001). Massin (2017) has a more ecumenical approach, that tends towards privileging component forces. For (roughly) resultant forces are residual component forces. 28 See Cartwright (1980) and (1983) and J. Wilson (2009b). 29 See A. Wilson (2009a), Moore (2012) and Massin (2017) (but see note 26). 30 For some doubts, see Bigelow, Ellis, Pargetter (1988) and Massin (2009). On the ontology of forces, see also J. Wilson (2007). 31 On this problem, see J. Wilson (2009b). Since facts are typically taken to have constituents/parts, it may be useful to think of resultant forces as relational modes, that is as particular relations that also depend for their identity and existence on their relata, even if their relata are not ‘parts’ of them (see Paolini Paoletti 2016). Modes play the roles typically attributed to facts. Therefore, they may count as fact-like entities. 32 Another option consists in claiming that the resultant force is not identical with the relational fact/fact-like entity that has the component forces as its relata. The resultant force may be an additional entity that owes its existence, its identity and some specific features (i.e., magnitude and direction) to the relational fact/fact-like entity involving the component forces. 33 Additionally, on my account, it is possible to apportion causal responsibility among distinct entities by taking into account the component forces in manifestations. Finally, it is not required to accept null forces (see Massin 2009).

204  Michele Paolini Paoletti References Anjum, R. L., Mumford, S. D. (2011). Getting Causes from Powers. Oxford: Oxford University Press. Anjum, R. L., Mumford, S. D. (2017). “Mutual Manifestation and Martin’s Two Triangles”. In: Jacobs, J. D. (ed.), Causal Powers. Oxford: Oxford University Press: 77–89. Anjum, R. L., Mumford, S. D. (2018). Causation in Science and the Metaphysics of Scientific Discovery. Oxford: Oxford University Press. Austin, C. J. (2016). “Is Dispositional Causation Just Mutual Manifestation?” Ratio, 29: 235–248. Baltimore, J. A. (2022). “Dispositionalism, Causation, and the Interaction Gap”. Erkenntnis, 87: 677–692. Bennett, K. (2007). “Mental Causation”. Philosophy Compass, 2: 316–337. Bigelow, J., Ellis, B., Pargetter, R. (1988). “Forces”. Philosophy of Science, 55: 614–630. Cartwright, N. (1980). “Do the Laws of Physics State the Facts?” Pacific Philosophical Quarterly, 61: 75–84. Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon. Cartwright, N., Pemberton, J. (2013). “Aristotelian Powers: Without Them, What Would Modern Science Do?” In: Groff, R., Greco, J. (eds.), Powers and Capacities in Philosophy: The New Aristotelianism. London-New York: Routledge: 93–112. Choi, S., Fara, M. (2018). “Dispositions”. In: Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/entries/dispositions/ last visited on June 7, 2021). Corry, R. (2019). Power and Influence. The Metaphysics of Reductive Explanation. Oxford: Oxford University Press. Creary, L. G. (1981). “Causal Explanation and the Reality of Natural Component Forces”. Pacific Philosophical Quarterly, 62: 148–157. Fischer, F. (2018). Natural Laws as Dispositions. Berlin: de Gruyter. Hüttemann, A. (2013). “A disposition-based process-theory of causation”. In: Tugby, M., Mumford, S. D. (eds.), Metaphysics and Science. Oxford: Oxford University Press: 101–122. Hüttemann, A. (2021). A Minimal Metaphysics for Scientific Practice. Cambridge: Cambridge University Press. Ingthorsson, R. D. (2021). A Powerful Particulars View of Causation. LondonNew York: Routledge. Kistler, M. (2012). “Powerful Properties and the Causal Basis of Dispositions”. In: Bird, A., Ellis, B., Sankey, H. (eds.), Properties, Powers and Structures. Issues in the Metaphysics of Realism. London-New York: Routledge: 119–138. Lewis, D. K. (1973). Counterfactuals. Oxford: Blackwell. Lowe, E. J. (2010). “On the Individuation of Powers”. In: Marmodoro, A. (ed.), The Metaphysics of Powers. Their Grounding and their Manifestations. LondonNew York: Routledge: 8–26. Lowe, E. J. (2011). “How Not to Think of Powers: A Deconstruction of the ‘Dispositions and Conditionals’ Debate”. The Monist, 94: 19–33.

The Composition of Naïve Powers  205 Marmodoro, A. (2017a). “Aristotelian Powers at Work: Reciprocity without Symmetry in Causation”. In: Jacobs, J. D. (ed.), Causal Powers. Oxford: Oxford University Press: 57–76. Marmodoro, A. (2017b). “Power Mereology: Structural Powers versus Substantial Powers”. In: Paolini Paoletti, M., Orilia, F. (eds.), Philosophical and Scientific Perspectives on Downward Causation. London-New York: Routledge: 110–127. Martin, C. B. (2008). The Mind in Nature. Oxford: Oxford University Press. Martin, C. B., Heil, J. (1998). “Rules and Powers”. Noûs – Philosophical Perspectives, 12: 283–312. Martin, C. B., Heil, J. (1999). “The Ontological Turn”. Midwest Studies in Philosophy, 23: 34–60. Massin, O. (2009). “The Metaphysics of Forces”. Dialectica, 63: 555–589. Massin, O. (2017). “The Composition of Forces”. The British Journal for the Philosophy of Science, 68: 805–846. McKitrick, J. (2018). Dispositional Pluralism. Oxford: Oxford University Press. Molnar, G. (2003). Powers. A Study in Metaphysics. Oxford: Oxford University Press. Moore, D. (2012). “A Non-reductive Model of Component Forces and Resultant Force”. International Studies in the Philosophy of Science, 26: 359–380. Nolan, D. (2015). “Noncausal dispositions”. Noûs, 49: 425–439. Paolini Paoletti, M. (2016). “Non-Symmetrical Relations, O-Roles, and Modes”. Acta Analytica, 31: 373–395. Paolini Paoletti, M. (2017) The Quest for Emergence. Munich: Philosophia. Paolini Paoletti, M. (2018) “Substance Causation”. Philosophia. Published in Online First on June 11, 2018. Paolini Paoletti, M. (2020) “Emergent Powers”. Topoi, 39: 1031–1044. Paolini Paoletti, M (2021) “Masks, Interferers, Finks, and Mimickers: A Novel Approach”. Theoria, 87: 813–836. Schaffer, J. (2015). “What Not to Multiply Without Necessity”. Australasian Journal of Philosophy, 93: 644–664. Spurrett, D. (2001). “Cartwright on Laws and Composition”. International Studies in the Philosophy of Science, 15: 253–268. Vetter, B. (2014). “Dispositions without Conditionals”. Mind, 123: 129–156. Vetter, B. (2015). Potentiality. Oxford: Oxford University Press. Williams, N. E. (2019). The Powers Metaphysic. Oxford: Oxford University Press. Wilson, A. (2009a). “Disposition-manifestations and Reference-frames”. Dialectica, 63: 591–601. Wilson, J. (2007). “Newtonian Forces”. The British Journal for the Philosophy of Science, 58: 173–205. Wilson, J. (2009b). “The Causal Argument against Component Forces”. Dialectica, 63: 525–554.

Part III

Power Mereology in Science

11 Quantum Dispositions and the Simple Theory of Property Composition Matteo Morganti

Introduction How do the properties of simple(r) things get together so as to compose (or determine, or give rise to, or whatever – mereology is not intended to play a particular role here) the properties of (more) complex things?1 According to what one may call the ‘Simple Theory’ of property composition (henceforth, ST), the answer is straightforward: the more complex properties are ‘nothing over and above’ the properties of their constituents. For instance, for a stone to have a weight of 600 kilograms nothing more is required than two stone-­parts of 300 kilograms each (the two pieces of stone, obviously enough, must be connected to each other).2 ST may be motivated in various ways. Most notably, one may find it compelling because they endorse a view, famously inspired by David Lewis, whereby – as per ‘Humean Supervenience’ – the world is a vast mosaic of local physical qualities, instantiated at specific points or regions, and related by spatial distance relations. Additionally, one may have in mind a particular story not only about what exists but also about what could exist. In particular, one could motivate ST on the basis of a ‘combinatorial’ view of modality, whereby the possible is determined simply by considering combinations of actual elements, without any restrictions on the admissible permutations other than consistency.3 A well-­ known defender of combinatorialism about modality is, for instance, David Armstrong.4 According to Armstrong, the basic ontology of reality is one of properties – as universals – instantiated by particulars within states of affairs, and possible worlds are just rearrangements of the particulars and properties that exist in the actual world. As for properties, more specifically, according to Armstrong, they are universals, and all complex universals are either conjunctive or structural. In the former case, the nature of complex properties is straightforward: it is just the logical conjunction of two simpler properties. In the latter case, a property of a mereological composite constituted by certain parts x, y, z, … can be analysed in terms of universals

DOI: 10.4324/9781003298830-15

210  Matteo Morganti instantiated by x, y, z, … individually, plus a relation acting as a structuring element – for instance, the binding relation that makes it the case that two instances of being hydrogen and one of being oxygen give rise to an instance of being water. Regardless of the details, in both cases the intuition behind ST seems to be satisfied: the fact that a ball is round and green is nothing over and above the fact that it is green together with the fact that it is round, and if an atom of oxygen and two of hydrogen exist and are connected by a certain relation described by physics and chemistry, then ipso facto a molecule of water exists. More precisely, the fact that an oxygen atom and two hydrogen atoms share electrons in chemical bonds, the oxygen atoms, having one electron in common with each one of the hydrogen atoms, is necessary and sufficient for the existence of a molecule of water.5 There has been considerable discussion concerning the exact details of Armstrong’s combinatorialism, and the precise formulation of the view more generally.6 The same holds for the other elements of the Hume– Lewis–Armstrong perspective that we just mentioned. We will say more about Humean Supervenience later on. However, what matters for the time being is that there seems to be little doubt that ST is internally consistent and can consequently be regarded as at least a possible way things are. Indeed, prima facie ST appears to be a plausible view of the way in which complex properties emerge in the world we live in. But consider now the following argument, where ‘@’ denotes the actual world: i ) ST is true in @; ii) At least some properties exemplified in @ are dispositions; c) Therefore, dispositions obey ST (and this claim is not simply vacuously true). Premise (i) concedes that ST may not be necessarily true, but is a significant philosophical thesis nonetheless, to the extent that it is a correct account of what goes on in the universe we happen to inhabit. Premise (ii) is, of course, true for friends of dispositions, while it would be rejected by opponents. If it is granted, a well-­defined thesis about the ‘mereology of dispositions’ – or, at any rate, about the way in which dispositions ‘behave’ so that things come to possess their more complex dispositional properties – follows. The thesis, expressed in (c), is interesting, among other things, because it is in principle open to empirical testing broadly understood7 – certainly a welcome result at least from the perspective of a naturalistic philosophical methodology. In what follows, I perform such a test. I first (in the next section) present reasons for regarding the properties described by the best theory of the

Quantum Dispositions and the ST of Property Composition  211 microphysical domain that we currently have available (i.e., quantum mechanics – henceforth, QM) as essentially dispositional. Then (in the third section), I argue that there are composite physical systems described by QM – so-­called entangled systems – that violate ST – that is, whose properties are, in fact, more than just the properties of the parts taken together. In particular, I argue against an interpretation of the properties of entangled systems in terms of Armstrong-­style structural sums of more basic parts and relations. Finally (in the fourth section), I briefly suggest a way of making sense of the peculiar features of quantum entanglement based on a general metaphysical theory, alternative to those that characterise the Hume–Lewis–Armstrong line of thought underpinning ST. More specifically, such theory diverges significantly from what is often called ‘metaphysical foundationalism’, which is the family of philosophical theories that share the assumption that the metaphysical structure of reality has a hierarchical, vertical structure bottoming out in a fundamental basis. The divergence is determined by the fact that within this alternative theory symmetric relations of ontological dependence are postulated that give rise to metaphysical structures characterised by a ‘horizontal’, same-­level arrangement which lacks, or at least may lack, a fundamental basis. This non-­standard metaphysical view has more or less recently come to be known as ‘metaphysical coherentism’.8 Here, I concisely describe the basic features of metaphysical coherentism and suggest that it naturally captures a (if not the) fundamental fact about the complex properties of quantum entangled systems, namely, that precise modal connections between distinct existents emerge upon physical interaction, so that not only the simpler properties of the parts determine the more complex properties of the whole but that the former are also in turn affected by the latter.9 Quantum Properties QM10 is a theory that has several puzzling features. It appears especially mysterious when it is compared with our earlier ways of describing the world, based on classical mechanics or just with common sense. One of its distinctive traits no doubt concerns the properties that quantum theory attributes to physical systems. While normally we expect questions concerning whether a system possesses a certain property to receive yes-­or-­no answers, typically QM provides probabilistic answers.11 So, for instance, in the classical domain a lump of matter occupies a specific region of space at a given instant, and this implies that it does not occupy any other region at that instant. In the quantum case, instead, the theory can (and, in fact, more often than not, does) tell us that the bit of matter is ‘here’ with a certain non-­zero probability but also that it is ‘there’ with a certain non-­ zero probability. These quantum probabilities are objective; that is, they

212  Matteo Morganti don’t just express our limited knowledge of physical facts: it is actually the case that there is, or may be, something located here but also there. In these sorts of scenarios, we talk about quantum ‘superpositions’. Superposition is, then, common in the quantum domain: indeed, only in limiting cases can we attribute determinate properties to physical systems. Now, the relevant probabilities, computed on the basis of the system’s ‘wave function’ and the so-­called Born rule,12 are often interpreted as dispositions. This is because the probabilistic assignments of the theory are naturally interpreted as indicating how things could be like, that is, that certain physical features of things are indeterminate and only acquire determinate values given certain conditions. More specifically, according to standard QM, measurement events make the wave function ‘collapse’ so that a system that has a certain non-­zero probability of being in state S1 but also a certain non-­zero probability of being in state S2 is at that point found to be either determinately in state S1 or determinately in state S2.13 It is therefore natural to take quantum probabilities to mirror dispositional features of quantum systems, measurement events (or, more generally, events that determine collapses of the wave function) to constitute the conditions for the manifestation of those dispositions and measurement outcomes to be their manifestations.14 Indeed, the literature contains a long series of proposals in this sense: Margenau, Heisenberg, Popper and other, more recent, authors all urged, although with significant differences, an interpretation of quantum properties as dispositions. According to Margenau, for instance, items belonging to a specific subset of quantum properties must be understood as tendencies or ‘latencies’. In the 1950s, he wrote: The contrast, or at any rate the difference, is now between … possessed and latent observables. Possessed are those, like mass and charge of an electron, whose values are ‘intrinsic’, do not vary except in a continuous manner, as for examples the mass does with changing velocity. The others are quantized, have eigenvalues, are subject to the uncertainty principle, manifest themselves as clearly present only upon measurement. I believe that they are ‘not always there’, that they take on values when an act of measurement, a perception, forces them out of indiscriminacy or latency. (1954: 10) A bit later, Heisenberg (1958) endorsed a conception of (some) quantum properties in terms of Aristotelian potentialities, while Popper (1959, 1967) talked about quantum-­mechanical ‘propensities’, identifying them with ‘virtual frequencies’, that is, with what will tend to happen upon repetition.

Quantum Dispositions and the ST of Property Composition  213 In later times, Maxwell (1988) identified quantum ‘propensitons’ with spread-­out three-­dimensional entities that become point-­like under certain conditions.15 Most recently, Suarez (2007) put forward an account based on ‘selective propensities’, according to which the relevant properties can be expressed as weighted sums of projectors corresponding to the eigenstates available to a system with respect to a certain observable. What this means is, roughly, that all the possible determinate values for any given property, as these can be ‘extracted’ from the system’s wave function, uniquely identify the system’s ‘propensity-­state’: a so-­called mixed state which is the origin of the determinate properties that we experience when we perform measurements. Upon measurement, Suarez claims, the physical process selects a particular value for a particular property, so making one or more dispositions manifest, with a corresponding change in the state of the system.16 There would, of course, be a lot more to say about the formulation and viability of an interpretation of QM (with wave-­function collapse) along the lines just sketched.17 In what follows, however, I will simply assume that quantum properties are indeed dispositions.18 The relevant question is whether these dispositional properties combine in agreement with ST. Let us see. Entanglement Another distinctive feature of QM is entanglement. The term entanglement denotes a class of composite systems19 which exhibit certain surprising features. In particular, entangled quantum systems are characterised by peculiar internal correlations. Consider, for instance, fermions – roughly, the particles that constitute matter. Like all quantum systems, fermions possess a typical property, called ‘spin’, which is roughly akin to a rotation relative to a spatial dimension.20 The absolute magnitude of spin is fixed and essentially characterises particles of a certain type: for fermions, only half-­odd-­ integer values of absolute spin are allowed (e.g., 1/2, 3/2, etc.). For any fermion p, and its spin along an arbitrary spatial axis; however, p can have either one of two specific values corresponding to such absolute magnitude. That is, one gets that

( )

( )

↑ Probp= ↓ 0.5, Probp= where the two alternatives, that is, the negative and the positive spin value in the relevant direction, are conventionally denoted as spin ‘up’ (‘↑’) and spin ‘down’ (‘↓’), respectively. What this entails is that p has the same probability of being found in each one of two available states upon

214  Matteo Morganti measurement.21 Now, in light of this, it is natural to think that for two fermions 1 and 2 one should get

(

)

(

)

(

)

(

)

, ↑2 Prob12 ↑1= , ↓2 Prob12 ↓1= , ↓2 Prob12 ↑1= , ↑2 0.25. Prob12 ↓1= Imagine for instance two fair coins. Since they both have the same probability of landing heads or tails, it is straightforward to conclude that there are four equally probable possible distributions when we toss them: two heads, two tails, the first coin heads and the second tails, and the first coin tails and the second heads. Indeed, this way for probability values to combine is somewhat intuitive, as it corresponds to the way in which things appear to behave at the level of common sense and ordinary experience. In terms of probabilities, this is often referred to as ‘factorisability’. If the probabilities of joint measurement outcomes factorise, more specifically, one gets that, for any two outcomes x, y of measurements performed, respectively, on distinct systems 1 and 2: Prob(x1, y 2 | S, m1, m2 ) = Prob(x1 | S, m1)Prob(y 2 | S, m2 ), where S denotes the pair’s state before measurement and m1 and m2 denote the states of the pieces of apparatus that measure system 1 and system 2, respectively. Notice how natural factorisability looks, in particular, from the point of view of ST, grounded as the latter is in the assumption that facts about the (properties/probabilities of the) whole are nothing over and above facts about the (properties/probabilities of the) parts. However, and here is the key fact, when we make two fermions of the same type interact so that they form a composite system,22 we observe that the following joint probabilities result instead:

( (

) )

( (

) )

, ↑2 Prob12 ↑1= , ↓2 0.5 Prob12 ↓1= , ↓2 Prob12 ↑1= , ↑2 0 Prob12 ↓1= This means that spin-­outcomes become ‘anti-­correlated’: whatever the outcome of a spin measurement on one fermion, the outcome for the measurement of the same spin component for the other fermion will be the opposite.23 Consequently, one gets that

( (

) )

( ) ( )

( ) ( )

Prob12 ↑1, ↓2 ≠ Prob1 ↑ Prob2 ↓ Prob12 ↓1, ↑2 ≠ Prob1 ↓ Prob2 ↑ .

Quantum Dispositions and the ST of Property Composition  215 That is, the relevant probabilities do not factorise.24 This is indeed the distinctive feature of entanglement and probably of QM more generally.25 The foregoing clearly suggests that the properties of entangled quantum systems are more than just the properties of their subsystems taken together: for, if the former were nothing over and above the latter, then the corresponding probabilities should factorise. If this is so, it follows that, at least in some cases, quantum dispositions violate ST, that is, that at least some actual properties do not obey the ST of property composition, contradicting the conclusion of our initial argument (conclusions (c) in the earlier argument). One first rejoinder is, however, readily available: it consists in the claim that ST is in fact not falsified by entangled quantum particles, as entanglement can be accounted for in terms of structural properties in Armstrong’s sense discussed earlier. In more detail, one can argue that even in the case of entangled objects the (dispositional) properties of the composite system are nothing over and above those of the parts, as the property-­structure of the whole directly mirrors its mereological structure: in particular, considering our two fermions from earlier, the entangled whole is nothing over and above the monadic properties of each fermion plus a peculiar relation of entanglement, which should be included in the list of relevant constituents. In relation to this, recall that (i) relations are explicitly counted among the components of structural properties, for example, by Armstrong (as in our example of the two hydrogen atoms composing water together with one oxygen atom and two relations corresponding to the relevant chemical bonds) and (ii) this is normally taken to be compatible with a combinatorial view of modality and, more generally, with a broadly Humean conception of reality. Indeed, that QM requires one to add one more relation to the ontological inventory does not seem to constitute a sufficient reason for giving up on the Humean programme: to the contrary, it was openly accepted as a theoretical possibility by Lewis himself.26 This view, however, faces important difficulties. Darby (2012) argues that adding entanglement relations to the supervenience basis does not violate the letter of Humean Supervenience, but it does violate its spirit, as it replaces a mosaic of local matters of fact with global matters of fact involving arbitrary numbers of particles and relations of varying n-­adicity. To this criticism, in what follows I will add another, which concerns specifically the nature of properties and the content of ST as a theory of property composition. To give an initial hint, the point to be made is the following: while in canonical examples of structural properties the relations between the parts ‘only’ play the role of the glue that puts the pieces together, in the quantum case something more happens, and novel constraints emerge on the original properties, that is, the simple(r) properties of the separate parts.

216  Matteo Morganti Consider again our water example: two hydrogen atoms and one oxygen atom interact and, via the addition of relations of spatial contiguity and chemical bonding, give rise to the structural property corresponding to the predicates ‘being water’ and ‘being H2O’. What can be said about the properties exemplified in this scenario? A crucial thing to point out is that, while, of course, the whole possesses novel properties, not possessed by the parts taken separately (for instance, a lone hydrogen atom does not have a molecular mass of 18,0153 Daltons, nor does it have the property of having two parts at a 104,45° angle from each other27), the basic properties of the parts are left essentially unchanged after the ‘merge’. The qualification ‘essentially’ is added here to leave out of the claim those contingent properties that are straightforwardly explained by the very fact that a molecule of water has been constituted. For example, each individual hydrogen atom has the same atomic number and the same constituents (one proton and one electron) after the bonding than it had before. It also has the same mass, modulo a slight decrease due to the conversion into the energy responsible for the bonding with the oxygen atom. Obviously enough, it no longer has the property of being able to share one electron, but this is entirely explained by the fact that the atom has entered an H2O structure, and the electron that was previously shareable is – contingently – no longer available. In the quantum case, things are quite different: in addition to something analogous to what happens in the water example, the entanglement structure crucially adds novel modal constraints on the monadic properties of the parts. In particular, as we have seen, when they become entangled previously separate particles acquire novel, correlated dispositions, and the corresponding unconditional probabilities turn into different, conditional probabilities. After the interaction that leads to the constitution of an entangled two-­fermion system, for instance, each fermion has the same disposition (being either spin up or spin down along axis …), but different stimulus conditions (a measurement performed on a distinct particle is now sufficient for the possession of a determinate spin value) and different possible manifestations (spin-­up and spin-­down still being the two equally probable outcomes but now conditional on the other particle’s turning out spin-­down and spin-­up, respectively). These correlations are certainly not mysterious in the sense that there is no science-­based explanation for them – entanglement is a well-­known physical phenomenon with a solid corresponding theoretical apparatus. They are surprising, however, in the sense that the fact that entanglement ‘feeds back’ on the properties of the parts, as it were, is a primitive, non-­further-­analysable fact that has no correlate in canonical cases of structural properties. While one may just insist that this is to be regarded as a peculiar characteristic exhibited by some complex wholes and not others, this does not seem very satisfactory,

Quantum Dispositions and the ST of Property Composition  217 especially once one recalls that, as mentioned at the beginning of the chapter, one of the basic motivations behind ST is a view of reality according to which (as per Hume’s Dictum) no primitive modal connection holds among the basic building blocks of reality. What this entails is that not only must the properties of more complex entities be fully analysable in terms of those of their simpler constituents, but it must also be the case that the latter do not affect the former in terms of what is possible/impossible. ‘Nothing over and above’ talk, that is, must be taken quite literally: if a mereologically complex entity has property P, then its simpler constituents have properties qq and, additionally, stand in relation R, and if certain entities have properties qq and stand in relation R, then there is a corresponding composite entity with property P. Representing this more concisely with a bi-­conditional: according to ST, for any complex property P, there is a plurality of simpler properties qq and an external relation R such that it is the case that P ↔ qq + R. As we have just seen, however, in the case of quantum entanglement new modal constraints arise instead on the state-­dependent properties of the simpler constituents, mirrored by the fact that previously independent, unconditional probabilities become correlated, conditional probabilities: not only qq + R → P at time t1 but also P→(qq→qq*) immediately after t1 – where of course qq* differs from qq in that a different, smaller set of possible values is available for the relevant properties, and the corresponding probabilities do not factorise. To repeat, it is certainly possible to say that all this due to relation R having a peculiar ‘modal power’ in the quantum case, but this seems to go in the exact opposite direction with respect to the theoretical framework underpinning ST. How to Make Sense of the Properties of Entangled Quantum Systems? Faced with the evidence just described, philosophers have reacted in various ways. Besides the option of ‘updating’ Humean Supervenience by adding entanglement relations to distance relations in the supervenience basis, which we have already discussed, the supporters of the Hume–Lewis– Armstrong approach (hence of ST) have explored two other possibilities. The first consists in re-­shaping it so that it occupies a four-­dimensional space endowed with sufficient structure to explain everything in terms of local properties;28 the second in transferring the Humean mosaic to a multidimensional configuration-­space.29 We don’t have the space, nor the need, here to embark on a detailed discussion of these attempts, as it is not our aim to provide a conclusive, knock-­down argument against ST.30 Let us briefly summarise, however, those that can be regarded as their basic shortcomings. On one hand, as we have seen in the previous section, adding entanglement relations to the

218  Matteo Morganti catalogue of parts available for building complex objects and properties won’t do unless one attaches to them a primitive power to set modal constraints on the relata, which goes against the basic assumptions underlying ST and the Hume–Lewis–Armstrong approach more generally. Something similar holds for the attempts to enrich the mosaic so that everything supervenes on local matters of fact: indeed, according to these proposals, our simplest and most informative description of reality includes not only a collection of local properties in space-­time but also some fundamental constraints that act at the global level. In this case, too, the mosaic is not really a simple mosaic anymore: the (properties of the) whole depend(s) on the (properties of the) parts plus certain basic facts about the universe as a whole, encoded in the laws of nature.31 On the other hand, as for the second option, the well-­known complaint is that assuming that reality is indeed analysable in terms of simple, local matters of fact but only in a 3N-­dimensional space may plausibly be regarded as too high a cost for preserving something which is only remotely akin to the initial intuition behind Humean Supervenience. Be this as it may, at any rate, here we will not discuss the Hume–Lewis– Armstrong approach to ontology, modality, and properties any further. Rather, in the remaining part of the chapter, we look at one particular way of making philosophical sense of the properties of quantum entangled systems, which constitutes a viable candidate in the context of the metaphysics of entanglement, and possibly beyond that: so-­called metaphysical coherentism. The basic idea underpinning metaphysical coherentism is the following. Most metaphysicians nowadays take the fundamental structure of reality to be determined by non-­causal relations whereby something is the case in virtue of something else being the case. And typically, in agreement with common-­sense intuition, we take such metaphysical structure to be layered and have a fundamental basis. This means that the key metaphysical relations give rise to what mathematicians refer to as well-­founded strict partial orders. Using the popular grounding vocabulary to refer to these relations,32 this can be summarised as follows: i) No element of reality grounds itself (irreflexivity); ii) If a grounds b then b does not ground a (asymmetry); iii) If a grounds b and b grounds c then a grounds c (transitivity); iv) Grounding chains have an ultimate, ungrounded basis (wellfoundedness).33 Metaphysical coherentism basically amounts to the abandonment of (iv) and (ii): there is no ultimate basis, and two entities may ground each other, i.e., be mutually dependent. Since (i) and (iii) together entail (ii), by modus

Quantum Dispositions and the ST of Property Composition  219 tollens, at least one of them must be given up as well. Transitivity is very intuitive, so it is natural to sacrifice irreflexivity and accept that some entities may ground/depend on themselves. The obvious worry immediately arises that one only gets trivial explanations of the form ‘a grounds a’. To neutralize it, coherentists can plausibly claim that only partial ground can be reflexive and non-­asymmetric. Assumptions (i)–(ii) can, therefore, be accepted in a qualified form: they apply to full ground but not, or at least not necessarily, to partial ground. This qualification is directly connected to the fact that metaphysical coherentism must not – or, at least, need not – be understood as the claim that ‘being’ is transmitted in loops so that a fully grounds b, b fully grounds c and c fully grounds a – hence a fully grounds itself. Rather, in analogy with sophisticated forms of coherentism about belief and justification in epistemology, it can – and should – be intended as the claim that certain groups of entities are (or may be) such that each of them requires the existence of all the others to be what it is, from which it follows that the plurality of all the entities in the domain is the full ground of each entity and each entity partially grounds itself and each one of the others.34 Notice, in this connection, that it is sufficient for the coherentist to talk about individual entities and pluralities of entities, and no commitment is required on their part to the whole composed by all the entities in question as an ontological addition to the latter. In the case at hand, for instance, this means that entangled quantum systems need not be regarded as distinct from, and additional to, the particles that give rise to them.35 Let us now replace generic talk of grounding with something more useful – for us, at least. What coherentism posits, as explained, is some sort of mutual, symmetric ontological dependence. Talk of ontological dependence itself requires further specification, however, as there are different possible respects of dependence, and consequently various, more fine-­ grained stories that the coherentist may tell about distinct scenarios. In particular, two or more entities may depend on each other with respect to their existence and/or their properties and/or their essence and/or their identity.36 When it comes to quantum entanglement and the relationship between simple(r) and complex properties, clearly it is ontological dependence involving non-­essential properties, that is, the ‘qualitative profile’ of things, but not their essence, that matters. Our explanandum, in particular, is the fact that, while ST claims that more complex properties are always nothing over and above corresponding sets of simpler properties (that is, for any complex property P and plurality of corresponding simpler properties qq, it is the case that P↔qq), there seem to be actual cases in which this is not true. Instead, the same simple properties that led to the constitution of the complex property in question are affected by the process in a primitive, non-­further-­analysable way. More specifically, the possible values of certain state-­dependent properties are

220  Matteo Morganti modified in ways that are directly mirrored by the relevant probability assignments, quantum probabilities turning out to be non-­factorisable (not only Simpleqq→ComplexP at time t1 but also ComplexP→(Simpleqq→ Simpleqq*) immediately thereafter). What the coherentist says (or, at any rate, should say) about this is the following: the supporter of ST invites us to think of a supervenience basis, including simpler monadic properties of quantum particles as well as irreducible relations of entanglement, but we ought instead to regard entanglement as a particular kind of physical process whereby a change in a certain set of monadic quantum properties is determined and new modal constraints arise. In the notation we just employed, considering for simplicity only two entities 1 and 2 and their property-­sets q1 and q2: Interaction12→(Simpleq1q2 → Simpleq1q2*). Any two exactly similar fermions 1 and 2, that is, are such that upon the right kind of interaction:37

• The existence and properties of 1 and 2 determine the existence and (novel) properties of the plurality 12 (which we interpret as a composite system in an entangled state without – importantly – the need to commit to the existence of the whole as an entity additional to 1 and 2); • 12, in turn, constrains the (possible) state-­dependent properties of 1, 2.

The key idea is that, since physical interaction determines novel correlations between properties, everything can be accounted for in terms of symmetric dependence with respect to qualitative profile arising among the interacting entities, none of these entities being in any sense prior or more fundamental than the other. Assuming, as we did here, that the qualitative profile of quantum systems corresponds to dispositions, what we get is what we were expecting: the dispositions of the separate fermions and the physical relations holding between them are not all it takes to determine the disposition of the whole – the latter is not an ontological free lunch with respect to the former. To the contrary, given certain conditions, the dispositions of the whole follow from the dispositions of the parts, but, at the same time, the very fact that the parts have given rise to such a whole sets certain modal constraints on the properties of the parts themselves, constraints which were not present in the original, separate dispositions. This clearly contradicts the intuition underpinning the Humean view of reality and its various ramifications, including ST. At this point, one may legitimately ask for more details about the symmetric dependence in question and the way in which it is determined by physical processes of interaction/composition. In particular, one could ask whether facts about entangled particles are determined by the laws of nature. In the case of fermions, one may argue that Pauli’s Exclusion

Quantum Dispositions and the ST of Property Composition  221 Principle, which roughly states that no two fermions can be in the same state, and subsequently requires the total spin of the system of two entangled fermions to be 0, together with the conservation of angular momentum, entails the observed anti-­correlation among the separate spin values of entangled fermionic particles. If this were the case, the laws of nature would turn out to be fundamental and not reducible to properties. On a different construal, instead, one may suggest that laws and principles of physics are in fact derivative of more fundamental facts about properties. In the case of quantum dispositions, this would no doubt be the viewpoint endorsed for instance by dispositional essentialists. For the aims of this chapter, however, it is not necessary to take a stance with respect to this particular issue. On the one hand, the objection to ST that we have considered does not rely on a particular understanding of the relationship between laws and properties.38 On the other hand, as for the positive proposal that was formulated in this section, metaphysical coherentism presupposes neither the ontological priority of properties over laws of nature, nor the converse. Whatever precise details one adds to the preceding analysis, thus, it seems fair to say ST fails as a general story about the properties of things in the actual physical universe, while metaphysical coherentism presents itself as an effective explanation. Concluding Remarks In this chapter, I have defined a ‘Simple Theory’ of property composition, according to which there is a precise sense in which the properties of composite wholes are reducible to, they are nothing over and above, those of their parts. Then I looked at the peculiar features of quantum entangled systems, pointing out, in particular, that entanglement seems to set modal constraints on the (dispositional) properties of the component sub-­systems of composite entangled systems. While, strictly speaking, there are ways to salvage ST, Humean Supervenience and the Hume-­ Lewis-­ Armstrong approach to metaphysics more generally in spite of this seemingly recalcitrant empirical evidence, we have considered reasons for finding these attempts unsatisfactory. In particular, one way of defending something like a simple mereological understanding of complex quantum dispositions would be to posit physical relations of entanglement as literal constituents of the relevant properties and encode the relevant modal connections into them. Another option would be to ‘expand the Humean mosaic’ by either adding global constraints on the distribution of its pieces, or making it 3N-­dimensional. However, I argued that both routes would clearly go against the spirit of the philosophical perspective under scrutiny.39 As an alternative, we have seen that an understanding of quantum properties is

222  Matteo Morganti available according to which they violate ST and behave in ways that are best captured by so-­called metaphysical coherentism. The exact details of the view, as well as more discussion of the pros and cons of the various options vis-­à-­vis quantum properties and the laws of nature that govern physical systems, are left for future discussions. Notes 1 This question, note, is independent of the existence of a fundamental level. A relative sense of fundamentality is sufficient for it to be meaningful and, consequently, to get the discussion going. 2 Of course, not all properties are additive like weight, but the basic intuition underlying ST is the same for non-­additive properties: complex properties of  things are a direct by-­product of the simple(r) properties of things taken together. 3 This is related to another broadly Humean assumption, known as ‘Hume’s Dictum’. According to Hume’s Dictum, there are no necessary connections between distinct entities. Indeed, in the context of Lewis’ philosophy, Humean Supervenience and Hume’s Dictum may be said to cooperate towards a combinatorial view of possibility (see Wilson 2015). 4 See Armstrong (1989). 5 Armstrong notoriously speaks of complex properties, and the corresponding states of affairs, in terms of ‘ontological free lunches’ with respect to basic properties, particulars and states of affairs. 6 See, for instance, Sider (2005). 7 That is, not (necessarily) in terms of experimental procedures, but rather of assessing philosophical hypotheses against the background of our best scientific theories. 8 For a more detailed presentation and discussion, see Morganti (2018) and Calosi and Morganti (2020), where coherentism is specifically applied to the quantum domain. 9 As it will become apparent in what follows, the present discussion is intimately connected with the well-­known dispute about Humean Supervenience. However, it specifically focuses on a lesser debated aspect, involving the nature of properties, and in particular dispositions. 10 In this paper, we will be only concerned with non-­relativistic QM. 11 Also, probabilities appear in different forms depending on the specific interpretation of the theory – or specific theory, alternative to the canonical textbook formulation – one endorses. Here, however, we will presuppose ‘standard’ QM, essentially based on the idea that physical systems evolve deterministically unless they undergo certain non-­deterministic physical processes (generically labelled ‘measurements’) that make them acquire precise, determinate properties. 12 Even though it is sometimes interpreted realistically, hence regarded as an actual physical entity, the wave function is primarily a mathematical description of the state of a quantum system. Indeed, it can be regarded as a complex-­ valued probability amplitude encoding all the relevant information about the properties of the system in question. The Born Rule is the postulate of QM that says that the probability of finding a particular value for a given property is equal to the square of the corresponding probability amplitude.

Quantum Dispositions and the ST of Property Composition  223 13 To repeat, this does not mean that the system was in a precise state before measurement. Rather, it was in a superposition of two states, and measurement somehow caused it to ‘pick’ one of the two. Of course, it is a crucial question why and how certain events qualify as measurements, and superposition doesn’t simply persist, in fact ‘spreading’ to other systems. This is the infamous ‘measurement problem’ besetting QM which, luckily, we don’t have to deal with here. Indeed, the discussion to follow only assumes the reality of the collapse of the wave function and the objective nature of quantum probabilities. Arguably, this means that the claims to follow also apply to Ghirardi-­Rimini-­ Weber-­type spontaneous collapse versions of QM, according to which the emergence of determinate values is not determined by anything and instead occurs randomly (in this context, it is worth mentioning, there are obvious reasons for preferring an analysis of dispositions whereby activating conditions are not necessary – on this, see Molnar (2003) and Vetter (2014). 14 In introducing the topic of dispositions in QM the notion of (ontic) determinacy/indeterminacy was used. To be precise, dispositional talk and talk of indeterminacy are by no means interchangeable, as properties of things could be indeterminate without being dispositional, and unmanifested dispositions may fail to correspond to anything, not even indeterminate. For a detailed presentation and discussion of indeterminacy in QM, see Calosi and Mariani (2021). 15 Obviously attempting to translate talk of the collapse of the wavefunction into something more familiar and intuitive. 16 Notice, however, that the part of the system’s state that corresponds to its propensities does not ‘jump’ due to collapse: in fact, it only follows the linear evolution dictated by the Schrödinger equation. 17 For more discussion, see Dorato (2006) and (2011). 18 A number of connected questions will have to be simply ignored here: for instance, whether or not quantum dispositions are ‘bare’, i.e., they lack a categorical, non-­dispositional, basis. 19 Here, and below, I will talk about wholes, parts and composition but, once again, no particular assumption needs to be made with respect to mereology including with respect to the actual existence of entangled wholes as additional entities with respect to their parts (more on this later). 20 It’s not exactly a rotation, though. For one thing, particles have spin components along all three spatial dimensions at the same time. 21 The actual value of spin in a particular direction is consequently to be regarded as an accidental, ‘state-­dependent’ property, in contrast with the above absolute value, to be regarded as an essential, ‘state-­independent’ property. Recall Margenau’s distinction between possessed and latent values above. 22 We said above that entanglement denotes a class of physical systems, but entanglement also has to do with physical interactions and processes, and the way in which systems of this kind are produced. 23 A bit like the results of a series of coin tosses in Rome being exactly the mirror image of a similar series of coin tosses in New York. Assuming that the tosses happen at the same instant, surely this is weird! Indeed, quantum correlations hold no matter the distance: this is the basis for the well-­known Einstein-­ Podolosky-­Rosen-­Bell results, which led to the conclusion that QM is in conflict with the theory of special relativity, that would instead require the correlation to be causally mediated, hence to take at least the time needed for light to travel from one particle to the other. Our focus here, though, is not on

224  Matteo Morganti quantum ‘non-­locality’ and the QM-­relativity relationship, but rather on the ontological nature of entanglement correlations. As for the sort of ‘non-­ separability’ that is often associated with EPR-­Bell-­type scenarios, instead, a suggestion will be formulated later. 24 The state of a two-­fermion entangled system like the one in our example is, in particular, labelled ‘singlet state’. 25 In the case of bosons, i.e., roughly, the particles that mediate the action of forces, whose absolute spin only has integer values, something similar happens, with a few differences that we don’t need to look at in detail here. Something worth mentioning, however, is that the total state of two entangled bosons is symmetric rather than anti-­symmetric. This entails that, unlike fermions, two bosons of the same type in the same composite system can also be in the same state. That is, bosons do not obey Pauli’s Exclusion Principle. 26 Lewis claimed that his proposal could “doubtless be adapted to whatever better supervenience thesis may emerge from better physics” (1994: 474). 27 I don’t mention here the properties typically associated to water (such as having a boiling temperature of 100 °C, being able to dissolve salt, quenching thirst etc.) for the obvious reason that they are not properties of single H2O molecules. 28 See Esfeld (2014) and Bhogal and Perry (2017). 29 See Loewer (2004). 30 For a more detailed discussion of Humean Supervenience and QM, see Calosi and Morganti (2016). 31 Bhogal and Perry, for example, claim that the mosaic of local entities and properties (the ‘M-­state’) must be kept distinct from those physical facts that do not belong to the mosaic but still supervene on it (the ‘L-­state’). Two electrons being in an entangled state is, according to them, a paradigm of what an L-­state consists of. It is easy to see that this two-­state Humeanism essentially consists in defining a theoretical ‘container’ for whatever doesn’t fit the original Lewisian picture, and that the peculiar nature of quantum properties is not effectively explained. As far as ST is concerned, the impression is confirmed that it can no longer be said that more complex properties are always nothing over and above the corresponding simpler properties. 32 Which I do only for ease of exposition and to connect to the literature. No particular assumption is made, nor needed, here with respect to the existence and precise features of grounding relations, and the meaning and actual usefulness of grounding talk. 33 Other properties are also often attributed to grounding, which we do not need to worry about in the present context: that grounding is hyperintensional (logically equivalent expressions may determine different truth values for grounding propositions), that the grounding necessitates the grounded, and that grounding is non-­monotonic (it may be the case that a and b ground c, yet a, b and d fail to ground c). What is important is that (i)–(iv) earlier express what is known as metaphysical foundationalism – the view that reality (or a part thereof) has a vertical, hierarchical structure with a fundamental ‘starting point’. Coherentism is one way of questioning foundationalism. 34 A related, useful notion here is that of quasi-­reflexivity. A quasi-­reflexive relation holds between something and itself only if it holds between that thing and something distinct from it. 35 This is useful for distinguishing coherentism from monistic forms of foundationalism, whereby (following here the mereological rendering of the view

Quantum Dispositions and the ST of Property Composition  225 suggested by Schaffer (2010)) the whole has parts but is ontologically prior to them. For an interpretation of quantum wholes along these lines, see Ismael and Schaffer (2020). 36 For a useful overview on ontological dependence, also in connection with grounding, see Tahko and Lowe (2020). 37 A further specification of which is an empirical matter that can be set aside here, as it is a job for scientists, not philosophers. 38 If anything, we granted for the sake of argument that everything (including laws) supervenes on local properties, which is instead an essential tenet of the Hume-­Lewis-­Armstrong perspective. 39 Moreover, going along this route would require us to regard entanglement relations as literal constituents of reality, which they are most plausibly not: indeed, entanglement is a particular way in which physical entities may exist, rather than an actual constituent of reality, and this is directly mirrored by the fact that physical theory describes entanglement as a feature of quantum states, i.e., a second-­order property of properties, not as a property of quantum systems. This point is, however, still open to debate: see, for instance, the arguments in Cinti, Corti and Sanchioni (2022).

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226  Matteo Morganti Ismael, J. and Schaffer, J. (2020): Quantum Holism: Nonseparability as Common Ground, in Synthese, 197, 4131–4160. Lewis, D. (1994): Humean Supervenience Debugged, in Mind, 103, 473–479. Loewer, B. (2004). Humean Supervenience, in Carroll, J. (Ed.): Readings on Laws of Nature, University of Pittsburgh Press, Pittsburgh, 176–206. Margenau, H. (1954): Advantages and Disadvantages of Various Interpretations of the Quantum Theory, in Physics Today, 7, 10, 6–13 Maxwell, N. (1988): Quantum Propensiton Theory: A Testable Resolution to the Wave/Particle Dilemma, in British Journal for the Philosophy of Science, 39, 1–50. Molnar, G. (2003): Powers: A Study in Metaphysics, Oxford University Press, Oxford. Morganti, M. (2018): The Structure of Physical Reality: Beyond Foundationalism, in Bliss, R. and Priest, G. (eds.): Reality and Its Structure, Oxford University Press, Oxford, 254–272. Popper, K.R. (1959): The Propensity Interpretation of Probability, in British Journal for the Philosophy of Science, 10, 25–43. Popper, K.R. (1967): Quantum Mechanics without ‘The Observer’, in Bunge, M. (ed.): Quantum Theory and Reality, Springer-­Verlag, New York, 7–44. Schaffer, J. (2010): Monism: The Priority of the Whole, in Philosophical Review, 119, 31–76. Sider, T., (2005): Another Look at Armstrong’s Combinatorialism, in Noûs, 39, 680–696. Suarez, M. (2007): Quantum Propensities, in Studies in History and Philosophy of Modern Physics, 38, 418–438. Tahko, T.E. and Lowe, E.J. (2020): Ontological Dependence, in Zalta, E.N. (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), https://plato. stanford.edu/archives/fall2020/entries/dependence-­ontological/ Vetter, B. (2014): Dispositions without Conditionals, in Mind, 123, 489, 129–156. Wilson, J. (2015): Hume’s Dictum and Metaphysical Modality. Lewis’s Combinatorialism, in Loewer, B. and Schaffer, J. (eds.): A Companion to David Lewis, John Wiley and Sons, Chichester, 138–158.

12 Dispositions, Mereology and Panpsychism The Case for Phenomenal Properties Simone Gozzano Introduction Powers (i.e. the causal tendencies of things) can be simple or complex. Very roughly, a power is (maximally) simple if it has just one kind of manifestation; if it has more than one kind of manifestation, it is complex. However, there are different ways in which a power can be complex. A rubber band, for instance, has both the power to keep its original length after being expanded and the power to break if exposed to cold conditions. These two are the two faces of the power or disposition1 of elasticity, and we may consider elasticity to be a complex power. Such complexity is not limited to physical properties, however. Some of our phenomenal states, those characterized by “what it is like” to have them (cf. Nagel 1974), are frequently complex ones. A bittersweet experience is one in which one seems to feel joy and sadness at the very same time, and these are two different emotional conditions. Another example is the taste of some wine: a white one may taste green apples and hay. In such a case, we have a complex taste, with two phenomenal properties belonging to the same sensory modality, perhaps by virtue of impinging on different receptors. (cf. Skrzypulec 2021) Complexity is tantamount to a phenomenal state being composed by, or resulting from, two or more phenomenally simple components. Is this the complexity proper of mereology? Inasmuch as there is nothing strictly spatial involved, it seems it is not for, as we will see, the concept of part, at the heart of mereology, requires spatiality. However, it seems that the components of these complex states or properties are “in” the state, are parts of it, such that the nature of the complex state would result modified without them. So, in this sense, they are mereological parts. Possibly, one issue here is that experiences are spatial in a very metaphorical sense, thus undermining them for being mereological entities. However, pain is an experience that has a spatial phenomenology. The cases of complex experiences lie at the crossroad of two topics: the metaphysics of powers, on the one side, and mereology – that is, the theory

DOI: 10.4324/9781003298830-16

228  Simone Gozzano of parts and wholes – on the other. My interest in this chapter is to investigate this crossroad as applied to mental properties, considered as powers. In particular, I scrutinize the possibility of taking the phenomenal property of feeling pain as a complex power or disposition. This possibility comes in handy in discussing panpsychism, the view that the ultimate elements of reality are phenomenal properties, which would ground physical properties as well. The link between panpsychism, dispositionalism and phenomenal properties has been clearly described by Hedda Mørch, that stresses that panpsychists think that all (or at least most) physical properties are dispositional. They then claim that dispositional properties require categorical grounds or realizers, and that phenomenal properties are the only categorical properties we know. This suggests that phenomenal properties could be the categorical realizers of all (or most) physical properties—as per what is known as Russellian panpsychism. (2020: 1) But are phenomenal properties suitable to fill this role? As Mørch herself notes, many have seen this as a reductio of dispositionalism, because it would make the theory that every property is captured in dispositional terms, hence relational, to be dependent on nonrelational categorical properties. But, again, is it possible to take phenomenal properties to be categorical and apt for the grounding role of physical properties, or should this role be played by some more fundamental property? To tackle this question, I consider the views relating phenomenal properties and physical properties, such as emergentism, panpsychism and protopanpsychism. I then consider how to get to the ultimates of reality by decomposing phenomenal properties into their ultimate elements. In doing so, I consider protopanpsychism as the only view that can be combined with mereology inasmuch as it posits that phenomenal properties manifest themselves in circumstances that could be analyzed along mereological principles. Finally, I consider if such mereological decomposition could take the burden of providing the categorical grounds that are needed by panpsychism to play the theoretical role assigned to it by Russellian monism. Russellian Monism and Three Views In order to solve the mind–body problem, Bertrand Russell (1927) argued that ontology is monistic and that there are fundamental entities that ground both physical and phenomenal – or more generally mental – properties. Such categorical bases are needed for grounding physical properties for, Russell argued, physics individuates physical properties by

Dispositions, Mereology and Panpsychism  229 describing their roles without specifying who is going to fill those roles, thus leaving us with a deep ignorance of the categorical bases of physical properties. Such categorical bases, however, are not only the right properties to fill the roles established by physics, but they also “have a significant role in explaining consciousness or experience” (Pereboom 2011: 89). So, the fruitful solution provided by Russellian monism was to fill the gap between the experiential (or mental) and the non-experiential, that is, physical, with properties good for both while giving full credit to the physicalist view according to which ontology is monistic. The resulting picture is one with three fundamental tenets: physical properties are described in structural and relational terms, that is, by their roles; there are inscrutables or ultimates that are neither structural nor relational; at least some inscrutables or ultimates are phenomenal or protophenomenal (we will see this in due time; cf. Alter and Nagasawa 2012).2 As Montero (2010) pointed out, a property is an inscrutable just in case we know little about it beyond the theoretical role it is supposed to play. So, ultimates are categorical entities, or quiddities, whose identity conditions are independent from, and not in relation to other entities. The general metaphysical framework engendered by Russellian monism leads us pretty naturally toward panpsychism: if phenomenal properties are the necessary grounds for physical properties, whenever a physical property is instantiated, its categorical ground, which is phenomenal, is instantiated as well. So, there is some mentality everywhere there is something physical. Three different views attribute to phenomenal properties the role of ultimates: panpsychism, emergentism and panprotopsychism. These views take different paths as regard the level of reality at which we should place phenomenal properties (cf. Goff 2017, Goff et al. 2022) and hence assume different relation between ultimates, which are categorical, and roleinvolving properties, which are dispositional. According to panpsychism, there are conscious phenomena all the way down. Chalmers (2015) considers the possibility that our consciousness is grounded in some simpler forms of consciousness present at the micro-level and calls this constitutive panpsychism. Entities such as quarks or others yet to-be-discovered fundamental particles or waves are the kernels of a rudimentary form of consciousness, such that “there is something it is like to be a quark or a photon or a member of some other fundamental physical type” (Chalmers 2015: 246–7). The most relevant consequence of panpsychism is that maximally simple physical properties are identical to maximally simple phenomenal properties. And since there are physical properties all over the natural domain, what there is in the natural domain (all the composing parts of it) is ipso facto phenomenal. Maximally simple phenomenal properties, then, are constitutive of reality, and “there is something that it is like to be a physical ultimate” (Goff 2009: 289).

230  Simone Gozzano However, it might be very difficult to accept that entities quite far away from us, like quarks, can have experiences as we have. To temper this point, one that determines an “incredulous stare” (Goff 2017), panpsychists may say that even if ultimates are the same kind of entities, experiences of these ultimates need not be of the same kind. We are not forced to admit that there is something it is like to be a quark or a photon: it seems plausible to say that such experiences bear just a theoretical and extremely pale resemblance with ours. To make this clearer, dark matter would be composed of massive particles, so subject to gravity, but the interaction with the gravity of these particles is incredibly far away from that of us and very far from that of super-massive bodies, like black holes. Basically, a difference in quantity could make a difference in quality. Galen Strawson has argued that the “real physicalist” should not be worried about this view, for she has simply to admit that conscious phenomena are part of the physical world and should not invoke any special miraculous character for these phenomena. Rejecting the idea of an emergence that pins down to be non-deducible, Strawson invites us to change the way in which matter – usually thought to be non-experiential – is conceived, by taking it to be experiential in some sense: “Real physicalist must accept that at least some ultimates are intrinsically experience-involving” (2008: 71). So, in the case of panpsychism, some ultimates and maximally simple phenomenal properties should be identified.3 The second option is emergentism, in Chalmers’s terms, non-constitutive panpsychism. Following the positing of maximally simple phenomenal states, emergentism argues that conscious phenomena, absent at some level of physical reality, emerge once the relevant physical entities get to a sufficient level of complexity and are in the proper interaction. This view entails a radical form of coming into existence: from nonconscious entities we arrive at the conscious ones. In such a case, there would be an “ontological jump”. Emergentism has that reality is composed by different levels and new fundamental powers come into existence at many levels. According to Strawson, this is the weak point of emergentism, because emergence cannot be brute: “For Y truly to emerge from X is for Y to arise from or out of X or be given in or with Y given how X is. Y must arise out of or be given in X in some essentially non-arbitrary, and indeed wholly nonarbitrary way” (2008: 66). Moreover, emergent novelty entails, in some way, the violation of the principle of causal closure, according to which in the natural world, if an event has a cause at time t, it has a purely physical cause at time t (cf. Kim 1998; Wilson 2021). Emergentism takes conscious states or properties as qualitatively different from nonconscious ones. A middle path is steered by a third option: panprotopsychism (Chalmers 2010, 2015). Nonconscious states or properties have the disposition, in a given condition of interaction, to manifest conscious states or properties.

Dispositions, Mereology and Panpsychism  231 The hypothesis stems from recognizing that phenomenal properties are somehow structured and dynamical. Consider the complex taste of our white wine or the listening to a musical passage: the perceptual experience has a structure and a dynamics that directly derive from the source of the experience itself and so from the structure and dynamics of the taste of the wine or the musical passage itself. If these phenomenal properties are so structured, then there are properties constituting them. These constitutive elements are called protophenomenal properties and are described as “properties that collectively constitute phenomenal properties when organized in the appropriate way” (Chalmers 2010: 151). Regarding this collective composition, “we need a much better understanding of the compositional principles of phenomenology: that is, the principles by which phenomenal properties can be composed or constituted from underlying phenomenal properties, or protophenomenal properties” (Ibid.: 136). So the passage from the nonconscious to the conscious is determined by principles or rules that we may discover. It is now time to take stock and compare these three doctrines in order to understand how the distinction between categorical and dispositional properties is considered and that, among these views, could give to phenomenal properties a dispositional role. First, panpsychism takes simple entities to be conscious without this being a matter of dispositionality: being conscious is a categorical property. Second, panpsychism may offer a way to explain the different varieties of consciousness: the more the entities and their interactions, the more complex consciousness is. According to panprotopsychism, vice versa, simple entities are not conscious in themselves, not even in some minimal or rudimentary form: they are disposed to generate consciousness when interacting or summing up in certain ways. Consciousness is there just in potency, but some conditions or interactions are required for it to manifest.4 One strain of emergentism, too, takes simple entities not to be conscious, but it takes them not to have the disposition to give rise to consciousness either; rather, consciousness is the result of some ontological jump, a radically nondeducible, hence unforeseeable, difference. Both panpsychism and panprotopsychism accept the presence of constitutive elements of consciousness, elements that panpsychism takes to be sufficient for phenomenal experiences, while panprotopsychism takes these elements as necessary composing parts of conscious experiences; both panprotopsychism and emergentism take the phenomenal experiences we are used to as a sui generis phenomena, either not present at lower levels (emergentism) or not properly manifested (panprotopsychism); both panpsychism and emergentism take phenomenal properties to be categorically different from all other kinds of properties and fundamental, with panpsychism positing fundamentality all the way down and emergentism positing it at some point in a yet-to-be-clarified ladder of levels. In the terms of our

232  Simone Gozzano discussion on maximally simple phenomenal properties and ultimates, only panprotopsychism clearly distinguishes between phenomenal properties and ultimates, with panpsychism and emergentism not being clear on that distinction. Moreover, only panprotopsychism fits with the dispositional view of pain proposed, in particular with the idea that pain is the combination of a simpler form of consciousness. So, let’s discuss panprotopsychism further. As we have already seen, according to panprotopsychism ultimates and maximally simple phenomenal properties are different: the former could arrange, according to principles and law, so to give rise to the latter. And it is only in panprotopsychism that mereology could be applied as a methodology that allows to better understand how phenomenal properties manifest themselves in the proper circumstances. Chalmers also argues that protophenomenal properties are not necessitated by physical properties even though they necessitate phenomenal properties, which are not fundamental: There are two possibilities here. First, it could be that consciousness is itself a fundamental feature of the world, like space-time and mass. In this case, we can say that phenomenal properties are fundamental. Second, it could be that consciousness is not itself fundamental but is necessitated by some more primitive fundamental feature X that is not itself necessitated by physics. In this case, we might call X a protophenomenal property, and we can say that protophenomenal properties are fundamental. (Chalmers 2010: 125) So, if we do not consider consciousness as fundamental in itself, we have physical properties not necessitating protophenomenal properties while these do necessitate the phenomenal ones. Moreover, Chalmers insists that protophenomenal properties are “special properties that are not phenomenal (there is nothing it is like to have a single protophenomenal property) but that can collectively constitute phenomenal properties, perhaps when arranged in the right structure” (2015: 260). So, we would have that constituting would be necessitating. In line with Russellian monism, Chalmers stresses that the underlying neutral properties X (the protophenomenal properties), [are] such that the X properties are simultaneously responsible for constituting the physical domain (by their relations) and the phenomenal domain (by their collective intrinsic nature) … [where] One could give the view in its most general form the name panprotopsychism, with

Dispositions, Mereology and Panpsychism  233 either protophenomenal or phenomenal properties underlying all of physical reality. (2010: 134) So, these protophenomenal properties, to be identified with the ultimates, could be the dispositional elements that, in the appropriate circumstances, necessitate, while constituting, the maximally simple phenomenal properties. At this point, we should consider two questions: one is whether and how mereology plays any role in making sense of the resulting metaphysical picture; the other is the metaphysical role that maximally simple phenomenal properties and their constituting protophenomenal parts play. Let me face these issues in turn. Experiences and their Parts Consider bodily pain. According to many scholars, pain is not a unitary phenomenon (see Corns 2014). Indeed, pain has, at least, both a proprioceptive and an affective component, also referred to as somatosensory and experiential, so it has two or more simpler phenomenal properties.5 While the former is responsible for the location and the spatial structure of pain – it can be modeled as a spot, an area, or a volume – the second one determines the axiological or hedonic value of pain, its being bad or unpleasant for us. At least one specific pathological condition, asymbolia for pain (see Grahek 2007), give us empirical evidence that the two can be taken apart, as some individuals are on average in saying where their pains are but are not affected by them: they don’t care about their own pains. Nonpathological individuals feel pain as having these two features or properties. Beyond being complex, pain can be regarded as a power or disposition. The dispositionality of pain, in particular, is revealed by its being the manifestation of our sensitivity toward certain phenomenal stimuli, those that appear most salient to us while impinging on our body and such to trigger potential self-care states.6 One may also support the dispositionality of pain indirectly by either adopting pandispositionalism, the view that all properties are dispositions (Mumford 1998, 2004; Mumford and Anjum 2011), or the identity view, according to which the distinction between dispositional and categorical properties is a superficial one and the two have to be identified (Molnar 2003; Heil 2012; Jacobs 2011). Taking the two assumptions together, pain being complex and being a disposition, we get to consider pain as a power composed of simpler powers: detecting and representing locations on the body and evaluating the most salient stimuli impinging on the body as of affective or having a hedonic nature and prompting for self-care.

234  Simone Gozzano We briefly introduced the concept of a simple phenomenal property, something we may call a phenomenal atom. A phenomenal state that is not simple in the given sense will be phenomenally complex or molecular, to add a piece of terminology. Taking phenomenal properties as atomic or molecular suggests that molecular phenomenal states can be considered as mereological entities, that is, entities that can be analyzed in terms of parts and wholes. Usually, mereology is applied to concrete entities, such as statues, books and the like, and phenomenal properties or states can be hardly considered in this way. However, many have applied or used mereology also to understand the internal relation among properties (Williams 1953; Paul 2002; Forrest 2016) So, we can use the relation of parthood, the fundamental relation of mereology, to analyze the components of our phenomenal states. We could say that the taste of hay is part of the taste of this white wine and that the tasting experience is composed by it and by the taste of green apple. Similarly, the feeling of pain is part of the overall feeling of pain-in-the-thumb, as I am considering sensory pain.7 So far, I have referred to simple phenomenal properties as our mereological atoms, the constitutive minimal elements that participate in some complex experiences as we have them. What is it to be such an atom? Here is a proposal: [ATOM] A phenomenal atom a – or a maximally simple phenomenal state – is a state such that any modification of it would change its phenomenal nature, either by undermining it (there is nothing that it is like to have a modified a, as a*) or by changing it (from a we would get to b). If atoms are as defined, since pain is structured, it is composed by more than one phenomenal atom, hence it is a phenomenal molecular property. Since I don’t think that phenomenal states can be free-floating, if they are tokened, it is in virtue of them being the content of someone’s experience. So, the tokening of a phenomenal property, either atomic or molecular, determines a corresponding phenomenal state. Notice that it is the content of an experience that is complex, not the quale in itself. When we are in pain, we experience both an affective (or hedonic) quale and a proprioceptive quale: these two determine the molecularity of our experience. Had we suffered asymbolia for pain, we would have experienced only the proprioceptive quale, thus having an atomic experience. Now, can these atoms play the role assigned to them by Russellian monism and by the various doctrines related to it? In particular, can they be the elements that ground everything else? The answer lies, in part, in whether mereology can help us in understanding how from these atoms we can get to molecular or complex states.

Dispositions, Mereology and Panpsychism  235 Mereology for Pain (or the Combination Problem) In order to tackle the so-called combination problem (how constitutive mental elements compose phenomenal states) we may take phenomenal atoms to be the new way to identify qualia.8 Since there are different types of qualia, there should be as many type-different phenomenal atoms. We may think of phenomenal atoms either as endowed with a structure or not. If phenomenal atoms have a structure, then the ultimates, or protophenomenal properties, are the elements of this structure. To secure this result there are two options: either there are type-different ultimates, so that each  type plays some specific role in composing a phenomenal atom, in analogy with physical subatomic particles and atoms, or the ultimates, while belonging to the same kind, in terms of determinability, are different in terms of determinate: say, they are all red but have a different shade. Their difference would make for the difference in the phenomenal atoms. If phenomenal atoms do not have a structure, we may think of them as mereologically flat, and in such a case, the simple sum of the ultimates is enough to give rise to type different phenomenal atoms, where such a sum would not count as either structural or functional. The contrast between sums versus structural/functional relations is a way to meet what Lando describes as the literal versus the metaphorical interpretation of mereology. The basic tenet of classical mereology is the relation of being part of, and this relation is reflexive, transitive and anti-symmetrical. So, reflexivity has that everything is part of itself; transitivity is such that if x is part of y and y part of z, then x is part of z; finally, antisymmetry is as follows: if x is part of y and y is part of x, then the two are identical or, to put it conversely, two distinct things cannot be part of each other (Lando 2017; Varzi 2019). Lando takes these formal features to characterize the relation of being part of along with two further principles: spatiality and nonselectivity. According to spatiality, being a part involves having a spatial feature, so having a physical location. Nonselectivity involves having clear boundaries without a specific function or role to be played: the leftuppermost brick of a wall has a location but not a specific function, so it is nonselective. John the trumpeter is part of the band, but he has a specific function, playing the trumpet, and so is selective. Hence, mereology is more literally construed if the three principles of formality, spatiality and nonselectivity are literally respected. Now, a mereological sum meets the three principles: the bricks of a wall are such a mereological sum. The subatomic particles of a physical atom, vice versa, are not a mereological sum; they rather obey structural relations, because they violate, at least, nonselectivity. Clearly, also the bricks bear some relation to each other or to the wall as a whole (the left-uppermost brick bear specific relations to the wall and other bricks), but this is not

236  Simone Gozzano intrinsic to them, for one can replace or relocate any brick, and no change either in the bricks or in the wall follows.9 So, apart from being parts of the wall, or constituting it, they do not bear any specific structural or functional feature. This is not the case with phenomenal atoms, and what is crucial in the structural and functional view of the phenomenal atoms is selectivity. The reason this is so is that in many phenomenal cases, we recognize the presence of a structure or a potential one. Let’s think about phenomenal atoms in analogy with type-different physical atoms. We need to imagine some difference in their protophenomenal elements, in analogy with the subatomic particles, so to justify why the atoms are different as well. We know that in the case of subatomic particles, there is a mix between type difference and summative difference: two atoms are type-different in virtue of a different number of typedifferent constituents, namely, electrons, neutrons and protons. So, we can say that phenomenal atoms have a structure realized also in terms of the number of elements. Imagining the protophenomenal elements as typedifferent does not necessarily leads to a regress, for we may take these as the ultimates and simply postulate that there are type different ultimates, whose combination is the subvenient base for type different phenomenal properties. The crucial upshot here is that there cannot be differences in phenomenal properties without differences in the protophenomenal ones.10 So, a supervenience relation holds between the phenomenal and the protophenomenal. Having these distinctions in place, we should consider the possible structure of phenomenal properties. Think again at the sip of white wine: the flavor is composed by the taste of green apple and that of hay. At the same time, that experience is stimulated by a single experience, and it is a taste having a composition, hence a structure. Let’s apply this point to the case of pain. We saw that pain is considered to be composed of two components: a perceptual and an affective one. The perceptual is about locating the pain, the affective is assessing it as determining self-care and to be negative on an axiological ladder (possibly in relation to its intensity). So, the instantiation of the phenomenal property of feeling pain is the instantiation of the properties of feeling a location as painful (location as primary) and having an affective or hedonic negative value as located (painfulness as primary). Can we take these two composing elements of pain as its protophenomenal composing properties? If we consider protophenomenal properties as non-experienceable, as Chalmers does, there is a sense in which the composing properties of pain could be experienced in isolation, as the case of asymbolia for pain reveals (Grahek 2007). As we saw, asymbolic subjects are on average in spotting the location of inflicted pain, even for those painful stimuli not directly observable (as those occurring at the center of the back), but they are not emotionally affected by them: the nocive

Dispositions, Mereology and Panpsychism  237 stimuli do not bother them. Since these properties are experienced, whether both or not, they aren’t admissible as protophenomenal properties. Rather, since these properties prima facie are not further decomposable, we may take them as phenomenal atoms. We could consider a potential issue by reasoning in disjunctive terms. Either pain is a molecular phenomenal property, with two composing phenomenal atoms, or those suffering from asymbolia experience a different phenomenal atom with respect to what non asymbolic subjects. Now, we can dismiss this second option by considering the following argument. If asymbolic subjects have a different phenomenal atom of pain as compared to that of non-asymbolic subjects, their protophenomenal properties would be different because, we established, phenomenal properties supervene on protophenomenal properties. Consequently, they would have different protophenomenal properties constituting the phenomenal atoms of pain. However, it seems that we have no reason, beyond the mere evaluation of simplicity itself, to suppose that the atoms are different. The only upshot of taking them to be different is in order to argue that the phenomenal is independent from the protophenomenal, which would be a step closer to say that the phenomenal is independent from the physical, as per Chalmers’s conceivability argument. So, postulating different phenomenal atoms begs the question about whether phenomenal properties are autonomous or reducible with respect to physical properties. Therefore, we should abandon the option of having different phenomenal atoms for pain and consider pain as a phenomenal molecule. As a consequence, the phenomenal atoms are two: one is the feeling of a location as painful (location as primary), and the other is the negative affective value as located (painfulness, the affective component prompting for self-care as primary). The asymbolic differs from the non-asymbolic in not feeling the second atom. If these are the atoms, what is their structure? Or, to put it in other terms, what are their protophenomenal components? In discussing what are the ultimates, Derek Pereboom (2011: 97 et passim) proposes perfect solidity as the categorical ground for all the physical properties that impenetrability, as a disposition, manifests. The proposal makes evident that the ultimates are to be thought of more as abstract and logical features rather than as precursors of our experiences. They have to fill the role established by the dispositions that manifestation we have described in psychological terms.11 However, we want that these ultimates, in the proper circumstances, give raise to experiences. In the case at hand, then, we can imagine that the ultimates underneath the phenomenal atoms of location and affective value are relative to self-location and self-safety. Here, “self” does not mean that there has to be an ultimate that refers to its own individuality as such but simply a logical feature such that the location or the affective value in question are to be related to some other

238  Simone Gozzano ultimate.12 Once these ultimates are in the circumstances in which, to make a case, the individual bearing them may take stance and action with respect to their occurrence, then these can be felt, thus determining the occurrence of a phenomenal atom. So, I am suggesting that the proper circumstances in which a protophenomenal property gives rise to a phenomenal one are those in which the subject of experience may take a stance – for instance, judging it in need of self-care or taking it to have a negative hedonic component – or may act – avoiding or searching again in the proximity of her own body – with respect to the content of the experience.13 The logical structure here is one of saturation; it is one in which a protophenomenal component of the form “x needs to take care of x with respect to stimulus a” and “point y is in need of care with respect to stimulus a” are saturated by x and y being replaced by the sense of the self and the sense of one’s own body of the very same individual, respectively. So, a phenomenal atom of having pain is one in which the protophenomenal property of something nocive for the body one has is considered as in need of care for one, and this occurs as a phenomenal atom and similarly, for a location where a point, area or volume of own’s body is considered as in need of action. Once these two occur together, we have the phenomenal molecule of, say, pain in the thumb. One of the crucial elements lurking behind this issue is whether ultimates or protophenomenal properties have a categorical nature, one that takes their nature to be independent of the way in which these ultimates are related to anything else. However, it is crucial to understand that the proper circumstances that determine the passage from the ultimate as a protophenomenal property to a phenomenal atom are part and parcel of what these ultimates are. So, this ultimate cannot be categorical all the way down. This brings us back to the fundamental question of this chapter and to the metaphysical structure imagined by Chalmers with respect to panprotopsychism. The Metaphysical Place of Phenomenal Atoms We saw that, according to Chalmers (2015), protophenomenal properties are not experiential; there is nothing it is like to have them. However, these properties necessitate and constitute phenomenal properties, which are fully experiential. Hence, there is a passage from the nonexperiential to the experiential. How can this passage be accounted for? Unless one endorses the identity thesis by Molnar (2003) and Heil (2012) – which somehow resolves the problem by fiat – or adopts a form of Russellian monism, the one invoked by Strawson – that requires the base properties to have some form of experientiality thus denying both Chalmers’s tenet on ultimates not being experiential – the only option left is to suppose that there is some

Dispositions, Mereology and Panpsychism  239 (to be determined) law or principle bringing, with some form of necessity, from the nonexperiential to the experiential. This problem has been recently debated by Alter and Coleman (2020) reacting to a double attack on Russellian monism by Brown and Morris. According to Brown (2017) and Morris (2016), protophenomenal properties are partly individuated by their role in constituting fully phenomenal properties. On the contrary, Alter and Coleman note that “protophenomenal inscrutables need not be individuated by any roles they play. … Instead, they might be individuated just by what they are in themselves, that is, by their intrinsic natures – natures that might be physical and not experience specific” (2020: 413) So, protophenomenal properties would be categorical properties, that is, quiddities, individuated by their intrinsic nature. Our original question, whether phenomenal properties or some more fundamental properties can ground physical properties, is now clarified, for phenomenal properties are grounded in the ultimates and by transitivity of grounding we should consider whether ultimates can play the role of grounding the physical and the experiential, as well, while being categorical. One familiar path followed by those who favor the idea of having quiddities as grounding properties, as David Armstrong, is to insist on the contingent nature of the relation established by these properties. The role that quiddities may happen to fill in a specific world is, typically, contingent. For, it could well be the case that the intimate nature of electrons, to make a classical example, is to stay in some repelling relation to same-kind particles in this world and in an attracting relation to same-kind particles in another world. Whether electrons turn out to be attracting or repelling to other same-kind particles depends on the laws of nature holding in the world they inhabit. (cf. Schaffer 2005) So, their quidditistic nature, their having the specific nature that characterize them, is contingently linked to the roles they play. The same, then, should hold for ultimates. Now, according to Chalmers, phenomenal properties are necessitated by protophenomenal properties. Consequently, if protophenomenal properties are quiddities and quiddities are contingently linked to the role they play, it seems that these protophenomenal properties can only contingently determine the phenomenal properties, contrary to the assumption. Therefore, either we abandon the idea that these properties are quiddities or we abandon the idea that they necessitate phenomenal properties, in particular phenomenal atoms. Perhaps Chalmers may weaken his view and take protophenomenal properties only to contingently necessitate phenomenal properties. This would mean that there could be different ways in which the protophenomenal could compose the phenomenal so to justify the iterated modality. The picture would be (put in possible worlds terms): in this world, necessitation goes according to certain laws of nature, but in some

240  Simone Gozzano other world, inasmuch as it is governed by different laws of nature, other principles rule the passage from the non experiential to the experiential. The weakening can be formulated as follows: protophenomenal properties nomologically necessitate the phenomenal ones, and laws of nature are contingent with respect to a variety of necessity stronger than nomological necessity. So, what is needed at this point is some formulation for how to make sense of this nomological necessitation. The view just sketched reminds of Armstrong’s view on the relation between properties and laws of nature. According to Armstrong (1983, 1997), properties are quiddities because they lack any modal character: there is no necessary entailment in virtue of having property P and property P is not necessarily entailed by any other property. At the same time, the laws of nature are contingent second-order relations on first-order properties, and they at most say that whenever something has property F it has property G, but no stronger modal relation is foreseen.14 Now, suppose to stick with Armstrong’s model, as Chalmers seems to do. How is it that the ultimates or protophenomenal properties necessitate a phenomenal property? To necessitate is to necessarily bring about. In the case of physical entities, this is tantamount to necessarily causing. Consider the protophenomenal component of location in the case of pain. This property has the intrinsic nature of determining a location, it is a pointer to a location. Once this encounters or interacts with a further protophenomenal ultimates of the proper type, one that attaches to the pointer a phenomenal value, it should necessarily bring about the phenomenal property of feeling some location as x. If the other ultimate is a negative affective value, one hedonic value that determines some self-care, then the location is a feeling of the location as one necessitating care because of a negative phenomenal value; if the other ultimate is a smell, the experience is one that locates the origin as a positive or negative smelling location, and similar for sounds and other phenomenal modalities.15 This tentative solution entails abandoning the quidditistic nature of protophenomenal properties. For, given the proposed solution, the ultimates are intrinsically relational: the locating ultimate is a spatial feature relating a place to something else; the phenomenal value ultimate has some axiological content, and these features are not independent from everything else; they do establish entailment relations, for the location establishes itself in a structural space while the axiological in a ladder of values. So, if protophenomenal properties are considered as elements composing powers – perhaps they are proto-powers – then we have a route for the necessitation of phenomenal properties and powers out of proto ones. But if the quidditistic nature is deemed nonnegotiable, then such a route is blocked because the modal character of the ultimates clashes with the modal character of their role. Finally, notice that the way in which I have imagined the role that the

Dispositions, Mereology and Panpsychism  241 ultimates have to fill is not phenomenal per se but, as needed, protophenomenal. It is a double role: a tracking one, the location, and an imposing one, if negative you should do this and that.16 Clearly, the imposing role may hold also in case of pleasure: you won’t get rid of the signal, but rather, you may want it to continue. Individuating ultimates through their roles allows one to repeat the classical Russellian’s move against anti-physicalist conceivability arguments. Those arguments maintain that we can conceive a world that is molecule by molecule identical to the actual one but is deprived of any phenomenal property, hence consciousness-free. However, duplicating the actual world entails also duplicating the ultimates of this world, and since these necessitate phenomenal properties, these properties would be tokened as well. To sum up, in this chapter, I provided reasons to maintain that some phenomenal properties, as the property of feeling pain, can be considered complex dispositional properties composed of simple phenomenal atoms. These atoms can be framed in the context of present-day discussions on Russellian monism and panpsychism. In such a framework, these properties are, in turn, composed of protophenomenal properties, which need to be individuated in relational terms, thus abandoning the quidditistic constrain that many want to impose on them. If taken as relational, protophenomenal properties allow the fulfilling of the typical Russellian reaction toward anti-physicalist arguments, such as the conceivability argument, thus vindicating physicalism. Acknowledgments For helpful comments on a previous draft of this chapter I wish to thank Donatella Donati and Giorgio Lando. Notes 1 I will use power and disposition interchangeably. 2 From now on, I use “ultimates”, for it seems that many non-ultimates could be inscrutable. 3 He parts company from views as those by Humphrey and Tim O’Connor. See also Strawson (2015) and Coleman (2006). 4 Vetter (2015) has that disposition may simply manifest even if no specific stimulus triggers them. 5 Assessing the phenomenal property as bad distinguishes it from other very intense properties, such as sexual pleasure. My view on the components of pain is tripartite: I take pain to be composed of three specific features: intensity (modeled as a quantity), location and dynamics (whether a burning, a pulsing or a throbbing pain, to name a few case). Finally, I take something as bad if it prompts for self-care dispositions (cf. Gozzano 2021). However, to keep things simple, in this chapter, I consider only the bipartite view.

242  Simone Gozzano 6 My view in noncommittal with respect to the relation between manifestation and stimuli: it could be the case that pain is sensitivity to certain phenomenal stimuli, as per the classical model of disposition (Mumford 1998), or that pain is the easiness in sensing certain phenomenal conditions, if the Vetter (2015) model is preferred. 7 Notice that I am here discussing phenomenal atoms from the same sensory modality (two tastes composing my phenomenal experience of wine tasting), but if one considers a phenomenal property as originating from different sensorial modalities, this problem is well recognized in the literature on consciousness as the binding problem, that is, the problem of explaining the sense of unity that we have in experiencing things through different sensory modalities, such as the taste, smell and color of the wine. Kant thought of this as the synthetical capacity of the mind, the one providing us with a single experience composed of different, and presumably autonomous, parts. More recently, Tim Bayne has elaborated a mereological theory of the unity of consciousness (Bayne 2010). All these theories, however, take for granted what are their fundamental parts. 8 See James (1890) and Chalmers (2017). 9 This entails denying composition as identity, for one may think that changing the position of a brick changes the wall as a whole, determining a new wall. See Lando for a defense of this view. 10 A further option is the following: while the phenomenal atoms are kind different, their composing elements are not: the difference in the atoms is given by the amount of protophenomenal ultimates composing them. We all know, for instance, that some sugar could be nice, too much sugar could be disgusting. So, a difference in quantity can determine a difference in quality, that is, in the qualia we experience. 11 Mørch (2020), with Chalmers (1996, 2010), takes these to be the positive and the negative conceivability: a negative one specifies only the theoretical role; a positive conception specifies how that role can be filled or imagined to be filled. 12 This presupposes that ultimates can be fully individuated. However, it is doubtful that, for instance, elementary particles can be so individuated. For instance, there is no clear sense, if not an outright falsity, for giving an electron a determinate position in space. 13 For the view that pain is a command for the body to act, see Klein (2015). 14 Against such a general view, Alexander Bird (2005) has argued that it is untenable. Either it collapses in a regularity view (“whenever something has F it has G”), and so losing any explanatory force, or it involves a vicious regress of weakly necessitating relations. 15 See Gallagher (2000) for taking ownership and action as basic elements in our cognitive life. See Coleman (2013) for the idea that phenomenal properties have both a qualitative and a subjective component that he thinks can be taken apart. 16 This is pretty much in line with Klein’s (2015) view according to which the content of our pain states is a command to the body, something like “Stop having this!” or “Remove the hand from that” and the like.

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Index

Pages followed by “n” refer to notes. Note: Where used synonymously, the terms ‘dispositions’, ‘potentialities’ and ‘powers’ have been brought under ‘powers’. activation 186 activation-causal-process 187; composite 199; multiplicity of 198, 199; non-fragile 188 activation conditions 186, 188, 193 activation-process see activation-causal-process aggregate 146 Alter, T. 239 Anjum, R.L. 52, 87, 144, 191 anti-Humeanism 85, 144 Aristotelian totals: additive 124; generative 124–125 Aristotelian wholes 125 Armstrong, D.M. 209, 239–240 Bennett, K. 117, 121, 153, 198 Bird, A. 16, 21, 100, 144 the Born Rule 212, 222n12 Brown, C.D. 239 Cameron, R. 91, 92, 93 Cartwright, N. 88 categorical-dispositional dualism 45 categorical-dispositional monism 57 causation: atemporal 117; as atemporal building relation 121; causal closure 230; causal exclusion 159–160; causal models 130, 131; causal overdetermination 18, 159–160, 198; causal powers see powers; causal process 185; causal

relations 130, 131; causal structures 134, 136; directed causal graphs 132; interventionism see interventionist theory of causation; token 132; type 132 centred worlds 48 Chalmers, D.J. 229, 232, 238 Coleman, S. 239 collective instantiation see plural instantiation collective powers 157; grounding of 152–154; and non-emergence 151 complex powers 11, 61, 227; and cooperative manifestations 75, 77; and determinate-determinable relation 66–67, 76; and emergence composition criterion 72–77; and essence composition criterion 68–72; extrinsic complexity of 64; and functional unity 75; and fusion 67–68; intrinsic complexity of 61–63, 64; and linguistic analysis 65–66; mereological complexity of 64; and reductionism 71; and unity 65, 70–72; see also composite powers; determinable powers composite powers 51, 118, 190, 198–199; and component powers 192–196, 200; vs. conjunctive powers 116; and derivative powers 192–196, 200, 203n23; see also power-composition

246 Index composition 153, 170; and causation 117, 121; characterization conditions of 161; as identity 69; moderate approaches see restricted composition; operational account of 161; of powers see powercomposition; of properties 142; restricted 88, 167; universal see mereological universalism; see also mereology conceivability arguments 241 consciousness 229, 231; grounding of 229 Cosmic Entanglement 175, 176, 180 determinable dispositions see determinable powers determinable powers 99, 100; and atelic events-in-progress 106; events-inprogress argument for 104–106; grounding argument for 100–103; vs. multi-track powers 106; and telic events-in-progress 106 disposition ascriptions 119 dispositional essentialism 143, 162n4 dispositionalism 89, 228; and contingentism about mereological laws 93; and contingentism about natural laws 91; and necessitarianism about mereological laws 93; and necessitarianism about natural laws 92 dispositions see powers Dixon, T.S. 43 downward causation 74, 75 the Eleatic Principle 83 emergence 72–73, 230; strong 80n14; weak 80n14 entity stage 45, 54 epistemological coherentism 219 essences: complex 162; and dependence 71; and grounding 69; THICK essentialism 68–69; THIN essentialism 69–71; and totality fact 70 event: atelic type 104–105; telic type 104–105 events-in-progress 104; atelic 105–106; dispositional account of 104; and marks of dispositionality 104;

resultant state of 104, 105; telic 105–106 experience see consciousness experiences: complex 227; mereology of 233; subject of 238 extreme resemblance nominalism 45, 55, 56–57; and indeterministic powers 57 factorisability 214 fact-powers 47; grounding mereology of 48; and groverlap 47; identity conditions of 48, 54; parametric conditional 56; partial grounding of 47; power parameter 54, 55; and proper ground-part 47; semantics for conditionals 48–50 facts: conditional 42; grounding mereology of 43–44; individuation of 44; mereologically coincident 42; power equivalent 42 Fine, K. 161 forces 192; component 200–201; and relational facts 201; resultant 200–201, 203n32 fusion 22, 67–68 the general composition question 170 graph-theoretic model of powers 14–18; directed graph 14; and homomorphism 25; manifestation arc 14; Manifestation Constraint 15; and monomorphism 25; Single-Track Constraint 16; sink 15; and sources 15; and substructure 25–26; triggering arc 14; see also labelled transition systems grounding 69, 151, 153, 218; argument for determinable powers 103; asymmetry of 218; bottom-up explanation 161; vs. composition 153; and essences 161; hyperintensionality of 224n33; irreflexivity of 218; necessitation by 224n33; non-monotonicity of 224n33; and ontological reduction 151; partial 43, 219; as a relation between truths 45; of specific powers 101–103; top-down explanation 161; transitivity of 218; wellfoundedness of 218

Index  247 grounding mereology 43–44; and ground-part 43; and groverlap 44 grounding-mereological axioms: Addition 56; Asymmetry 43; CA 51; Consequent Conjunction 50; CONTR 50; CSO 51; Equivalent Antecedents 50; Exercise 56; ID 50; MOD 50; Power Ponens 56; Reflexivity 44; Right Weakening 50; Strong Supplementation 44, 58–59; Transitivity 43, 44 Gruszczynski, R. 86 gunk 93 Heil, J. 57, 119, 144, 146–147, 157 Heisenberg, W. 212 holistic dependence 174, 175; of entangled systems 175, 177–178 Hume’s Dictum 217, 222n3 Humean Supervenience 209, 222n3 Humeanism 11 the Hume-Lewis-Armstrong approach 211 hylomorphism 146 Hypotheticalism 57 idempotency 123 interventionist theory of causation 130, 132–133; and causal powers 138; causal relevance 132, 134, 136; confounding 133; disjunctive variables 135, 136; intervention variable 132–133; interventionist criterion of 132; interventionist criterion as existential condition 134; and necessity 140; pragmatic approach to 134; the problem of disjunctive causes 133–137; and unambiguous effects 139 Ismael, J. 176, 177 Kroll, N. 104 labelled transition systems 18–20, 36n22; and Asymmetry Constraint 21; and automorphism 21; and bisimulation coordination 33; and clustering approach 27–30; and coordination approach 30–34; and coordination property 32; and c-parthood 29, 33; and

Deterministic Constraint 19; and Manifestation Constraint 19; and multipartite graph 31; and natural homomorphism 31; and partitions 27–29; and quotienting 31; and reciprocal partners 20; and Single-Track Constraint 19; and subcollection approach 22–25; and subgraphs 23; and untriggered powers 19 Lando, G. 235 latencies see quantum dispositions laws of nature 220–221, 239, 240; and ceteris paribus clauses 88; as descriptions of powers 88; and mereological laws 89–90 levels conception of reality 157 Lewis, D.K. 25, 48, 209 the manifest image 146, 155 manifestations 186, 187; collective 158–159; complex 1; continuous 17, 75, 80n17; and contributions to effects 191; determinable 97–100; determinate 97–100; emergent cooperative 77, 80n18; impossible 15; joint see collective manifestation; mutual 17; mutual partners see reciprocal partners; non-combinatory 77; non-fragile 187; non-ordinal 76; parts of 119–120; untriggered 17 Margenau, H. 212 Marmodoro, A. 83, 90, 168, 172–175 the Marmodoro Condition 168, 172–175, 179 Martin, C.B. 17, 57 Maxwell, N. 213 mereological axioms 89; analyticity of 12; and contingentism 91; Anti-symmetry 23, 169, 235; Complement Principle 122, 127n16; metaphysical ground of 86; and necessitarianism 91; non-selectivity 235; pluralism about 86, 112; Reflexivity 23, 169, 235; Remainder 23; spatiality 235; Strong Supplementation 93n1, 127n16; topic neutrality of 12, 86; Transitivity 23, 169, 235; Unrestricted Fusion 23; Weak

248 Index Supplementation 33, 93n1, 121, 127n16, 128n17 mereological laws see mereological axioms mereological nihilism 87, 156, 167 mereological principles see mereological axioms mereological regulation 86 mereological sum 65, 235; see also fusion mereological universalism 70, 87, 117, 118, 167 mereology: building metaphor of 12; carving metaphor of 12; classical 23, 112, 235; classical extensional 67, 88; and exceptions 90; four-layered 33; literal vs. metaphorical interpretation of 227; non-classical 33, 112; and spatiality 115; unity via necessity 70 metaphysical coherentism 211, 218–221, 224n35 metaphysical foundationalism 211, 224n33 metaphysical indeterminacy 103 metaphysical unification 172, 173–174 modal dispositionalism 118 modality: combinatorialism about 209–210, 222n3; dispositional account of see modal dispositionalism Molnar, G. 17, 25, 83, 84, 99 Morch, H.H. 228 Mormonn, T. 25–26 Morris, K. 239 multi-track powers 1, 16, 36n17, 62, 79n8, 99–100, 107n1, 191 Mumford, S. 52, 87, 91, 144, 191 natural classes 46–47 nomological necessitation 240 Oliver, A. 149 ontological dependence 173, 219; symmetric 211, 219, 220 organicism 93 overlap 22 pain 233; asymbolia for 233, 234, 236; complexity of 233; as a phenomenal molecule 237; as a power 233; structure of 236–237, 241n5

pandispositionalism 20, 57, 191, 233 parthood 235; detachability 85; mutual 85; proper 22, 85; and spatiality 227 Pauli’s Exclusion Principle 221, 224n25 phenomenal atom 234; and selectivity 236; and structure 235–236 phenomenal molecule 234 phenomenal state 234; see also properties, phenomenal physical unity 173 pleiotropy 62, 79n3; qualitative 62; quantitative 62; see also multi-track powers plural instantiation 147, 149–151, 153, 155, 156 plural predication 148–149 polygeny 61–62, 79n2 Popper, K.R. 212 potentialities see powers the power mereology view 167; and entangled universe 175, 178–179; and priority monism 182 power structuralism 83 power-composition 170, 189–190; direct composition 111, 114; direct composition and co-location 116–117; direct composition and extensionality 118; direct composition and mereological axioms 121–123; direct composition and monotonicity 118; direct composition by realisation 117–123; the general question of 170; indirect composition 111, 114, 123–126, 127n5; moderate approach 168, 172; power-nihilism 168, 170; power-universalism 168; power-universalism and the Eleatic Principle 171; power-universalism and physical unity 171; the special question of 167; the special question and realisation 118 the powerful cosmos 168, 175, 180, 181–182; argument for 175–180 powerful qualities theory 57 powers 11; abundantism 15, 119, 162n2; and background conditions 193, 202n7; basic 193; and causal profile 112; coinstantiated 127n10; complex see complex powers;

Index  249 composite see composite powers; power-composition; as collections of counterfactuals 63; collective see collective powers; co-location of 84; complementary 122; conflicting 53, 54; conjunctive 24, 116; constellation model of exercising 191; derived see composite powers; determinable see determinable powers; directedness of 106–107; disjunctive 24, 99; emergent 190; as equivalence classes of conditional facts 42, 56; essential see powers, primary; fragile 187; free 43; as functions 14, 154; fundamental 11; and fundamental properties 144; general 97–98, 100–103; and graph-theoretic modelling see graph-theoretic model of powers; grounding theory of 143; higher-level 142, 144, 150; identity conditions of 20; identity theory of 143, 162n4, 233; indeterministic 52; intrinsic 84, 158; irreducibility of 112; joint 42, 45, 191; see also collective powers; as lawmakers 88, 94n7; lower-level 142; macro 144; marks of 13; and mereological axioms 89–90; mereological complexity of 12; mereology of 1; see also power-composition; and modality 11; monism see pandispositionalism; multi-track see multi-track powers; mutually concordant 42; naïve view of 185, 187; as natural classes of facts see fact-powers; network of 22; as parts 84; phenomenal 240; as portable properties 83; and possession conditions 202n7; and prevention 195–196; primary 47; probabilistic 99; and probabilistic conditionals 53; protophenomenal proto-powers 240; and qualitative space 22; rational 52; as resemblance classes of particulars 57; secondary 48; simple 227; single-track 1, 16; sparsism 119; sparsism and compositional nihilism 119; specific 97, 98, 100–103; stochastic see powers, indeterministic; structuralism about identity 20;

substantial 173; and sui generis conditional 46; teleological account of 107; teleological directedness of 107; tertiary 48; and triggers 17–18, 20; and truthmaking 63–64; uninstantiated 114; unmanifestable 15; untriggered 36n19; vector model of exercising 191; and vicious regress problem 20; way-non-specificity of 96–99; and weighted connections 30; see also quantum dispositions predicates: collective 148–149; distributive 148 priority monism 177, 182 propensities see quantum dispositions properties: anti-realism about 147; atemporal determination between 117; categorical 11, 229; clustering of 68; collective 145, 147, 149–151; collective properties and relations 156; disjunctive 137–138; disjunctivity and naturalness 137; eliminativism about 147; emergent 145; episcopalian 147; inscrutables 229; non-distributive see collective properties; non-relational property 156; phenomenal 228, 229, 231; phenomenal atomic see phenomenal atom; phenomenal molecular see phenomenal molecule; physical 228; protophenomenal 231, 232, 238; structural 215; ultimates 229 property composition: Simple Theory of 209 quale see qualia qualia 234, 235 quantum dispositions 212, 213 quantum entanglement 176, 180, 213–217, 225n39; coherentist view of 180; and composite plurality 220; and conditional probabilities 216, 217; holistic approach to 177; and Humean Supervenience 215; and Hume-Lewis-Armstrong approach 217; and internal correlations 213, 223n23; and modal constraints 216; and non-factorisability 215; and

250 Index non-locality 178; and spin anticorrelations 214; and statedependent properties 220, 223n21; structuralist view of 180 quantum mechanics 211 quantum non-locality 223n23 quantum probabilities 211, 222n11; and quantum dispositions 212; and quantum indeterminacy 212 quantum superposition 212 quasi-mereology 26 quasi-properties 147 quiddities 229, 239; non-modal character of 240 real physicalism 230 realisation 117–118, 121 reciprocal partners 17, 45, 191 reduction 151; Changing the Predicate strategy 148; Changing the Property strategy 149–151; Changing the Subject strategy 149; Changing the Substance strategy 149 re-individuation 174, 179 relations 215; building 117, 126; determinate-determinable 66–67; non-causal 218 Russell, B. 228 Russellian emergentism see Russellian panpsychism, non-constitutive Russellian monism 228–233; and the combination problem 235 Russellian panprotopsychism 230–231, 232–233; and combination problem 237–238; and necessitation by constitution 232; and necessitation of phenomenal properties 232, 239–240; and supervenience 236 Russellian panpsychism 228, 229–230, 231; constitutive 229; nonconstitutive 230, 231

saturation 238 Schaffer, J. 176, 177 Schrodinger’s equation 176 the scientific image 155 self see experiences, subject of Shoemaker, S. 57, 138 Sider, T. 90, 93 Simons, P. 122 singular instantiation 155 Smiley, T. 149 the special composition question 94n4, 167 state of affairs: determinable 107; determinate 107 Strawson, G. 230 Suarez, M. 213 substance 145, 146; anti-realism about 147; composite 146, 163n8; composite substance and higher-level powers 146; eliminativism about 147; mereologically complex see composite substance; simple 146 teleological directedness 107 tendencies 52 token-parsimony 198 truthmaking 147, 152 Tugby, M. 15, 17, 18, 161 type-parsimony 198 universal entanglement see Cosmic Entanglement van Inwagen, P. 93, 118 Varzi A. 86 Vetter, B. 98, 99, 101–102, 191 wave function 176, 180, 212, 222n12; collapse of 212, 223n13 Williams, N.E. 20, 30, 119, 158, 191 Wilson, J.M. 103 Woodward, J. 130, 132, 139