Top-Down Causation and Emergence (Synthese Library, 439) 3030718980, 9783030718985

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Synthese Library 439 Studies in Epistemology, Logic, Methodology, and Philosophy of Science

Jan Voosholz Markus Gabriel   Editors

Top-Down Causation and Emergence

Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 439

Editor-in-Chief Otávio Bueno, Department of Philosophy, University of Miami, USA Editors Berit Brogaard, University of Miami, USA Anjan Chakravartty, University of Notre Dame, USA Steven French, University of Leeds, UK Catarina Dutilh Novaes, VU Amsterdam, The Netherlands Darrell P. Rowbottom, Lingnan University, Hong Kong Emma Ruttkamp, University of South Africa, South Africa Kristie Miller, University of Sydney, Australia

The aim of Synthese Library is to provide a forum for the best current work in the methodology and philosophy of science and in epistemology. A wide variety of different approaches have traditionally been represented in the Library, and every effort is made to maintain this variety, not for its own sake, but because we believe that there are many fruitful and illuminating approaches to the philosophy of science and related disciplines. Special attention is paid to methodological studies which illustrate the interplay of empirical and philosophical viewpoints and to contributions to the formal (logical, set-theoretical, mathematical, information-theoretical, decision-theoretical, etc.) methodology of empirical sciences. Likewise, the applications of logical methods to epistemology as well as philosophically and methodologically relevant studies in logic are strongly encouraged. The emphasis on logic will be tempered by interest in the psychological, historical, and sociological aspects of science. Besides monographs Synthese Library publishes thematically unified anthologies and edited volumes with a well-defined topical focus inside the aim and scope of the book series. The contributions in the volumes are expected to be focused and structurally organized in accordance with the central theme(s), and should be tied together by an extensive editorial introduction or set of introductions if the volume is divided into parts. An extensive bibliography and index are mandatory.

More information about this series at http://www.springer.com/series/6607

Jan Voosholz • Markus Gabriel Editors

Top-Down Causation and Emergence

Editors Jan Voosholz Center for Science and Thought University of Bonn Bonn, Germany

Markus Gabriel Center for Science and Thought University of Bonn Bonn, Germany

ISSN 0166-6991 ISSN 2542-8292 (electronic) Synthese Library ISBN 978-3-030-71898-5 ISBN 978-3-030-71899-2 (eBook) https://doi.org/10.1007/978-3-030-71899-2 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Introduction

In Honour of George Francis Rayner Ellis George Ellis is universally recognised as one of the leading cosmologists of our time. A gifted applied mathematician and theoretical physicist, he is a worldrenowned expert on the theory of relativity, space-time, complexity, and causality. In addition, however, his rare depth of insight combined with an uncanny knack for grasping the deep systematic import of any given scientific issue also makes him what can only be described as a true philosopher of nature, however much that term might have fallen out of fashion. Throughout his career, he has been an embodiment of the scientific ideal, cherished as a model teacher by his students and held in the highest esteem by his colleagues. For many of us philosophers, at least, it is difficult to appreciate the sheer range and complexity of George’s numerous contributions, let alone to grasp the significance of his work across such a variety of scientific fields. To be sure, we members of the scientific laity are likely to know his classic collaboration with Stephen Hawking on space-time, The Large Scale Structure of Space-Time (1973). Likewise, he is widely known for having co-authored standard works on relativistic cosmology, including Relativistic Cosmology (2012) with Roy Maartens and Malcom MacCallum, as well as for the famous Dynamical Systems in Cosmology (1997), co-edited with John Wainwright. Yet these three books represent only the tip of the iceberg: George is responsible for a series of highly influential monographs, collections and journal articles spanning the fields of general relativity, relativistic cosmology, cosmological models, and complex systems, which together make up an overall contribution that has proved to be as groundbreaking as it is vast. To assess the whole body of George’s work in a brief introduction would therefore be a hopeless endeavour. Yet, even if we limit ourselves to the field of philosophy, George has been responsible for significant innovations in a number of different subdisciplines. For well over two decades, his interests in causation, emergence and cosmology have taken a distinctly philosophical turn, and he has published what are perhaps the most influential pieces on top-down causation in recent scholarship, successfully bridging philosophy, physics, the life sciences and v

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mathematics in a way that few—if any—can hope to emulate. The remarkable theory of the causal structure of the universe, complexity and emergence, that he put forward in his much-discussed How Can Physics Underlie the Mind? Top-Down Causation in the Human Context (2016) together with numerous highly regarded articles, has sparked widespread academic discussion. In addition, his keen interest in ethics, moral philosophy and theology has been equally productive, resulting in the publication of a volume of collected papers, numerous articles, book chapters and monographs including, among others, the highly regarded On the Moral Nature of the Universe: Cosmology, Theology, and Ethics (1996), co-authored with Nancey Murphy. All these achievements contribute to his status as one of the most outstanding scientists and scholars of recent decades. They are the fruits of a highly impressive career of which we can here mention only a few of the key landmarks: Following his graduation with distinction in physics at the University of Cape Town in 1960, he went on to study at St. John’s College, Cambridge, where he was awarded a PhD in Applied Mathematics and Theoretical Physics in 1964. His first academic positions were at the University of Texas, Austin, and the University of Cambridge, where he became a lecturer in the Department of Applied Mathematics and Theoretical Physics in 1970. In the following years, he was a visiting professor at the University of Chicago’s Fermi Institute, the University of Hamburg and the University of Boston, before his appointment as Professor for Applied Mathematics at his alma mater in Cape Town in 1974, a chair he occupied until 2004, when he became Emeritus Professor and Honorary Research Associate at the very same department. Since taking up his position in Cape Town, he has been invited as a distinguished visiting professor at a number of illustrious institutions: the University of Alberta at Edmonton, the University of Texas at Austin, Specola Vaticana at Castel Gandolfo, Queen Mary College at the University of London, the University of Oxford, the University of Cambridge and, as a frequent visitor, the Max Planck Institute for Astrophysics in Munich. From 1988 to 1993 he was Professore Ordinario of Cosmic Physics at the International School for Advanced Studies in Trieste, and in 1988 he also became GC MacVittie Visiting Professor of Astronomy at Queen Mary and Westfield College of the University of London, a position he holds to this day. In light of his manifold scientific achievements, contributions to philosophy and theology, and social and political engagement, he has been the recipient of multiple honours. To name but a few: since 1983, he has been a Fellow of the Royal Society of South Africa, of which he was also President between 1992 and 1996; he was appointed a Fellow of the Royal Society in 2007; and naturally, he has been decorated with the highest possible recognition of the National Research Foundation of South Africa. For his contributions to furthering the dialogue between science and religion, he was awarded the Templeton Prize in 2004. Beyond the scholarly sphere, he was recognised with the Order of the Star of South Africa in 1999 for his history of vocal opposition of Apartheid. In addition, he was President of the International Society for General Relativity and Gravitation as well as of the International Society for Science and Religion. As a founding and council member of the Academy of Science of South Africa and a Fellow of the Third World Academy of Science, he

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has served the academic communities in South Africa and the Global South. He holds honorary doctorates at seven different universities spanning three continents: Africa, North America and Europe. As we have known him for only a few years, we can only bestow George with a much more modest honour: for his 80th birthday, we would like to offer him the small, belated gift that is this collection. Of his many accomplishments, it was his theory of top-down causation and emergence which first led our paths to cross. This part of George’s work, which is truly interdisciplinary in the best sense of the term, forms the focal point of the following contributions. The many colleagues who have participated in the creation of this volume have conceived their respective contributions as expressions of their respect and admiration for George’s industry, intellectual example and human kindness. This Festschrift assembles a diverse and distinguished group of collaborators. The transdisciplinary diversity it represents is only fitting for a collection compiled in honour of George, and the volume is intended to reflect both the scope of his own scientific and philosophical interests and his talent for perceiving unlikely yet consequential connections between different topics and fields. Furthermore, many of the essays that follow are parts of ongoing discussions: many of the contributing authors were able to discuss the questions raised in the volume with George himself at a conference held at Bonn in the summer of 2018 on his theory of top-down causation and emergence. In the following section, we outline the structure of this anthology and offer a preview of each of the contributions. This also affords us an opportunity to briefly introduce the reader to the debate on top-down causation and emergence, with a particular focus on George’s own outstanding contributions to the field.

The Contributions to This Festschrift Applications of George Ellis’s Theory of Causation, the first of five parts of this anthology, contains three chapters. Each of these focuses on a different aspect of the grand theory of complexity, causality and the structure of nature proposed by George Ellis. Of the many recent theories of the causal structure of the universe, whether proposed by scientists or philosophers, only a small handful are truly applicable to all areas of nature and within all scientific disciplines that are in the business of making causal claims. And even fewer theories have the additional advantage of shedding philosophical and scientific light on the emergence of genuine complexity and thus of counting as contributions to the study of complex systems. In this respect, Ellis’s theory seems to represent a genuine rarity, and the task of applying it to a range of different test cases—from philosophy through to the social and natural sciences—promises to be especially fruitful. The first chapter, by George F. R. Ellis and Markus Gabriel, entitled Physical, Logical, and Mental Top-Down Effects, is a multidisciplinary essay exploring the architecture and applicability of the theory of top-down causation in three different

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contexts. The first is the physical universe: here, Ellis and Gabriel assess how topdown effects are possible in the case of physics, with reference to the fact that the physical universe is not closed at the lower levels. They argue for the importance of contextual effects, which include examples from both biology and neuroscience. In a second step, citing a number of examples from such different fields as logic, mathematics and the social sphere, they argue that abstract objects have causal effects on material-energetic systems. They conclude that only a theory of top-down causation is able to account for the role played by abstract objects in knowledge acquisition, which in turn has the consequence that strict reductionism about abstract objects undermines the possibility of knowledge. In a concluding section, Ellis and Gabriel tackle the problem of mental causation by sketching a model for mind– body interaction that arises from both Ellis’s theory of causation and complexity and Gabriel’s neo-existentialism in the philosophy of mind. This lead chapter thus takes up various threads in the work of both authors; it attempts to provide a suitable philosophical language and framework for certain well-established components of Ellis’s theory while also expanding it into new subject domains. The second chapter, by Sara Green and Robert W. Batterman, Making Sense of Top-Down Causation: Universality and Functional Equivalence in Physics and Biology, investigates a key aspect of Ellis’s theory: the relationship between the notion of top-down causation and functional equivalence classes. The latter is the conceptual tool that allows Ellis to explain how a specific higher-level behaviour can be multiply realised by different lower-level systems or states. By highlighting what Green and Batterman call causal slack between levels, they explain the apparent independence of higher-level phenomena from lower-level conditions. Through exploring cases from physics and biology, Green and Batterman argue for an extension of Ellis’s account of mechanical top-down causation and top-down causation by information control which involves causal slack. The authors argue that this modification to the theory of mechanical top-down causation has the additional merit that it presents an even greater challenge to reductionism. The third chapter, by Otávio Bueno, is entitled Mathematics and Measurement: Causation and the Mind. It tackles the question of what causal roles mathematical structures could play in causal processes and the linked question of how to construe measurements in light of Ellis’s theory. Bueno argues that while mathematical structures might be important for causal processes it is not clear that they need to be causally efficacious, as Ellis suggests. Guided by an empiricist understanding of scientific theorising, the first part of Bueno’s article aims to support the idea that while mathematical structures are causally inactive in virtue to their abstractness, they play a role in causal processes via their interpretation and use as representations by agents. The second topic of the paper, how measurement should be understood in light of Ellis’s theory, is connected to this insight: According to Bueno, agents play the same causally active role in a measurement process, making it an example of top-down causation. The second part of our collection, The View from Physics, explores Ellis’s theory from the perspective of different subdisciplines of physics. It contains two quite distinct contributions:

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The fourth chapter, by Barbara Drossel, is entitled Strong Emergence in Condensed Matter Physics. It investigates whether a micro-physicalist reductionism, which argues for causal closure and determination in a bottom-up fashion, or a theory of top-down causation, is best suited to explain the effects and laws central to condensed matter physics. Drossel argues for the conclusion that Ellis’s theory is superior from this perspective. She begins by giving a series of examples of condensed matter systems that show emergent phenomena. After drawing a distinction between weak and strong emergence, she investigates texts by three Nobel laureates in condensed matter theory and demonstrates how condensed matter research is conducted in practice, supplemented by insights from her field of expertise, statistical physics. Based on this analysis, she presents a list of reasons for accepting strong emergence in physics and discusses certain widespread objections to the view. The fifth chapter, by Thomas Luu and Ulf-G. Meißner, takes a completely different route: in On the Topic of Emergence from an Effective Field Theory Perspective the authors start from the vantage point of effective field theories in theoretical physics. Such theories have been successfully used to provide a bottom-up description of phenomena whose intrinsic degrees of freedom behave at length scales far different from their effective degrees of freedom. As an example from the theory of quantum chromodynamics, Luu and Meißner focus on the behaviour of quarks and gluons and how they combine to form protons and neutrons or, collectively, nucleons, in order to justify an approach that moves from a fundamental description that makes use of quarks and gluons to an effective field theory description of nuclei. The length scales traversed by this explanation span at least two orders of magnitude. The authors thus provide an effective field theory viewpoint on the topic of emergence, arguing on the side of reductionism and weak emergence. The chapter closes with comments on Anderson’s interpretation of constructionism and strong emergence and Ellis’s antireductionist theory, which they criticise as non-falsifiable. The third part of our collection, The View from the Life Sciences, explores the theory of top-down causation from the perspectives of physiology, biology and neuroscience. It presents three pieces, each operating on a different level. The sixth chapter, by Denis Noble, is entitled The Principle of Biological Relativity: Origins and Current Status and has a particular significance: its topic, the biological relativity for which Noble is famous—among other notable contributions to medicine and biology, such as his mathematical model of the human heart—is inspired by his exchange with George Ellis. The chapter thus starts by outlining the origin story of the principle of biological relativity and its subsequent history. It was first formulated by distinguishing between the causal properties of initial and boundary conditions, regarded as a formal cause, as compared to the dynamics of the differential functions themselves, regarded as an efficient cause. The concepts of organisational level and of boundaries between levels and environmental factors are also central to the principle. Noble argues that work on the properties of boundaries reveals two important features: the nature of causation differs significantly between different levels of organisation, and the top-down and bottom-up forms must act

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simultaneously. These developments of the principle are used to clarify the reasons why bottom-up causation alone is inadequate in multi-level biology. The seventh chapter, by Larissa Albantakis, Francesco Massari, Maggie Beheler-Amass and Giulio Tononi, A Macro Agent and its Actions, draws on Ellis’s theory to argue for an antireductionist account of causal interactions in complex, dynamical systems in general and in the case of autonomy and agency in particular. From the perspective of computational neuroscience, the authors argue (1) that agents require causal borders separating them from the environment which, in the context of biological agents, are (2) associated with complex, dynamical macro systems and (3) that such macro agents are supposed to act on their environment. As proponents of integrated information theory, the authors offer an antireductionist account of causation, specifically for the case of (neurological explanations of) agency. Albantakis, Massari, Beheler-Amass and Tononi demonstrate the framework of integrated information theory by using the example of a simulated agent equipped with a small neural network. The eighth chapter, by George F. R. Ellis, is entitled Physics, Determinism, and the Brain. Here Ellis provides us with a deeper understanding of his account of how physics underlies the brain. Ellis begins by establishing the differences between synchronic and diachronic emergence in order to counter the idea that brain function is determined solely by microphysics in a bottom-up fashion. He then proceeds to spell out how his account of causation relates to the life sciences, especially biology and neuroscience, and gives arguments for understanding the brain as an open system. In doing so, he highlights the significance of diachronic emergence and brain plasticity. In the final paragraphs of the essay, Ellis discusses the role of randomness and its connection to agency and gives arguments pertaining to the idea of the causal closure of the universe and the topic of free will. The chapter thus provides not only new arguments defending Ellis’s view of the brain against counterarguments, but also a detailed overview of his conception of the relationship between physics and the life sciences and how this bears on the connection between the human brain and the human mind. The fourth part of this anthology The Debate on Top-Down Causation and Emergence, is dedicated to discussions of Ellis’s theory in the context of surrounding debates on causation and emergence. It consists of five essays. The ninth chapter, by James Woodward, entitled Downward Causation Defended, argues—as its title suggests—against certain lines of criticism directed at top-down/downward causation. Working from within the context of machine learning and computer science and drawing on work from Ellis and Noble, Woodward begins by offering the possibility of integrating his own interventionist account of causation with the aforementioned perspectives. He then illustrates the resulting philosophical account of top-down causation with the aid of examples from various sciences. The first widespread criticism Woodward refutes is that “wholes” cannot act downwardly on their “parts”, because the synchronous wholepart relationship is not a diachronic causal relationship. He then turns to other objections, such as causal exclusion arguments, by outlining the mistakes common to different forms of such arguments. Woodward does not limit himself to rebutting

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these critiques: he goes on to sketch a more positive account of the work that can be done by the notion of downward causation. The tenth chapter, by Richard Healey, is entitled A Pragmatist Perspective on Causation, Laws and Explanation. Working from a pragmatist perspective in the philosophy of science, it offers an explanation of how it is possible to abandon what he calls the Laplacean vision of causation, according to which the existence of global laws of nature determines the evolution of the world by determining the motion of its basic physical parts, in favour of a pragmatist understanding of (topdown) causation. For Healey, this goes hand in hand with a pragmatist conception of laws and explanation. As a consequence, he argues for a local understanding of causation, which does not reference any laws—contra the Laplacean vision— but focuses instead on the function played by the notions of causation, laws and explanation in our practical and theoretical undertakings. By looking at emergence and top-down causation through the lens of John Conway’s Game of Life, he argues that these notions are better suited to make sense of the phenomena when compared to the Laplacean vision of causation. The eleventh chapter, by Jan Voosholz, entitled Top-Down Causation Without Levels, examines an apparent prerequisite of Ellis’s theory of top-down causation: the idea that nature is ordered by distinct and finitely many levels, each with their own types of entities, relations, laws and principles of behaviour as well as causal relations to their respective neighbouring top- and bottom-levels. Voosholz’s analysis of this “level-picture” of nature makes explicit certain key premises presupposed by this overall framework. He maintains that a closer examination of the relevant issues leads to two surprising conclusions: On the one hand, he argues that a potential critic of Ellis could attack the level-picture, exploiting its vulnerability to certain objections in order to refute the overall theory of topdown causation, genuine complexity and emergence. On the other hand, Voosholz’s investigation reveals that such a manoeuvre on the part the critic would ultimately prove futile. He shows that the theory can be defended by abandoning the levelpicture and that adjusting certain important premises in light of the objections allows us to retain the key features of Ellis’s broader account. The twelfth chapter, by Simon Friederich and Sach Mukherjee, is entitled Causation as a High-Level Affair. It argues against one of the most dominant reductionist arguments against accounts of top-down and higher-level causation, the causal exclusion argument, in favour of non-reductive physicalism as championed by Jaegwon Kim. The counterargument presented by the authors concludes that higher-level causation is a legitimate notion even if non-reductive physicalism holds; indeed, causal relations at the micro-physical level obtain either in a derivative sense, parasitic on higher-level causation, or are so dependent on background conditions as to dilute the term “causal”. This counterintuitive conclusion is supported by first summarising the interventionist response to this particular version of the causal exclusion argument and then focusing on how the difference between sensitive and insensitive background conditions allows the derivation of an argument for the robustness of higher-level causality. Finally, they show how this surprising outcome derives from the previous steps.

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The thirteenth chapter, by Max Kistler, entitled Models of Downward Causation, takes on the causal exclusion arguments for physicalism and against any downward causation from the mind. His conclusion and solution diverges from Friederich’s and Mukherjee’s, yet he also argues for the possibility of downward causation. Kistler holds that we could not make sense of downward causation, especially from the mental and the abstract to the physical, in physicalist terms, because we have not yet found the right model for downward causation. In this chapter, Kistler now analyses two models of causal influences that provide this missing framework. The first model utilises the notion of phase space from dynamical systems theory. Kistler constructs such a model for a case of mental causation, showing that the causal exclusion arguments pose no threat and that downward causation is an unproblematic occurrence. The second model builds on the framework of structural equations which are used in the computer modelling of complex systems to find causal dependencies. Kistler argues that this model respects the principle of causal closure but the exclusion principle, the second premise of causal exclusion arguments, does not hold in this model. He concludes that in both models the exclusion premise is false and takes this as a sign that even physicalists should not endorse it. In the fifth and final part of this Festschrift, George F. R. Ellis replies to each of the contributions in turn. In revisiting each chapter, he not only provides incisive and balanced responses to the assembled perspectives on his work, but also takes the opportunity to situate the multitude of issues that have been raised within a broader scientific and philosophical landscape. We hope that readers will derive as much enlightenment from these contributions as we have and take them as an incentive to continue exploring the implications of George’s unique work. It remains to express our thanks to everyone who has supported us during the process of editing this volume. Special thanks goes to Otávio Bueno, who has time and again—and with astonishing promptness—answered innumerable questions, and to Alex Englander, who has helped immensely with the revision of this introduction and provided frequent advise on our contributions. Finally, we would like to take this opportunity to congratulate you, George, on your birthday—we hope you will continue to provoke and inspire us for many years to come. Institute for Philosophy, University of Bonn, Bonn, Germany

Markus Gabriel

Institute for Philosophy, University of Bonn, Bonn, Germany

Jan Voosholz

References Barbara Drossel and Ellis, George F.R. 2018. Contextual Wavefunction Collapse: An Integrated Theory of Quantum Measurement. New Journal of Physics 20:113025. Clarissa-Marie Claudel, Kumar S. Virbhadra, and Ellis, George F.R. 2001. The Geometry of photon surfaces. Journal of Mathematical Physics 42.2:881–838.

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Clarkson, C., Ellis, G., Larena, J., & Umeh, O. 2011. Does the Growth of Structure Affect our Dynamical Models of the Universe? The Averaging, Backreaction and Fitting Problems in Cosmology. Reports on Progress in Physics 74.11:112901. Ellis, George F.R. 1967. Dynamics of Pressure-Free Matter in General Relativity. Journal of Mathematical Physics 8.5:1171–1194. Ellis, George F.R. 1970. Topology and Cosmology. General Relativity and Gravitation 2.1:7–21. Ellis, George F.R. 1993. Before the Beginning: Cosmology Explained. New York: Bowerdean/Boyars Publishing. Ellis, George F.R. 1995. The Covariant and Gauge Invariant Approach to Perturbations in Cosmology. NATO Science Series C: Mathematical and Physical Sciences 467:1–37. Ellis, George F.R. (ed.). 2002. The Far-Future Universe: Eschatology from a Cosmic Perspective. Philadelphia, London: Templeton Foundation Press. Ellis, George F.R. 2005. Physics, complexity, and causality. Nature 435:743. Ellis, George F.R. 2006. On the Nature of Emergent Reality. In: The Re-Emergence of Emergence. The Emergentist Hypothesis from Science to Religion, eds. Philip Clayton, and Paul Davies, 79–107. Oxford: Oxford University Press. Ellis, George F.R. 2007. Issues in the Philosophy of Cosmology. In: Philosophy of Physics, eds. Jeremy Butterfield, and John Earman, 1183–1285. Amsterdam, Oxford: Elsevier. Ellis, George F.R. 2008. On the Nature of Causation in Complex Systems. Transactions of the Royal Society of South Africa 63:69–84. Ellis, George F.R. 2009. Relativistic Cosmology (Reprint of Varenna Lectures 1971). General Relativity and Gravitation 41.3:581–660. Ellis, George F.R. 2009. Top-Down Causation and the Human Brain. In: Downward Causation and the Neurobiology of Free Will, eds. George F.R. Ellis, Nancey Murphy, and Timothy O’Connor, 63–81. Berlin, Heidelberg: Springer. Ellis, George F.R. 2011. Inhomogeneity Effects in Cosmology. Classical and Quantum Gravity 28.16:164001. Ellis, George F.R. 2012. Top-down Causation and Emergence: Some Comments on Mechanisms. Interface Focus 2:126–140. Ellis, George F.R. 2013. The Arrow of Time and the Nature of Spacetime. Studies in History and Philosophy of Science Part B: Modern Physics 44:242–262. Ellis, George F.R. 2014. On the Philosophy of Cosmology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46:5–23. Ellis, George F.R. 2016. How Can Physics Underlie the Mind? Top-Down Causation in the Human Context. Berlin, Heidelberg: Springer. Ellis, George F.R., and Malcolm A.H. MacCallum. 1969. A Class of Homogeneous Cosmological Models. Communications in Mathematical Physics 12.2:108–141. Ellis, George F.R., and Andrew R. King. 1973. Tilted Homogeneous Cosmological Models. Communications in Mathematical Physics 31.3:209–242. Ellis, George F.R., and Bernd G. Schmidt. 1977. Singular Space-Times. General Relativity and Gravitation 8.11:915–953. Ellis, George F.R., and Marco Bruni. 1989. Covariant and Gauge Invariant Approach to Cosmological Density Fluctuations. Physical Review D 40.6:1804–1818. Ellis, George F.R., and Mark S. Madsen. 1991. Exact Scalar Field Cosmologies. Classical and Quantum Gravity 8.4:667–676. Ellis, George F.R., Macro Bruni, and Peter K.S. Dunsby. 1992. Cosmological Perturbations and the Physical Meaning of Gauge Invariant Variables. The Astrophysical Journal 395:34–53. Ellis, George F.R., Antonio Lanza, and John Miller (eds.). 1993. The Renaissance of General Relativity and Cosmology: A Survey to Celebrate the 65th Birthday of Dennis Sciama. Cambridge, New York: Cambridge University Press. Ellis, George F.R., Nazeem Mustapha, and Charles Hellaby. 1997. Large Scale Inhomogeneity Versus Source Evolution: Can We Distinguish them Observationally? Monthly Notices of the Royal Astronomical Society 292:817–830.

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Ellis, George F.R., and Henk van Elst. 1999. Cosmological Models: Cargese Lectures 1998. NATO Science Series C: Mathematical and Physical Sciences 541:1–116. Ellis, George F.R., and Ruth M. Williams. 2000. Flat and Curved Space-Times. Oxford, New York: Oxford University Press. Ellis, George F.R., and Roy Maartens. 2004. The Emergent Universe: Inflationary Cosmology with no Singularity. Classical and Quantum Gravity 21.1:223–232. Ellis, George F.R., Jeff Murugan, and Christos G. Tsagas. 2004. The Emergent Universe: An Explicit Construction. Classical and Quantum Gravity 21.1:233–250. Ellis, George F.R., David J. Mulryne, Reza Tavakol, and James E. Lidsey. 2005. An Emergent Universe from a Loop. Physical Review D 71.12:123512. Ellis, George F.R., Roy Maartens, and Malcolm A.H. MacCallum. 2012. Relativistic Cosmology. Cambridge, New York: Cambridge University Press. Ellis, George F.R., Denis Noble, and Timothy O’Connor. 2012. Top-Down Causation: An Integrating Theme Within and Across the Sciences? Interface Focus 2:1–3. Ellis, George F.R., Michael Heller, and Tadeusz Pabjan. 2013. The Causal Universe. Krakow: Copernicus Center Press. Ellis, George F.R., and Barbara Drossel. 2019. How Downwards Causation Occurs in Digital Computers. Foundations of Physics 49.11:1253–1277. Gennaro Auletta, Ellis, George F.R. and Luc Jaeger. 2008. Top-Down Causation by Information Control: From a Philosophical Problem to a Scientific Research Program. Interface 5.27:1159– 1172. Hawking, Stephen W., and Ellis, George F.R. 1965. Singularities in homogeneous world models. Physics Letters 17:246–247. Hawking, Stephen W., and Ellis, George F. 1968. The cosmic black-body radiation and the existence of singularities in our universe. The Astrophysical Journal 152:25. Jean-Philippe Uzan, Chris Clarkson, and Ellis, George F.R. 2008. Time Drift of Cosmological Redshifts as a Test of the Copernican Principle. Physical Review Letters 100.19:191303. Jeff Murugan, Amanda Weltman and Ellis, George F.R. (eds.). 2012. Foundations of Space and Time: Reflections on Quantum Gravity. Cambridge, New York: Cambridge University Press. John Wainwright and Ellis, George F.R. (eds.). 1997. Dynamical Systems in Cosmology. Cambridge, New York: Cambridge University Press. Kumar S. Virbhadra and Ellis, George F.R. 2000. Schwarzschild Black Hole Lensing. Physical Review D 62.8:084003. Nancey Murphy and Ellis, George F.R. 1996. On the Moral Nature of the Universe: Theology, Cosmology, and Ethics. Minneapolis: Fortress Press. Nancey Murphy, Ellis, George F.R. and Timothy O’Connor (eds.). 2009. Downward Causation and the Neurobiology of Free Will. Berlin, Heidelberg: Springer. Peter Coles and Ellis, George F.R. 1997. Is the Universe Open or Closed? The Density of Matter in the Universe. Cambridge, New York: Cambridge University Press. Sara I. Walker, Paul C.W. Davies and Ellis, George F.R. (eds.). 2017. From Matter to Life: Information and Causality. Cambridge, New York: Cambridge University Press. Stephen W. Hawking, and Ellis, George F.R. 1973. The Large Scale Structure of Space-Time. Cambridge, New York: Cambridge University Press.

Contents

Part I Applications of George Ellis’s Theory of Causation 1

Physical, Logical, and Mental Top-Down Effects . . . . . . . . . . . . . . . . . . . . . . . George F. R. Ellis and Markus Gabriel

2

Making Sense of Top-Down Causation: Universality and Functional Equivalence in Physics and Biology . . . . . . . . . . . . . . . . . . . . Sara Green and Robert W. Batterman

3

Mathematics and Measurement: Causation and the Mind . . . . . . . . . . . . Otávio Bueno

3

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Part II The View from Physics 4

Strong Emergence in Condensed Matter Physics . . . . . . . . . . . . . . . . . . . . . . . Barbara Drossel

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5

On the Topic of Emergence from an Effective Field Theory Perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Thomas Luu and Ulf-G. Meißner

Part III The View from the Life Sciences 6

The Principle of Biological Relativity: Origins and Current Status . . 117 Denis Noble

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A Macro Agent and Its Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Larissa Albantakis, Francesco Massari, Maggie Beheler-Amass, and Giulio Tononi

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Physics, Determinism, and the Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 George F. R. Ellis

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Contents

Part IV The Debate on Top-Down Causation and Emergence 9

Downward Causation Defended . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 James Woodward

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A Pragmatist Perspective on Causation, Laws and Explanation . . . . . . 253 Richard Healey

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Top-Down Causation Without Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Jan Voosholz

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Causation as a High-Level Affair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Simon Friederich and Sach Mukherjee

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Models of Downward Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Max Kistler

Part V Responses 14

Responses to Part I: Applications of George Ellis’s Theory of Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 George F. R. Ellis

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Response to Part II: The View from Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 George F R Ellis

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Response to Part III: The View from the Life Sciences . . . . . . . . . . . . . . . . 363 George F. R. Ellis

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Response to Part IV: The Debate on Top-Down Causation and Emergence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 George F. R. Ellis

Part I

Applications of George Ellis’s Theory of Causation

Chapter 1

Physical, Logical, and Mental Top-Down Effects George F. R. Ellis and Markus Gabriel

Abstract In this paper, we explore the architecture of downward causation on the basis of three central cases. (1) We set out by answering the question of how topdown causation is possible in the universe. The universe is not causally closed, because of irreducible randomness at the quantum level. What is more, contextual effects can already be observed at the level of quantum physics, where higher levels can modify the nature of lower-level elements by changing their context, or even creating them. As one moves up through higher levels, contextual effects on lower levels occur on various scales within nature, which is crucial in biology in general and the brain in particular. (2) We then argue that there are important logical downward causes. Abstract objects (such as logical principles of intelligibility) have causal effects on material-energetic systems. It can be shown that abstract objects (institutions, numbers, intentionality etc. as well as algorithms and plans) have measurable effects on lower levels, which needs to be accounted for by successful explanations of real phenomena such as intentional action. Intentional action has the form of deductive causation from logical structures to human agency. Without this assumption, we would not be warranted in believing that our physical theories latch onto a universe that is essentially the way we discover it to be. Denying topdown causation on account of the idea that the universe permits only bottom-up constitution of wholes from lower-level elements leads to undermining the very possibility of knowledge and science. Thus, it can be rejected as a global form of explanation. (3) We sketch a model for mind-body interaction according to which the various levels of a human organism together enable the emergence of mental top-down effects. They are necessary conditions for the emergence of human mindedness. Once it is clear that downward causation is a widespread natural phenomenon, the apparent mystery of mental causation (how abstract objects can

G. F. R. Ellis Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] M. Gabriel () Center for Science and Thought, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_1

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cause measurable changes in the universe via our mental representations of them) is, in principle, solved.

1.1 Introduction Compared to weak (epistemic) emergence, strong (ontic) emergence remains a contentious issue (see Humphreys 2016 and references therein as well as Chalmers 2006). One prominent way of drawing the distinction relies on the notion that, in the case of many systems at least, we are incapable of telling whether causally relevant behavior at some higher level can in principle be reduced to causally relevant behavior at some lower level. While it is in fact impossible for us to carry out reductions, even in cases that many philosophers (wrongly) identify as obvious cases for reductionist accounts of relations between levels, some conjecture that in some cases reduction might be impossible in principle. Yet, we reject the idea that the burden of proof is typically on the side of anti-reductionism, because we can know that metaphysical reductionism, i.e. the reduction of all higher levels to one fundamental level, does not correspond to the facts (against the idea that temperature can be given the mechanical description required to demonstrate its reducibility both in principle and in fact, see Atmanspacher (2016) and Bishop and Atmanspacher (2006); for the equally misused example of the alleged identity of water and H2 O, see Chang (2012)). Particular problems concerning the very concept of strong emergence are based on the idea of the causal closure of the physical and the associated claim that topdown-causation from non-physical levels to the physical (paradigmatically mental causation) would at best amount to a form of overdetermination. In addition to this kind of worry, which is ultimately question-begging against the evidence for strong emergence, one might argue that top-down causation is not genuine efficient causation. However, in this article we argue that these worries are side-effects of identifying efficient causation with push-and-pull mechanisms in the universe. For instance, standard ways of formulating counterfactual accounts or interventionist accounts of causation need not assume that efficient causation has this shape. The ontological framework within which we are operating here is pluralistic in the following sense: There really are different domains of objects, which we will label fields of sense (following Gabriel 2015). Claiming that some field of sense is causally closed does not entail that its structure is not constrained by processes on higher levels. These higher levels in turn can have genuine causal powers in all relevant senses, which is associated with the idea of a realistic notion of inference to the best explanation. Causes are what you discover if you identify the best explanation for a phenomenon. To illustrate with a rough example: If Bill is thirsty and is offered a glass of water and a glass of orange juice, he can begin to make up his mind about which drink to accept. Let’s assume he picks the water and drinks it. Then the best available explanation for why a bunch of elementary particles changes its arrangement will

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have to invoke the fact that Bill decided to drink the water. This is a better explanation than one operating on a lower, maybe physically more fundamental level, for it identifies an epistemically more relevant cause for the change of states of the elementary particles. Bill’s decision to drink the water does not undermine the explanatory power of physics at the lower level; he does not violate any law of nature. However, taking his decision to drink the water into account is still a better explanation for why the elementary particles are arranged in a certain way than any explanation of those events that does not take Bill’s decision into account. Thus, there is mental causation in this straightforward sense. This fact becomes most salient in cases where metaphysical reductionism of all causation to an alleged fundamental physical level turns out to involve forms of performative self-contradiction: The scientific, epistemic activity of attempting to reduce one’s own activity of scientific reduction to the fundamental level is unable to so much as grasp what one is doing in theorizing. Reducing theorizing to the fundamental level simply does not make sense. Therefore, at some point or other in any hierarchy of levels, the very idea of metaphysical reductionism evidently becomes incoherent (see Gabriel 2018a). Of course, this argument does not settle the issue of where top-down causation begins. Following Ellis (2016), one prominent option we will pursue in this article maintains that the occurrence of strong emergence requires top-down causation in order that higher levels can have genuine causal powers. In brief, the higher levels decide what can be done, the lower levels do the work, and compatible causation allowing this to happen occurs at all levels simultaneously. There is no privileged level of causation, as emphasized by Noble (2012) in the case of biology (building on the literature starting with Wimsatt (1976a, b), followed by the influential Prigogine and Stengers (1985)). Top-down effects occur across science in general (Ellis 2012a), and in physics in particular (Ellis 2016), even though this is not often sufficiently highlighted. There is currently no scientific evidence that the manifold cases of weak, epistemic emergence could in principle be replaced by models that allow us to construct further models in which all levels are reduced to exactly one fundamental level such that nothing strongly emerges. At least, no such metaphysical account is based on current, actual science. As far as we know, then, strong emergence occurs in the physical sciences’ hierarchy of particles, atoms, crystals, rocks, planets, solar systems, galaxies and so on (see Sect. 1.2 below), in the case of structure formation in the universe, for example, and in phenomena such as superfluidity. As is emphasized by Noble (2008), it is also crucial in biology in general, where epigenetic effects occur, and specifically in evolution, where adaptation to the environment takes place, as emphasized by Campbell (1974). It is not possible to seriously consider the brain without taking top-down effects into account (Ellis 2016, 2018), because perception is contextually embedded and the mind has causal powers. David Chalmers puts it this way:

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G. F. R. Ellis and M. Gabriel The best way of thinking of this sort of possibility [strong emergence] is as involving a sort of downward causation. Downward causation means that higher-level phenomena are not only irreducible but also exert a causal efficacy of some sort. Such causation requires the formulation of basic principles which state that when certain high-level configurations occur, certain consequences will follow. (Chalmers 2006, p. 248)

Chalmers is right that downward causation might occur in the brain, requiring causal incompleteness at the underlying levels for consistency; but he does not take into account that physics itself speaks in favor of such incompleteness because of its quantum foundations. Quantum theory states that outcomes from initial data are determined only statistically; specific outcomes are unpredictable even in principle, meaning that there is sufficient logical and causal space for pervasive top-down causation, which is mediated by time dependent constraints and top-down selection effects, as discussed below. Top-down causation is also a core feature of the functioning of digital computers. It is key to realize here that there are two orthogonal hierarchies: logical hierarchies, such as occur in language and computer programs, and implementation hierarchies, which are realized in physical structures such as the physical structure of brains and computers. Top-down causation takes place in both in a compatible way: the implementation hierarchy enables the logical hierarchy to be causally effective at each level.1 However the idea of top-down causation has been criticized because of the reductionist views of many physicists (see Batterman 2018), and particularly because of the alleged causal completeness of physics at the bottom level (Kim 1998, 1999, 2002), which implies that apparent higher-level emergence must in fact be an epiphenomenon. It is alleged that supervenience triumphs and makes downward causation impossible. The purpose of this paper is to make a solid philosophical case, based on current science on the one hand and the ontology presented in Gabriel (2015) on the other, that top-down causation not only can occur, but indeed does occur across the natural, biological, and social sciences. In particular, we will counter the supervenience argument below (Sect. 1.3.5). In what follows, we discuss the ontology of downward causation and why it is possible (Sect. 1.2). We will include a rebuttal of arguments based on supervenience (Sect. 1.3), contextual arguments as to why it must indeed exist (Sect. 1.4), and a discussion of top-down effects in logical hierarchies (Sect. 1.5).We also suggest a model for mind-body interaction and for social ontology (Sect. 1.6). The conclusion follows in Sect. 1.7.

1 In

the case of computers, this magic is performed by compilers or interpreters linking abstract machines at different levels (Ellis 2016, ch. 2).

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1.2 The Ontology of Top-Down Causation Ontology is the systematic response to the question of what exists (Gabriel 2015). To exist within the universe is to be an entity that stands in causal relations: an entity that exists must have a causal effect on something else. Both physical entities (objects) and abstract entities (non-objects) exist. Examples of the former are planets, bricks, tables, machines, animals, crystals, and molecules; we take their existence as our foundation (all levels are equally real, (Wimsatt 1976a, b, 2007): see Eddington (1927) for the case of physics, and Noble (2012) for the case of biology). Examples of the latter are algorithms, plans, corporations, laws, and money; we take their existence as proven by their demonstrable causal effects on the former. The property of existence is multiply realizable: what it is for an entity to exist depends on the level on which it is encountered. This applies to both physical entities (objects) and abstract entities. Physical entities and abstract entities can stand in causal relations, which is most evident in the case of intentional action and social contexts (Friedel 2019).

1.2.1 Levels and Scales In light of this background, we can clarify the language of levels/scales for the universe in terms of an ontology of fields of sense or interaction. Fields (or domains) are defined (Gabriel 2015) by local parameters of intelligibility (a logic) for their entities, such that all entities in the field are related to at least one other entity in the field by such parameters;2 if they are physical objects, they will3 be restricted in both space and time. A sense is a rule for individuating a domain. A scale is a field of sense/interaction with its specific objects related by the same kind of interaction logic (see Ellis and Kopel 2019 for examples). The various scientific disciplines and their branches are ideally ordered across an axis of levels/scales: particle physics, nuclear physics, atomic physics, chemistry, and so on, branching at higher levels into branches characterized by physical causation on the one hand and biological causation on the other (see Table 1.1). Micro/macro-distinctions are not limited to physics, but play an equally important role in biology,4 sociology, economics, as well as in abstract relations (language, mathematics, and algorithms, for example) and in artefacts constructed by design (Simon 1996). Generally, the logic for the objects of a given arrangement of target systems defines causal parameters for the elements in the field. There is no overall theory for all fields such that it would even be possible in principle 2A

field must have boundaries that define its limits. If an entity is not related to something in the field, it does not belong in it. 3 Except perhaps in the case of the entire Universe. 4 For details in the case of biology, see Campbell and Reece (2005).

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Table 1.1 The basic hierarchy of structure and causation for inanimate matter (left) and for life (right) as characterized by academic disciplinesa Level 10 Level 9 Level 8 Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1

Inanimate matter Cosmology Astronomy Space science Geology, earth science Materials science Physical chemistry Atomic physics Nuclear physics Particle physics Fundamental theory

Living matter Sociology/economics/politics Psychology Physiology Cell biology Biochemistry Chemistry Atomic physics Nuclear physics Particle physics Fundamental theory

From Ellis (2016, p. 6) a This representation has higher length scales at higher levels, which in physics terms correspond to lower energies. The physics literature tends conversely to represent higher energies (smaller length scales) at the top. We stick with the convention used in biology (e.g. Campbell and Reece 2005)

to reduce explanations of the behavior of elements in all fields to just one field (say fundamental physics). There is no maximal discipline studying absolutely everything there is. Computer algorithms, for example, cannot be explained in physical terms (Knuth 1973); but they nowadays have key causal effects, for example in factories, aircraft, social media, and Artificial Intelligence applications. Objects are embedded in facts, i.e. in structures (specific features), that can in principle become realizations of a theory that applies to generic features, of which the specific features are special cases. Causation should not be modelled on macroscopic push-and-pull mechanisms, which do not even include electromagnetism or gravity in physics, for example, let alone the cell signaling networks and metabolic networks of biology or the causal effects of computer programs. Therefore, in this paper we adopt a counterfactual theory of causation that is capable of characterizing causation by both physical and abstract entities. The relation of causation that can hold between entities consists in the fact that variation of properties in one object systematically changes the properties in the other object. This includes abstract objects: if the logical structure of a given field were different, its objects would be different too. The actual number or distribution of objects in a given space of mutual influence can have decisive consequences for the behavior of a target system theoretically constructed out of the elements. Some mathematical structures carve the universe at its joints in such a way that referring to mathematical objects and structures is an irreducible part of the right explanation of certain phenomena; for example, this occurs in physics (Newton’s laws of motion, Maxwell’s equations of electromagnetism, and so on). In other cases, a causal network may give the best explanation (Pearl and MacKenzie 2018), as for example in the case of metabolism (Rosen 1958). According to the counterfactual theory we adopt, elements in a network

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sufficiently individuated by a theory are causally related to each other if and only if facts would have been different, had one of the elements behaved otherwise or been different. To be an element in a causal order is to make a theoretically significant difference (see Beebee et al. 2017 for a state-of-the-art overview).

1.2.2 Abstract Objects and Human Agency There is no known physical fact that rules out that abstract objects can stand in causal relations. Hence, causation is not restricted to spatio-temporal relations among determinate material-energetic objects. In addition, no combination of known natural-scientific facts yields naturalism, i.e. the view that all there is, is the spatio-temporal manifold best explained by natural science (Gabriel 2017). The humanities and social sciences explain the behavior of phenomena whose existence depends on the concepts deployed by the elements of their target systems, which are often not of a physical nature (shame and pride, for example, or nationalism and sense of identity) but are manifestly causally efficient. Computer science explains outcomes, such as symbols on a screen, through concepts such as programs and algorithms (Knuth 1973), which are not in themselves physical, although they must be realized in physical terms in order to be causally effective. Many such realizations are possible. Human agency can be demonstrated to have a causal effect on the physical world (Ellis 2005, 2016; Drossel 2021): without it, the existence of aircraft, houses, tables and chairs, wine and wine bottles, books, scientific knowledge-acquisition and so on is inexplicable. If human agency (which includes the construction of scientific theories and associated knowledge claims concerning the causal order of a given target system) had no causal effect on the physical world, we could not so much as formulate the interventionist picture of causation at the heart of modern science. In order for there to be experiments, measurements, and theories, the human practice of scientific discovery and documentation has to be in place. Via technology, abstract science has a causal impact on the universe. Science is not a mirror of the world, but itself a complex target system, which essentially relies on the stability of social systems that can be investigated by the humanities and social sciences. Science itself is among the target systems of science.

1.2.3 Top-Down Causation and the Reality of Levels Scientific theories, humans, mathematical structures, etc. are among the objects that stand in causal relations. The concept of top-down causation (Campbell 1974; Noble 2012; Ellis et al. 2012; Ellis 2016) describes causal effects from a higher level of reality to a lower level of reality. What counts as a higher level in comparison with a lower level is the outcome of scientific research on a given field. There is therefore

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no overall hierarchy of levels running through the universe, but rather different levels relative to different explanatory endeavors. The various subdisciplines of physics are related to each other by a physical scaling system (physical size) related to an inverse scale of binding energy (smaller entities are more tightly bound than larger ones). An example of how one defines such levels in physical terms is given by Rueger and McGivern (2010). The separation of levels with emergent autonomy is possible because of the multiple realizability of higher levels at lower levels (Batterman 2018), as discussed below. Within this physical scaling system, it turns out that there is no conclusive evidence for a reduction of macro-levels to lower levels. On the contrary, assuming the causal closure of physics on an as-yet undiscovered ultimate micro-level is incompatible with current physics because of quantum uncertainty at the lower levels, both in terms of the Heisenberg uncertainty principle (one cannot set data on particle positions and momenta with arbitrary accuracy) and because of the occurrence of quantum events: collapse of a wavefunction superposition to an eigenstate involves irreducible uncertainty. This takes place in a contextual way (Drossel and Ellis 2018), for example, whenever a quantum measurement takes place. Thus, this is itself a key example of top-down causation. Chemistry is a key case of emergence: for example, the “aromaticity that characterises the benzene molecule is obviously not present at the level of the atomic components; it is a property arising in the ensemble of the particular atomic configuration, it is an emergent property” (Luisi 2002, p. 188). Furthermore, the classic supposed prime example of bottom-up emergence in physics – the kinetic theory of gases, whereby molecular properties at the micro level are coarse grained to give macroscopic properties of a gas – fails to account for the crucial Second Law of Thermodynamics: the entropy S of an isolated system increases with time: dS/dt > 0 (Eddington 1927). This is because of Loschmidt’s Paradox: Boltzmann’s beautiful derivation of the H-theorem works equally well for both directions of time (set t → t : = −t, and the same proof that showed dS/dt > 0 will show that dS/dt > 0). An assumption about large-scale correlations in the past has to be added to the local physical description in order to derive the H-theorem in the forward direction of time (Penrose 2016). Local arrows of time are determined in a contextual way by the conjunction of the cosmological direction of time and special low-entropy initial conditions for the matter in the universe (Albert 2009; Drossel and Ellis 2018). This top-down effect has to function in this way, because the relevant microphysics is time symmetric.5 Upward emergence, downward realization, and horizontal causation occur at every level according to the logic governing individual levels and relationships between specific levels. All levels are equal in that respect. The principle of biological relativity (Noble 2012) can be generalized to ontology: each level is equally real. There is no privileged standpoint from which we can present a complete system of levels, with their local structure as emerging from one particular

5 The

weak time asymmetry of the weak interaction has no effect on the ongoing physical interactions that underlie chemistry and biology on Earth.

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level. Strong emergence abounds: at higher levels causal facts are established that cannot be deduced from knowledge of the causal structure of a lower level; an important physics example is superconductivity (Laughlin 1999). There is no a priori knowable architecture of the universe such that we are entitled to assume that there is only one causally active level on the basis of some meta-physical insight. Reality is not exhausted by any known theory designed to explain the behavior of elements within its explanatory reach. According to the epistemic theory of reality, the hallmark of the real is that it can become the object of fallible knowledge claims (Gabriel 2018a, b). Scales and causation across scales are real. The division of scientific labor ideally adapts itself to the structure of reality, because different kinds of relations hold in each of the special sciences, each characterized by its own vocabulary and concepts. We have no good reasons to deny either ontology pluralism (there are many scales causally connected by downward and upward processes, including non-physical objects and systems) or epistemological pluralism (there are different disciplines with local logical standards and methods, designed to latch onto the objects in their target domain).

1.2.4 Effective Laws and Causal Closure A key point here is that any effective theory ETL at a level L, stating a phenomenological description of a verifiable effective law, is about an ontological reality and valid at that level. Yet this is not at all the same thing as claiming that that level is causally closed. Indeed, precisely because of the mix of upward and downward causation that occurs, this is never the case (Ellis 2020). What is true is that given the effective theory ETL at level L, it gives a unique map (exact or statistical) (1) between initial data and outputs at that level. But what entities occur in that theory, where the initial data comes from, and the source of any constraints that occur in the theory (1), all have to be specified in order to attain causal closure; and that, as is discussed in depth in Ellis (2020), is an inter-level affair (see also the discussion in Paoletti and Orilia 2017). An example is digital computers (Ellis and Drossel 2019) where the purposes of the algorithms (processing pictures, sending emails, analyzing user preferences, controlling an aircraft, and so on) determine which electronic gates open and close and so allow currents to flow at the physical level. Another example is that the COVID-19 pandemic has resulted in airline regulations (abstract entities), which have resulted in thousands of aircraft (macro-level entities, corresponding to Level 9 in Table 1.1) not flying, which has in turn caused billions of particles making up those aircraft (Level 1) to have different spacetime trajectories than would otherwise have occurred. Causal closure involves all levels from Level 1 to Level 10 (where that decision was taken). The decision regarding flying was an outcome of Final Causation, the goal of saving lives reaching down to have material consequences. Thus, it is simply not true that either level 1 or level 2 is causally closed, as these examples conclusively demonstrate (and see Ellis 2020). The alleged

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overdetermination at Level 1 does not occur, because it is based on a false premise (causal closure occurring at a single level). This does not happen, because of interlevel causation; mechanisms enabling this are discussed in Sect. 1.3.2. In any case, physics is not causally closed, because of quantum uncertainty at its foundations. Efficient Causation An interesting question is how this all relates to the idea of efficient causation. We propose that validity of (1) at a level L is a statement of the existence of Efficient Causation at that level: that is, the idea of efficient causation is a level-dependent idea, and it in fact occurs at each well-characterized emergent level. For example, in a famous quote, Francis Crick attributes real causal powers to neurons and genes (see Sect. 1.4.3): he sees them as doing real causal lifting – even though they are enabled by underlying physical interactions and forces. Thus, he attributes efficient causation to level 6, despite it emerging from levels 1 and 2. We maintain that the decisions leading to COVID policy also do real causal lifting. Thus Noble’s Principle of Biological Relativity (2012) can be restated: Efficient Causation occurs at each level.

1.3 Why It Is Possible Top-down effects occur in physical and biological systems between each pair of adjacent levels, chaining down from higher to lower levels (Noble 2008, 2012; Ellis 2017) and thereby reaching down from the biological to basic physical levels (Ellis and Kopel 2019). Note that we are not claiming that there is either a topmost level or a bottom-most level; rather, we are claiming that causation can occur between any two neighboring levels, thus chaining down, for example, from the mental or social level to the level of electrons and protons. In order to establish that this is possible, Sect. 1.3.1 states the basic way top-down effects occur in physical and biological systems via constraints. Section 1.3.2 argues that there is no causal closure at the bottom levels; Sect. 1.3.3 considers various ways that top-down effects alter the nature of lower levels; Sect. 1.3.4 considers the key issue of the multiple realization of higher-level structure and function at lower levels, and Sect. 1.3.5 uses the concept of diachronic emergence to counter the argument from supervenience. Finally, Sect. 1.3.6 looks at attempts to determine higher-level outcomes in truly complex systems in a purely bottom-up way.

1.3.1 Constraints on Lower Levels The first basic way in which top-down effects occur is via higher-level constraints on lower levels in modular hierarchical structures (Salthe 1993; Juarrero 1998, 2000;

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Blachowicz 2013). In Aristotelian terms, this is Formal Causation. Note that this does not override the lower-level physics or violate physical causation in any way: it rather conscripts lower-level processes to higher-level purposes due to the specific nature of the constraints (Juarrero 1998, 2000; Ellis 2016). This may occur in straightforward physical terms, as with constraints due to physical entities such as physiological systems or neural networks (Campbell and Reece 2005) or biomolecules (Ellis and Kopel 2019) or wiring connectivity in digital computers; or in terms of networks of interactions such as cell signaling networks (Berridge 2005), which occur because of the presence of particular families of molecules in settings such as a cell cytoplasm contained within a cell wall. They are conveniently studied by graph-theoretic representations of networks, which are widely employed in systems biology and neuroscience. “As a result of such interconnections mechanisms often exhibit complex dynamic behaviors that constrain how individual components respond to external inputs, a central feature of top-down causation” (Bechtel 2017, p. 253). They can often be usefully summarized in diagrams of the phenomenon or mechanism which integrate a variety of data to construct a single, coherent representation (Sheredos and Bechtel 2017). Overall, this is a form of structural explanation (McMullin 1978). The results are very complex: for example, parts and operations of mechanisms provide constraints that direct the flow of free energy, enabling the mechanism to perform work. Many of the constraints in mechanisms are flexible, capable of being altered through work performed by other mechanisms. These other mechanisms exercise control. They too involve flexible constraints that are capable of being operated on by yet other mechanisms. (Bechtel 2018, p. 590)

The result is the kind of top-down causation emphasized by Juarrero (1998, 2000) and Noble (2008, 2012), based on his detailed modelling of heart physiology (Noble 2002), and by Kandel in the case of the brain (Kandel 1998, 2001). Thus, biological variables can reach down to the physics level and co-opt physical processes (proceeding according to the laws of physics, such as energy minimisation in molecular systems) to fulfil biological purposes. An example is chemotaxis: bacteria moving towards food and away from poisons (Müller et al. 2002). The concept of “food” and “poison” are not physics concepts: they are essentially biological and have no physics definition (see Brandom 2001). However, their gradients have causal effects in terms of bacterial motion, enabled by the underlying physics. This is enabled by the complex physical structure of the bacteria (Wadhams and Armitage 2004), in turn enabled by time-dependent potential terms in the underlying Hamiltonian at the microphysics level. The result is very sophisticated: Despite its relative simplicity, the operation of the E. coli chemotaxis network is highly refined and evolutionarily optimized at many levels. For example, recent studies revealed that the network adjusts its signaling properties dependent on the extracellular environment, apparently to optimize chemotaxis under particular conditions. The network can even utilize potentially detrimental stochastic fluctuations in protein levels and reaction rates to maximize the chemotactic performance of the population. (Sourjik and Wingreen 2012, p. 262)

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1.3.2 No Causal Closure of the Bottom Levels Top-down causation to the physics level is possible because, despite what is often claimed, physics is not causally complete at the bottom levels. Hence lower-level causation is not overdetermined. This is so for three reasons: existence of quantum uncertainty, time-dependent constraints, and time-dependent higher variables that influence lower-level outcomes. (a) Firstly, quantum uncertainty prevents the causal completeness of physics at the bottom level (Drossel and Ellis 2018). If one tries to deny this by interpreting quantum theory in a way that keeps it causally closed against all odds, the measurement problem becomes unsolvable (it is not a unitary process). If physics were complete at the lowest level currently known (quantum physics), nothing above that level could enter into horizontal, let alone vertical causal relations. Therefore, measurements would not really take place, because they would not take place on the lowest level currently known, which means even if the universe were causally complete on the lowest level, this could not be scientifically known. This shows that the idea of causal closure on the bottom level of quantum physics is incoherent. Quantum physics outcomes are crucially affected in a top-down way (Drossel and Ellis 2018): consider, for example, whether the apparatus used to detect radiation measures intensity or polarization, the experimenter’s act of designing and constructing the apparatus with particular sensitivities, and the act of initiating the relevant interactions by turning the apparatus on at a specific time. Contextual Wavefunction Collapse (CWC) is a possible solution to the measurement problem, which combines the Copenhagen interpretation with a realistic contextual account of the role of measurements. Given that the quantum level is neither causally complete nor causally sealed off from measurement (which would make quantum physics as a discipline impossible), downward causation from the classical level of the laboratory to the quantum level has to occur. Actually, even classical physics is not deterministic, because it is not possible to set initial data with infinite precision (Del Santo and Gisin 2019). (b) Secondly, time-dependent constraints change lower-level dynamics in Hamiltonian systems. What happens at lower levels is channeled by constraints C(xi ) = 0 on the lower-level variables xi due to higher level structures or boundary conditions. For example, a ball of mass m free to move in an unconstrained way falls vertically to the ground if released from rest, but if it is constrained by a rod to move at constant distance L from a hinge, it will move on a circular arc instead: the constraint is C (x, y) := x 2 + y 2 − L2 = 0, L = L0 = const.

(1.1)

The constraint changes free fall of the ball into the motion of a pendulum (consequently altering the motion of all the billions of particles that comprise the

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ball). However, Hamiltonian dynamics can be subject to time-dependent constraints C(xi ,V(t)) = 0, driven by higher-level variables V(t). This is true, for example, if the distance of the ball from the hinge is controlled by an activator so that L = L0 in (1) is replaced by L = L(t), altering the motions of all the particles comprising the ball. The existence and uniqueness theorems for Hamiltonian systems (which are the basis for the claim of the causal completeness of physics: the initial data uniquely determines outcomes) do not hold for systems with time-dependent constraints C(t). It is the time variation of these constraints that then determine the outcomes, rather than just the initial conditions (see Ellis and Kopel (2019) and Ellis and Drossel (2019)).6 Commonplace physics examples are turning on and off a light switch and alteration of the setting of a thermostat coupled to a heater in a hot water cylinder (the setting of the thermostat is the higher-level variable that controls lower-level outcomes: flow of electrons in a wire and speed of motion of water molecules). In biology, constraints on molecular flows and hence electron movements are controlled by biological macro-variables in cell signaling networks (Berridge 2005) and gene regulatory networks (Noble 2012; Ellis and Kopel 2019). Specific examples in the case of the heart are given by Manning (2019), and in the case of the brain by Kandel (2001). Ellis and Drossel (2019) discuss the case of digital computers. In each case, the causal powers of mechanisms are grounded in timedependent, variable constraints (Winning and Bechtel 2018). (c) Thirdly, time-dependent macro variables act down to the physical level. What happens at lower levels may depend on higher-level dynamics through the values of macro variables VJ (t) that control the lower-level dynamics,7 and change with time according to higher-level dynamics. In that case, it is again true that what happens at the micro level is not determined by the initial data (xi (t0 ),p i (t0 )) alone. Examples are: • Nucleosynthesis in the early universe, where the temperature-time relation T(t) = a t-1/2 determines nuclear outcomes (amounts of Helium, Deuterium, and Lithium produced) and is itself controlled by the cosmological density parameter ρ(t) at that time: a top-down effect from cosmological parameters to nuclear scales (Dodelson 2003; Peter and Uzan 2013). • Structure formation in cosmology, where physical outcomes depend both on the rate of expansion of the universe (the Hubble parameter H(t)) at that time as well as the cosmological densities ρ bar (t), ρ dm (t), ρ rad (t) and pressure prad (t) (Dodelson 2003, Peter and Uzan 2013). It is because of this top-down effect on astronomical structures that measuring matter and radiation power spectra is the best way to determine the basic cosmological parameters (Ellis 2017).

6 The

relevant equations for a simple example are given in the Appendix of Ellis and Kopel (2019). difference from the previous case is that it was focussed on Hamiltonian dynamics. In this case it can be far more general, for example cell signalling networks or neural networks.

7 The

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• A biological example is the control of the reading of the genome in a cell through the epigenetic processes mediated by gene regulatory networks, which through signaling molecules respond to higher-level conditions (Gilbert and Barresi 2020; Noble 2008, 2012; Kandel 2012; Berridge 2005). Thus, gene regulatory networks control tissue-specific expression of proteins through “go-between” molecules (Gilmour et al. 2017). • An ecological example is the increasing acidity of our seas, which is threatening many species of marine life because of the increased concentrations of atmospheric CO2 due to global climate change (Deweerdt 2017). • A neuroscience example is the behavior of C Elegans neural networks during sleep (Nichols et al. 2017). A global brain state underlies sleep, which is an emergent property of neuronal networks; their dynamics then converge towards a fixed point. Also, circadian rhythms in humans are controlled at a systems level via the central clock in the suprachiasmatic nucleus which controls expression of core clock genes (Bass and Lazar 2016). • The logical analogue in the functioning of digital computers is passing of global variables to program’ submodules.

1.3.3 Top-Down Alteration of Lower Levels Another basic way top-down effects occur is via alteration of lower-level entities and variables. In Aristotelian terms, this is Material Causation, and the key point is that in real biological circumstances, it has a time-dependent element. It sets the stage for Efficient Causation at each level, shaping physical outcomes by altering the elements on which physical laws act. The “billiard ball” model of emergence, based on the kinetic theory of gases which leads to an understanding of gas properties by coarse graining (Penrose 1979), is highly simplified to explain very special circumstances and is incorrect in many emergent situations. This is because there are three key ways in which higher-level features alter lower-level elements to suit higher-level purposes. (a) Nature of lower-level elements Higher-level contexts alter the nature or properties of lower-level elements in key ways (Ellis 2016). A physics example is that a neutron is unstable with a half-life of 10 min when on its own; when bound into a nucleus, its half-life is billions of years; indeed, the internal structure of a nucleon—a proton or a neutron—depends on its environment (Feldman 2019). Again, a free electron interacts with radiation completely differently than when bound in an atom, or in the conduction band in a metal. A biological example is that cells in a multicellular animal are pluripotent at birth (they can become anything) but then become specialized to particular types (bone, hair, skin, neurons, etc.) through developmental processes (Gilbert and Barresi 2020), so as to fulfil their physiological function. The properties of

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the stem cells alone cannot account for the specialization, which is evidence of top-down causation. (b) Existence of lower-level elements Higher-level contexts can create lower-level elements or relations (Ellis 2016), and/or provide the essential context for their existence. A first physics example is the band structure of solids (Simon 2013), the bands (determining if it is a conductor or insulator) being fixed by the specific crystal structure. A second is super-conductivity: the Cooper pairs of electrons that underlie this effect (Phillips 2012) can exist only because of a specific crystal structure whose distortions allow the existence of the Cooper pairs. The same is true for the phonons that underlie many effects in condensed matter physics (Simon 2013) and all the other quasiparticles that occur (Venema et al. 2016). A third are the topological states that are of such interest at present in solid state physics (Qi and Zhang 2011; Keimer and Moore 2017; Tokura et al. 2017). These are irreducible to lower-level terms precisely because they are topological and hence non-local. Particularly striking is the existence of fractionally charged quasi-particles in the Quantum Hall Effect (Laughlin 1999). In biology, the component entities in all symbiotic relationships cannot survive without the other; an obvious example is the human body, where the individual cells depend for their existence on the body as a whole, and specifically on the functioning of the heart, pumping blood so as to reach every single one of the 1013 cells in the body. Within minutes of the heart failing, those cells die. We suggest that a good way to describe all these effects is Top-down Emergence, for the relevant lower-level entities emerge because of particular higher-level conditions. (c) Top-down selection: tamed randomness A key form of top-down action is that of the selection of entities from an ensemble, resulting in a more ordered ensemble according to the selection criterion. This can take place in two ways: direct selection of lower-level elements, and selection of lower-level elements via selection of higher-level elements. In both cases, the phenomena resemble those discussed in (a) and (b): the nature, and even existence, of lower-level elements is determined by the higher-level context, so ordered states come into existence that were not there before. 1. Direct selection of lower-level elements: the classical physics example is Maxwell’s Demon, where molecules are let through a selection gate if and only if their speed v is greater than some selection level v0 . Separation and purification processes are a key part of physics, chemistry, microbiology, and engineering, for they require pure materials or specimens to work on: thus centrifuges, mass spectrometers, and so on are important parts of a lab (Ellis 2016). This is top-down action from the apparatus to the lower-level constituents, with a key causal aspect being the separation criterion. A key quantum physics example is state vector preparation (Ellis 2012b), which is a non-unitary process.

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2. Multi-level selection: Indirect selection of lower-level elements via selection of higher-level elements is key to all biology. Survival occurs at the level of the individual, who either lives to reproduce or does not; if she does, that fact chains down to the genome she has inherited and will in turn pass on (in modified form) to her children. However, the survival of the individual is conditioned (in social animals) and then enhanced by being a member of a group, so group characteristics (such as a symbolic ability leading to development of language, money, and mathematics) enhances the survival chances of individuals in the group who have the genes that firstly underlie such capacities and secondly underlie the will to form such groups (Dunbar 2009, 2016). Selection is for genotypes that will lead to the needed metabolic networks, gene regulatory networks, and proteins (Wagner 2014) that will enable the necessary physiology to allow this all to happen to come into being through appropriate developmental processes. 3. There is a huge degeneracy in the genotype to phenotype map (Wagner 2014), and one only has to select one genotype from all those in the equivalence class that lead to necessary higher-level functions (such as sight); this is the multiple realizability of higher-level needs at lower levels, as discussed in Sect. 1.3.4. Biology has a huge random element at the molecular level; it is this variability that provides the ensemble of possibilities from which higher-level needs can be satisfied (Noble and Noble 2018). The lower-level elements are then adjusted to those needs.

1.3.4 Multiple Realization Higher-level functions and structures are multiply realized at lower levels, both in physical and abstract cases (Rosen 1958; Mikulecky 2000). This allows for the emergence of autonomy of higher levels (Batterman 2018). Whenever such a multiple realization occurs, this is an indication that top-down causation is occurring (Auletta et al. 2008); varying a macro variable causes selection of any one of the equivalence class of lower-level changes that correspond to this higher-level change. For example, in classical physics, the same pressure P and temperature T of gas in a volume V can be realized by billions of different arrangements of molecules at the lower levels (Penrose 1979); the associated top-down causation is decreasing the volume V so that billions of molecules at the lower-level move at higher speeds v, resulting in a higher pressure P and temperature T according to the perfect gas law at the macro scale. As regards biology, in the case of genetics, vast numbers of different genotypes can lead to the same phenotype (Wagner 2014); Darwinian selection takes place in terms of phenotype properties, which then chain down to select any one of the billions of genotypes that result in this more adapted phenotype. In the case of neural networks, there are many different detailed connectivity patterns that can result in the same higher-level performance, such as letter recognition.

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The true causal elements at lower levels are equivalence classes that all correspond to the same higher-level element (Ellis 2016, pp. 19–122); these are the ‘natural kinds’ in terms of which relationships between elements of a field can be defined.

1.3.5 Supervenience and Diachronic Emergence The classic argument against strong emergence is based on the idea of supervenience, as stated particularly strongly by Kim (1998, 1999, 2002). However, this argument has been countered in various ways, see e.g. McGivern (2008). Our view is shown in Fig. 1.1. Synchronic emergence is trivially subject to supervenience in those cases where the current state L1 (t0 ) of the lower-level variables at time t0 uniquely determines higher-level outcomes L2 (t0 ) at that time in a bottom-up way: L1 (t0 ) → L2 (t0 ) L2(t0)

L2(t-1)

(1.2)

L2(t0)

L2(t-1)

L1(t0)

L1(t-1)

L2(t0)

C(t)

L1(t0)

(a)

L1(t-1)

(b)

L1(t0)

(c)

Fig. 1.1 Synchronic and diachronic emergences (a) (Left) Synchronic emergence: The lowerlevel state L1 (t0 ) at time t0 uniquely determines the higher level state L2 (t0 ) at the same time (vertical solid line) (b) (Middle) Diachronic emergence mechanism: The lower-level state L1 (t−1 ) at time t−1 uniquely determines the higher-level state L2 (t−1 ) at that time. The later lower-level state L1 (t0 ) at time t0 (t and a lower case number 0) depends both on L1 (t−1 ) and on time-dependent constraints C(t) on dynamics at the lower level that are determined by higherlevel variables at time t−1 (Sect. 1.3.1b, and Ellis and Kopel 2019). The lower-level state L1 (t0 ) at the later time t0 then determines the higher-level state L2 (t0 ) in a way that has been determined by the higher-level state L2 (t−1 ), resulting in the higher-level dynamics L2 (t−1 ) → L2 (t0 ) given by combining L1 (t−1 ) → L1 (t0 ) and L1 (t0 ) → L2 (t0 ) (c) (Right) Diachronic emergence outcome: The resulting higher-level action L2 (t−1 ) → L2 (t0 ) is carried out according to the relevant higherlevel logic, enabled by the underlying constrained lower-level map L1 (t−1 ) → L1 (t0 ) as in (b). The emergent diachronic map L1 (t−1 ) → L2 (t0 ) (purple diagonal line upwards to the right) is thus controlled by the initial higher-level state L2 (t−1 ) which determines L1 (t0 )

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(that is the essential core of supervenience; see Fig. 1.1a). Note here that historic events will, in essence, be coded in L1 (t0 ); for example, the complete state of a living cell is determined in every detail (not just the DNA and RNA) by its past history; similarly, the detailed state of a brain (its neuronal connections plus current state of excitation) fully represents past memories and learnt abilities; this is the foundation of synchronic emergence (Fig. 1.1a). However, diachronic emergence is quite different (determined by relevant timescales, see Ellis, Chap. 8). The issue is how the state L1 (t0 ) arose in the first place. As indicated above (Sect. 1.3.1b), it was determined from the lower-level state L1 (t−1 ) at a previous time t−1 via lower-level dynamics controlled by timevariable constraints C(xi ,t) or macro variables VJ (t). Thus, diachronic emergence is the map {L1 (t→1 ) → L2 (t0 )} given by L1 (t−1 ) → L1 (t0 ) → L2 (t0 ) .

(1.3)

Consequently, in general there is no unique map L1 (t→1 ) → L2 (t0 ) comparable to (1.2), because (see Sect. 1.3.1) the map L1 (t→1 ) → L1 (t0 ) is not, in general, uniquely determined by the lower-level dynamics: it may be shaped in a top-down way. Thus, diachronic emergence does not lead to unique higher-level outcomes at a later time from lower-level states at an earlier time (see Fig. 1.1b): top-down causation determines diachronic outcomes (Fig. 1.1c). An application in the case of the brain is as follows: knowledge of Maxwell’s equations in an engineer’s mind is causally effective in the real world, for example through her design of a cell phone. One can claim that if you were to reproduce every neuron and synapse in her brain B together with their states of excitation in a duplicate brain B , then this brain would be in an identical state and hence have identical thoughts, whereby Maxwell’s equations would be equally causally effective in both brains. This is synchronic emergence, which is thus claimed to show that those thoughts are epiphenomenal consequences of the electronic and ionic activity in either B or B , which are identical: they are “nothing but” consequences of these lower-level phenomena. However, the question is: how did Maxwell’s equations come to be realized in the precise details of the neural networks in brain B (and hence in brain B )? That came about through processes of social learning, through which the engineer learned about the discoveries of the nature of electromagnetism over time, via the communal efforts of many scientists, culminating in their formalization in Maxwell’s equations. Both these discoveries and her learning about them were processes of adaptive selection of hypotheses and their adoption or rejection in the light of evidence: the processes of scientific discovery and of learning respectively. The initial states of the brains were the result of a plethora of top-down processes. Without these processes of diachronic emergence there would be no detailed neural network underlying the thought experiment. Multiple realization is possible (Sect. 1.3.4); the mathematical form of Maxwell’s equations can be represented in the brain through a huge number of alternative synaptic connections between the 1011 neurons in the cortex. Knowing

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Maxwell’s equations is thus diachronically conditioned (caused) by top-down effects and multiply realizable at later stages after their discovery.

1.3.6 Modularity and Interactions Between Levels The result of all the above is complex interactions between levels that depend on the modular nature of the hierarchical structure, which underlies stability (SalesPardo 2017). An analysis of how this multilevel interaction occurs in biochemical networks is given by Boogerd et al. (2005), who demonstrate in detail how [i]n general, the (dynamic) behavior of A is not simply the superposition of the (dynamic) behaviors of its subsystems studied in isolation. Dynamic interactions can bring about qualitatively new behavior in complex systems. This is precisely where prediction of system behavior on the basis of simpler subsystems fails. We cannot predict the behavior of the components within the entire system and so cannot predict systemic behavior. This is emergence, with novel system behaviour that cannot be predicted on the basis of the behavior of simpler subsystems. (Boogerd et al. 2005, p. 156)

Similarly, it takes place in physiology, as is discussed in depth by Noble (2002, 2008), and specifically in the case of the brain (Scott 1999) and hence the mind (Donald 2001; Gabriel 2017).

1.4 Contextual Considerations: Evolution, Cosmology, and the Bottom Level The necessity of the existence of strong emergence is shown by two examples: emergence in an evolutionary context (Sect. 1.4.1) and emergence in a cosmological context (Sect. 1.4.2). These examples give conclusive proof that the downward causation needed for strong emergence to be possible must indeed occur. Furthermore, emergence takes place in a context where the bottom level is unknown (Sect. 1.4.3), which clearly creates grave problems for any claim that higher-level effects are a bottom-up consequence of conditions “at the bottom-most level”. If one makes that claim, what level is supposed to be the bottom level at which the “real action” occurs? The only standpoint that makes sense is that genuine causation takes place at each level (Noble 2012).

1.4.1 The Evolutionary Context The impact of top-down causation can be illustrated with recourse to the Swampman thought experiment (Davidson 1987). According to that thought experiment, we are to imagine that lightning strikes a dead tree in a swamp while Davidson is

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standing nearby. As Davidson’s body dissolves due to the causal circumstances, the tree’s molecules by coincidence turn into his replica, which begins to behave like Davidson, moves into his house, writes articles in his name etc. We maintain that Swampman is physically impossible. No molecule by molecule duplicate of a person could arise spontaneously from inanimate matter. The evolutionary prehistory and the adaptation of an organism to its causally local environment (its niche) are essential for the organism’s existence. The organism controls local patterns of causation in a top-down way. The organism is prior to the causal order of its elements (Mossio and Moreno 2010; Moreno and Mossio 2015). If we copied the causal order of an organism’s elements, we would still not have copied the organism. To be more precise, we would have to copy the causal order of an organism’s element in the right way in order for a Swampman to be alive, which means that the contextual, social constraints on his production set the conditions for the lowerlevel elements to realize Swampman. Random physical structure is not enough for “Swampman” to be so much as alive for any amount of time. Hence, there could not be a Swampman replica of Davidson. Our use of the material of the thought experiment is supposed to illustrate that evolutionary causal history, including its niche and social contexts, is essential for the causal constitution of human life and thought. Even if we could replicate human organisms by some hitherto unavailable procedure, this would not be evidence for a bottom-up process, as the relevant causal context would, of course, include us and the technical apparatus needed in order to achieve the feat of bringing organic matter into shape.

1.4.2 The Cosmological Context It is not remotely plausible that what happens today on Earth, such as the existence of the iPhone and Facebook or the occurrence of a debate about Brexit, is determined uniquely by the initial state of the early universe (Ellis 2016). Firstly, the quantum fluctuations during the inflationary era that are supposed to lead to classical fluctuations at the end of that era (Dodelson 2003; Peter and Uzan 2013) are subject to quantum uncertainty. The specific outcomes that actually occurred at the Last Scattering Surface are not uniquely determined by data at the start of inflation. Secondly, the transfer function from the Last Scattering Surface to the occurrence of astronomical structures such as our cluster of galaxies has difficulty even in accounting for the structure of galaxies. It simply does not operate on a scale relevant to the human mind. Thirdly, since life began, the course of evolution of life on Earth has been altered by radiation damage caused to DNA by cosmic rays; and the emission of cosmic rays is a quantum event, subject to quantum uncertainty. Strong emergence of a brain capable of logically working out the nature of electromagnetism on the basis of scientific data must occur, else how could the molecules in the early universe have encoded the logic of Maxwell’s equations and deterministically written them into Maxwell’s brain? Something new – the logical structure of those equations – has been added to the physical universe since its

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early stages. There is no way that that logical structure could have been written into the data on the last scattering surface, which are modulated random Gaussian fluctuations.8 The issue of strong emergence does not arise at a late stage (with the formation of organic molecules, say), but is present at the earliest known stages of the cosmological evolution of the universe. Here is what we call the argument from “transcendental ontology” (Gabriel 2011): the actual scientific context of discovery takes place on a level of reality that has run through various layers of emergence, including the emergence of meaning and theory-construction. The early universe cannot encode anything that has the logical form of a theory. Otherwise, the universe could not be known, because the heuristic process of theory-discovery relies on the free exchange of data between scientists together with conceptual capacities that develop historically. Science essentially has a history of discoveries building on each other in a chain of rational improvement. Science progresses neither randomly nor deterministically.

1.4.3 The Problem of the Bottom Level Currently, we do not even know if there is a bottom level of reality. If there is a bottom level, it will almost certainly not consist of completely isolated elements (philosophical atoms). If there are relations on the bottom level, they form a context, meaning that it is currently at least equally rational to believe that there is contextual (downward) causation on the bottom level as to try to circumvent it by thinking of the bottom level as metaphysically granular. To be sure, these speculations have zero explanatory power, because we have not even settled on the best-known candidate for a bottom level. The scientific status of the most popular candidate – String theory or M-theory – is in any case questionable (Ellis and Silk 2014). Given the lack of an established bottom level, scientists in practice choose some arbitrary intermediate level and argue for reduction to that level. An example is the statement by Francis Crick in his book The Astonishing Hypothesis: ‘You,’ your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules. (Crick 1995, p. 3)

He is thus claiming (see Fig. 1.1) that what happens at Level 9 can be reduced to what happens at level 6 and 7; Level 9 is epiphenomenal. This is obviously a halfhearted form of reductionism. Following his reductionist logic, what happens at the cellular and molecular levels 6 and 7 is “nothing but” the behavior of electrons and ions at Level 2. So why does he stop at the levels he does? Evidently, because he believes that real causal powers reside at those levels (they are the levels at which he studies causality). But this is only possible if they act down to the underlying 8 And

suppose that was possible, the question would arise: who or what wrote them into that initial data? The processes of physical cosmology cannot possibly do so.

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physical levels to cause the electrons and ions at lower levels to flow in accord with the dictates of cellular and biomolecular logic (see Figure 6 in Ellis and Kopel 2019). But if that top-down causation is possible, then there is no reason why it should not similarly occur from Level 9 to levels 6 and 7 – as we claim, and as is required to fulfill the dictates of Noble’s Principle of Biological Relativity, namely that all levels equally have real causal powers (Noble 2012).

1.5 Top-Down Effects in Logical Hierarchies So far, we have looked at top-down (contextual) effects in physical hierarchies. However, they occur equally in logical hierarchies: the logic of lower levels, and even the nature of lower-level components, usually depends on higher-level contexts. The point is simply that no logical statement takes place in isolation: it always assumes a context which shapes both the language and logic that occurs. In all cases, one has a Modular Hierarchical Structure, because this is the only way that one can build up true complexity (Sect. 1.5.1). Contextual effects occur in mathematics (Sect. 1.5.2), computer programs (Sect. 1.5.3), and the logic that underlies society and daily life (Sect. 1.5.4).

1.5.1 Modular Hierarchical Structures All complex abstract structures are modular hierarchical structures,9 where each word is important (see Booch 2006 for a very enlightening discussion, developing from Simon 1996). • Structures constrain what is possible: they will be of the form of specifications of general classes of objects from which specific instances (‘tokens’) can be realized, together with modifiers specifying the possible nature of specific objects, and procedures for acting on the various classes together with modifiers for the actions and rules constraining what is allowed.10 The objects and actions are dual to each other, in that they jointly lead to logical outcomes: a specification may prioritize procedures or object classes. • Hierarchies: emergent levels of abstract structure will occur out of lower-level objects and actions, each with their own variables and effective laws of behavior,

9 This

is also true for biological complexity and complex artefacts (Ellis 2016); it is the only way to generate true complexity. 10 This is stated with structures as primary. There is a duality between entities and processes: both are needed to get outcomes. One can emphasize whichever one wishes to get an analysis of causes and outcomes.

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•

•

•

•

25

with higher levels formed by concatenating lower entities and combining or black boxing lower-level logical operations. Modularity: at each level, modules will occur with specialized functions and content. This allows abstraction, describing the function of the module from an exterior view (its effective logic as an entity in its own right), and information hiding: many internal variables can be hidden from the external view that is looking at the module as an abstract object. An important aspect of abstraction is naming the module and its variables and actions. Proper naming is essential for ease of understanding what is represented. Interfaces matter: internal information is only used locally and is hidden from outside, but properly formatted higher-level variables can control the functioning of the lower-level modules. Similarly, the kind of information the module sends back to higher levels needs careful specification. In general, only summary reports will be needed. Top-down (contextual) effects: in general, the higher levels will constrain or shape lower-level meanings and actions in crucial ways. This will enable higherlevel entities to shape lower-level entities and interactions so that the higher-level logic can be achieved. Multiple realizability: the lower levels can fulfil higher-level purposes in many different ways. All that is required is that they satisfy the requirements of their abstraction. For example, if you have a list sorting module, it can be realized via bubble sort, quick sort, heap sort, etc.; which is used does not matter from an external viewpoint, except in terms of performance (such as time taken to complete a sort of a long list). This is obviously in parallel to what happens in biology.

1.5.2 Mathematics Any book or paper on mathematics sets up a set of definitions and symbols that form the framework for what is then done. These will categorize the nature of variables and the operations that can be performed on them, thereby structuring what is possible in the following argumentation. Each Lemma or Theorem that follows assumes as a context both this overall basis and the preceding Lemmas and Theorems, which thereby form a hierarchically structured whole in which the parts can be understood only in the light of the whole, and indeed in the light of series of understandings and conventions that have been adopted by the mathematical community as a whole.

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1.5.3 Computer Programs Computer programs consist of a main program and subroutines, usually with subsubroutines, each made of lines of code made of elements (variables, constants, instructions) that form logical sections aimed at particular outcomes. Global parameters and variables are passed to the subroutine and determine what happens, thereby enabling top-down control of the subroutines. Locally defined internal variables do the work using the logic of the subroutine and then pass the result back to the main program. This is all discussed in depth by Knuth (1973) and the case of objectoriented programming in the very enlightening book by Booch (2006). This all takes place at one level of the hierarchy of abstract machines (Tannenbaum and Austin 2013). Precisely the same logic gets chained down from higher to lower levels of that hierarchy through compilers, assemblers, and linkers, rewriting it in a different formalism at each level. However, the basic logic represented by the relevant language at each level, as expressed in its algorithms (Knuth 1973), is the same. It is these algorithms – abstract entities – that control what the computer does, because at the machine code level they determine which transistors in the CPU are on or off at any one time, and hence control the flow of electrons at that level (Ellis and Drossel 2019). They then have key causal effects in the world (MacCormick 2011).

1.5.4 Logical Systems of Society and Daily Life Laws, procedures, rules, and so on structure society and business. These again form logical modular hierarchical structures, where top-down (contextual) effects take place. For example, in the case of a contract, one will have an overall aim and associated major section (e.g. is it for letting a house or employing a person?) that then determines what subsections are required (paying of rent, care of the house, putting out rubbish, etc.), the meaning of each of which is set within the overall context of what the contract is about (if it is for hiring a car, all will be different). Similarly, sports are based on rules realizing a logical system with a hierarchical structure, e.g., in the case of Rugby, the different contexts of playing the ball, a lineup, a scrum, or a penalty shoot set different contexts where the actions of the players are quite different. Games like Bridge or Chess similarly involve an abstract set of rules that sets the context as to which actions are allowed and which are not under which circumstances.

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1.6 A Model for Mind-Body Interaction Physical hierarchies enable the realization of logical hierarchies, thus enabling the emergence of the mind and society. In the natural sciences we find physical modular hierarchical structures that are necessary prerequisites for the emergence of non-physical phenomena, including the mind and social interaction. Nonphysical phenomena such as thoughts and intentions trivially supervene on physical structures: Nothing takes place in fields of sense populated by mental processes without something taking place in physical fields of sense, because physical objects are necessary conditions for the realization (strong emergence) of minded creatures. The fact that minded creatures strongly emerge from lower levels of the universe does not mean that their internal organization is detached from physics. There is no variation in mental and social phenomena without physical correlates, where this does not mean that the correlation is one-to-one. This is ruled out by the fact that the mind and society are strongly emergent phenomena; not only is the relevant form of supervenience diachronic, not synchronic (Sect. 1.3.4 above), but the nature of emergent phenomena (qualia, thoughts) are also completely different than what is described at the underlying physical levels, and we do not even know how to start solving the hard problem of consciousness. However, we do understand in depth its neural correlates (Kandel et al. 2013). The issue of the mind-brain relation is discussed in depth in Gabriel (2017). Top-down causation and the mind are discussed in depth in Ellis (2016, 2018), and the way mental causation reaches down to the level of electrons is clarified in Ellis and Kopel (2019). The model we propose for mind-body interaction can be called “conditionalism” (Gabriel 2018a, pp. 39–45). According to this model, any actual token mental state a human subject realizes can be analyzed into necessary and jointly sufficient conditions for its obtaining. A token state of a human subject is “mental” to the extent to which some of its elements (some of its ontological parts) exist in virtue of the subject’s implicit or explicit account of its position in the animal kingdom and the wider universe. Phenomenal and intentional consciousness are prerequisites for human mindedness, but they do not exhaust it. Consciousness is not the exclusive “mark of the mental”, but one type of process realized via organic structures, which probably are identical with a subset of the nervous system. However, the nervous system’s features cannot be exclusively explained with reference to neural tissue or the synchronized firing of neurons, as neurons depend on a larger organic environment for realizing their potential contribution to mental states. The function of conscious mental states in animals is to track processes in the environment (sensation, perception of distal objects) on the one hand and processes internal to the organism (pain, the immune system, probably dreams etc.) on the other hand. A full mental state in an adult, neurotypical human being involves many more layers than phenomenal consciousness. Some of these layers exist as a consequence of social interaction, which includes the very structure of nervous tissue in humans which emerges during pregnancy. Mother and baby causally interact before and after birth, a process which sets parameters for the specific development of nervous tissue and

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other cell types in a human organism. Consciousness itself is thus a social product, causally tied to social contexts without which it would not exist in the way we are able to observe it in ourselves and other animals. Human mindedness is self-conscious in the specific sense that humans sometimes act in light of a conception of humans and their mental states. More specifically, human institutions articulate a conception that human beings have of themselves at a certain time and age. Human mindedness is thus part of a complex social web without which humans could neither survive nor flourish. The articulation of this structure is subject to norms of rationality, to primary and secondary emotions which co-evolve historically. The overall token mental state a subject is in, essentially involves the environment (as so-called semantic externalists like Tyler Burge, Hilary Putnam, and Donald Davidson have demonstrated). Human minds track facts in their environment that significantly go beyond their immediate sensory scene, as we successfully think about galaxies, events on micro-scales, laws of nature, mathematical truths, the past, the future, etc. We, therefore, propose a generalized form of externalism, according to which the human mind is fallibly in touch with physical and non-physical aspects of reality. This connection is causal given that causation ought not to be reduced to push-and-pull mechanisms or relations between physical objects (see Churchland 2012). In this section we look at mental top-down causation (Sect. 1.6.1); social ontology and causal effectiveness (Sect. 1.6.2); and the way the highest level of intention (values/ethics) is causally effective (Sect. 1.6.3).

1.6.1 There Is Genuine Mental Top-Down Causation There are various axes along which human mindedness is involved in mental top-down effects (Ellis 2018). Mental states and processes, such as adjusting one’s attitudes (beliefs) to the expected attitudes of agents in the same situation, have consequences in action. Human action (including the activity of scientific measurement and experiment) has significant and measurable causal impact on prior, lower levels within the physical parts of the universe. This occurs in the case of perception and attention, planning and action, higher-level cognition, and health. (a) Perception and attention Adult human perception (such as the idealized and trained perception of the scientist, the art connoisseur etc.) cannot be adequately described without taking the sociality of humans into account. Humans can perceive cars, artworks, friendly faces, architecture, bubble chambers and socially complex dangers. What we know from social training contexts (the role of education) affects what we perceive and how we perceive it. Language affects our perceptual field. We can distinguish between mere sensation, blind/non-conscious perception, conscious perception and the actual full-blown perceptual situation of a trained individual. It does not make sense to reduce the highest known level of perception (which we can call “expert

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Fig. 1.2 Triangle Illusion We cannot but help seeing two triangles in this diagram: but there are no triangles there, just three angular segments and three partial filled circles. The brain fills in missing lines to make it seem that there are two triangles

perception”) to some lower level. This does not mean that the lower levels are also expert systems. Human expert perception requires sensory systems whose operations do not as a whole require conscious control and orientation. Within the perceiving mind, there are top-down effects across its levels. Overall, the brain is a predictive machine (Clark 2013; Hohwy 2013), continually filling in missing information on the basis of expectations (Frith 2007; Purves 2010), thus making meaningful patterns by top-down processing of information (Kandel 2012). We have learnt how to “see” on the basis of past experience; on this basis, our mind automatically fills in what we expect to see. This is shown in the case of vision by Fig. 1.2, where we cannot help seeing two triangles although there are none there. Many other visual illusions confirm that this is the nature of vision (Purves 2010). Similar effects occur in reading, as is shown by our ability to read miswritten text: Y u c n re d this evn tho gh it is not phonem cally correct and this thuogh lwtters are wron g And this though words missing The fact that you could read the above proves that the mind continually guesses and fills in, all the time searching for meaning. An ongoing holistic process takes place whereby the cortex predicts what should be seen, fills in missing data, and interprets what is seen on the basis of expectations in the current context. This process is driven in a top-down way as a ‘psycho-linguistic guessing game’ (Goodman et al. 2016) – else it could not work. Furthermore, by attention and conscious action we can change what we perceive: for example, by focusing our gaze in particular directions. (b) Top-down effects in action: We can make choices of what we will do, e.g. walking across the room, and that intention gets translated into the motion of billions of electrons in our muscles that

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cause that action to happen. By focusing attention, we can attain very fine control of how this happens, e.g. in athletics and gymnastics. It is possible to think of the realization of practical syllogisms in human action as a form of deductive causation. Thinking about what one ought to do for a reason is part of human motivation insofar as we are rational agents. Rationally guided action is ontologically grounded in the implementation of deductive causation, which means that there is no strict fact/value or nature/norm-dichotomy. We have practical knowledge of what we are doing that differs in category from observational knowledge (see, for instance, Anscombe 2000; Rödl 2007) and hypothesis-formation. We can do something in order to achieve a goal. Human action is self-consciously teleonomic: we can know what we are doing by doing it. For instance, if a scientist is reading off a measurement from an instrument, she does not need a further instrument or experiment to figure out what she is doing. There is thus non-observational, yet fallible, knowledge of what we are doing. Some forms of self-consciousness realize this structure too, as we can become aware of our modes of thinking by practicing them. We can know laws of logic and pure mathematics in virtue of exercises of our capacities to make them explicit without thereby referring to observational knowledge of processes in our organism. When activity of the mind results in physical outputs such as the construction of an aircraft or a computer or house or writing a letter, one has logical causation (see section 6.3. of Ellis and Kopel 2019), whereby, through the neural network structure of the brain, evidence-based logical deduction together with choice of goals leads to choice of outcomes in terms of an action plan. A decision to act then leads to action potentials in the motor cortex sending signals to muscles that control hand motion and so result in a physical output. (c) Higher-level cognition Thinking about one’s situation results in overall attitudes and the selection of higher-level goals that shape all lower-level outcomes (these in turn are affected by values and meaning, see Sect. 1.6.3). An example of how this works in primate brains is that parallel metamemory streams supervise recognition networks for remote and recent memory, without contributing to recognition itself. (d) Health An example of top-down causation as regards health is the causal power of placebos: The brain predicts that you ought to get better: and you do, even if you know that they are placebos and so have no active ingredients (Kaptchuk et al. 2010; Kaptchuk and Miller 2015).11 Beliefs have causal powers over the physical state of the body. They alter movements of biomolecules and electrons.

11 See

Sifferlin (2018) for a description.

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1.6.2 Social Ontology and Causal Efficacy Institutions, social roles, the economic system, moral value, etc. are abstract (nonphysical) entities that exert causal power over events in the physical universe (Searle 1997; Elder-Vass 2010; Ismael 2016; Gabriel 2020a). Human agents do not distort or cancel the laws of nature. Yet, they genuinely interfere with the course of natural, physical events on their scale of interaction with the universe. Human interaction with the universe presupposes social training and participation. Human education is a precondition of survival of our offspring. Adult perception, as we know it, does not take place without necessary social conditions that are external to any given individual organism without being further mental states. They are encoded in documents that guide the mutual attitude adjustments of humans that form a norm-circle (Elder-Vass 2010). Norm-circles have top-down effects on individual mental states because human mindedness is normative: we assess the course of thinking and acting in light of norms. These norms are the objects of the humanities and social sciences, which study their structure and causal powers, as well as their diachronic and synchronic variation over different groups (normcircles). To be sure, these top-down effects are restricted by their necessary physical prerequisites, with which they causally interfere without breaking any laws of nature. The laws of nature cannot be broken because they describe events on an idealized level that does precisely abstract away from human interaction. Apart from language and mathematics, the causal powers of money and of social organizations such as companies or corporations are also crucial (Harari 2014; Mayer 2018). These are abstract entities that have transformed human history. Neither is a physical entity: they are abstract entities that exist through social agreement, and then have causal powers in terms of changing physical outcomes: leading to the existence of buildings, roads and dams, aircraft, motor cars, and so on (Albeverio et al. 2007).

1.6.3 The Highest Level of Intention [Values/Ethics] Is Causally Effective The highest level of causation in mental processes is the choice of criteria for what are acceptable goals, based on a value system and view of ethics. This controls all lower-level goal choices by setting out what is desirable on the one hand and placing limits on permissible actions on the other, thus separating the ethical from the unethical. This is based on an overall world view or concept of meaning (‘telos’), which guides what we do with our lives. Thus, the options we choose between are shaped by ethical standpoints/values, which act top-down to guide all mental and physical outcomes (see Gabriel 2018a, 2020a, b). In terms of Aristotelian causation, this is Final Causation. It is the highest level of causation, shaping what happens at all lower levels by determining the direction of purposeful activity (Ellis and Noble 2021).

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A specific case of considerable contemporary relevance is climate change, which is speeding ahead because of the values of those opposed to its mitigation (a topdown effect from values to the physical world)12 and which will then in turn have a top-down effect from global mean temperature increases to ecology (Ulanowicz 1977, 1990, 1997, 2009, 2019; Deweerdt 2017) and health (Woodward et al. 2014).

1.7 Conclusion Why is this argument about reductionism and emergence important? Because in biology, reductionist views that are supposed to conform to what physics says have had a fundamentally debilitating effect on understandings of biology (Woese 2004), even while many aspects of physics have moved away from reductionism: as argued above, one cannot, for example, understand many aspects of condensed matter physics from a reductionist viewpoint (Simon 2013). Proper understanding of biology is holistic (Weiss 1973), incorporating its systems aspects and top-down effects (Noble 2012). As Weiss states: [T]he basic characteristic of a system is its essential invariance beyond the much more variant flux and fluctuations of its elements or constituents. [ . . . ] This is exactly the opposite of a machine, in which the pattern of the product is simply the terminal end of a chain of rigorously predefined sequential operations of parts. In a system, the structure of the whole coordinates the play of the parts; in the machine, the operation of the parts determines the outcome. Of course, even the machine owes the coordinated functional arrangement of its parts, in last analysis, to a systems operation - that of the brain of its designer. (Weiss 1973, p. 41)

The universe is not causally closed on some fundamental level, as we have argued: irreducible quantum uncertainty denies this. Strong emergence already takes place in non-human reality, but is particularly visible in the realm of human social interaction, which builds on the assumption of free will or social freedom in the sense of mutual attitude adjustment in the context of systematic (economic) action coordination (a society or norm-circle of norm-circles).

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12 For

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Moreno, A., & Mossio, M. (2015). Biological autonomy: A philosophical and theoretical inquiry. Dordrecht: Springer. Mossio, M., & Moreno, A. (2010). Organisational closure in biological organisms. History and Philosophy of the Life Sciences, 32, 269–288. Müller, S. D., Marchetto, J., Airaghi, S., & Kournoutsakos, P. (2002). Optimization based on bacterial chemotaxis. IEEE Transactions on Evolutionary Computation, 6, 16–29. Nichols, A. L. A., Eichler, T., Latham, R., & Zimmer, M. (2017). A global brain state underlies C. elegans sleep behavior. Science, 356(6344), e6851. https://doi.org/10.1126/science.aam6851. Noble, D. (2002). Modeling the heart – From genes to cells to the whole organ. Science, 295, 1678–1682. Noble, D. (2008). The music of life: Biology beyond genes. New York: Oxford University Press. Noble, D. (2012). A theory of biological relativity: No privileged level of causation. Interface Focus, 2, 55–64. Noble, R., & Noble, D. (2018). Harnessing stochasticity: How do organisms make choices? Chaos, 28(10), 106309. https://doi.org/10.1063/1.5039668. Paoletti, M. P., & Orilia, F. (Eds.). (2017). Philosophical and scientific perspectives on downward causation. New York: Routledge. Pearl, J., & MacKenzie, D. (2018). The book of why: The new science of cause and effect. New York: Basic Books. Penrose, O. (1979). Foundations of statistical mechanics. Reports on Progress in Physics, 42(12), 1937–2006. Penrose, R. (2016). Fashion, faith, and fantasy in the new physics of the universe. Princeton: Princeton University Press. Peter, P., & Uzan, J.-P. (2013). Primordial Cosmology. Oxford: Oxford University Press. Phillips, P. (2012). Advanced solid state physics. Cambridge: Cambridge University Press. Prigogine, I., & Stengers, I. (1985). I: Order out of Chaos. New York: HarperCollins. Purves, D. (2010). Brains: How they seem to work. Upper Saddle River: FT Press Science. Qi, X.-L., & Zhang, S.-C. (2011). Topological insulators and superconductors. Reviews of Modern Physics, 83(4), 1057–1110. Rödl, S. (2007). Self-consciousness. Cambridge, MA: Harvard University Press. Rosen, R. (1958). A relational theory of biological systems. The Bulletin of Mathematical Biophysics, 20(3), 245–260. Rueger, A., & McGivern, P. (2010). Hierarchies and levels of reality. Synthese, 176(3), 379–397. Sales-Pardo, M. (2017). The importance of being modular. Science, 357, 128–129. Salthe, S. N. (1993). Development and evolution: Complexity and change in biology. Cambridge, MA: MIT Press. Scott, A. (1999). Stairway to the mind: The controversial new science of consciousness. New York: Springer. Searle, J. (1997). The construction of social reality. Oxford: Oxford University Press. Sheredos, B., & Bechtel, W. (2017). Sketching biological phenomena and mechanisms. Topics in Cognitive Science, 9(4), 970–985. Sifferlin, A. (2018). People are now taking placebo pills to deal with their health problems – And it’s working. Time. http://time.com/5375724/placebo-bill-health-problems/. Accessed 15 Jan 2021. Simon, H. A. (1996). The sciences of the artificial. Cambridge, MA: MIT Press. Simon, S. H. (2013). The Oxford solid state basics. New York: Oxford University Press. Sourjik, V., & Wingreen, N. S. (2012). Responding to chemical gradients: Bacterial chemotaxis. Current Opinion in Cell Biology, 24(2), 262–268. Tannenbaum, A. S., & Austin, T. (2013). Structured computer organisation. Boston: Pearson. Tokura, Y., Kawasaki, M., & Nagaosa, N. (2017). Emergent functions of quantum materials. Nature Physics, 13(11), 1056–1068. Ulanowicz, R. E. (1977). Growth and development. New York: Springer. Ulanowicz, R. E. (1990). Aristotelean causalities in ecosystem development. Oikos, 57, 42–48.

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Ulanowicz, R. E. (1997). Ecology: The ascendant perspective. New York: Columbia University Press. Ulanowicz, R. E. (2009). The dual nature of ecosystem dynamics. Ecological Modelling, 220(16), 1886–1892. Ulanowicz, R. E. (2019). Information across the ecological hierarchy. Entropy, 21(10), 949–955. https://doi.org/10.3390/e21100949. Venema, L., Verberck, B., Georgescu, I., Prando, G., Couderc, E., Milana, S., Maragkou, M., Persechini, L., Pacchioni, G., & Fleet, L. (2016). The quasiparticle zoo. Nature Physics, 12, 1085–1089. Wadhams, G. H., & Armitage, J. P. (2004). Making sense of it all: Bacterial chemotaxis. Nature Reviews Molecular Cell Biology, 5(12), 1024–1037. Wagner, A. (2014). Arrival of the fittest: How nature innovates. New York: Penguin Random House. Weiss, P. A. (1973). The science of life: The living system–A system for living. Mount Kisco: Futura Publishing Company. Wimsatt, W. C. (1976a). Reductive explanation: A functional account. In A. X. Michalos, C. A. Hooker, G. Pearce, & R. S. Cohen (Eds.), PSA-1974 (Boston studies in the philosophy of science, volume 30) (pp. 671–710). Dordrecht: Reidel. Wimsatt, W. C. (1976b). Reductionism, levels of organization, and the mind-body problem. In G. G. Globus, G. Maxwell, & I. Savodnik (Eds.), Consciousness and the brain: A scientific and philosophical inquiry (pp. 199–267). New York: Plenum. Wimsatt, W. C. (2007). Re-engineering philosophy for limited beings. Cambridge, MA: Harvard University Press. Winning, J., & Bechtel, W. (2018). Rethinking causality in biological and neural mechanisms: Constraints and control. Minds and Machines, 28(2), 287–310. Woese, C. R. (2004). A new biology for a new century. Microbiology and Molecular Biology Reviews, 68(2), 173–186. Woodward, A., Smith, K. R., Campbell-Lendrum, D., Chadee, D. D., Honda, Y., Liu, Q., Olwoch, J., Revich, B., Sauerborn, R., Chafe, Z., Confalonieri, U., & Haines, A. (2014). Climate change and health: On the latest IPCC report. The Lancet, 383(9924), 1185–1189.

Chapter 2

Making Sense of Top-Down Causation: Universality and Functional Equivalence in Physics and Biology Sara Green and Robert W. Batterman

Abstract Top-down causation is often taken to be a metaphysically suspicious type of causation that is found in a few complex systems, such as in human mindbody relations. However, as Ellis and others have shown, top-down causation is ubiquitous in physics as well as in biology. Top-down causation occurs whenever specific dynamic behaviors are realized or selected among a broader set of possible lower-level states. Thus understood, the occurrence of dynamic and structural patterns in physical and biological systems presents a problem for reductionist positions. We illustrate with examples of universality (a term primarily used in physics) and functional equivalence classes (a term primarily used in engineering and biology) how higher-level behaviors can be multiple realized by distinct lowerlevel systems or states. Multiple realizability in both contexts entails what Ellis calls “causal slack” between levels, or what others understand as relative explanatory autonomy. To clarify these notions further, we examine procedures for upscaling in multi-scale modeling. We argue that simple averaging strategies for upscaling only work for simplistic homogenous systems (such as an ideal gas), because of the scaledependency of characteristic behaviors in multi-scale systems. We suggest that this interpretation has implications for what Ellis calls mechanical top-down causation, as it presents a stronger challenge to reductionism than typically assumed. Keywords Functional equivalence class · Multiple realizability · Reductionism · Top-down causation · Universality · Constraint

S. Green () Section for History and Philosophy of Science, Department of Science Education, University of Copenhagen, Copenhagen, Denmark e-mail: [email protected] R. W. Batterman Department of Philosophy, University of Pittsburgh, Pittsburgh, PA, USA © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_2

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2.1 Introduction The problem of top-down causation refers to how and whether changes of higherlevel variables can have causal effects on lower-level behaviors (Campbell 1974; Ellis 2008). Top-down causation remains a contested issue in science and philosophy of science alike (Ellis 2005; Auletta et al. 2008). A common assumption is that if macroscale systems consist of “no more than” physical-chemical components, it should be possible to describe higher-level phenomena bottom-up from more fundamental lower-level descriptions (e.g., Oppenheim and Putnam 1958; Crick and Clark 1994; Bedau 1997). This chapter comments on and adds to important insights from George Ellis’ work that challenge this assumption. Ellis has been one of the key figures emphasizing that topics such as reductionism and top-down causation are not only philosophically interesting but have important practical implications for science and medicine. We examine further examples in support of this view, by stressing an even stronger interpretation of what Ellis (2012) calls mechanical top-down causation. An important precondition for the existence of top-down causation is that explanations of phenomena at higher scales or levels are (relatively) autonomous of explanations at lower levels. If higher-level explanations and parameters were fully reducible to or derivable from more “fundamental” ones, appeals to top-down causation would be unnecessary or even misleading. In arguing against bottom-up determination of higher-level properties, Ellis (2008, 2012) appeals to the existence of multiple realizability, illustrated through the existence of equivalence classes in different scientific domains. In the following, we therefore examine the connections between multiple realizability, equivalence classes, and top-down causation. Multiple realizability means that a higher-level state or property is realized by different heterogenous states or properties at a lower level. The term is often introduced in discussions about the ontological or explanatory autonomy of higher-level phenomena and models. For instance, Putnam argues against physical reduction of mental states by highlighting that mental kinds are multiple realized by distinct physical kinds (Putnam 1980). Others have appealed to multiple realizability in discussions about explanatory unification (Fodor 1974; Sober 1999; see also Brigandt and Love 2017). However, for the purpose of the discussion of top-down causation, the most important aspect of multiple realizability is that it supports the explanatory autonomy of more general higher-level models that capture similarity in behaviors of heterogenous systems (see also Batterman 2000, 2018). Ellis connects the issues of multiple realizability and top-down causation as follows: Top-down causation takes place owing to the crucial role of context in determining the outcomes of lower level causation. Higher levels of organization constrain and channel lower level interactions, paradoxically thereby increasing higher level possibilities. A key feature here is multiple realizability of higher level functions, and consequent existence of equivalence classes of lower level variables as far as higher level actions are concerned. An equivalence class identifies all lower level states that correspond to the same higher level state. (Ellis 2012, p. 128, emphasis added)

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We unpack with further examples the claims that (i) multiple realizability supports explanatory autonomy of higher-level features, and (ii) top-down causation can be interpreted as the effects of higher-level constraining relations that determine outcomes of lower level causation. Equivalence classes are also sometimes called universality classes in physics. Both concepts highlight how systems with distinct microstructures often display general or universal patterns of behavior. Describing these behaviors does not require reference to microscale details – in fact, generic models and explanations are often identified through procedures that abstract from or selectively leave out irrelevant details (Batterman 2000; Green and Jones 2016). We illustrate the relation between multiple realizability and universality through the example of thermodynamics near critical points in Sect. 2.2.1. We then examine what Ellis terms functional equivalence classes in biology, exemplified through feedback control (Sect. 2.2.2). Functional equivalence can be interpreted as an instance of universality that applies only to engineered and living systems, since equivalent behaviors here are characterized in functional terms such as information, robustness, homeostasis, control, etc. (Ellis 2008, 2012). Functional equivalence classes typically are more context-dependent than classical examples of universality in physics, a point we shall elaborate on further below. For multiple realizability to be possible, Ellis holds, there must be causal slack between lower and higher levels (Ellis 2012). The notion of causal slack usefully highlights how the explanatory autonomy of higher levels is justified by empirical demonstrations of conditional independence of upper-level behavior on many lower-level details (see also Woodward forthcoming and this volume). The term implies that the autonomy is relative to certain conditions that hold for a given equivalence class. Just like a sail can be slack within certain length limits of the sheets, so do relations of conditional independence hold within certain boundaries or parameter spaces. Hence, the autonomy of macro-level explanations is not absolute, but relative (see also Batterman 2018). Critics may argue that this threatens the explanatory autonomy of higher-level explanations, and hence the possibility of top-down causation. Instead, we believe that the notion of relative autonomy avoids many problems afflicting strong accounts of top-down causation (such as difficulties in understanding how different levels are connected), and therefore also offers a better description of how scientists develop multi-scale models in practice. The emphasis on relative explanatory autonomy parallels Ellis’ distinction between his account of top-down causation and a “stronger” interpretation in which top-down causation is described as efficient causation operating across levels. A strong account has been criticized for giving rise to the problem of causal overdetermination or to mysterious cause-effect relations, which would violate the lower-level laws of physics (Kim 1998, 2000). However, if we interpret topdown effects as higher-level constraining-relations on the possible lower-level states of a given system, top-down causation becomes a matter of understanding how higher levels define the boundary conditions of lower-level dynamics (see e.g., Ellis 2008, 2012, 2016; Green 2018; Moreno and Mossio 2015; Mossio and Moreno 2010). Constraints are here understood as physical conditions that limit the

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degrees of freedom of a dynamic process, thus enabling only selected system states (Christiansen 2000; Hooker 2013; Juarrero 1998, 1999). Constraints are typically regarded as being at a higher spatial scale than the entities and operations of the constrained processes. In biology, constraints are often further defined according to functional levels in a hierarchically organized system (Pattee 1971, 1973; Salthe 1985; Wimsatt 2007). For instance, the shape and size of blood vessels enable efficient circulation by limiting the degrees of freedom of liquid motion, or blood flow. The interpretation of top-down causation as the ability of upper-level variables to set the context for lower-level ones may be seen as a “weaker” form of topdown causation (Emmeche et al. 2000). Yet, it allows for an understanding of how constraints productively can channel system states that are not possible to reach for an unconstrained system. The productive aspect of constraints can be illustrated by how an open respiratory system would not be able to provide sufficient gas exchange for a large organism. Similarly, the constraints provided by a sail on wind flow enable a sailboat to move. When one increases the drag by trimming the sail, one does not (effectively) change the operating cause (the wind). Rather, one modifies the structural constraints that channel a pressure difference across the windward and leeward side of the sail. Constraints thus have causal power by delimiting the space of possibilities for lowerlevel causes. Without appeals to top-down constraints, we would not be able to explain why specific states are realized among multiple possible lower-level states and through such selections give rise to emergent properties. Ellis distinguishes between several types of top-down causation. The most basic form of top-down causation is mechanical top-down causation, exemplified by how the rigid boundaries of a gas container constrains the degree of freedom of the lower-scale movement of gas molecules (see also Christiansen 2000). Elsewhere, Ellis also refers to this form as algorithmic top-down causation, because top-down causation can be understood mathematically as the effects of boundary conditions on the solution to equations describing lower-level dynamics (Ellis 2012). A similar account is defended by the systems biologist Denis Noble in the context of multiscale cardiac modeling (Noble 2012, 2017; see also Emmeche et al. 2000; Green 2018). Whereas physical or chemical systems can exhibit mechanical or algorithmic top-down causation, living systems display multiple additional types such as nonadaptive information control, adaptive selection, and intelligent top-down causation (Ellis 2008, 2012). These are often considered as stronger forms of top-down causation, because biological functions must be understood through goals of whole organisms and species, which again depends on higher-level features such as the environmental and evolutionary background (Ellis and Kopel 2017). These “stronger” types of top-down causation, specific to biological systems, are not the focus of our chapter.1 Rather, our aim is to show that the ideal of “bottom1 Readers

interested in these types of downward causation, as well as debates on the metaphysical implications of downward causation, may find Paoletti and Orilia’s (2017) comprehensive anthology on downward causation interesting. For examples of downward causation in ecology, see also (Allen and Star 1982; Ulanowicz 1986, 1997).

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up reductionism” (Gross and Green 2017) can also be challenged with examples of mechanical top-down causation. Our chapter responds to a common view or concern that in the contexts of physics and chemistry, “it is not always clear whether traditional reductionist point of view is actually overcome, since these [high-level variables] can again be understood as a complicated effect of more elementary processes” (Auletta et al. 2008, p. 1162). We draw on examples from both physics and biology to argue that higher-level variables used to model many multi-scale systems are, in fact, not reducible in the sense often assumed. Hence, we think that mechanical top-down causation presents a stronger challenge to reductionism than typically assumed. The analysis is structured as follows. After clarifying the concept of universality in physics and relating it to Ellis’ notion of equivalence class, we further elaborate on Ellis’ suggestion that feedback control and network motifs are examples of functional equivalence classes (Sect. 2.2). We then compare top-down causation based on information control to mechanical or algorithmic top-down causation (Sect. 2.3). Drawing on examples of multi-scale modeling in physics and biology, we argue that high level variables used to describe heterogeneous systems cannot be derived from micro-scale details through coarse-graining. We end the chapter with reflections on the practical implications of the autonomy of scales and top-down causation for science and medicine (Sects. 2.4 and 2.5).

2.2 Universality and Functional Equivalence One way to expresses the challenge to the reductionist is to ask: “how can systems that are heterogenous at the microscale exhibit the same pattern of behavior at the macro-scale?” (Batterman 2018, p. 861). We can answer this question by demonstrating that details of the heterogenous realizers are to a large extent explanatorily irrelevant, and thus that we are justified in idealizing (and thereby effacing) many lower-scale details when our explanatory target is at higher scales. Similarly, Ellis highlights that if an upper-level behavior is multiply realized, we do not have to appeal to micro-level details but can explain higher-level patterns through the generic characteristics of the equivalence class. For Ellis, the features explaining the characteristics of equivalence classes are higher-level constraining relations that channel similar outputs in heterogenous systems. Such effects can be interpreted as instances of top-down causation (Ellis 2012; Sect. 2.3).

2.2.1 Universality and Multiple Realizability in Physics A paradigmatic example of universality is found in thermodynamic behavior near critical points. Various fluids consisting of different chemical elements will have different critical temperatures and pressures. That is to say, they will undergo so-

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called continuous phase transitions at pressures and temperatures that depend upon the micro details of the molecules. However, the behavior of many different fluids at the critical point of phase transitions are identical and can be characterized by the same critical exponents. During a phase transition, e.g., when water boils in a pot, the densities of the liquid water and the vapor (steam) will differ. And, in fact, there will be regions of liquid and regions of vapor that coexist in the pot. If one plots the difference in the densities of the liquid and the vapor, one notices that as the temperature approaches a critical value, this difference exhibits power law scaling behavior. Remarkably, when one plots for a certain class of fluids in   this behavior dimensionless (reduced) coordinates ρρ , TTc , one can show that they all exhibit the c same scaling behavior. See Fig. 2.1 for a dramatic display of this behavior. Thus, there is a universal property (shared behavior at macroscales by systems distinct at microscales) for systems near their respective critical points. More remarkable still is the fact that systems like magnets near criticality also display very similar coexistence curves. (For magnets the order parameter is the net magnetization2 but the scaling exponent is identical.) Part of the reason for this universal behavior is the fact, noted explicitly by Kadanoff (1971) that the closer the system is to criticality, the less the macroscopic/continuum properties depend on the dynamical details of the system. If we wish to understand why many different systems exhibit such similar behaviors, we are unlikely to find the answer in reductionist appeals to fundamental force laws for each chemical component. Rather, the answer is given by the socalled renormalization group explanation of the universality of critical phenomena (henceforth RG explanation). This explanation takes advantage of the fact that near criticality systems exhibit self-similar, fractal-like, behavior. Thus, one can introduce a transformation on the space of Hamiltonians that throws away details via a kind of coarse-graining. Repeated application of this transformation eliminates details that genuinely distinguish the different systems from one another. The hope is to find a fixed point of the transformation from which one can determine the value for the scaling exponent. All systems that evolve under this transformation to the fixed point for the universality class of systems exhibit the same macroscopic scaling behavior. The RG explanation thus extracts structural features that stabilize macroscopic phenomena irrespective of changes in or perturbations of microscopic details. This example from physics not only gives a concrete interpretation of multiple realizability, but also allows for a better understanding of why some very simple models (Ising models, for example) can be used in quite varied contexts to help explain the behaviors of real systems (fluids and magnets) (Batterman 2000, 2018). Phase transitions illustrate the emergence of new macroscopic features through the different characteristics of liquid water, steam, and crystalline ice. They involve discontinuous alterations in higher-level behaviors through the influences of higher-

2 The

net magnetization can also be understood as a difference in densities. The densities of upspins vs. down-spins. This difference vanishes at the critical temperature, as the high temperature randomizes the directions of the spins.

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Fig. 2.1 Vapor-liquid coexistence curve for various  fluids. The figure shows the difference in densities at temperatures in reduced coordinates. At ρρ , TTc = (1,1) liquid phase (left) and vapor c phase (right) have the same density, thus their difference vanishes. (Reprinted from Guggenheim 1945 with the permission of AIP Publishing)

level variables (such as temperature and pressure) on lower-level interactions (Ellis 2016, 139). In Ellis’ view, environmental variables triggering phase transitions should be interpreted as coarse-grained higher-level variables, because temperature and pressure cannot be attributed to isolated molecules. Like order parameters, these point to collective properties arising in a constrained system, such as a gas container (see also Christiansen 2000). Yet, pressure and temperature are interpreted as coarse-grained because they can be identified through averaging of lower-level details (see Sect. 2.3). Accordingly, phase transitions of this type represent the most basic (or weak) form of top-down causation (Ellis 2016, pp. 224–225). We shall return to this point in Sect. 2.3, after examining some examples from biology for comparison.

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2.2.2 Functional Equivalence and Information Control in Biology Ellis uses the term functional equivalence class when referring to models in the life sciences that identify correspondence (or equivalence) of lower-level states or systems with respect to the corresponding higher-level variables and behavior (Ellis 2008, 2012). Examples of these are recurring network motifs and feedback control, which exemplify multiple realizability in biology. We further unpack examples from systems biology that support this view. A hallmark of living systems is homeostasis, i.e., the ability of organisms to maintain a relatively stable internal environment despite external perturbations (Bernard 1927/1957; Cannon 1929). The robustness of functional steady states in organisms is typically explained with reference to feedback control, a concept imported to biology from engineering in the 1920s and later formalized by the mathematician Norbert Wiener (Wiener 1948). Wiener’s book was ground-breaking in suggesting that the same mathematical models can be used to describe feedback control in very different oscillatory systems, from electrical circuits to metabolic regulation in different organisms. The hope for generic systems principles was highlighted also in Rachevsky’s mathematical biology and Bertalanffy’s general system theory (Green and Wolkenhauer 2013). In recent years, systems biology has further strengthened and elaborated on this view by using generic models from control theory and graph theory to describe so-called organizing or design principles in living systems (Alon 2007; Green 2015). An example of a design principle is integral feedback control, which is used to explain robust perfect adaptation in bacterial chemotaxis. The example is described in further detail in other publications (Green and Jones 2016; Serban and Green, 2020), and we shall here focus only on why integral feedback control can be seen as an instance of multiple realizability. An important question in biology is how various functions are maintained despite environmental perturbations. For instance, biologists are interested in understanding how motile bacteria can detect changes in the concentrations of nutrients or toxins in their environment and optimize their movements according to those changes. Remarkably, chemotactic bacteria have receptor systems that can detect and respond to concentration changes in their environments with the same precision before and after stimulus. In engineering terms, the receptor system is said to display robust perfect adaptation (RPA), i.e., the system will return to its pre-stimulus value and regain sensitivity over a large range of parameter values (Alon et al. 1999). Achieving this kind of robustness is a hard problem in engineering. Engineers are often interested in designing systems that asymptotically track a fixed steady-state value, so as to maintain system function despite noisy input signals (or changes in initial conditions). In engineering, robust adaptation to pre-stimulus steady-state values can be achieved through a design principle called integral feedback control (IFC). IFC refers to a quantifiable feedback relation in which the difference between the desired output (steady-state activity) and the actual output is fed back to the system as the

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integral of the system error. Strikingly, the mathematical description of bacterial receptor systems has been found to be equivalent to formal models of integral feedback control in engineering. Systems biologist John Doyle and colleagues derived the principle through a mathematical analysis in which they reduced a mechanistically detailed model of the receptor system to a generic description involving only relations sufficient for the higher-level property of robust perfect adaptation (Yi et al. 2000).3 As a result, IFC was proposed as a design principle that generically constrains functional behaviors and enables robust perfect adaptation, regardless of the causal details of the heterogenous systems realizing this capacity. In Ellis’ terms, we can say that there is sufficient “causal slack” between higherlevel behaviors and lower-level realizers to allow for the same principle to apply to systems as different as bacteria and engineered thermostats. We shall comment further on this example below. Similar examples of multiple realizability in biology are so-called network motifs in gene regulatory networks (Ellis 2012; Fang 2020). Network motifs are small sub-circuits of regulatory connections that have been found to be frequent in biological regulatory networks and have been hypothesized to display characteristic generic functions (Alon 2007).4 For instance, a so-called coherent feedforward loop, cFFL, has been shown to implement a sign-sensitive delay of outputs in response to input signals. This function was first demonstrated mathematically through a simple Boolean input function (see Fig. 2.2), and the hypothesized function was subsequently confirmed experimentally in living bacteria (Mangan and Alon 2003). In biological systems, it can function as a persistence detector that can filter out noisy input signals, such as brief fluctuations in the concentration of nutrients available in a bacteria’s environment. This ensures that protein synthesis of metabolizing enzymes is only activated when the activating signal (availability of sugars) is persistent (for further details, see Alon 2007). Systems biologists more generally use the term design principles to highlight that generic network structures instantiate general dynamic patterns that i) are independent of specific realizations in different causal systems, and ii) serve functional or goal-oriented roles in engineering and biology (Green 2015). In other words, the characteristics of functional equivalence classes are explained with reference to how network structures constrain dynamic outputs to enable generic types of functions such as sustained oscillations, noise filtering, robust perfect adaptation, signal amplification, bi-stable switching, etc. (Doyle and Stelling 2006; Tyson et al. 2003; Tyson and Novák 2010). The quest for design principles highlights the hope in systems biology that any network circuit with a specific structure, regardless of the specific details of its causal constituents, will belong to a more general functional equivalence

3 This

aspect is analyzed in further detail in (Green and Jones 2016). of the stabilizing aspects of global constraints in networks have been explored much earlier, e.g., by Stuart Kauffman’s demonstrations of how the structure of Boolean networks constrains the possible network states (Kauffman 1969, 1993).

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class. If so, this would allow gene regulatory functions to be predicted and explained independently of detailed knowledge about the lower-level genetic and molecular details of specific systems. Generic functions of network motifs have been demonstrated in various contexts (Alon 2007). In the neighboring field of synthetic biology, multiple realizability through network motifs is exploited as a design heuristic for the synthesis of synthetic circuits with pre-defined functions (Koskinen 2017, 2019). Similarly, systems biologists have recently explored the global properties of gene regulatory networks, following up on Kauffman’s (1969, 1993) insight that even complex networks often converge to a limited set of stable states. Using the framework of dynamical systems theory, systems biologists have demonstrated that many different molecular mechanisms can lead to the same attractor states (representing biological functions or states of cell differentiation), thus moving the focus from the details of causal pathways to system trajectories (Huang 2011). This approach can potentially explain biological robustness (via top-down causation), because it can show how stable functional states are largely independent of the specific states (or initial conditions) of specific network nodes.

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Functional equivalence classes in biology are, however, more contested than the classical examples of universality in physics (Auletta et al. 2008). Analyses of global network topologies and network motifs have shown that functions of genetic circuits are dependent on the contexts of the gene regulatory network, the environment, and organisms as a whole (DiFrisco and Jaeger 2019). It has therefore been debated to what extent the structure of network motifs determines gene regulatory functions (Isalan et al. 2008; Jiménez et al. 2017). Similarly, systems biologists have debated whether biological systems exhibiting robust perfect adaptation necessarily realize integral feedback control (cf., Yi et al. 2000; Briat et al. 2014). Importantly, however, conditional independence is compatible with some degree of context-dependence within defined boundaries. We further clarify this below. The discovered complexity has sparked an interest in understanding how wider system contexts can influence the characteristic functioning of specific network motifs. This can for instance be done through simulations where parameter spaces for the strengths of inputs and weighting of regulatory connections are varied (Tyson and Novák 2010). Hence, an aim here is to explore the conditions under which generic functions can be inferred from structural network types. Systems biologists have also used computer simulations to explore the possibility spaces for network structures that can realize specific functions of interest. For instance, they explore how many network topologies fall within a functional equivalence class and which structural features characterize the class. As an example, Ma et al. (2009) conducted a computational search for networks capable of performing robust perfect adaptation and investigated their regulatory wiring patterns. From a starting point of 16,038 possible network topologies, they found that only 395 were capable of performing RPA, and that they all fell into two generic structural classes (one is a negative feedback loop with a buffer node, the other is an incoherent feedforward loop). Interestingly, all known biological examples of RPA are instantiations of the negative feedback control type, as described by Yi et al. (2000). The example thus highlights how structural constraints may realize functions that are multiply realized in distinct systems and thus “unify the organization of diverse circuits across all organisms” (Ma et al. 2009, p. 760).5 The complexity and diversity of biological systems presents a major challenge to provide an analysis in this context similar to the RG explanation in physics. But despite the limitations for universal laws in biology, generic models have proven useful for explaining why characteristic dynamic patterns arise in causally different systems. An ideal in systems biology is to shift the focus from inherent properties of specific genes or proteins to how those are interconnected through stabilizing regulatory structures that give rise to similar higher-level behaviors. In physics and chemistry as well as biology, an important part of scientific analysis is thus 5 This

necessarily involves abstraction from lower-level details. In the words of Ma et al.: “Here, instead of focusing on one specific signaling system that shows adaptation, we ask a more general question: what are all network topologies that are capable of robust adaptation?” They further state that the aim to “construct a unified function-topology mapping [ . . . ] may otherwise be obscured by the details of any specific pathway and organism”. (Ma et al. 2009)

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to determine “how many values of hidden variables can underlie the same higherlevel description” (Ellis 2016, p. 120). In the following, we examine further how the causal slack of “hidden variables” supports a relative explanatory autonomy of higher-level models.

2.2.3 Causal Slack and Explanatory Autonomy The notion of hidden variables can be understood as a domain of lower-level causal details that would not change the output of a higher-level function, e.g., because the system trajectory would converge to the same fixed point or attractor in an abstract phase space.6 As Ellis highlights, for a given equivalence class “it does not matter which particular lower level state occurs, as long as the corresponding higherlevel variables are in the desired range” (Ellis 2008, p. 74). This has important implications for the way natural phenomena are represented and explained. A notable feature of systems biology textbooks, compared to those of molecular biology, is that molecular details are almost absent in the figures and diagrams (cf., Alon 2007; Lodish et al. 2008). The use of highly abstract illustrations not only highlights how the functional descriptions are (relatively) independent of molecular details, but also that functional equivalence classes are identified through procedures of what Ellis (2012) calls information hiding. Akin to how we arrive at explanations for universal behaviors in physics by the use of RG explanations, systems biologists must necessarily abstract from molecular details in order to make the generic patterns of network organization visible (Levy and Bechtel 2013; Green 2015). Some would argue that information hiding strips the abstract network models of their explanatory power, and that these are explanatory only in so far as details are added back to explain the workings of specific systems. For instance, Matthiessen (2017) argues that design principles such as IFC are not explanatory if they do not allow us to distinguish between different species of bacteria or between organisms and thermostats. But while fine-graining by adding details would serve the explanatory purpose of how specific systems work (what we can call a type-I question), it would not address the (type-II) question of what these systems have in common or why the same abstract model or principle applies to causally diverse systems (Batterman 2002, p. 23). The reductionist would hence have to explain how higher-level descriptions can be relatively autonomous from changes of lower-scale details (see also Wimsatt 2007). To respond to the type-II question, it is important to highlight two implications of what Ellis calls causal slack, and others understand through scale separation of multi-level systems. Scale separation refers to the manifestation of different dominant behaviors at different length scales, which accordingly must be described through different types of mathematical models (Batterman 2012). If, for instance,

6 It

goes (almost) without saying that this notion of “hidden variables” is not quantum mechanical.

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one is interested in modeling the bending properties of a material such as steel, it would not be useful for take the lowest (atomic) scale as the starting point. Instead, one typically starts with variables at the mesoscale and upscales to higher-level variables (such as elastic material parameters) that are used in continuum models. In fact, a detailed microscale models would often be irrelevant if the aim is to describe upper-scale continuum behaviors, as upper-level behaviors are literally invisible at the lowest scales. Scale separation explains why meso- and macroscale models often work well, despite ignoring or even misrepresenting many lower-level details. Indeed, mesoscale parameters are often dependent on some microscopic details, and these are accounted for through so-called homogenization strategies (see also Sect. 2.3). One can interpret the use of such strategies as a way to determine the degree and kind of causal slack between different spatial scales. Top-down causation implies that higher-level features are not just relatively autonomous from lower-level description but also influence the latter through constraining relations. An objection to this view may be that since higher-level features primarily select among possible lower-level states, higher levels are not really autonomous after all. If lower levels define the possibilities, and if emergent features are always realized through materials at lower levels, what does autonomy really consist in?7 Our response is as follows. First, causal slack implies that higher levels are not fully controlled or determined by lower-level features but also by the structuring of the system. Second, the requirement of higher-level boundary conditions to constrain the space of causal possibilities implies that some lowerlevel states cannot be accounted for without the boundary conditions imposed by higher-level structures. For instance, Noble (2012) and this volume highlights how a phenomenon such as the heart rhythm is not possible without top-down causation, because the constraining relations of a membrane (understood mathematically as cell voltage) are required to produce oscillations of ionic currents. Noble’s example illustrates how constraints, as indicated in the introduction, must be understood in an enabling as well as limiting sense, as they allow for stable system behaviors or robust functions that would be impossible to reach in an unconstrained system (Pattee 1971, 1973). Another example illustrating this point is how our rigid skeleton enables upright movement on land by delimiting the possible directions of muscle contraction (Hooker 2013). It would be misleading to say, in this context, that the top-down constraints of the bone primarily provide a (non-explanatory) background for the lower-level states or operations of molecular muscle cells. Rather, as in the case of cardiac cells, certain emergent properties become possible only when constraining relations are applied on lower-level states. The causal power of top-down constraints can also be clarified through “negative” examples, where the constraints are removed and functions as a result

7 This

concern was for instance raised after a talk by Ellis entitled “On the Nature of Causality in Complex Systems”, at the conference The Causal Universe, Krakow, Poland, May 17–18, 2012. Available online: https://www.youtube.com/watch?v=nEhTkF3eG8Q. In the following we further elaborate on a possible response to this question.

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become impossible to obtain. Breaking a bone has immediate effects on the causal possibilities for muscle performance, just like a ripped sail immediately changes the speed and control of a sailboat. Similarly, Noble mathematically demonstrates how removal of the top-down constraints of cell voltage causes oscillations to cease in a simulation of the heart rhythm (Noble 2012). Generally, many biological processes would not be possible without inter-level constraining relations (see DiFrisco and Jaeger 2020 for further examples).

2.3 Top-Down Causation and High-Level Variables For Ellis, a crucial feature of top-down causation is how coherent higher-level actions emerge from top-down constraints on lower-level dynamics (Ellis 2012, p. 128). Such constraints are often mathematically described as boundary conditions that delimit the set of lower-level variables (e.g., the set of initial conditions as inputs to the dynamics) within which a given function can be realized. Top-down causation should thus not be understood as causal effects that are completely autonomous from lower-level dynamics. The organizing or design principles defined at higher scales nevertheless have causal effects that constrain the distributions or values of lower-level constituents or states, thus enabling emergent behaviors of lower levels (cf. Emmeche et al. 2000). As mentioned in the introduction, Ellis (2008, 2012) distinguishes between several types of downward causation. Following up on Sects. 2.2.1. and 2.2.2, we focus only on two, namely top-down causation by information control and mechanical or algorithmic top-down causation. Feedback control loops in biology are instances of what Ellis calls top-down causation by information control (Auletta et al. 2008; Ellis 2012). The IFC-principles and the proposed generic functions of network motifs highlight a basic condition for equivalence classes, namely that many different input situations or causal “realizers” would give rise to equivalent operational outcomes, as long as basic structural requirements are obeyed. Importantly, a feedback loop is here interpreted as a structural constraint that delimits the space of possibilities for lower-level dynamics. Hence, feedback control consists in information selection. For instance, the structure of a feedforward loop motif determines whether a genetic circuit should respond only to persistent input signals (coherent feedforward loop) or immediately to any nutrient detected (incoherent feedforward loop). As illustrated in Fig. 2.2, coherent feedforward loops control transcription by introducing a time difference between direct and indirect transcription activation routes. Similarly, incoherent feedforward loops can minimize the response to disturbance by simultaneously activating the transcription of an output product and an intermediary transcription factor that inhibits output protein production. Hence, structures such as network motifs constrain the dynamic possibilities of gene regulation at a lower scale in a hierarchy (see also Bechtel 2017). Ellis defines top-down causation by information control as follows:

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Top-down causation by information control occurs thanks to the connection between equivalence classes and information control [ . . . ] In this case, the feedback control circuits produce reliable responses to higher level information (Ellis 2006, 2008), allowing equivalences classes of lower level operations that give the same higher level response for a certain goal. (Auletta et al., pp. 1169–1170).

Different lower-level operations are here considered as controlled by information from above in the sense that the control circuits are considered as higher-level entities in two senses. First, the functions are implemented by networks that cannot be reduced to the operation of lower-level entities in isolation (Ellis 2008). Second, functional goals are higher-level concepts referring to the properties of a whole system (an organism, metabolic system, or circuit of interacting processes or entities). The second feature requires some clarification. Ellis (2008) argues that: “[t]he goals in biological systems are “intrinsic higher-level properties of the system considered, and determine the outcome (unlike the usual physical case, where the initial state plus boundary conditions determine the outcome). [ . . . ] The initial state of the system is then irrelevant to its final outcome, provided the system parameters are not exceeded” (Ellis 2008, p. 74). Ellis stresses that top-down relations in biology include considerations of part-whole relations, which do not necessarily translate to the physical context. While we agree with this characterization, we do not view downward causation primarily as a compositional relation between parts and wholes (see also Woodward, forthcoming). Rather, we view top-down causation as relations between higherlevel and lower-level variables. Thus understood, we find it potentially misleading to consider the relative independence from initial conditions as a prime feature that separates physical and biological systems. As we have seen, universality in physics is characterized through insensitivity to lower scale details, and both biological and physical systems can be described through equivalence classes within certain boundaries of system parameters. Accordingly, we suggest, that “bottom-up reductionism” can also be challenged by examples of mechanical or algorithmic top-down causation in both physics and biology. Although typically considered a “weaker form” of top-down causation, compared to top-down causation by information control, cases of multi-scale modeling in both domains highlight the limitations of a bottom-up approach (Batterman and Green 2020). Mechanical or algorithmic top-down causation refers to a ubiquitous form of top-down causation that occurs whenever “high-level variables have causal power over lower level dynamics through system structuring or boundary conditions, so that the outcome depends on these higher level variables” (Ellis 2012, p. 128). With Ellis, we believe that this form of top-down causation is much more common than typically recognized.

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2.3.1 Revisiting Mechanical Top-Down Causation As mentioned, Ellis views mechanical top-down causation as a phenomenon occurring also in physical and chemical systems. This was exemplified in the way changes in higher-level variables (such as pressure or temperature) can lead to changes in lower level interactions in gases and fluids, enabling new properties such as gas ignition or phase transitions (Sect. 2.2.1).8 In these examples, Ellis seems to assume the correspondence between lower- and higher-level variables is given by a relatively simple relation between these, i.e., that higher-level variables can be derived from coarse-graining of lower-level ones (Auletta et al. 2008). Ellis broadly defines high level variables as follows: A high level variable is a quantity that characterizes the state of the system in terms of a description using high level concepts and language – it cannot be stated in terms of low level variables. Use of such variables involves information hiding, for they are the relevant variables for the higher level description, e.g., the pressure, temperature and density of a gas, without including unnecessary lower level details (such as molecular positions and velocities). (Ellis 2008, p. 70)

Ellis further distinguishes between coarse-grained higher-level variables and irreducible higher-level variables. The pressure of an ideal gas exemplifies the former, whereas feedback loops or the tertiary structure of protein folding illustrate the latter (see also Brigandt and Love 2017). Coarse-grained variables can be obtained by averaging over a set of lower level variables, and they are therefore in principle possible to derive from lower-level details (although this is often not done for practical reasons). This has implications for the strength of mechanical top-down causation because Ellis views all the high-level variables concerned with this type of top-down causation as coarse-grained. He further writes: “The resulting high level relations are then an inevitable consequence of the low level interaction, given both the high level context and the low level dynamics (based in physics)” (Ellis 2008, p. 72). As a friendly amendment to this view, we suggest that the scope of mechanical or algorithmic top-down causation be expanded to include cases that go beyond instances of simply coarse-grained higher-level variables. While we agree that the high level variables are coarse-grained in the case of homogeneous systems such as ideal gases, there are many multi-scale systems in physics where mesoand macroscale parameters cannot be obtained via simple averaging procedures (Batterman and Green, 2020). This presents a further challenge to the reductionist point of view. Indeed, in the case of an ideal gas, we can assume that the system is homogenous, and we can therefore upscale to the higher-level thermodynamic behavior by relatively simple averaging over micro-scale details (such as molecular spatial and velocity distributions). However, whenever multi-scale systems are heterogenous 8 Other

2018).

examples from physics are discussed in (Bishop 2012; Christiansen 2000; see also Ellis

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and display more complicated limit behaviors, this approach would fail. For instance, if the task is to develop a multi-scale model of the bending behaviors and relative strength of heterogenous materials such as a steel beam or vertebrate bone, complex homogenizations strategies are typically adopted to account for mesoscale structures that are not observable at lower scales (Batterman and Green 2020). In both contexts, simple averaging over lower-scale variables would not enable scientists to predict macroscale material properties. For multi-scale systems that are heterogeneous (e.g., composites of materials with different conductivities or elastic behaviors), the aim of upscaling is to find effective (continuum scale) parameters (like Young’s modulus) that code for microstructural details of the composites.9 Typically this involves the examination of a representative volume element (RVE) that reflects the nature of heterogeneities at scales (mesoscales) where those structures are deemed to be important. One introduces correlation functions to characterize (primarily) the geometric and topological aspects of the mixture in the RVE (Torquato 2002). The mathematics that enables one to find the effective parameters that characterize the behavior of the composite at the continuum scale is called “homogenization theory.” (Batterman and Green 2020 discusses some aspects of this in the context of materials science and biology. See also Batterman forthcoming.) Note that the relative autonomy of the homogenized system (at the continuum scale) from the atomic lower scale details reflects a kind of emergence. This sense of emergence is weaker than that associated with higher-level variables characterizing the human mind or social phenomena. Yet, the higher-level parameters cannot be reduced to or derived from lower-level details. Consider Young’s modulus, an example of a higher-level parameter of central importance in materials science and biophysics. Young’s modulus parameterizes the stiffness of a material and is identified as the slope (or coefficient of proportionality) of a stress-strain curve of a given material. Stiffness is understood as the resistance of a material to deformation in response to applied force and cannot be understood or defined at atomic scales. More generally, material parameters describe mechanical properties of a larger continuum of structure that cannot be measured or defined at the level of individual “parts”. As stressed by developmental biologist (and biophysicist) Lance Davidson and colleagues, material parameters of relevance for modeling of the development of an embryo are inherently higher-level concepts: The capacity of the notochord to resist bending as it extends the embryo comes from the structure of the whole notochord. Measurements at the level of the individual collagen fiber or fluid-filled cells that make up the structure would not reveal the mechanical properties of the whole notochord. (Davidson et al. 2009, p. 2157)

We can interpret this as a form of (mechanical) top-down causation, because biomechanical features influence the development of vertebrate embryos through constraints on motility and bending of cells (Green and Batterman 2017). As in the case of feedback loops, the higher-level material parameters cannot be achieved 9 Note

that “microstructure” here refers to structures far above the atomic and far below the continuum.

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through coarse-graining but requires measurements where the whole structure must be intact. Similarly, the action potential in neurons is a mesoscale parameter that cannot be measured or understood at the molecular or sub-cellular level because the property depends on the whole cell structure (Noble 2012). We should therefore not think of higher-level variables in this context as merely “smeared-out versions” of a more fundamental lower-level description. At the same time, the explanatory autonomy should not be overemphasized as there is clearly some connection between microstructure and material parameter values. In both physics and biology, modeling of materials over large spatial scales requires that scales are bridged, e.g., via the identification of RVEs. In biology, the relations between higher and lower-scale variables are often illustrated in diagrams through feedback relations going both up and down (see e.g., Noble 2012; Lesne 2013). Thus, the idea of a scale dependent relative autonomy offers an alternative to more extreme positions (reductionism or anti-reductionism), while capturing aspects of how scientists deal with multi-scale systems. In summary, examples of multi-scale systems that are heterogenous (unlike ideal gases) support a stronger interpretation of the causal role of higher-level variables in the context of mechanical top-down causation. Higher-level variables in such contexts are not coarse-grained in the weaker sense that they can be derived from lower-level details via simple averaging. Rather, the requirement for homogenization strategies in multi-scale modeling highlights how higher-level variables are relatively autonomous from lower-level descriptions. The examples thus challenge an assumption in the definition of mechanical top-down causation (Ellis 2008, 2012), but in doing so they also strengthen Ellis’ point about the importance and ubiquity of top-down causation and emergence in science.

2.4 The Practical Importance of Top-Down Causation Debates on the possibility or strength of top-down causation are often assumed to primarily be of theoretical interest to philosophers. However, as emphasized by Ellis and others, top-down causation and equivalence classes have important practical implications (Auletta et al. 2008; Ellis et al. 2012; see also Wimsatt 1976, 2007). Top-down causation, for Ellis, is not a mysterious metaphysical concept, but an empirical phenomenon that can be demonstrated through experimental intervention. He defines the following operational criteria for top-down causation: To characterize some specific causal effect as a top-down effect, we must demonstrate that a change of higher level conditions alters the sequence of processes at lower levels; we do this by changing higher level conditions and seeing what happens at the lower levels (Ellis 2012).

Thus, top-down causation is here given a concrete interpretation as a relation between system variables at different spatial scales or levels (see also Ellis 2016, p. 16, and Woodward forthcoming). If intervening on macroscale variables can change

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the dynamic states of microscale processes, it has important practical implications for the design of experiments, for multi-scale modeling, as well as for discussions about where and how to intervene to control and change future outcomes (such as disease definitions and treatment modalities in medicine, for instance). In the following, we present further examples of this view.

2.4.1 Top-Down Causation and Multi-scale Modelling Scientific explanations often highlight molecular activities (biology) or the role of laws and initial conditions (physics), but boundary conditions are often equally important for understanding system behaviors. In the context of multi-scale cardiac modeling, Noble (2012) argues forcefully that that the models describing the processes at the lowest scale, i.e., ordinary differential equations describing ionic currents, cannot be solved without the boundary conditions determined by the cell voltage. It is important to note here that cell voltage is a parameter that cannot be defined at the molecular or subcellular scale. Similarly, models of the action potential at the level of cells depend on inputs from models at the tissue scale (defined via partial differential equations), which describe how biophysical features of the tissue can influence the propagation of electrical currents through the 3D structure of the heart (Qu et al. 2011; Green 2018). Although parameters such as the cell voltage, or the geometrical and electrical properties of different tissue types are “nothing but” properties of physical structures, they are not reducible to or derivable from lower-scale variables. In fact, one cannot measure or even conceptualize these variables at lower scales. They also cannot be reduced to explanatory background conditions for descriptions of causal efficacy at lower scales, because the boundary conditions and higher-level parameters in general are required to channel the lower-level behaviors in the first place. As highlighted by Noble: “without the downward causation from the cell potential, there is no [heart] rhythm” (Noble 2012, p. 58). A reductionist perspective thus faces great difficulties in terms of showing that a bottom-up analysis is itself sufficient. In the context of developmental biology and cancer research, the importance of top-down causation is also increasingly acknowledged. New experimental techniques to manipulate higher-level biomechanical cues have revealed that macroscale biomechanical properties (e.g., tissue stiffness) can influence gene expression, molecular signaling pathways, as well as cell differentiation (Miller and Davidson 2013). This has important implications for understanding how biomechanical constraints can buffer genetic “noise”, and how there is sufficient causal slack between macroscale biomechanical models and molecular details to allow modelers to efface many lower-scale details. Moreover, it has (negative) implications for the view that genetic or molecular causation has a privileged role in developmental biology (this is further discussed in Green and Batterman 2017). The biases of such perspectives can also have important social implications, as we now clarify.

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2.4.2 Research and Treatment Modalities in Medicine Ellis (2012) highlights the existence of different treatment modalities in medicine, depending on whether one commits to a reductionist (bottom-up) perspective or to a more holistic view. This is particularly apparent in the case of mental disorders, where the focus can span from genetic susceptibilities and molecular dysfunctions to how states of the mind can impact physical health (see also Ellis 2016). Philosophical assumptions concerning the possibility and relative importance of topdown causation (vs. bottom-up causation) does, in fact, influence which research questions and treatment regime are seen as most promising. Attention to top-down causation can fruitfully point to the missed opportunities of the prioritized focus on reductionist research programs – and positively highlight the potential benefits of a broader perspective (Fuchs 2018). In closing, we provide a few examples to illustrate this view. Cancer is often understood as a disease caused by accumulation of somatic mutations. However, increasing evidence suggests that tissue-scale properties can sometimes overrule genetic instructions (Soto et al. 2008; Bissell and Hines 2011). The constraints of the tissue can either promote or reduce cell proliferation and motility, depending on the biomechanical properties of the tumor microenvironment, which is another important example of top-down causation (Green, forthcoming). Hence, the reductionist perspective may create unfortunate blind spots, such as the opportunity to develop treatment strategies that target tissue-scale properties (Stylianopoulos 2017). Similarly, the criticism of reductionism is highly relevant in the context of preventive medicine. With the promotion of precision medicine, the research focus on genetic factors that increase an individual’s susceptibility for developing complex diseases like cancer, depression, or dementia has intensified. But a focus on genetic factors is neither sufficient for understanding and treating such complex diseases, nor is it necessarily more precise. An important concern is that genetic risk profiling at the individual level shifts attention away from structural causes at the population level, such as socio-economic disparities, that may be more efficient to intervene on (Hoeyer 2019; Olstad and McIntyre 2019). Top-down causation is therefore not only of theoretical philosophical interest, but it is an empirical phenomenon with profound scientific and social implications.

2.5 Concluding Remarks Explanatory autonomy of levels or scales is often defended with reference to the existence of universality or functional equivalence classes. Universal or functionally equivalent behaviors are described through macroscale models and parameters that cannot be reduced to lower-level models. Examples examined in this chapter include thermodynamics near critical points as well as feedback control in biology. The examples illustrate how models can be explanatory without specifying how

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a behavior is causally realized in any specific system. In fact, generic models are explanatory because they show how many causal details are explanatorily irrelevant as long as stabilizing structures defining an equivalence class are in place. The notion of information hiding highlights that there is enough “causal slack” at the bottom to make the inclusion of all possible lower-level details irrelevant or even counterproductive for the purpose of explaining higher level or multi-scale systems. A key issue in discussions of reductionism and top-down causation is whether higher-level variables can be derived from lower-level details. Mechanical topdown causation is often seen as a weak form of top-down causation, because the high-level variables are taken to be nothing but coarse-grained correlates of lowerlevel variables. Thus understood, it is unclear whether reductionism is overcome. We have argued that upscaling of variables via coarse-graining only works for simple homogenous systems, such as an ideal gas. For systems with complex microstructures at the mesoscale (such as steel or bone), more involved upscaling techniques are required. The reason is that physical systems at different scales display distinct physical structures and behaviors, and that higher-level behaviors are dependent on some microstructural details that are best studied at the mesoscale. Mesoscale parameters (such as material parameters) differ from what Ellis calls coarse-grained high-level variables in being identified via homogenization strategies. The need for such strategies signals a stronger explanatory autonomy of high-level variables also in physical examples than often assumed. Hence, attention to scale-dependency of characteristic behaviors in multi-scale systems offers support to Ellis’ account by further extending the scope and significance of mechanical top-down causation. Top-down causation is not a suspicious, rare form of causation, but is ubiquitous in physical and biological systems alike. This has important practical implications not only for scientific modeling and explanation, but also for how we best approach complex socio-scientific problems.

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Chapter 3

Mathematics and Measurement: Causation and the Mind Otávio Bueno

Abstract In this paper, I discuss two aspects of top-down causation in George Ellis’s compelling account of this complex concept. I first examine whether mathematical structures can enter into any causal relations, and argue that it is unclear that they can. I highlight instead the role played by the interpretation of mathematical theories in the context of applied mathematics. Second, I consider the role played by top-down causation in measurement, especially in quantum mechanics but also elsewhere, and identify the importance of the observer in this context. I am in large agreement with Ellis’s overall message, but we may understand certain details a bit differently. I articulate the message within a broadly empiricist setting. Keywords Measurement · Top-down causation · Interpretation · Mathematics · Observer · Dirac

3.1 Introduction In How Can Physics Underlie the Mind? (Ellis 2016), George Ellis provides a compelling case for the importance of top-down causation across the sciences (in particular, physics, biology, computer science, and cognitive sciences) and beyond. It is a wide-ranging work, with a very clear thesis that is supported by a variety of examples. The thesis, in a nutshell, insists on the importance not only of the familiar bottom-up causation (from basic physical levels to non-physical domains), but especially of top-down causation (from the mental to the physical) in the characterization of hierarchical structures. As Ellis notes: It is the combination of bottom-up and top-down causation that allows genuinely complex behaviour to emerge out of simple components combined together to form modular hierarchical structures. As well as bottom-up causation, top-down causation takes place in these structures [ . . . ] through the crucial role of context in determining the outcomes of lower level causation. (Ellis 2016, p. 5; italics added)

O. Bueno () Department of Philosophy, University of Miami, Coral Gables, FL, USA © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_3

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It is this “crucial role of context” that I want to focus on by engaging with two cases that Ellis examines: the causal role of mathematical structures and the role of topdown causation in measurement (especially in quantum mechanics). I am in large agreement with his overall message, although we may disagree on matters of detail and I will articulate the message within a broadly empiricist setting.

3.2 Mathematics and the Mind The ontology of mathematics is typically presented as one that involves objects and structures that are neither located in spacetime nor causally active (see Lewis 1986; Hale 1987; Colyvan 2001). One of the interesting consequences of emphasizing the role of top-down causation is that mathematics becomes, at least under a certain interpretation, causally active. In fact, according to Ellis, the abstract world of mathematics is causally efficacious: This abstract world is causally efficacious in two ways. First, it can be explored by the human mind and the resulting relationships shared and represented in many ways. One can, for example, print graphic versions of the Mandelbrot set in a book, resulting in a physical embodiment of this abstract pattern in the ink printed on the page. (Ellis 2016, p. 367)

It is the exploration of mathematics by the human mind that allows one to uncover new relations among abstract objects, and to represent such relations in the physical world, such as with a printed representation of an abstract pattern in the case of the Mandelbrot set. But this is not the only way in which the abstract world is causally efficacious. Ellis continues: Second, the resulting relations [among abstract objects] can be used in commerce, physics, and engineering to analyse possibilities and so make changes in the world. For example, mathematics underlies decisions in commerce and construction projects in building and engineering that alter the world around us. It also underlies the way physics underpins engineering, e.g., the way Maxwell’s equations underlie the telecommunications industry [ . . . ]. Thus mathematical relations make a real difference to what happens in the world. (Ellis 2016, p. 367)

By using mathematics in the analysis of possibilities, changes in the world can be acted on. An engineering project, such as the construction of the Golden Gate bridge, designed and guided by careful mathematical considerations, embody the kinds of changes in the world that mathematics can bring about. Properly understood, this is a plausible view. There is no doubt that mathematics plays a crucial role in our ways of representing, understanding, and changing the world. Popper (1972) also defended the view that the mathematical world (part of his World 3) is causally efficacious. But it is not clear to me that that the mathematical world itself needs to be causally efficacious for mathematics to play such role in our understanding and changing of the world. After all, the same mathematical structures are compatible

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with radically different physical situations, with distinct causal profiles. So, it is not clear that mathematics is causally active and responsible for the effects in the physical world, given the compatibility between the relevant mathematical structures and no corresponding causal change. Consider, for instance, the case of the Dirac equation in quantum mechanics: this is a significant equation that has negative energy solutions. The issue is then how to interpret such solutions. As it turns out, the equation and its solutions are compatible with three very different physical situations. The first is one in which the negative energy solutions are taken not to correspond to anything in the physical world. This was Paul Dirac’s initial reaction to the equation that now bears his name after he first encountered it 1928. The reaction is quite reasonable, and in fact it is the same reaction one typically has when facing negative solutions to equations in classical mechanics. By 1930, however, Dirac proposed a different interpretation of the Dirac equation: the negative energy solutions correspond to “holes” in spacetime. But as it was promptly pointed out by Werner Heisenberg and Hermann Weyl, among others, on this interpretation, electrons and protons would have the same mass, which is clearly empirically inadequate. Unperturbed, in 1931, Dirac advanced a third interpretation of the same equation, according to which the negative energy solutions correspond to a new particle that has the same mass as the electron but the opposite charge. In the following year, 1932, Carl Anderson produced a cloud chamber image of cosmic radiation that, suitably interpreted, can be taken as supporting the existence of such particle: the positron had been discovered. (For further details and references, see Bueno 2005). This example illustrates a common feature of mathematics: a radical form of underdetermination in which the same mathematical relations are compatible with radically different empirical situations. The Dirac equation and its negative energy solutions are compatible with three very different physical circumstances: (i) one situation in which the solutions do not correspond to anything physically real, and so no causal outcome is expected or observed; (ii) another situation in which the solutions are connected to “holes” in spacetime, and end up introducing something that is empirically inadequate, and finally, (iii) yet another situation in which the solutions refer to a new particle, for which some empirical evidence is eventually produced. Given such underdetermination, it seems that the relevant mathematical structures do not determine uniquely a causal outcome in the world. The fact that the Dirac equation is also compatible with the absence of any causal change, as the first situation above clearly illustrates, seems to question the adequacy of attributing causal powers to the mathematics. The issue then is whether it is the abstract world of mathematics that is causally efficacious or whether it is one’s actions in the world, in some cases informed by suitable interpretations of a mathematical formalism, that ultimately are. The fact that the same mathematics is compatible with very different physical states in the world seems to question that a direct causal link between the abstract world and physical circumstances can be established. Any such link is mediated by suitable interpretations of the mathematical structures, with the consequence that rather than the mathematics, it is its interpretations, connecting the relevant

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abstract structures to corresponding physical processes, that are playing the crucial role. The mathematics, important as it is, provides an overall framework only, one that is silent about the causal processes of what goes on in the physical world. The hard work of connecting this framework to concrete physical processes requires apt interpretations, which often are not unique and lead to very different causal outcomes. As an additional illustration, consider the case of the axiom of choice, which, in one of its many formulations, specifies that any collection of non-empty sets has a choice function, that is, a function that yields a corresponding element from each set in the original collection. As is well known, it follows from this axiom that every set can be well-ordered. The choice function provides the existence of a well-ordering even if it cannot exhibit the particular well-ordering in question. This is a result that Ernst Zermelo established in the early days of set theory (Zermelo 1904). In fact, in light of the controversy generated by the explicit formulation of the axiom of choice, the well-ordering result eventually led Zermelo to articulate the first axiomatization of set theory (Zermelo 1908; for a discussion, see Kanamori 1997). But the axiom of choice also has unexpected consequences, and the so-called Banach-Tarski “paradox” is a significant example. According to this result, given a solid sphere, it is possible to decompose it into finitely many pieces that can be put together to form two solid spheres of the same size as the original one. (For further discussion of consequences of the axiom of choice, see Bell 2009.) The sense of paradox emerges from the confusion generated by considering that a physical sphere (perhaps an orange) could be sliced and reassembled into two spheres (two oranges). Clearly, this is not possible, and the Banach-Tarski theorem in no way states otherwise. In fact, the theorem applies to abstract objects only: the spheres in question do not have a volume (they are, rather, infinite scattering of points), and the theorem has nothing to say about what can or cannot be done with concrete objects, such as fruits. Once again, there is no direct causal link from abstract entities to concrete configurations in the physical world. Perhaps it could be argued that mathematics has only a dispositional causal role: it us only under suitable circumstances that the causal effect of mathematics would be felt in the world. Humans (or creatures with corresponding intentional capacities) need to be present and able to interpret appropriately the relevant mathematical structures and to implement the corresponding actions in the world (building bridges, aircrafts, particle accelerators) based on the abstract patterns provided by the mathematics in question. But the point is that without the relevant mathematics, several such constructions could not be created at all. This brings the issue of the indispensability of mathematics to scientific, engineering, and technological practices (Colyvan 2001). I certainly grant that mathematics is indeed indispensable to much of these practices and even in those cases in which it can be dispensed with (such as in simple arithmetical calculations that can be carried out in terms of logic alone), there is no question that mathematics provides powerful representational devices that simplify enormously the inferential processes involved. However, even granting the indispensability of mathematics, an

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additional step is needed to conclude that mathematics needs to be causally active in order for it to play such indispensable role. Here is a different account of the situation: Mathematical structures are abstract and, as such, are causally inactive and are not located in spacetime. They do not specify anything directly about the physical world, since physical processes are concrete: they are spatiotemporally located and causally active. Simply put, if mathematical structures specify relations among functions, numbers, and sets, and if all of these entities are taken to be abstract, none of them are part of the physical world, assuming, as is usually the case, that the latter is taken to be concrete. At best, mathematical structures impose cardinality restrictions only. Presumably, if all the models of a given mathematical theory are finite, they would not be adequate to accommodate phenomena that involve infinitely many items. Cardinality considerations aside, it is unclear that abstract mathematical structures per se can be causally efficacious (or have any causal power), despite their undeniable role in the representation of physical phenomena and in the analysis of possibilities involved in the design and construction of buildings and artefacts in the world. Rather than describing this process as a form of top-down causation from abstract structures to physical phenomena, processes, and events, it can be accounted for in terms of the inferential role played by mathematics in the representation of the physical world. Mathematical structures provide information about possible (or impossible) configurations in a given abstract domain. Once suitably interpreted, as Dirac did when he was trying to connect to the physical world negative energy solutions to the Dirac equation, mathematical results can be used to draw inferences about concrete objects. Describing the inferential process as a form of top-down causation is, no doubt, highly suggestive, but it seems to require that abstract structures themselves be causally efficacious. For that to be the case, such structures would need to be part of the causal network of the concrete world, being spatiotemporally located and causally active. The difficult is how to make sense of these traits in the context of abstract entities. Perhaps it could be argued that mathematical objects and structures are located wherever the concrete objects they are applied to are located. In this sense, abstract structures would have causal powers provided that the concrete objects they apply to have such powers and are, thus, causally efficacious. As long as there is a tight connection between the abstract and the concrete (in terms of colocation and identification), it is not difficult to understand how the former can have precisely the same powers as the latter. The difficulty, however, is that mathematical theories typically have far more structure than any of its potential physical instantiations do. Part of the reason why mathematical theories can be so useful in applications to the physical world is due to the additional, surplus structure they provide (Bueno and French 2018). The example from the Dirac equation above also illustrates this point, given the role played by a mathematical feature that initially was thought to be entirely otiose (namely, negative energy solutions), and thus was considered to be just part of a structural surplus, but which, with proper physical interpretation, turned out to be

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heuristically quite fruitful, eventually leading to the discovery of a novel particle (the positron). Interestingly, when Anderson was asked whether he knew of Dirac’s work, he acknowledged his awareness of Dirac’s papers, but noted that he was so busy dealing with his instruments that, as far as he was concerned, the discovery of the positron was “an accident” (for references, see Bueno 2005). Since mathematical theories typically provide structures whose size is much larger than anything found in the concrete world, it is unclear how such structures can be physically located in the regions they are applied to. In the case of infinite mathematical structures, they can never be fully instantiated in any portion of the physical world (assuming that it is finite). As a result, it may not be possible to determine uniquely which mathematical structure is, in fact, being applied. After all, there are several non-isomorphic structures that overlap with the initial segment of the one that is allegedly being applied, but which diverge from it elsewhere, with the result that it is undecided which structure is ultimately at stake. For these reasons, it seems less problematic to accommodate the use of mathematics and abstract structures in the sciences and beyond by examining, as suggested above, the role played by interpretations of the relevant structures rather than by emphasizing the potential causal connections between mathematical structures and physical phenomena. This allows one to acknowledge, with Ellis’s topdown causation approach, the immense and decisive significance of mathematical structures in shaping the concrete world, albeit by emphasizing the role played by proper interpretations of the structures in question, without the commitment to the existence of direct causal connections between the abstract world and physical reality.

3.3 Measurement and Top-Down Causation Another domain in which top-down causation is also crucial, according to Ellis, is in microphysics, particularly in the context of measurement in quantum mechanics. It is usual and important to distinguish the evolution of a quantum system, which evolves in accordance with the Schrödinger equation, from the measurement process, which, after suitable preparation, aims to determine the system’s state. As Ellis points out: Measurement is a process with significant parallels to the process of state preparation, in that both can change a wave function that is a superposition of states to an eigenfunction. Hence, they are non-unitary processes that are not equivalent to action by the Schrödinger equation. (Ellis 2016, p. 273)

It is also usual and important to distinguish the observer from the quantum system under study; otherwise, instead of a measurement of the system, the interaction between the measurement apparatus and the system to be measured would simply amount to just another physical interaction to be accounted for by quantum mechanics. But measurement is not just any interaction: it involves something special in light of the presence of an observer and the observer’s ability to influence

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certain aspects of the measurement process. It is precisely at this juncture that topdown causation enters. Ellis stresses this aspect: The experimental viewpoint is that the macro observer and apparatus have an existence as macro entities that can be taken for granted, and that can influence quantum states both in terms of enabling state vector preparation, and in terms of determining the context for outcomes of a measurement, for example, by determining the axes along which spin will be measured. These are of course both cases of top-down causation. (Ellis 2016, pp. 273–274; italics added)

Ellis is exactly right in identifying both types of influences that an observer can have in the measurement process (namely, to enable state vector preparation and to provide a context for measurement outcomes) as instances of top-down causation. After all, both cases involve, roughly speaking, influences from the mental to the physical. Both cases are also fairly sensible, unlike to engender perplexing difficulties or challenges specific to quantum mechanics. After all, one finds, mutatis mutandis, similar instances of them in other kinds of measurements in the sciences. For example, in order to use transmission electron microscopes, biologists need first to prepare the sample properly, on pain on not being able to detect anything useful through the measurement process. Measurements can yield minimally adequate outcomes only after the proper interaction between the sample and the microscope has been set. In other words, sample preparation is an indispensable step, which informs the entire process of measurement. This includes cutting a piece of the studied material in the proper size, gluing the piece to the glass plate, grinding and polishing the sample, and finally placing it into the sample holder. The choices and apt actions of the observer, performed in each stage of the process, clearly illustrate the role played by top-down causation in the measurement process. Had the choices been different (a different portion from the studied material; a misplaced sample on the sample holder), and the outcome of measurement (the corresponding micrograph) would be correspondingly different. The observer clearly enables and implements the sample preparation. Similarly, the determination of the “context for outcomes of a measurement” is central in electron microscopy as well. After all, the way in which the material in the sample is cut may yield significantly different outcomes, which are eventually exhibited by different micrographs. One may think, in light of the information provided in a micrograph, that the shape of a given cellular structure is oblong, whereas if one takes into account its three-dimensional structure, the relevant shape is closer to a cylindrical form. The context for outcomes of a measurement is, thus, crucial for the proper determination of the relevant measurement outcomes, so that one can understand properly the significance of the results that are obtained. Consider, for instance, the determination of the shape of mitochondria on the basis of suitable micrographs. Attention to the proper context for measurement outcomes is central to avoid improper inferences being drawn from the results of the measurements. But should outcomes of the use of electron microscopes be considered measurements? I think the answer is affirmative, but it depends, of course, on the underlying conception of measurement. Such a conception should be broad enough to allow one

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to understand how measurements are involved in different practices not only across physics, chemistry, and biology, but also throughout several other representational activities, such as lithic illustrations in archeology (Lopes 2018, Chapter 10) and perspectival drawing in the fine arts (van Fraassen 2008, Chapters 1–3). In its most general form, a measurement has two traits (van Fraassen 2008, p. 91): (a) it is a particular kind of physical interaction, and (b) it is a process of collecting relevant information, appropriate for that kind. Condition (a) guarantees that measurements are physical processes and, thus, in principle the kind of thing that is able to provide information about the physical world. Condition (b) specifies the purpose of measurement as a process of obtaining relevant information. Of course, what counts as relevant is a highly context-sensitive matter, and this, in principle, allows for measurements to operate across a variety of domains—in fact, anywhere in which physical information (broadly understood) can be obtained. As Bas van Fraassen emphasizes: A measurement is at the same time a physical interaction and a meaningful information gathering process. (van Fraassen 2008, p. 91)

On this conception, to obtain a measurement is to represent the relevant phenomena in a certain way, from the perspective of the measuring device or technique in question. And van Fraassen continues: measurement falls squarely under the heading of representation, and measurement outcomes are at a certain stage to be conceived of as trading on selective resemblances in just the way that perspectival picturing does. (van Fraassen 2008, p. 91)

A perspectival drawing provides a particular technique to transform, or to transfer, a three-dimensional scene into a two-dimensional surface. The technique involves a process, the steps involved in achieving the proper result, and a product, the final drawing, implemented up to perspective. Both have close ties with measurement. According to van Fraassen: Perspectival drawing provided us with a paradigm example of measurement. The process of drawing produces a representation of the drawn object, which is selectively like that object; the likeness is at once at a rather high level of abstraction and yet springing to the eye. While the information about spatial configuration is captured in an invariant relationship that is quite difficult to formulate in words or equations, it is conveyed to us in a userfriendly fashion. The example is paradigmatic also in that it displays so clearly that the representation (the measurement outcome) shows not what the object is like ‘in itself’ but what it ‘looks like’ in that measurement set-up. The user of the utilized measurement instrumentation must express the outcome in a judgment of form “that is how it is from here”. And finally, the coin has another side: it is precisely by a process engendering a judgment of that form—that is to say, by a measurement!—that any model becomes usable at all. (van Fraassen 2008, pp. 91–92)

Interestingly, the observer in a perspectival drawing selects the angle from which the scene is going to be depicted and the measurement outcome, the drawing itself, will display how the scene looks like from that angle: “that is how it is from here”. The selection of that angle (the framing of the scene) corresponds to a form of preparation for a measurement, and the resulting selectivity (only what can be seen from the perspective of the viewer is displayed on the drawing) provides the context

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for outcomes of a measurement. In this way, both forms of top-down causation identified by Ellis in measurement (2016, pp. 273–274) seem to be present in perspectival drawings. Continuing his discussion of measurement in quantum mechanics, Ellis notes: Here by a measurement, we mean a process whereby quantum uncertainty is changed into a definite classical outcome that can be recorded and examined as evidence of what has happened. (Ellis 2016, p. 247)

Clearly, as Ellis indicates by situating the discussion within quantum mechanics, if measurement is understood in these terms, it becomes a concept specific to quantum theory, since it involves the shift from quantum uncertainty to the definiteness of a classical outcome. But in light of the discussion above, despite the crucial role played by measurement in quantum theory, other scientific domains, and many other areas beyond the natural sciences, including perspectival drawing and lithic illustrations, also provide and rely on measurements, which is a key source of information about the world. As a result, a notion of measurement that is not exclusively tied to quantum mechanics, or that does not take quantum mechanics as the paradigmatic case, is also needed. Ellis does emphasize an aspect of measurement that offers a broadening of the concept by removing the need of an observer: measurement, he notes, is primarily a physical process that can, in fact, take place independently of observers. On his view: It is not necessary for an observer to actually make any measurements. For example, it happens when a photon falls on a physical object such as a screen, a photographic plate, or the leaf of a plant, and deposits energy in a particular spot on the object at a particular time and place. In more technical terms, it occurs generically when some component of a general wavefunction collapses to an eigenstate of an operator [ . . . ]. (Ellis 2016, p. 247)

There is no doubt that in order for measurements to yield relevant information, they need to be physical processes of a suitable kind. Without a proper physical interaction, it is unclear that a measurement could take place. However, until an observer decodes the relevant information, the measurement will fail to yield any such result. If measurement involves “a meaningful information gathering process” (van Fraassen 2008, p. 91), an observer with intentionality seems to be required. Otherwise, only a physical interaction would have occurred, rather than a measurement. The very role played by top-down causation in measurement, clearly highlighted by Ellis, seems to demand observers in the measurement process, in light of the two kinds of influences, discussed above, that observers can have in measurement: they enable state vector preparation and provide a context for measurement outcomes (Ellis 2016, pp. 273–274). To a certain extent, this point is emphasized by Ellis himself. As he notes: We cannot pronounce on the measurement process itself, because quantum physics is still unable to explain how this happens. This, too, may be contextually dependent. What is clear is that the local context (such as what type of experimental apparatus is used) influences quantum measurement outcomes [ . . . ]. For example, if we measure spin, the resulting final state is different than if we measure momentum. The lower level physics is not immune to higher level influences. (Ellis 2016, p. 239)

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In this passage, there is a clear and correct acknowledgment that the kind of measurement to be performed influences the measurement outcome via the selection of the magnitude to be measured. Also highlighted are the differences of the various kinds of measurements: spin measurements are clearly distinct from momentum measurements. Taken together, these considerations seem to support, once again, the importance of the observer in the measurement process. After all, the choice of the distinct kinds of measurement to be performed is the observer’s choice. Significantly, and still in the context of quantum mechanics, measurements, and thereby observers, are involved in an additional key feature of quantum theory: the uncertainty of measurement outcomes. According to Ellis: It is a fundamental aspect of quantum theory that the uncertainty of measurement outcomes is unresolvable: it is not even in principle possible to obtain enough data to determine a unique outcome of quantum events [ . . . ]. This unpredictability is not a result of a lack of information: it is the very nature of the underlying physics. This uncertainty is made manifest when a measurement takes place, and only then. Without measurements, there is no uncertainty in quantum processes. (Ellis 2016, p. 247)

Ellis echoes here a point Anthony Leggett emphasizes: [ . . . ] it is the act of measurement that is the bridge between the microworld, which does not by itself possess definite properties, and the macroworld, which does. (Leggett 1991, p. 87; quoted in Ellis 2016, p. 247)

Given the centrality of measurement in quantum theory and the role of observers in top-down causation, it seems that observers are ultimately required in the measurement process after all.

3.4 Conclusion As the considerations above should make clear, there is much in Ellis’s insightful approach to top-down causation that I admire, and there is much to be learned from. Although I have expressed some concerns about causation in the context of mathematics, and tried to suggest a friendly amendment to Ellis’s considerations in that context, I fully agree with his emphasis on top-down causation in measurement more generally. It just seems to me that observers should then be a key component of the measurement process throughout.

References Bell, J. L. (2009). The axiom of choice. London: College Publications. Bueno, O. (2005). Dirac and the dispensability of mathematics. Studies in History and Philosophy of Modern Physics, 36, 465–490. Bueno, O., & French, S. (2018). Applying mathematics: Immersion, inference, interpretation. Oxford: Oxford University Press.

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Colyvan, M. (2001). The indispensability of mathematics. New York: Oxford University Press. Ellis, G. (2016). How can physics underlie the mind? Top-down causation in the human context. Berlin: Springer. Hale, B. (1987). Abstract objects. Oxford: Blackwell. Kanamori, A. (1997). The mathematical import of Zermelo’s well-ordering theorem. Bulletin of Symbolic Logic, 3, 281–311. Leggett, A. J. (1991). Reflections on the quantum measurement paradox. In B. J. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in Honour of David Bohm (pp. 85–104). London: Routledge. Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell. Lopes, D. (2018). Aesthetics on the edge: Where philosophy meets the human sciences. Oxford: Oxford University Press. Popper, K. (1972). Objective knowledge: An evolutionary approach (Rev. ed., 1979). Oxford: Oxford University Press. van Fraassen, B. C. (2008). Scientific representation: Paradoxes of perspective. Oxford: Oxford University Press. Zermelo, E. (1904). Neuer Beweis, dass jede Menge Wohlordnung werden kann (Aus einem an Herrn Hilbert gerichteten Briefe). Mathematische Annalen, 59, 514–516. (English translation in J. van Heijenoort (Ed.), From Frege to Gödel: A source book in mathematical logic, 1879– 1931 (pp. 139–141). Cambridge, MA: Harvard University Press, 1967). Zermelo, E. (1908). Untersuchungen uber die Grundlagen der Mengenlehre. Mathematische Annalen, 65, 107–128. (English translation in J. van Heijenoort (Ed.), From Frege to Gödel: A source book in mathematical logic, 1879–1931 (pp. 199–215). Cambridge, MA: Harvard University Press, 1967).

Part II

The View from Physics

Chapter 4

Strong Emergence in Condensed Matter Physics Barbara Drossel

Abstract This chapter argues that the physics of condensed matter, such as crystals, superconductors, magnets, liquids, cannot be fully reduced to the supposedly fundamental quantum mechanical theory for all the atoms of which the system consists. The author holds the view that there are in fact many reasons to reject the idea that the world of physics is causally closed with everything being determined bottom-up by fundamental microscopic laws. A considerable part of the chapter is devoted to showing how condensed-matter theory is done in practice. It is never done by starting with a microscopic theory for the interaction of all the atoms of the system. Instead, approximations, plausible assumptions, intuitive models, and phenomenological theories are used to mathematically describe and explain the properties of systems that consist of a macroscopic number of particles. The author argues that this is not merely a matter of convenience, but that there are fundamental and qualitative differences or even contradictions between the microscopic theory and the theory that is used in practice. These differences are in many cases due to the fact that the world is classical, with spatially localized objects, on the macroscopic scale, while quantum mechanics leads to superpositions of objects being in different locations. Concordantly, the theories used in condensed matter physics contain elements from classical physics as well as from quantum physics. The outline of the chapter is as follows: 1. Introduction: The author tells how she struggled as a physics student trying to understand how the calculations presented in the lectures relate to the supposedly fundamental theory, until she came to see many years later that there are fundamental and interesting issues behind the questions she asked herself as a student. 2. Example systems: Several examples from condensed-matter physics are given to illustrate the types of phenomena addressed in the chapter. A distinction is made

B. Drossel () Institute for Condensed Matter Physics, Darmstadt, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_4

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between equilibrium systems, which can be separated from their environment without losing their properties, and nonequilibrium systems. Defining reduction and emergence: These concepts are defined with an emphasis on the difference between weak and strong emergence. It is explained that the reductionist method has been extremely successful in physics, but that nevertheless a discussion is needed concerning the quality of this reduction: is it complete (which means that emergence is weak), or is it incomplete (which means that emergence is strong). The relation to top-down causation is explained. Condensed matter research in practice: By quoting three Nobel laureates, it is shown how condensed-matter research is done in practise. These authors provide good arguments against a reductionist view. These three examples are supplemented by the author’s expertise in statistical physics, showing that the supposed reductionist explanations made in this field import ideas that are foreign to the microscopic theory. Arguments for strong emergence in physics: Based on the information provided so far, the author now gives six reasons for strong emergence, including dependence on the environment, stochasticity, and insensitivity to microscopic details. Answers to objections: The author responds to several objections that she often hears in discussions about reduction and emergence. The main objection is that future progress of physics might yield the missing full microscopic explanations. The author counters that her arguments give generic reasons why a full reduction is not possible in principle.

4.1 Introduction When I was a physics student, I often had the impression that I did not really understand the material that was presented. The reason was that the presented calculations were claimed to be based on the ‘fundamental theory’, usually quantum mechanics, but many of the steps that were made did not seem to really follow from the equations of quantum mechanics. These equations are deterministic, linear in the wave function, and invariant under reversal of the direction of time. In contrast, the calculations presented in the classes appeared to involve concepts that are incompatible with these features. Time reversal symmetry was broken when dealing for instance with the scattering of a quantum particle at a potential: the incoming particle is assumed to be not affected by the potential, but the outgoing particle is. Chance is introduced when basing all of statistical physics on probabilities, or when transition probabilities between quantum states are calculated, as for instance in scattering theory. The supposedly ‘simple’ Hartree-Fock theory, a socalled mean-field theory that is used for calculating approximately the quantum mechanical ground states of many-electron atoms, is nonlinear in the wave function. Furthermore, elements from classical mechanics and quantum mechanics are often mixed, for instance when describing electrons as balls when explaining the origin

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of the electric resistance, or when calculating the configuration of molecules by assuming that the atomic nuclei have well-defined positions in space. Whether on purpose or unintentionally, many courses and textbooks made us students believe that in principle everything follows from a set of fundamental laws, but that in practice it is unconvenient or unfeasable to do the exact calculation, and therefore approximations, plausible assumptions, intuitive models, and phenomenological arguments are made. Only years later, I slowly began to understand that my problems had not primarily been due to a lack of talent and understanding on my side, but that there are indeed fundamental and interesting issues behind all these questions, some of which are the subject of lively discussions in the philosophy of physics. Probably the most important factor that made me change my views was becoming a physics professor and teaching these courses myself. In particular the courses on statistical physics and condensed matter theory showed me that even the most advanced textbooks and research articles contain concepts, arguments, and steps that are a far cry from a strict derivation of the phenomena exclusively from a set of basic axioms or mathematically expressed laws. Looking back to my time as a student, I wish I had been taught about the interesting philosophical questions surrounding physics. Because we were lacking this information, I and probably many of my fellow students thought that physics is the most fundamental science, and that by learning quantum physics and particle physics we would learn the laws that rule nature at the most fundamental level. As a consequence of this experience, I adopted in the meantime the habit of pointing these philosophical issues out to students when presenting the course material or when teaching seminars. When writing down the deterministic, timesymmetric equations of classical mechanics, electrodynamics, or quantum mechanics, I address the question whether this implies that nature is indeed deterministic or time-symmetric. When mentioning probabilities in statistical mechanics, I address the question how this relates to the supposedly more ’fundamental’, deterministic microscopic theories. When presenting the various models and methods of condensed-matter theory, I discuss how these models contain a mixture of elements from quantum and classical physics. Furthermore, I now have discussed the issue of emergence and reduction for a couple of years in a seminar that I teach during the winter semester to master students of physics. The following pages will explain in a more detailed manner that condensed matter physics cannot be fully reduced to the supposedly ’fundamental’ theory, which is quantum mechanics of 1023 particles. This means that many properties of condensed-matter systems are strongly emergent. It also means that the macroscopic properties of condensed matter systems have a top-down causal influence on their constitutents. In this way my contribution relates to the overall topic of this book and the workshop from which it results, which is top-down causation. The outline of this paper is as follows: First, I will give a series of examples of condensed-matter systems that show emergent phenomena and that illustrate the issues to be discussed subsequently. Then, I will define the concepts of reduction and emergence, with a focus on the distinction between weak and strong emergence, as

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they will be used later in the article. Next, using the texts by three Nobel laureates in condensed matter theory, I will show how condensed matter research is done in practice, and I will supplement it with insights from my own field of expertise, which is statistical physics. Based on all this information, we will then obtain list of reasons for accepting strong emergence in physics. Finally, I will deal with some widespread objections.

4.2 Example Systems Solids, liquids and gases are systems of 1023 particles that show many properties that the particles themselves don’t possess: pressure, temperature, compressibility, electric conductivity, magnetism, specific heat, crystal structure, etc. It is an important goal of statistical physics and condensed matter theory to explain or even predict these properties in terms of the constituent atoms or molecules and their interactions. And these two fields of physics have indeed been very successful at relating these properties to the microscopic makeup of the respective system. One reason for this success is that these systems can be discussed without need to refer explicitly to their context. The listed properties are properties of an equilibrium system. The wider context enters only implicitly as it determines which objects are present, how they are arranged, and what are the environmental variables, such as temperature or pressure or the applied electrical or magnetic field. Other condensed matter systems are open systems or driven systems: they can show patterns and structures that depend crucially on their being embedded in a certain context, as they obtain a continuous input of energy and/or matter from their environment and pass energy and matter to their environment in a different form. An important example is thermal convection: when a gas or liquid is heated from below such that it is cooler at the upper surface than at the lower, the gas or liquid can be set into motion to form of convection rolls and thus transports heat efficiently from the warm to the cool surface. Such differences in temperature drive to a considerable part the weather and climate on earth. In this case, the temperature differences are due to the sun’s radiation heating the earth surface more at some places than at others. A particularly fascinating example of patterns in open systems are spiral patterns. They are for instance observed in the Belousov-Zhabotinsky reaction, which is an oscillating chemical reaction that cycles through three different reaction products, with the presence of one aiding the production of the next one. When put in a petri dish, one can observe spiral patterns. This pattern persists only for a limited time unless reaction products are continually removed and reaction educts are continually added. The most complex open systems are living systems. They require a continuous supply of resources from which they obtain their energy, for instance oxygen and food, and they pass the reaction products, such as carbon dioxide and water, to the environment. More importantly, they communicate continuously with their environment, obtaining from it cues about danger and food, and shaping it for instance by building burrows, farming lice, exchanging information with their

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conspecifics and other species, and by pursuing the production and survival of their offspring. Driven systems are also investigated by theoretical physicists, employing theories that refer to the parts of the systems and their interactions, however, such theories use a different level of description and don’t usually refer to quantum mechanics. In this article, we will mainly focus on the first class of systems, as they appear to be less complex and more easily accessible to a description by a fundamental microscopic theory.

4.3 Defining Reduction and Emergence As already indicated, the natural sciences, in particular physics, work in a reductionist way: they aim at explaining the properties of a system in terms of its constitutents and their properties, and they are very successful at this endeavor. More precisely, physicists perform a theoretical reduction (and not an ontological reduction), which means that the property that one wants to explain is obtained mathematically by using elements of a microscopic theory that deals with the constituents of the system. Thus, for instance, the pressure of a gas is expressed in terms of the force that the atoms exert on the surface when they are reflected from it, and the temperature in terms of the kinetic energy of the atoms. The electrical resistivity is obtained from a mathematical description of the collisions of electrons with lattice vibrations and crystal defects. The oscillations and waves observed in the BelousovZhabotinsky reaction are reproduced from a set of chemical reaction equations for the concentrations of the molecules occurring in the system. Even beyond the realm of physics proper this type of approach is successful: the occurrence of traffic jams can be calculated based on models for cars that follow simple rules involving preferred velocities and preferred distances, the dynamics of ecosystems from biological populations feeding on each other, and stock market crashes from models of interacting agents. Emergence in a very general sense is the occurrence of properties in a system that the constituents don’t have. In the previous section, examples for such emergent properties were given. So far there is nothing contentious about these general concepts of emergence and reduction. The discussion starts when one wants to assess the extent and nature of this reduction or emergence. Broadly speaking, there are two possible points of view: Either reduction is complete, at least in principle, and therefore emergence is weak; or reduction is incomplete and emergence is strong. Complete reduction means that the property or phenomenon to be described is completely contained in and implied by the microscopic theory. Incomplete reduction means that although the microscopic theory is successfully used, one invokes additional assumptions, approximations, hypotheses, or principles that are not part of the microscopic theory. Concordantly, weak emergence means that although the system has new properties, which are the emergent properties, these are fully accounted for by the microscopic theory. Strong emergence, in contrast, means

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that there is an irreducible, generically new aspect to the properties of the system as a whole that is not contained in or implied by the underlying theory. Strong emergence is closely associated with top-down causation. If higher-level properties are not fully accounted for by the lower-level theory, but if they affect the behavior of the system, then they also affect the way in which the constituents behave. This means that there is a top-down causation in addition to bottom-up causation. The picture underlying these concepts of emergence and reduction is that of a hierarchy of entities and systems, with the objects of one hierarchical level being the parts of the objects on the next level. Several such hierarchies can be constructed. One hierarchy that leads up to human societies is the following: Elementary particles—atoms—molecules—cells—individuals—societies. Another hierarchy that stays within the world of physics is this one: Elementary particles— atoms—solids and fluids—planets and stars—solar systems—galaxies—universe. In this article, we will mainly deal with condensed matter systems such as given in the first group of examples above. This means that we focus on the relation between the physics of mesoscopic or macroscopic systems and the relevant microscopic theory, which is a quantum mechanical description of approximately 1023 atomic nuclei and their surrounding electrons. In terms of the hierarchy of objects, we discuss the relation between atoms and solids.

4.4 Condensed Matter Research in Practice In the following, I will quote three Nobel Laureates in condensed matter theory as they explain how research in their field proceeds and how it is related to the supposedly fundamental quantum theory. All of them present strong arguments against a reductionist view. Nevertheless, two of them make surprisingly ambivalent statements concerning the nature of reduction. Since condensed-matter physics often uses methods from statistical mechanics and since statistical mechanics is my field of expertise, I will present additional arguments against the reductionist view by explaining how statistical mechanics relates to quantum mechanics and also to classical mechanics (which is for historical reasons still often used as a fundamental microscopic theory when justifying the laws of statistical mechanics).

4.4.1 Philip Warren Anderson and the Topic of Symmetry Breaking In his famous paper ‘More is different’, Anderson (1972) begins with the following sentences:

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The reductionist hypothesis may still be a topic for controversy among philosophers, but among the great majority of active scientists, I think it is accepted without question. The workings of our minds and bodies, and of all the animate or inanimate matter of which we have any detailed knowledge, are assumed to be controlled by the same set of fundamental laws.

Somewhat further on, he explains: [. . .] the reductionist hypothesis does not by any means imply a ‘constructionist’ one: The ability to reduce everything to simple fundamental laws does not imply the possibility to start from those laws and reconstruct the universe. (..) At each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.

Then he gives the reason why this is so: It is because of symmetry breaking. The microscopic theory is invariant under spatial translation or rotation and thus for instance forbids the occurrence of nonzero electrical dipole moments or of crystal lattices. This is because in an electrical dipole the negative charges have a different center than the positive charges, which means that a particular direction—that in which the negative charges are shifted—is singled out. Similarly, the atoms on a lattice have preferred positions, and the lattice has main axes that point in specific directions. When a direction is singled out, rotational symmetry, which treats all directions equally, is broken. When lattice positions are singled out, translational symmetry, which treats all positions equally, is broken. Another important case of symmetry breaking is the handedness of many biological molecules. This is an example that Anderson focuses on: While very small molecules, such as ammonia, can tunnel between the two tetrahedral configurations with a high frequency, and thus have on average zero electrical dipole moment, larger molecules, such as sugar, cannot tunnel during any reasonable time period. Symmetry breaking is very important in condensed matter physics: When the energetically favored state is a symmetry-broken state, the system chooses spontaneously one of these possible states, all of which have the same energy, as is analyzed in depth in the theory of phase transitions. This is relevant to phenomena such as superconductivity, magnetism, and superfluidity. Anderson’s conclusion is that because of symmetry breaking the whole becomes different from the sum of its parts. There is an interesting dichotomy in this article: on the one hand, Anderson emphasizes more than once that he accepts reductionism (in the sense that ‘everything obeys the same fundamental laws’), on the other hand he gives great arguments why reductionism does not work. Even more, he admits that there is a logical contradiction between the laws of quantum mechanics and the fact the molecules have symmetry-breaking structures. Since he wrote his article, there has been a lot of progress in this field, and several authors have pointed out that in fact the problems of symmetry breaking and of molecular structure are closely related to the problems of interpreting the quantum mechanical measurement process and of understanding the relation between quantum mechanics and classical mechanics (Primas 2013; Chibbaro et al. 2014; Matyus 2018). We will address this problem further below.

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4.4.2 Robert Laughlin and Higher-Order Principles In his often-cited article with Pines “The Theory of Everything” (Laughlin and Pines 2000), and also in his popular-science book “A different universe” Laughlin (2008) expresses a similar view to Anderson. Laughlin and Pines (2000) label the Schrödinger equation that describes all the electrons and nuclei of a system as the “Theory of Everything” for condensed-matter physics and explain: We know that this equation is correct because it has been solved accurately for small numbers of particles and found to agree in minute detail with experiment. However, it cannot be solved accurately when the number of particles exceeds about 10. No computer [. . .] that will ever exist can break this barrier because there is a catastrophy of dimension. (. . ..) We have succeeded in reducing all of ordinary physical behavior to a simple, correct Theory of Everything only to discover that it has revealed exactly nothing about many things of great importance.

Just as Anderson, the authors first appear to commit to reductionism, and then explain why it is of no use for many important problems in condensed matter theory. Confusingly, they do not clarify what they mean by “correct” or “accurate”; they cannot possibly mean that the theory is exact as they write themselves that it neglects several effects (such as the coupling to photons). Apparently they think that these effects are unimportant even when dealing with solids consisting of 1023 atoms. Their arguments why the “Theory of Everything” is useless for condensed matter theory include symmetry breaking, but are more general: In his book, Laughlin calls the principles determining many emergent features ‘Higher-order principles’ (HOPs). In the article, he and Pines explain it as follows: Experiments of this kind (i.e., condensed-matter experiments that allow us to measure the natural constants with extremely high precision) work because there are higher organizing principles in nature that make them work. The Josephson quantum1 is exact because of the principle of continuous symmetry breaking. The quantum Hall effect2 is exact because of localization. (. . ..) Both are transcendent, in that they would continue to be true and to lead to exact results even if the Theory of Everything was changed.

They go on to explain that “for at least some fundamental things in nature the Theory of Everything is irrelevant.” They introduce the concept of a quantum protectorate, a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. [. . .] The low-energy excited quantum states of these systems are particles in exactly the same sense that the electron in the vacuum of quantum

1 The

Josephson quantum is due to the fact that magnetic flux surrounded by a superconducting current can only be an integer multiple of a basic flux unit. This is because the magnetic flux affects the phase of the superconducting wave function, but the wave function must have a again the same phase after going around the flux line once. 2 The Hall effect gives rise to a transverse electric field in a two-dimensional conductor to which a magnetic field is applied that is perpendicular to the current. The Hall resistance is the ratio of the transverse electrical field to the electrical current, and it takes quantized values when the material is cooled down sufficiently. The explanation of this effect involves considerations about the topology of the wave function.

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electrodynamics is a particle. [. . .] The nature of the underlying theory is unknowable until one raises the energy scale sufficiently to escape protection.

In fact, even though they do not mention this, the Theory of Everything, i.e., the many-particle Schrödinger equation, is also such a quantum protectorate, valid at low energies, obtained from general considerations, and independent of more microscopic theories, such as quantum field theories or string theories. All this raises the question whether it is logically consistent to claim that a system is determined by a micropscopic law and to claim simultaneously that this law is irrelevant since higher-order principles govern the behavior of the system. This is in my view the most interesting question raised by the article, but the authors don’t address it. We will come back to this question later. While the examples chosen by Anderson were taken mainly from the room-temperature classical world, the examples used by Laughlin and Pines are mainly quantum phenomena. Therefore, the issue now is not primarily the relation between the quantum description and the classical description, but the relation between different quantum descriptions (the microscopic one and the one based on HOPs) of the same system.

4.4.3 Anthony Leggett and the Quantum-Classical Transition In his article “On the nature of research in condensed-state physics”, Leggett (1992) writes No significant advance in the theory of matter in bulk has ever come about through derivation from microscopic principles. [. . .] I would confidently argue further that it is in principle and forever impossible to carry out such a derivation. [. . .] The so-called derivations of the results of solid state physics from microscopic principles alone are almost all bogus, if ‘derivation’ is meant to have anything like its usual sense.

So he agrees with Anderson and Laughlin that the microscopic theory is useless for deriving the properties of solids. He illustrates this by using the example of Ohm’s law, i.e. the law for the electrical resistance: Consider as elementary a principle as Ohm’s law. As far as I know, no-one has ever come even remotely within reach of deriving Ohm’s law from microscopic principles without a whole host of auxiliary assumptions (‘physical approximations’), which one almost certainly would not have thought of making unless one knew in advance the result one wanted to get, (and some of which may be regarded as essentially begging the question). This situation is fairly typical: once you have reason to believe that a certain kind of model or theory will actually work at the macroscopic or intermediate level, then it is sometimes possible to show that you can ‘derive’ it from microscopic theory, in the sense that you may be able to find the auxiliary assumptions or approximations you have to make to lead to the result you want.

But if auxiliary assumptions and approximations are involved in the derivation of Ohm’s law, the theory or even the phenomenon might not be contained in the microscopic theory. This becomes even clearer in the next paragraph:

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B. Drossel But you can practically never justify these auxiliary assumptions, and the whole process is highly dangerous anyway: very often you find that what you thought you had ’proved’ comes unstuck experimentally (for instance, you ‘prove’ Ohm’s law quite generally only to discover that superconductors don’t obey it) and when you go back to your proof you discover as often as not that you had implicitly slipped in an assumption that begs the whole question. [. . .]

This experience makes him skeptical with respect to the validity of his calculations: Incidentally, as a psychological fact, it does occasionally happen that one is led to a new model by a microscopic calculation. But in that case one certainly doesn’t believe the model because of the calculation: on the contrary, in my experience at least one disbelieves or distrusts the calculation unless and until one has a flash of insight and sees the result in terms of a model.

Now comes the most interesting part about the nature of theories in condensedmatter physics: I claim then that the important advances in macroscopic physics come essentially in the construction of models at an intermediate or macroscopic level, and that these are logically (and psychologically) independent of microscopic physics. Examples of the kind of models I have in mind which may be familiar to some readers include the Debye model of a crystalline solid, the idea of a quasiparticle, the Ising or Heisenberg picture of a magnetic material, the two-fluid model of liquid helium, London’s approach to superconductivity [. . .] In some cases these models may be plausibly represented as ‘based on’ microscopic physics, in the sense that they can be described as making assumptions about microscopic entities (e.g. ‘the atoms are arranged in a regular lattice’), but in other cases (such as the two-fluid model) they are independent even in this sense. What all have in common is that they can serve as some kind of concrete picture, or metaphor, which can guide our thinking about the subject in question. And they guide it in their own right, and not because they are a sort of crude shorthand for some underlying mathematics derived from ‘basic principles.’

This is reminiscent of the higher-order principles mentioned by Laughlin, but is more general: One needs to identify the important features that are responsible for the phenomenon to be explained. These features are discovered by an intuitive understanding of the system, often in terms of pictures and metaphors. They form the basis of a model, which in turn is the basis of an effective mathematical description. Further on, he explains that these models in fact often are incompatible with the microscopic theory: [. . .] not only is there no good reason to believe that all the properties of condensed-matter systems are simply consequences of the properties of their atomic-level constituents, but that there is a very good reason not to believe it. [. . .] Indeed, I would be perfectly happy to share the conventional reductionist prejudice were it not for a single fact [. . .] which is so overwhelming in its implications that it forces us to challenge even what we might think of as the most basic common sense. This fact is the existence of the quantum measurement paradox.[. . .] this argument implies that quantum mechanics, of its nature, cannot give a complete account of all the properties of the world at the macroscopic level. [. . .] It follows that somewhere along the line from the atom to human consciousness quantum mechanics must break down.

I fully agree with his characterization of how condensed matter physics is done in practice and with his diagnosis that there must be limits to the validity of quantum mechanics. In fact, together with George Ellis, I have written a paper that interprets

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the quantum measurement process in terms of top-down effects from the classical world on the quantum world (Drossel and Ellis 2018).

4.4.4 Statistical Physics and the Concept of Probabilities After these three examples from solid-state physics, I want to conclude this section with an example from my own field, which is statistical mechanics. Statistical mechanics does not deal with a particular system, but provides a framework for calculating properties of systems of 1023 particles at finite temperature, be they solids, liquids, or gases. Condensed matter theory often uses concepts and calculations taken from statistical mechanics, for instance when calculating the specific heat of a system, the phase transition between a paramagnet and a ferromagnet, or the conditions (temperature, magnetic field, or size of electrical current) that destroy superconductivity. This means that one does not use the supposedly ‘fundamental’ theory but a theory that brings with it new concepts. The basic concept of statistical mechanics is that of the probability of a state of a system or a subpart of the system. For instance, a fundamental theorem of statistical mechanics, from which almost everything else can be derived, is that in an isolated system in equilibrium all states that are accessible to a system occur with the same probability. Such an equilibrium state has maximum entropy, and therefore this theorem is closely related to the second law of thermodynamics, which states that entropy increases in a closed system until the equilibrium state is reached. Part of the textbooks of statistical mechanics and articles of the foundations of statistical physics aim at deriving these probabilistic rules from a microscopic deterministic theory, either classical mechanics (where the atoms of a gas are treated as little hard balls) or quantum mechanics. A close look at these derivations, however, reveals that they in fact always put in by hand what they want to get out: randomness. The initial state of the system must be a ’random’ state among all those that cannot be distinguished from each other when specifying them only with finite precision. The apparent randomness in the future time evolution then follows from this hidden, unperceivable initial randomness. This means that the randomness of statistical mechanics is not reduced to a deterministic ’fundamental’ theory, but it is only moved back to the initial conditions and hidden there. Of course, a truly deterministic world would not leave us the freedom to say that the precise initial state does not matter because the real one can be any of them. The initial state would be the state it is and not care about our ignorance of finer details. It is amazing that nature conforms to our ignorance and behaves as if there was nothing special to the initial state that would later lead to surprising effects in the time evolution. The natural conclusion, which however goes against the reductionist agenda, would be to say that the mathematical concept of infinite precision underlying the equations of the ’fundamental’ theories has no support from empirical science. In fact, when there are no specific top-down effects since the system is isolated, the system becomes maximally indifferent as to the state in which it tends to be. This is what

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the second law of thermodynamics states. This topic is discussed in more detail in publications by Gisin (2017, 2018) and by myself Drossel (2015, 2017). Interestingly, there is a close relation between the quantum measurement problem and the problem of relating statistical mechanics to quantum mechanics: quantum measurement and statistical mechanics both involve probabilities and irreversibility. Both deal with systems of a macroscopic number of particles (in the case of quantum measurement this is the measurement apparatus). Concordantly, the theories dealing with the two problems involve similar ideas and types of calculations: they are based on decoherence theory which explains why quantum mechanical superpositions vanish when a quantum particle interacts with a macroscopic number of other particles. These calculations—not surprisingly—again need to invoke random initial states. In contrast to theories that ‘derive’ statistical mechanics from classical mechanics, these random initial states are however not sufficient in order to ‘derive’ statistical mechanics from quantum mechanics, because the calculations give all possible stochastic trajectories simultaneously instead of picking one of them for each realization. So we arrive again at the point emphasized by A. Leggett: Quantum mechanics is not consistent with physics of macroscopic, finite-temperature objects. This means that there must be limits of validity to quantum mechanics.

4.5 Strong Arguments for Strong Emergence in Physics 4.5.1 A Full Reduction to a Microscopic Theory Cannot be Done The foregoing quotations and discussions have made clear that a full reduction is never done in practice, and that it is impossible for several reasons. The more trivial reason is limited computing power, not just at the present time but for all future since the calculation of the time evolution of the quantum state of as few as 1000 particles would require more information than contained in the universe (Kohn 1999). This means that the belief in full reduction is a metaphysical belief, as it can never, even in principle be tested. In contrast, physics is an empirical science rooted in what can be measured and observed. But beyond this, I think there are good reasons why reductionism even when taken as a metaphysical belief is wrong. As most clearly stated by A. Leggett, there is a logical incompatibility between quantum mechanics, which leads to superposition of macroscopic objects being in different locations, and the observation that macroscopic objects are localized in space. It is my impression that in fact all the effective theories and models and approximations made in order to obtain the properties of macroscopic systems, involve assumptions and steps that are in contradiction with the supposedly fundamental theory. For instance, the derivations of the phonon (lattice vibration) spectrum of solids starts by separating the equation for the electrons from that for the nuclei by

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using the so-called Born-Oppenheimer approximation. This approximation is in fact a mixture of quantum theory and classical theory, as it assumes that the atomic nuclei are localized in space and not in superpositions of different locations. It is also the basis of quantum chemistry and the widely-used density functional theory. A nice discussion of this can be found in the book by Chibbaro et al. (2014). Similarly, other theories in condensed matter make assumptions and approximations that deviate from the linear, deterministic, microscopic Theory of Everything. It appears to me that they all put in contextual information that is not intrinsic to the Theory of Everything and that contains elements from classical physics and oftentimes also of statistical physics. If have discussed this in detail in a recent article (Drossel 2019). And there are many more reasons why full reductionism is wrong, as listed in the following subsections.

4.5.2 The Parts Have Never Existed Without the Whole The mental picture that many people have when they think of emergence is that there are first the parts, and then they get together and form the whole. But this picture is only half the truth. These parts would not be there without a larger context that permits their existence and determines their properties. Which types of elementary particles exist in the universe depends on the properties of the quantum vacuum, namely its symmetries and degrees of freedom. Whether these particles can combine to create larger objects, is again determined by the context: In the early universe, the temperature and density of the universe determined which types of objects existed in it: quarks and gluons, or nuclei and electrons, or atoms and radiation, or stars and galaxies and planets. On smaller scales, one observes the same extent of context dependence, and many examples are listed in the book by Ellis (2016): The lifetime of a neutron depends on whether it is a free particle or part of a nucleus. In a crystal, the presence of the crystal structure permits the existence of phonons, and the symmetries of the crystal determine their properties. The mass of an electron depends on the band structure of the metal in which it is. Whether a substance is liquid or solid depends on the environmental conditions, such as temperature and pressure.

4.5.3 The Laws of Physics are Not Exact Full reductionism could only be correct if the supposedly fundamental laws were extremely accurate. Otherwise, even minute imprecisions could become magnified in macroscopic system to the extent that the fundamental theory cannot predict correctly the properties of the macroscopic system. But we know that our present theories are not fully exact: They are idealizations that leave aside many influences

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that affect a system. Newtonian mechanics, for instance, ignores the effect of friction, or includes it in a simple way, which is neither exact nor derived from a microscopic theory. A large part of thermodynamics is based on local equilibrium, which is not an exact but only an approximate description. Quantum field theory is burdened with exactly the same problems as nonrelativistic quantum mechanics, namely the discrepancy between a unitary, deterministic time evolution applied after preparation of the initial state and before measurement of the final state, and the probabilities and nonlinear expressions featuring in calculations of cross sections and transition rates. Furthermore, it could not yet be harmonized with Einstein’s theory of general relativity, which describes gravity. Batterman argues convincingly that physics theories are asymptotic theories that become exact only in an asymptotic limit where a quantity goes to zero or infinity (Batterman 2001). Newtonian mechanics is a good example of how the applicability of a theory depends on certain quantities being small or large: The velocity of light must be large compared to the velocities of the considered objects (otherwise one needs to use the theory of special relativity), energies must be so large that quantum effects can be ignored (otherwise one needs quantum mechanics), and distances must be small compared to cosmic distances on which the curvature of space is felt (otherwise one needs general relativity). In earlier times, there was a widespread belief that Newtonian mechanics is an exact theory, only to realize in the last century that on all those scales that could not be explored before (such as the very small, the very large, and the very fast) Newtonian mechanics becomes invalid, and that it is a very good approximation, but not exact, on those scales that had been explored. We can expect that our present theories will also turn out to become inappropriate when new parameter ranges, which we could not explore previously, become accessible to experiments. In fact, it appears impossible to have exact, comprehensive microscopic laws that govern everything that happens, and to have at the same time a complete insensitiveness to these microscopic laws in systems that are determined by higher-order principles.

4.5.4 The Microscopic World Is Not Deterministic One of the main shocks caused by quantum mechanics is the insight that the microscopic nature is fundamentally indeterministic, as for instance visible in radioactive decay where nothing in the state of an atom allows one to predict when it will decay. Only the half life can be known and be calculated from a microscopic theory. The same hold for the quantum-mechanical measurement process, where the experiment gives one of the possible outcomes with a probability that can be calculated using the rules of quantum mechanics, but the process itself is stochastic with nothing in the initial state determining which of the outcomes will be observed. In order for full reductionism to hold, the microscopic theory must be deterministic. Only then does the microscopic theory determine everything that happens. Otherwise the microscopic theory can at best give probabilities for the different

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possible events. When dealing with a system of many particles, one likely outcome of such stochastic dynamics is ergodicity, where the system goes to an equilibrium state that is characterized by a stationary probability distribution. This is what happens for instance when a thermodynamic system such as a gas reaches its equilibrium state, which has maximum entropy. The macroscopic state variables characterizing this equilibrium state, such as volume or pressure, are independent of the initial microscopic state and are essentially determined by the constraints imposed from the outside. Thermodynamic systems are in fact a nice example for top-down causation, as they do essentially nothing else but to adjust to whatever state is imposed on them by manipulations from the outside, such as volume change or energy input. But even when chance does not lead to ergodicity, top-down causation is involved. When a quantum measurement event happens, the measurement apparatus determines the possible types of measurement outcomes (for instance whether the z component or the x component of the spin is measured). When an excited atom goes to its ground state by emitting a photon, it can do so only because the surrounding medium, the quantum vacuum, can take up that photon. When the atom is enclosed in a small cavity the size of which is not a multiple of the photon wavelength, the photon cannot be emitted. It thus appears that all instances of quantum chance are in fact strongly dependent on top-down causation. A quantum object by itself, when it is carefully isolated from interacting with the rest of the world, evolves according to the ‘fundamental’, deterministic, and linear quantum mechanical equations. Karl Popper made the interesting suggestion that chance at the lower level is necessary for top-down causation from the higher level (Popper and Eccles 1977), and he has been criticized for it (O’Connor and Wong 2015). However, I think that he is right. Only when the entities at the lower level are not fully controlled by the microscopic laws can they respond to the higher level. It is often argued that random changes are as little susceptible to top-down effects as are deterministic changes. But this is based on the wrong premise that stochasticity is an intrinsic property of the lower-level system, while it arises in fact from the interaction of the lower-level constituents with the larger context.

4.5.5 Emergent Properties are Insensitive to Microscopic Details As mentioned above in Sect. 4.4.2, Laughlin has emphasized a lot that emergent properties are insensitive to microscopic details. It is the higher-order principles that determine the behavior of the systems he discusses. There are indeed many examples where systems that are microscopically different show the same macroscopic behavior and are described by the same mathematical theory. For instance, the phase transition from a paramagnet to a ferromagnet below the Curie temperature is described by the same mathematics as the Higgs mechanism that can successfully

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explain how particles obtain their mass. Furthermore, within one type of systems, for instance a ferromagnet made of iron, the mathematical description in the form of macroscopic or effective variables is independent of the precise microscopic arrangement of atoms and defects. There exist many microscopic realizations of the same macroscopic state. In fact, all “fundamental” theories of physics, such as quantum mechanics, quantum field theory, electrodynamics, general relativity, thermodynamics, are derived or justified by applying a small number of basic principles. This is most apparent in quantum field theory, where all terms that reflect the symmetries and conservation laws of the system to lowest order in the fields are included in the Lagrangian. So even this theory, which is considered by some as the most fundamental one, is based on higher-order principles (Laughlin and Pines 2000) and asymptotic reasoning (Batterman 2001) (see Sect. 4.5.3 above) and can therefore not include information on the structure of matter at even more microscopic scales. This structure is only revealed when energies are so high that the more microscopic degrees of freedom become activated. This is also the reason why the quantum field theories discussed by particle physicists and those discussed by solid state physicists (where these theories refer to quasiparticles), are formally equivalent. Laughlin refers so such theories also as quantum protectorates, as mentioned above. A different facet of this is emphasized in the book by George Ellis when he mentions the concept of ‘multiple realizability’ of a macroscopic state by microscopic states. For instance, a thermodynamic state characterized by state variables such as pressure and volume and temperature is realized by many different microscopic states, where the positions and velocities of particles are specified. An impressive biological example of multiple realizability is convergent evolution (Morris 2003). The evolutionary process has given rise to the same “solutions” many times. For instance, the camera eye evolved independently in vertebrates, cephalopds, snails and other organisms, with the general concept being always the same but the microscopic realization being different in each case. Another wellknown example are the very similar traits evolved in masurpials and plecental mammals that fill the same ecological niche. Multiple realizability means that the time evolution can be expressed in terms of the macroscopic variables much more transparently than in terms of the microscopic variables. This in turn means that the causal processes responsible for this time evolution can be described on the level of the macrostate. A natural conclusion is that causality does indeed occur at the level of the macrostates and that the microstates merely adjust to the constraints or requirements given by the macrostate.

4.5.6 Many Systems are Inseparable from Their Environment So far, we have mainly addressed equilibrium systems, which can be cut off from their environment without losing their properties. In fact, this is an approximate statement, as no system can be completely cut off from the environment; the best

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one can do is putting a system into a closed box or lab with no directed input or output of energy or matter. The typical solid-state systems discussed by the abovecited Nobel Laureates remain what they are under such conditions, at least on time scales relevant for experiments. On the very long run, they will be changed by surface reactions, by radioactive radiation, and ultimately by the sun turning into a red giant and burning everything on earth. In contrast to these relatively stable systems, open (or dissipative) systems require an ongoing input and output of energy and/or matter in order to remain what they are. We have given in Sect. 4.2 the examples of convection patterns, oscillating reactions, and living organisms. For these systems, the idea that they are determined by their parts and the interactions of their parts, is completely wrong, as they are what they are only in contact with their environment: Convection patterns require an input of heat at one end and a cooling surface at the other end; oscillating reaction can only be sustained when certain reactants are continually supplied and certain reaction products removed; living beings need to breathe and feed, and they respond in a complex way to cues from their environment. Since all these systems exist only due to being continually sustained by their environment, it is completely wrong to think of them merely in terms of their parts and the interactions of their parts. The emergent features of these systems are therefore clear-cut cases of top-down causation.

4.6 Answers to Objections When discussing the issue of strong emergence in physics, a variety of objections are being made, which shall be dealt with in the following.

4.6.1 We Will Find a More Fundamental Theory Quite a few scientists hope that even if our present microscopic theories are not yet the final, correct theories, the progress of physics will ultimately lead to such final theories. If such theories will ever be found, they must achieve a lot: They must solve the quantum measurement problem, and they must also establish a relation between general relativity and quantum physics. In the light of the arguments presented in this article, it seems impossbile that such a theory exists. The top-down effects of the larger, macroscopic context on the microscopic constituents cannot be captured by a purely microscopic theory. Some people argue that even if the ultimate theory might be unknowable, nature might nevertheless be governed by basic laws which are known to us only in approximate versions. This is a valid philosophical position, but it appears to be rooted more in a metaphysical commitment than in empirical evidence. This commitment is to physicalism and to causal closure. Both are very restrictive

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assumptions that can be doubted on philosophical grounds. The strongest arguments against physicalism are based on human consciousness, and are brought forward by authors such as Falkenburg (2012), Nagel (2012), or Gabriel (2017). All the arguments brought forward by George Ellis in favor of top-down causation are also arguments against causal closure. These arguments show that material systems are susceptible even to non-material influences such as goals, ideas, or man-made conventions.

4.6.2 You Argue from Our Lack of Knowledge, This Is Dangerous In the nineteenth and early twentieth centure, the British emergentists argued in favor of strong emergence based on chemistry and biology (McLaughlin 1992; O’Connor and Wong 2015). They could not imagine that chemistry of biology obeys the laws of physics, and they assumed that complex objects are subject to different laws. But after the successes of quantum chemistry at explaining the periodic table and calculating molecular structures, and the success of biology at reducing inheritance to the properties of the DNA molecule, these emergentist positions came in discredit. By analogy, those who hold to strong emergentist views, are told that progress of science will probably prove them wrong. If we cannot explain a macroscopic feature in terms of a microscopic theory today, it might become possible in the future. However, the arguments presented in this article are not arguments from ignorance, but from the very nature of the systems under study. Even the claimed reduction of chemistry or biology to (quantum) physics is incomplete. It is a partial reduction that invokes a collection of models and arguments that includes features from the quantum world as well as from the classical world, as explained in Sect. 4.5.1. In particular life is so dependent on its environment that the reductionist enterprise is doomed to failure on principal grounds.

4.6.3 There are Fully Reductionist Explanations for the Quantum-Classical Transition and the Second Law of Thermodynamics This is an expert discussion that goes into the details of the theories offered. As I have tried to convey above, all these theories need to invoke additional concepts beyond the ‘fundamental’ Theory of Everything. In one form or another, they all rely on some type of randomness of initial states or environmental states. Furthermore, since quantum mechanics is a linear theory, one cannot avoid the resulting superpositions of macroscopic states. Pointing out that these superpositions can

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look like a classical combination of the different possible outcomes with their associated probabilities does not fully solve the problem, as nature realizes in each instance only one of the possible outcomes (Schlosshauer 2005). Of course, there are interpretations of quantum mechanics that deal with this issue (such as the manyworlds interpretation, the statistical interpretation, consistent histories, relational interpretation), but all of them give up on the goal of science of accounting for an objective, observer-independent reality with its contingent, particular history. I am not willing to abandon this goal, and I think that abandoning this goals hampers the progress of science and distracts from the open problems that await solutions.

4.6.4 All Supposed Top-Down Effects can Equally Well be Expressed in Terms of a Microscopic Theory The idea behind this objection is that the context that produces the top-down effects is itself composed of atoms and can be described by a microscopic theory. Instead of having the description in terms of a system and a context, one could describe both system and context microscopically. However, apart from being impossible in practice, there are several reasons why this is not possible in principle: First, there is no isolated system, since every system emits thermal radiation to the environment, which in turn passes it on to open space. Furthermore, every system is exposed to the influence of gravitational forces, which cannot be shielded by any means. Third, having a closed system leads again to all the problems related to interpreting quantum mechanics. Some authors hold that the universe as a whole is a closed system and can therefore be described by a microscopic theory for all its particles and their interactions. However, the driving force behind everything that happens in the universe is the expansion of the universe, starting from a very special initial state. Neither the initial state, nor the expansion results from the interaction of the particles, and therefore the claim that the universe is determined by its parts and their interactions is wrong.

4.7 Conclusion To conclude, I see many reasons to reject the view that the world of physics is causally closed with everything being determined bottom-up by fundamental microscopic laws. As stated in the book by George Ellis: The lower (microscopic) level enables everything and underlies everything, but does not determine everything. The higher hierarchical levels have an important say at what happens in nature. Anthony Leggett writes in his above-cited article that the non-reductionist view is a minority view among professional physicists. In fact, I am not so sure about this. Clearly, the

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majority of people who write and talk on such foundational topics, have a more-orless reductionist view. However, when I talk to colleagues it appears to me that many of them are aware that the world described by physics is not a monolithic block that is controled by a small set of rules. Maybe that those people who have not simple clear view but think that physics is more complex usually don’t write papers on this topic. This is one of the reasons why I decided to write this paper.

References Anderson, P. W. (1972). More is different. Science, 177(4047), 393–396. Batterman, R. W. (2001). The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence. Oxford: Oxford University Press. Chibbaro, S., Rondoni, L., & Vulpiani, A. (2014). Reductionism, emergence and levels of reality, Ch. 6. Berlin: Springer. Drossel, B. (2015). On the relation between the second law of thermodynamics and classical and quantum mechanics. In Why more is different (pp. 41–54). Berlin: Springer. Drossel, B. (2017). Ten reasons why a thermalized system cannot be described by a many-particle wave function. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 58, 12–21. Drossel, B. (2019). What condensed matter physics and statistical physics teach us about the limits of unitary time evolution. Quantum Studies: Mathematics and Foundations, 7, 1–15. Drossel, B., & Ellis, G. (2018). Contextual wavefunction collapse: An integrated theory of quantum measurement. New Journal of Physics, 20(11), 113025. Ellis, G. (2016). How can physics underlie the mind?: Top-down causation in the human context. Heidelberg: Springer. Falkenburg, B. (2012). Mythos determinismus: Wieviel erklärt uns die Hirnforschung? Berlin: Springer. Gabriel, M. (2017). I am not a brain: Philosophy of mind for the 21st century. Hoboken: Wiley. Gisin, N. (2017). Time really passes, science can’t deny that. In R. Renner & S. Stupar (Eds.), Time in physics (pp. 1–15). Basel: Birkhauser. Gisin, N. (2018). Indeterminism in physics, classical chaos and bohmian mechanics. Are real numbers really real? Preprint arXiv:1803.06824. Kohn, W. (1999). Electronic structure of matter-wave functions and density functionals, nobel lecture. Reviews of Modern Physics, 71, 1253. Laughlin, R. B. (2008). A different universe: Reinventing physics from the bottom down. New York, NY, USA: Basic Books. Laughlin, R. B., & Pines, D. (2000). The theory of everything. In Proceedings of the National Academy of Sciences of the United States of America (pp. 28–31). Leggett, A. J. (1992). On the nature of research in condensed-state physics. Foundations of Physics, 22(2), 221–233. Matyus, E. (2018). Pre-born-oppenheimer molecular structure theory. Preprint arXiv:1801.05885. McLaughlin, B. (1992). The rise and fall of british emergentism. Emergence or reduction (pp 49– 93). New York, NY, USA: De Gruyter. Morris, S. C. (2003). Life’s solution: Inevitable humans in a lonely universe. Cambridge: Cambridge University Press. Nagel, T. (2012). Mind and cosmos: Why the materialist neo-Darwinian conception of nature is almost certainly false. Oxford: Oxford University Press. O’Connor, T., & Wong, H. Y. (2015). Emergent properties. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. Metaphysics Research Lab, Stanford University, summer 2015 edition.

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Popper, K. R., & Eccles, J. C. (1977). The self and its brain: An argument for interactionism. Berlin: Springer. Primas, H. (2013). Chemistry, quantum mechanics and reductionism: Perspectives in theoretical chemistry (vol. 24). Heidelberg: Springer. Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern Physics, 76(4), 1267.

Chapter 5

On the Topic of Emergence from an Effective Field Theory Perspective Thomas Luu and Ulf-G. Meißner

Abstract Effective Field Theories have been used successfully to provide a “bottom-up" description of phenomena whose intrinsic degrees of freedom behave at length scales far different from their effective degrees of freedom. An example is the emergent phenomenon of bound nuclei, whose constituents are neutrons and protons, which in turn are themselves composed of more fundamental particles called quarks and gluons. In going from a fundamental description that utilizes quarks and gluons to an effective field theory description of nuclei, the length scales traversed span at least two orders of magnitude. In this article we provide an Effective Field Theory viewpoint on the topic of emergence, arguing on the side of reductionism and weak emergence. We comment on Anderson’s interpretation of constructionism and its connection to strong emergence.

T. Luu () Institute for Advanced Simulation (IAS-4), Institut für Kernphysik (IKP-3), and Jülich Center for Hadron Physics, Forschungszentrum, Jülich, Germany Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Rheinische Friedrich-Williams-Universität Bonn, Bonn, Germany e-mail: [email protected] U.-G. Meißner Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Rheinische Friedrich-Williams-Universität Bonn, Bonn, Germany Institute for Advanced Simulation (IAS-4), Institut für Kernphysik (IKP-3), and Jülich Center for Hadron Physics, Forschungszentrum, Jülich, Germany Center for Science and Thought, Rheinische Friedrich-Williams-Universität Bonn, Bonn, Germany Tbilisi State University, Tbilisi, Georgia e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_5

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5.1 Emergent Phenomena in Nuclear Physics The term emergence is a multi-faceted concept whose exact meaning depends on context and invariably the field of study. In the field of (low-energy) nuclear physics, emergent phenomena are always associated with highly complex and highly nonlinear behavior. Such phenomena are deemed non-perturbative; their descriptions at the fundamental (lower) level are not amenable to simple paper and pencil calculations. An example, which we will go into more detail later, is the behavior of quarks and gluons (the fundamental particles at the lower level) and how they come together to form protons and neutrons, or collectively nucleons. The theory of the interactions of these lower level particles is known as quantum chromodynamics (QCD). It is a seemingly simple theory which can be written down in one line. However, the manner in which three quarks interact (via the exchange of gluons) and thus bind themselves to form nucleons is the quintessential non-perturbative problem. The explanation of the observation that quarks and gluons are never seen as free particles but are rather confined within strongly interacting particles, the hadrons such as the proton and the neutron, constitutes one of the grand challenges in theoretical physics1 . Complicating matters is the fact that gluons, which are considered the force carrier2 of the “strong interaction" between quarks, can also interact with themselves. This has profound implications on the generation of mass. Gluons are massless, and while quarks do have mass, their masses are roughly two orders of magnitude smaller than the mass of a nucleon. Thus most of the mass of the nucleon does not come from the masses of its (matter) constituents; rather, it is generated dynamically by the interactions of the gluons. This extends to the elements built from nucleons. Indeed, 95% of the mass of the observable universe is generated from interactions between massless particles (gluons). The term holistic might be an understatement in this case. Emergent nucleons from bound quarks subsequently bind and form heavier elements, such as deuterium, helium, carbon, oxygen, and so on. These processes are themselves emergent and non-perturbative. And the phenomena that emerge from such elements are vast and complex. Nuclear breathing modes for example, where large groups of nucleons within a nucleus move in a collective motion, lead to oscillatory behavior called giant dipole resonances. Such resonances, when coupled with electromagnetism and the weak interaction, play an integral role in nuclear fission. Another example and one that is not unique to nuclear physics, involves closed three-body systems known as Borromean states. The constituents of these states, when only considered pairwise, are not bound. However, when a third constituent is included, the system becomes bound and the resulting spectrum is extremely rich and diverse. Examples of nuclear Borromean states are 6 He, whose constituents are

1 Clay 2 The

(2020). http://www.claymath.org/millennium-problems photon is the analogous force carrier for quantum electrodynamics (QED).

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and two neutrons and the Hoyle state of carbon, whose constituents in the case are three separate 4 He nuclei.3 The examples of emergent phenomena above have little to no resemblance to their lower level constituents, which in this case are quarks and gluons. And since their description at the lower level via traditional calculations is essentially all but impossible, physicists instead turn to the powerful tool of effective field theory, where instead of using the lower level constituents to frame the problem, they instead work directly with the emergent phenomena as the relevant degrees of freedom.4 This effective field theory (EFT) is not an ad hoc description of the emergent phenomena, however. If developed properly, the EFT represents an equally valid representation of the phenomenon and can be used to predict new phenomena as well as to verify the lower level theory. We remark in passing that nowadays it is widely accepted that all field theories are effective field theories, which makes the phenomenon of emergence even more “natural”. In the following section we give a cursory primer on effective field theories whereby we enumerate the ingredients and conditions for constructing a successful EFT. We give examples of EFTs both from a historical point of view and from a modern viewpoint. In Sect. 5.3 we discuss the relationship between EFT and Emergence/Causation. We pay special attention to both strong and weak forms and argue on the side of weak emergence and reductionism. In Sect. 5.4 we provide our own interpretation of Anderson’s thesis in his seminal paper “More is different” Anderson (1972), whereby we compare with Ellis’ interpretation given in Ellis (2016). We continue our discussion in Sect. 5.5 on the apparent dichotomy of physics and biology due to “purpose", as motivated by Ellis in Ellis (2016), but argue that such reasoning is false and misleading. In Sect. 5.6 we invoke Popper’s falsifiability argument to gauge the “scientific merit" of strong emergence. Finally, we recapitulate our arguments in Sect. 5.7.

5.2 Primer on Effective Field Theory Since emergent phenomena preclude simple calculations from their constituent basis, physicists instead use effective degrees of freedom to describe these systems. In EFT terms, these are dubbed the “relevant degrees of freedom”, as will become clearer later on. Nucleons (protons and neutrons), rather than quarks and gluons, for example, form the basis for describing nuclear phenomena. The interactions between nucleons are not disconnected from the interactions of quarks and gluons, however. They are related to their constituent parts in a rigorous, systematic manner. This procedure of relating the effective degrees of freedom to the dynamics of constituent parts collectively falls under the purview of effective field theory. We 3 Such 4 We

states are only truly Borromean if we neglect the weak and electromagnetic interactions. remark that in an EFT, the lower-level theory indeed acts at higher energies and vice versa.

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discuss tersely the necessary and sufficient ingredients for constructing an effective field theory below. These are: Identification of effective, or active degrees of freedom: Here the emergent phenomena (e.g. protons, pions, nuclei, breathing modes in large nuclei, etc. . .) dictate the active (relevant) degrees of freedom, despite the fact that such phenomena can be expressed as collections of more fundamental degrees of freedom (i.e. constituents). The energy scales at which the emergent phenomena operate are considered low compared to the intrinsic energy scales of its constituents. This is very obvious in nuclear physics, while nuclear excitations involve energies of say tenth of MeV, to investigate (see) the quark-gluon substructure of nucleons or nuclei requires probes with multi-GeV energies, i.e. three orders of magnitudes larger. This identification of the relevant degrees of freedom can also be understood from the principle of resolution: The finer details of a system one wants to investigate, the larger energy (momentum) is needed, as follows simply from Heisenberg’s uncertainty principle. Therefore, as stated before, energies of relevance to nuclei can never reveal their quark-gluon substructure, it is simply irrelevant at these energies. Separation of length scales: The separation of length (or: energy) scales is implicit in all EFTs. By their very definition, emergent phenomena occur at length scales that are larger than their constituents’ intrinsic scales. Put another way, the energy required to resolve the emergent phenomenon is insufficient to resolve its constituents. Such separation in length scales, or equivalently energy scales, allows one to express an EFT as an expansion in the ratio of scales (e.g. the ratio of the energy scale of the emergent phenomenon to its constituents’ intrinsic energy scales). The larger the separation of scales, the more effective the EFT description as such an expansion converges faster. Identification of symmetries: Symmetries play a fundamental role in the construction of any EFT of some emergent process. The symmetries that the emergent phenomenon respects are identical to the symmetries of its constituents and their interactions. Examples of such symmetries are Lorentz invariance (physics does not depend on the observer’s frame), gauge invariance (local transformations of quantum fields that leave the Lagrangian invariant), and the discrete symmetries of parity (e.g. mirror symmetry), time-reversal invariance (a reaction happening forward in time is equal to its counterpart happening backward in time), and charge conjugation (particles turn into anti-particles). The identification of such symmetries provides strong constraints in the types of expressions that show up in an EFT, and in many cases, simplifies and reduces the number of terms by providing relations between different expressions. Despite these constraints on the form of terms, each term has an associated coefficient that is not determined by symmetry alone and must be either empirically determined or derived from the lower level theory. It should also be noted that symmetries can be realized differently in the EFT compared to its underlying theory or can be broken upon quantization. Such phenomena happen indeed in QCD and its corresponding EFT, but we will not discuss them any further here.

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Power counting scheme: Even with the identification of all terms with the relevant symmetries of the system in question, there still exists myriads of terms5 that make any EFT calculation futile unless there is some systematic way of organizing the expressions in terms of relative importance. Here one employs the concept of power counting, where the different terms are enumerated in hierarchical importance related to some expansion parameter (usually related to the ratio of some soft momentum scale to a hard scale). A desired accuracy of calculation then dictates the number of terms to be calculated. Thus there is a finite number of terms that are needed for any EFT calculation. Note, however, the following ramification of such a procedure: no EFT calculation will ever be exact since there is always an associated uncertainty (due to the truncation of terms). Also, it should be noted that any realistic calculation in physics can never be exact (unless in very simplified toy models).

5.2.1 Examples of Effective Field Theories Here we give a few examples of well known EFTs. These examples are by no means exhaustive, they are simply selected because of their inherent clarity. Heisenberg-Euler Theory: In the early 1930s Heisenberg, Euler and Kockel considered a theory Heisenberg and Euler (1936); Euler and Kockel (1935) describing photons with energies ω that are much lower than the mass of the electron, i.e. ω  me (= .511 MeV).6 As there are no other electromagnetically charged particles with masses less than the electron, the only active degrees of freedom are thus the low-energy photons. All other heavier particles, here electrons and their anti-particles, have been integrated out. Their theory, constrained by Lorentz symmetry and parity, constitutes essentially an EFT expansion in (ω/me )2 (odd powers are forbidden by parity), and was used to investigate the cross section for light-by-light scattering at low energies. Note that their effective theory allows for a direct interaction between photons, whereas in the more fundamental theory, quantum electrodynamics (QED), a photon cannot interact directly with another photon, but only through an intermediary charged particle. The corresponding full calculation in QED including electrons as active degrees of freedom was only done in 1951 (Karplus and Neuman 1951), and found to agree with the EFT result in the energy range ω  me . Fermi’s Theory of Beta Decay: Also during this time Fermi proposed a theory (Fermi 1934) for beta (weak) decays that utilized a direct four-fermion coupling (dubbed four-Fermi interaction later). An example of such a process is the decay of a neutron into a proton, an electron, and an anti-neutrino, n → pe− ν¯ e The theory worked amazingly well at low energies, but was shown to break down at energies of order ∼100 GeV. In light of our understanding today of the more

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principle there are an infinite number of expressions. MeV = 1 mega-electronvolt = 106 eV.

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Fig. 5.1 Neutron decay as seen from the fundamental weak interaction theory, where a down (d) quark turns into an up (u) quark with the emission of a heavy W − -boson that then decays into an electron and an anti-neutrino. At energies much below the W -mass, the propagation of this virtual particle can no longer be resolved and the interaction collapses into a four-fermion point coupling. Not shown a the up and down quarks not participating in the decay, as a neutron is made from quarks as |udd and a proton as |uud

fundamental theory of weak interactions, such a breakdown is not surprising. The particles that mediate the weak interaction are the W and Z-bosons, whose masses are approximately MW ∼ 80 GeV. At energies well below this mass, these particles cannot be resolved (as discussed above) and Fermi’s effective four-fermion coupling is an excellent approximation to the weak processes, as shown in Fig. 5.1. But at energies comparable or larger to MW , these particles are now resolvable and the effective field theory breaks down. At these high energies one is forced to work with the more fundamental theory and its constituents. Chiral Perturbation Theory: Despite knowing the more fundamental (lower level) theory of its constituents, the above examples provide two effective theories that are just as good at describing, and predicting, processes related to their emergent phenomena (i.e. light-by-light scattering and beta decay), as long as one is willing to work at low enough energies. Indeed, calculations with the effective theory are more often than not simpler to perform in these low energies. But given the theoretical advances in our understanding of QED and the weak interaction, today’s physicists prefer to work directly with the more fundamental theory when it comes to photons and weak decay. We stress, however, that either representations (EFT or fundamental theory) are valid descriptions of these emergent phenomena. On the other hand, Chiral Perturbation Theory Weinberg (1979); Gasser and Leutwyler (1984) is an EFT that serves as a more modern example where, despite knowing its underlying theory of Quantum Chromodynamcs (QCD), one cannot directly perform calculations with the fundamental theory (at energies  250 MeV)7 but must utilize its corresponding EFT. More precisely, there are two distinct EFTs for QCD, one refers to the sector the the light quarks (up, down and strange) and the other to the heavy quarks (charm and bottom). In what follows, we will consider the the light quark sector only. In this sector, the active degrees of freedom are nucleons (neutrons and protons) and pions, and the interaction between these degrees of freedom originate from the interactions of their constituents, the light quarks and

7 Such

calculations can be done on a finite volune space-time, known as lattice QCD, but this requires state-of-the-art supercomputers and will not be discussed further.

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Fig. 5.2 Chiral perturbation theory provides an effective multi-nucleon interaction LN N (right) that is constrained by the symmetries and interactions LQCD between the lower level, fundamental quarks and gluons (left). Note the length scale traversed by these systems, ranging from sub-femtometers (left) to 10s of femtometers (right). The size of the nucleon (center) is approximately 1 femtometer

gluons. It is important to note the length scales encompassed by these systems, which range for sub-femto8 (quarks and gluons) to 10s of fermi (nuclei), as depicted in Fig. 5.2. The form of the interaction terms is dictated by a chiral symmetry9 of the quarks (in the massless limit), the coefficients of which are constrained by empirical data. The diverse separation of scales, coupled with a consistent power counting scheme, provides the organizational tools to perform calculations that both postdict and predict nuclear emergent phenomena (Epelbaum et al. 2009). Coupled with high-performance computing, calculations of nuclei up to the mid-mass region (∼50 nucleons) are now possible (Lähde and Meißner 2019). The Standard Model of Particle Physics: The Standard Model of Particle Physics (SM), which encompasses the strong (QCD), weak, and electromagnetic (QED) interactions, is in and of itself an incomplete theory since it does not include gravity. We know that new physics must occur at least at the Planck energy scale,10 1.2 × 1025 MeV, and most likely before this. Relative to this energy scale, the standard model is itself a low-energy EFT. This means that the QCD, weak, and QED interactions are not exact, but low-energy approximations of some grander theory. Still, the accuracy of these “effective" theories is very high due to the large separation to the Planck scale (or, more generally, the scale of physics beyond the SM, which is estimated to be in the TeV region).

femto(meter) is 10−15 m. symmerty refers to the fact that in massless QCD, one can write down two independent theories in terms of left- and right-handed quarks, respectively. This symmetry is explicitly broken due to the small quark masses. 10 The Planck scales signifies the point where gravity and the SM forces have equal strengths. 8 One

9 Chiral

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5.3 EFT in Relation to Emergence and Causation The EFT description provided above naturally leads to a bottom-up approach, where upper-level emergent phenomena and their associated larger length scales/lower energies are built from lower-level (more) fundamental constituents. The level below the EFT is required to calculate certain properties from more basic constituents, like e.g the values of the low-energy constants (LECs). This is fully consistent with the reductionist point of view. The entire field of particle physics, whether it is consciously aware of this or not, follows the reductionist line of reasoning, at least in methodological and theoretical forms: we build experiments and theories that probe lower level physics in an attempt to investigate currently unexplainable phenomena. Such phenomena, if deemed “emergent”, serve as parametrizations of our ignorance. It is natural to think then that causation follows this same bottom-up (or upward) direction as well. Indeed, within the EFT prescription, it is the symmetries of the lower level that dictate the allowed interaction terms at the higher level, but not the other way around. However, as the EFT description is a fully consistent and equally valid representation of emergent phenomena, any prediction it makes, regardless of how “disconnected” or “unexpected” when viewed from the lower level theory, is consistent with the laws that govern the lower level constituents. Such predictions, and the associated causal impacts that accompany them, are in principle11 deducible from the lower level constituents. This is consistent with the notion of weak downward causation (Bedau 1997). When it comes to emergence, the same applies for EFTs. In principle, calculations at the lower level using QCD would be preferable, all things being equal. Indeed, the LECs required by an EFT can only be calculated from the lower level theory. But once the LECs are determined and the desired accuracy specified, any description of the emergent phenomena with an EFT stands on equal footing with the description using the lower level constituents. We note that the EFT can operate by itself, if one accepts to determine the LECs by a fit to data, that is with no recourse to the underlying theory. Any facts or predictions (or collectively, truths) obtained via the EFT, no matter how unexpected or seemingly disconnected from the lower level point of view, is in principle deducible from the lower level domain. Thus weak emergence (Chalmers 2006) is automatically encompassed by EFTs. There is a plethora of examples where EFT predictions provided unexpected deeper insights into the workings of lower level physics. A set of such EFT predictions refer to the chiral limit of QCD (i.e. setting the light quark masses to zero), where it can be shown that certain quantities like the pion radius, the nucleon isovector radius or the electric and magnetic polarizabilities of the nucleon diverge, see e.g. Pagels (1975); Bernard et al. (1995). Such a behavior appears very unnatural (and can not be calculated in any way) from the point of view of QCD in terms of quarks and gluons, but can be explained rather naturally in the EFT, where the

11 In

practice, such a deduction might be impossible due to computational constraints.

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Yukawa-suppressed pion cloud turns into a quantity of infinite range sampling all space and thus diverging. Another beautiful example is the EFT investigation of the validity of carbon-oxygen based life on earth, where the amount of required fine-tuning to keep the so-called Hoyle state in the spectrum of carbon-12 in close proximity to the three alpha-particle threshold, thus enabling sufficient carbon and oxygen production in stars, under changes of the fundamental parameters of the SM could be pinned down, see Meißner (2015) for details and more references. Again, even though these predictions were made with EFTs operating at the higher levels, there is no question that they can, in principle, be deduced from lower-levels, but in practice, this is currently impossible and might be so for a long time.

5.4 Anderson’s “More is different” Anderson’s seminal paper “More is different" Anderson (1972) has been often used by philosophers and scientists (mostly condensed matter physicists, see contribution of B. Drossel in this volume) alike as one of the main sources for the emergentist “resurgence” (Mainwood 2006). In his book How Can Physics Underlie the Mind (Ellis 2016), George Ellis appears to interpret Anderson’s position as an anti-reductionist one (Ellis 2016, p. 4), even misquoting Anderson’s paper (Anderson 1972) on the very same page. However, Anderson, in his own words, is a reductionist (Anderson 1972), As I said, we must all start with reductionism, which I fully accept. (p. 394),

which runs counter to the strong emergence mantra. Anderson uses the term reductionism as synonymous with what is referred to in metaphysics as microphysicalism (Mainwood 2006). However, the discrepancy between Anderson’s statement and Ellis’ presentation of Andersons article (Anderson 1972) is more than a liberal translation from one terminology into another. The mismatch in terminology between Ellis and Anderson becomes obvious in Andersons statement: (. . . ) the reductionist hypothesis does not by any means imply a constructionist one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. (p. 393).

Anderson argues further that, due to complexity, it may be impossible practically to compute the higher level phenomena starting from the lower level constituents. He states, Surely there are more levels or organization between human ethology and DNA than there are between DNA and quantum electrodynamics, and each level can require a whole new conceptual structure. (p. 396).

This position alone does not imply anti-constructionism, because what can be meant by requiring a new conceptual structure is the use of a new, more convenient basis for the description of relevant degrees of freedom much along the lines of effective field theory. It is also not anti-reductionist, because Anderson states that the novel

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concepts in physics are explained from fundamental laws (even when it takes thirty years to do so, as in the case of superconductivity). However, the placement of this statement in Anderson’s paper (he used it to argue against an approach by some molecular biologists at the time “to reduce everything about the human organism to ‘only’ chemistry, from the common cold and all mental disease to the religious instinct” (p. 396)) had likely attracted the interpreters in favour of strong emergence. While it is clear that Anderson’s position maintains that the new conceptual structure in complex systems may not in practice be derived from the interaction of its constituents, interpreting it as an argument for strong emergence would be equivalent to neglecting Anderson’s full acceptance of reductionism. To “start with reductionism” (p. 394) matters here, even if one interprets Anderson’s term “reductionism” as “anti-constructionism”. Anderson at no point argues that the new conceptual structure of the higher level of organization cannot be deduced from the lower-level constituents in principle. On the other hand, strong emergent phenomena are not deducible even in principle from the “truths in the low-level domain” (Chalmers 2006). Thus, Anderson’s argumentation in Anderson (1972) is aligned with weak emergence.

5.5 “Purpose" in Life and Physics In his book How Can Physics Underlie the Mind (Ellis 2016) Ellis argues for strong emergence in the case of consciousness and a number of other phenomena. For example, in the case of biology, he argues that Biology cannot be reduced to physics, because it has an ineliminable teleology component to its explanations. . . (p. 373).

In other words, biology, and biological organisms by extension, have purpose, whereas physics does not. Thus biology can not be reduced to physics. He continues further, Purposeful design underlies all the features we expect in life today (. . .). But that physics knows nothing of these plans and theories. (pp. 414–415).

Again, the argument seems to be that since physics lacks the capacity to “know” the purpose of life, strong emergence must exist. We find such statements reminiscent of the arguments made by proponents of intelligent design (just replace the word Purposeful with Intelligent in the sentence above) (National Academy of Sciences 1999). We also caution in using terminology that may be precise at one level, e.g. purpose, but ill-defined at another level, as this ultimately adds confusion. However, it may very well be that the “purpose” of some biological organism, seen from our limited point of view, is procreation and the continuation of its species, but at the same time is equivalent to the minimization of energy in some very complex phase space. The latter explanation is fully consistent with a physical interpretation of phenomena. Neither our explanation nor Ellis’ explanation is sufficient to argue for one case or the other. Our present ignorance of the intricate

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workings of biological organisms, or even the consciousness of such beings, and its connection to physics is not a sufficient argument for the existence of strong emergence. Furthermore, we have not even come close to exhausting all possible research connections between physics (and even lower levels) and biology. Bohr writes (Heisenberg 1996) The richness of mathematical forms present in the quantum theory is perhaps by now sufficient to represent also biological forms.

And, perhaps surprisingly here, Schrödinger makes a statement (Schrödinger 1944) which clarifies his position better than Ellis’ citation on p. 4 of Ellis (2016), We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics. For that is just what is to be expected from the knowledge we have gained of the structure of living matter. We must be prepared to find a new type of physical law prevailing in it. Or are we to term it a non-physical, not to say a super-physical, law? (. . . ) No. I do not think that. For the new principle that is involved is a genuinely physical one: it is, in my opinion, nothing else than the principle of quantum theory over again.

The proposition that quantum mechanics plays an integral part in the emergence of life (and by extension, consciousness) is evoked quite often, though admittingly we find such a connection hard to imagine. But then again, we are limited by our lack of imagination.

5.6 Popper’s Falsifiability Test Any new scientific paradigm must be testable from a scientific point of view. New (and even currently accepted) theories make predictions which are subsequently tested empirically. If the tests fail, then the theories are either abandoned in favor of others or, more commonly, modified to better reflect reality. Either way, such testing provides better insight into Nature and her workings. This process repeats itself over and over, and is the basis for scientific progress. The great philosopher Sir Karl Popper argued that to be deemed “scientific”, a paradigm has to be falsifiable (Keuth 2019). The argument at first seems counterintuitive, but Popper’s own example in Popper (1962) serves as an excellent explanation. Popper, at the beginning of the twentieth century, considered the scientific worth of Einstein’s theory of general relativity compared to Astrology. Both made predictions: Einstein’s theory, for example, predicted the bending of light from distant stars traversing near our sun (Einstein 1915a,b), while astrologists predicted marriage probabilities, lottery winnings, horse races, and so on, based on the alignment of planets and other heavenly objects. Einstein’s theory could be easily falsified: it made a prediction about the exact amount of deflection about our sun of light originating from the Hyades star cluster that could be directly empirically verified. A false finding would directly lead to abandonment. On the other hand, false predictions by astrologists could always be argued away (“Venus

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and Mars were aligned, but Jupiter was slightly askew . . .”). History tells us the rest (Eddington 1919): general relativity is one of mankind’s greatest theories that has profoundly shaped our understanding of space and time. Sadly, astrology is still with us. Using Popper’s scrutiny the concept of strong emergence is not “scientific”. We are not aware of any predictions its theories have made. To be very clear on this issue, we refer to a prediction by a quantifiable statement of a theory or model that is amenable to an experimental test, like the abovementioned light bending in general relativity. Furthermore, if there are any predictions, it seems that the mere complexity of the systems in which it is intended to be applied to leaves very little room for direct falsifiability: there is always some conditional statements which can be concocted (after the fact) to “argue away” negative findings. Under these circumstances strong emergence does not appear worthier than astrology.

5.7 Conclusion Effective field theories provide powerful tools for modern day physicists to understand and describe emergent phenomena. Though the lower-level theory can be preferable to work with since it can calculate certain quantities, e.g. LECs, that are not accessible to an EFT, in practice calculations at the lower level are usually much more difficult or nearly impossible. Fortunately, once certain low-energy constants are determined from the lower-level theory or from data, an EFT is an equally valid description of the higher-level phenomena. Furthermore, EFTs can, and do, make predictions of the behavior of emergent phenomena that can be tested and falsified. We have listed the necessary and sufficient conditions for the construction and applicability of EFTs, and have argued that the principles underlying EFTs are fully consistent with the methodological and theoretical reductionist point of view coupled with the weak form of emergence and causation. History is replete with examples of phenomena that have seemingly no connection to the laws of nature known to man at that time. A classic example is the formation of the rainbow.12 During biblical times, such a phenomenon could surely be used as fodder for strong emergence. But through the passage of time, as our understanding of light refraction via water molecules has improved, our need to invoke strong emergence disappeared and instead became weak emergence. Indeed we can deduce the connection between light scattering and the colorful arcs in the sky. In this sense, strong emergent phenomena, if you will, are only fleeting designators for unexplainable phenomena to be superseded by weak emergent phenomena as our understanding of Nature improves.

12 For

us, a rainbow is a physical phenomenon, it can be measured and artificially produced, and does not require the discussion of human impression. Or stated more simply: A rainbow is a rainbow is a rainbow.

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As the separation of scales between levels widens, it becomes invariably more difficult to see the “connections” between these levels. Nothing annoys, yet motivates, physicists more (and presumably all scientists and philosophers) than phenomena that are currently inexplicable with our current knowledge of fundamental laws. Indeed, such instances (e.g. dark matter and dark energy) hint at the possibility that our current knowledge is insufficient, or our expected view of how nature works is too limited. Most likely it is a combination of both. In these cases it is tempting to propose a new scientific paradigm that somehow absolves us of our ignorances and lack of imagination, but to do so in a manner that is not testable and verifiable inevitably does more harm (scientifically) than not. Acknowledgments We thank Markus Gabriel for helpful comments. TL also thanks E. Berkowitz, C. Hanhart, J.-L. Wynen, and A. Wirzba for insightful discussions related to this manuscript. TL especially thanks M. Hru˘ska for her careful reading of this manuscript and analysis. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD" (Grant No. TRR110), by the Chinese Academy of Sciences (CAS) through a President’s International Fellowship Initiative (PIFI) (Grant No. 2018DM0034) and by the VolkswagenStiftung (Grant No. 93562).

References Anderson, P. W. (1972). More is different. Science, 177, 393. Bedau, M. A. (1997). Weak emergence. Nous, 31(s11), 375–399. Bernard, V., Kaiser, N., & Meißner, U.-G. (1995). Chiral dynamics in nucleons and nuclei. International Journal of Modern Physics E, 4, 193. Chalmers, D. J. (2006). Strong and weak emergence. In P. Davies & P. Clayton (Eds.), The reemergence of emergence: The emergentist hypothesis from science to religion Oxford: Oxford University Press. Eddington, A. S. (1919). The total eclipse of 1919 May 29 and the influence of gravitation on light. The Observatory, 42, 119–122. Einstein, A. (1915a). Grundgedanken der allgemeinen Relativitätstheorie und Anwendung dieser Theorie in der Astronomie. Preussische Akademie der Wissenschaften, Sitzungsberichte, (1915) (part 1), 315 Einstein, A. (1915b). Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie. Preussische Akademie der Wissenschaften, Sitzungsberichte, 1915 (part 2), 831839 Ellis, G. (2016). How can physics underlie the mind? Top-down causation in the human context. Berlin: Springer-Verlag. Epelbaum, E., Hammer, H. W., & Meißner, U.-G. (2009). Modern theory of nuclear forces. Reviews of Modern Physics, 81, 1773–1825. Euler, H., & Kockel, B. (1935). Ueber die Streuung von Licht an Licht nach der Diracschen Theorie. Naturwissenschaften, 23, 246. Fermi, E. (1934). An attempt of a theory of beta radiation. 1. Zeitschrift für Physik, 88, 161–177. Gasser, J., & Leutwyler, H. (1984). Chiral perturbation theory to one loop. Annals of Physics, 158, 142. Heisenberg, W. (1996). Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik. Piper Taschenbuch, Piper.

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Heisenberg, W., & Euler, H. (1936). Consequences of Dirac’s theory of positrons. Zeitschrift für Physik, 98, 714 (1936). Karplus, R., & Neuman, M. (1951). The scattering of light by light. Physical Review, 83, 776. Keuth, H. (2019). Karl Poppers Logik der Forschung (pp. 45–63) Wiesbaden: Springer Fachmedien Wiesbaden. Lähde, T. A., & Meißner, U.-G. (2019). Nuclear lattice effective field theory : An introduction. Lecture Notes in Physics, 957, 1. Mainwood, P. (2006). Is More Different? Emergent Properties in Physics. PhD thesis, Merton College, University of Oxford. Meißner, U.-G. (2015). Anthropic considerations in nuclear physics. Science Bulletin, 60, 43. National Academy of Sciences (1999). Science and creationism: A view from the National Academy of Sciences, 2nd ed. Washington, DC: The National Academies Press. Pagels, H. (1975). Departures from chiral symmetry: A review. Physics Reports, 16, 219. Popper, K. (1962). Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge. Schrödinger, E. (1944). What is life? The physical aspect of the living cell. Cambridge: Cambridge University Press. Weinberg, S. (1979). Phenomenological Lagrangians. Physica A, 96, 327.

Part III

The View from the Life Sciences

Chapter 6

The Principle of Biological Relativity: Origins and Current Status Denis Noble

Abstract This chapter describes the origin of the principle of biological relativity and its development since 2012. It was first formulated by distinguishing between the causal properties of initial and boundary conditions, regarded as a formal cause, compared to the dynamics of the differential functions themselves, regarded as an efficient cause. The concept of organisational level, and of boundaries between levels and environmental factors are also central to the principle. Work on the properties of boundaries reveals two important features: the nature of causation differs significantly between different levels of organisation, and the top-down and bottom-up forms must act simultaneously. These developments of the principle are used to clarify the reasons why bottom-up causation alone is inadequate in multilevel biology. Keywords Biological relativity · Top-down causation · Boundaries between levels

6.1 Introduction: How Did the Principle Arise? Nearly a decade ago I was invited by George Ellis to contribute to a meeting at The Royal Society in London on Top-Down Causation (Ellis et al. 2012). I already knew George’s great reputation as mathematician, cosmologist and relativity theorist. My initial reaction therefore was that I was hardly qualified to set even a foot inside the door of the powerful group of contributors from various walks of science and philosophy that he was assembling. And, even worse, there was the question “what could I possibly contribute that would be worth doing and of interest to that group?” In a rash moment I sent him the title “A Theory of Biological Relativity”. It was a gamble.

D. Noble () Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_6

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I was using my instinct rather than any very clear idea of where this would be leading. Those instincts told me two things. First, that my own work on the rhythm of the heart involved a form of Top-Down causation called the Hodgkin Cycle. Global electrical and chemical properties at the level of the whole cell are necessarily involved in the differential equations I had used to reconstruct the processes involved. Hodgkin and Huxley had paved the way for this kind of analysis in their ground-breaking 1952 paper on nerve (Hodgkin and Huxley 1952). Second, that there must be a difference between the Top-Down and the Bottom-Up forms of causation. But, when I sent in my title for the meeting I did not fully know how to characterise that difference. This is not the first time in my career that I have “lived on the edge”, meaning that I had an instinct for the direction of travel, but no complete route map to get me there. I first experienced that kind of “edge” when trying to convince the computer scientists at UCL in 1960 to let me have time on their huge, expensive and precious, Ferranti Mercury Computer. Precious, because in those days there was only a single computer machine of that power in the whole of London. My knowledge of mathematics is almost entirely self-taught so it has always been easy for me to be overawed by those with far greater mathematical and computational skills than me. That feeling was reinforced by the fact that, initially, the guardians of Mercury declined my application. I had to attend a lecture course on the mathematics of matrices before they eventually became convinced that I could do what I was proposing. One of their problems was that they assumed that, if I was going to reproduce heart rhythm, there would need to be an oscillator function somewhere in the equations. There wasn’t. On the contrary, in my mind as a physiologist, I imagined that the interactions within the model would themselves produce the rhythm. Of course, that meant attributing the origin of the rhythm to a high-level property and that it would arise from the solution to the equations. In other words, it is an attractor. My problem in 1960 was that, as a young graduate student, I knew nothing about the science and maths of attractors! I just sketched the presumed interactions on the back of an envelope. I didn’t have the mathematical skill to formulate it as an attractor. Almost 60 years later, I still feel surprised that I succeeded in constructing the first mathematical model of heart rhythm (Noble 1960, 1962a, b) with so little understanding of the significance of what I had done. It was George Ellis’ invitation and my rashly-proposed title that forced me to think more deeply about it. The only regret I have about the title is that it should have referred to a principle rather than a theory. It is not itself a theory. It is a principle of general application to multi-level organisation of organisms.

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6.2 The Silos of Academe Before I outline my own proposed solution, I wish to thank a referee of this article for drawing my attention to the fact that if, a decade ago, I had wandered a bit outside my own specialised field of cardiac electrophysiology I could have found a wealth of material on multi-level organisation. Notable amongst these is Allen & Starr’s 1982 book Hierarchy, republished as a second edition in 2017. There is a brilliant chapter 12 “Scale as an investigative tool” drawing attention to the inadequacy of thinking that, following sequencing of the human genome, “we had a whole ecosystem in a computer.” Sadly, in the 1980s I had no idea a book like this on multi-scale approaches existed. Biological science in those days was strongly imbued with reductionist dogma (including notoriously the Central Dogma of molecular biology). That dogma has now been deconstructed, notably by the Chicago biochemist James Shapiro in relation to molecular biology (Shapiro 2011), and more recently by me in relation to physiology (Noble 2018). But it was very difficult indeed to challenge the mind-set of reductionism within biological science itself in the twentieth century. There are many reasons for this, not least the fact that academe works in silos. The extent of knowledge and practical skills required to remain a front-line researcher in any field of biology is so large that we all have to focus on the literature that is absolutely necessary for us to succeed and to continue to obtain funding for our research teams. I want also to draw attention to a valuable collection of articles in the 2017 volume Philosophical and Scientific Perspectives on Downward Causation (Paoletti and Orilia 2017). Of special relevance to my arguments is the article by Luciano Boi (2017), which emphasizes the interlacing of upward and downward forms of causation: “upward and downward causation are in different ways and in both directions deeply interlaced.” Absolutely correct. They do not compete, they mesh together (Noble et al. 2019; Noble and Noble 2020). The siloisation of academe is the reason why interdisciplinary meetings of the kind organised by George Ellis are so important. They encourage new and deeper ways of thinking. That is particularly true in the context of challenging prevailing interpretations of biology.

6.3 First Tentative Solution to the Problem To understand why deeper thought is required we have first to acknowledge the strength of the alternative, reductionist explanation for any Top-Down causation

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theory. If, like James Watson, you really believe “there are only molecules”1 then you have also to dispense with the idea of different levels of organisation and claim that a mathematical model involving only molecular-level dynamics is at least conceivable. I think it is, and necessarily so. Wherever we draw the boundaries of what we are modelling it must always be conceivable that the boundaries could be extended to include all relevant molecular-level interactions on a wider scale. Notice that in that sentence I used the relatively neutral word ‘scale’, not the philosophically-loaded word ‘level’. A purely molecular theorist could use the term ‘scale’, meaning simply the physical dimensions of the model, but cannot use the term ‘level’ since that would involve already having the concept of a boundary between levels of organisation. Once the existence of a level of organisation with specific constraints on its components has been admitted I don’t think there is any escape from the application of the biological relativity principle. That principle then automatically excludes a purely molecular level model from explaining the phenomena. A purely molecular reductionist would therefore have to maintain that he doesn’t need to identify boundaries. All he needs to claim is that provided he extends the scale of his molecular level model sufficiently wide he will always be able to produce a molecular dynamics computation that reproduces the experimental observations. This was essentially also Spinoza’s position in the seventeenth century. Spinoza correctly saw that a whole (e.g. the whole body) could constrain its parts (its particles). He wrote: Let us imagine, with your permission, a little worm, living in the blood, able to distinguish by sight the particles of blood and to reflect on the manner in which each particle, on meeting with another particle, either is repulsed, or communicates a portion of its own motion. This little worm would live in the blood, in the same way as we live in a part of the universe, and would consider each particle of blood, not a as a part but as a whole. He would be unable to determine, how all the parts are modified by the general nature of blood, and are compelled to adapt themselves, so as to stand in a fixed relation to one another. (Elwes 1951)

But Spinoza still maintained that the universe itself, as a whole, is deterministic (Hampshire 1956). That is the reason why I have argued that Spinoza’s idea of constraint of particles by the whole is correct but that this alone is not sufficient to arrive at the principle of Biological Relativity. Two further assumptions are required: (1) that the concept of levels can be used to define causative organisation, including the existence of boundaries, and (2) that the universe is not determinate. The justification for those assumptions can be found in my recent book Dance to the Tune of Life (Noble 2016, pp. 174–176). Admitting that a purely molecular dynamics model is conceivable does not mean that it could be achieved. The sheer number of molecules involved may make it impossible. A cubic centimetre of water contains around 1022 molecules. If it was water in a living organism it would also have innumerable other molecules

1 https://www.edge.org/response-detail/11940

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dissolved in it. We don’t have the computational capacity to deal with such large numbers of molecular components interacting over any period of time relevant to a living organism. The equations for a theory of everything that could be relevant to ordinary experience are known (Laughlin & Pines, 2000). The problem is that, beyond computing the interactions of about 10 micro- components, it is impossible to solve those equations. That must also be true for matter in biology. That is why we introduce global properties of molecules like concentrations, pressures and potentials. The important point here is that, to do that, we need the concept of a boundary and therefore of a level of organisation. We can’t know those parameters without knowing what boundary constrains the molecules to generate a concentration, a pressure or a potential. Yet, once we do that we automatically also have a level of organisation. It is the level at which that boundary operates. In practice that is what I was doing with the heart rhythm computations on the Mercury computer in 1960. The boundary was a cell membrane, inside of which it was possible to define concentrations of ions, and across which there could exist an electrical potential. Those global properties necessarily constrain the dynamics of the protein molecules that form ion channels in the cell membrane. The resulting interaction is a version of the Hodgkin Cycle (Fig. 6.1). That model has now been superseded by much more extensive models of heart rhythm (Garny et al. 2002a; Noble et al. 2012). All necessarily involve use of the Hodgkin cycle. Now, in multicellular organisms, cells are organised into tissues, organs, and systems. We can therefore represent an organism as a series of levels each containing the levels below it. We then have the situation represented in Fig. 6.2.

Fig. 6.1 Left: The Hodgkin cycle represents the fact that global cell properties, such as electric potential, control molecular level properties, such as ion channel proteins, which in turn determine changes in cell properties. Right: Solution to the Noble 1962 equations showing the global rhythmic membrane potential (top) and the variations in conductance of the ion channels at a molecular level (bottom) (Noble 1962b)

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Fig. 6.2 Original multi-level causation diagram illustrating some of the forms of downward causation, including controls of gene expression, triggers of cell signalling and the protein machinery that reads and corrects gene sequences. Upward causation begins with a reading of genes to enable RNAs and proteins to be made. Those then generate networks and sub-cellular machinery. Cells then co-ordinate to form tissues organs and systems. Redrawn from (Noble 2006)

The question that then arises is how these arrows of causation are represented in the equations used in any multilevel model? The answer I gave in the 2010 Royal Society meeting was that the top-down causation arrows must be represented in the initial and boundary conditions at each level of organisation. And, indeed, so they are. In the differential equations I was using for heart rhythm there are no specific solutions to the equations without inserting initial conditions, and the constants in the ordinary differential equations are a representation of the boundary conditions constraining the molecular ion channels. These are the contextual forces within which the channel proteins operate. They will arise from many processes by which the protein dynamics are constrained, including the cellular properties that made their amino acid chains fold in the way they did, through to the lipid membrane forces across which the cell electrical potential develops, and which controls the opening and closing of the ion channels. Mossio and Moreno (2010) call this form of causation ‘Organisational Closure”. Montevil and Mossio (2015) also refer to the “closure of constraints” as characteristic of biological organisation. I think we are referring to the same process. It produces closure in the sense that, together with the differential equations for the dynamics, nothing more is needed for the description to be complete. That situation is represented diagrammatically as a formal algorithm in Fig. 6.3. It is a mathematical necessity that, without specifying the initial and boundary conditions, no specific solutions to the differential equations can be obtained. The

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Fig. 6.3 Diagram showing the formal relationships between initial conditions, boundary conditions, the differential equations and the solutions (output). Each integration step in the calculation goes through this sequence many times to achieve high accuracy. (Redrawn from Noble 2012)

principle of Biological Relativity is therefore itself a mathematical necessity. All open systems, as living systems must be, are subject to the external restraints that exist precisely because they are open systems. We can now address the question what would be missing from a purely molecular level model. It would be precisely the explanation for why the initial and boundary conditions are what they are. Without the concept of levels between which both upward and downward causation occur those conditions would be a completely unexplained set. This is not just a feature of models in biology. It is also a feature of models in physics. The big bang model of the universe has completely unexplained constants (Rees 2001). In contemplating the universe, we are therefore rather like the little worm of Spinoza, with no idea what constrains the universe to be as it is, and for us to exist (Noble 2016, chapter 9).

6.4 How Do Bottom-Up and Top-Down Forms of Causation Differ? One answer to that question is obvious from Fig. 6.3. The initial and boundary conditions are clearly a different form of causation from the differentials themselves. To use Aristotle’s famous categories of causation (Noble 2016, pp. 176–181),

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the conditions are a formal cause, the state of affairs in which the components find themselves, whereas the differentials are the efficient cause representing the dynamics of the components. But the diagrams I have reproduced so far can give a false impression through the use of separate arrows to represent the bottom-up dynamics and the top-down constraints. In fact, there is no sequence of causation with one occurring before the other. They must both act at the same time. This fact is also a mathematical necessity. In any programming of the integration procedure used to obtain solutions to the differential equations, the precise algorithm used depends on the integration formula used. Usually this consists in successive iterations until a preset level of accuracy is achieved. But it would not make sense to divide the integration step up into parts. The step itself is just an approximation to an infinitesimally small step. Everything computed in each step can be regarded as an approximation to true simultaneity. We should not be confused by the fact that we have to use finite steps to perform the integration into thinking that this represents reality. Any sequence by which the computer instructions are obeyed within each step is simply a computational convenience. Another way to appreciate this point is that a nano-size observer, if such could exist, would not see two separate forms of causation. This was the point of Spinoza’s ‘little worm’ thought experiment.

6.5 Boundaries and Simultaneity These issues form the subject of an article published recently in Frontiers in Physiology (Noble et al. 2019). In place of the separate arrows we constructed the diagram shown in Fig. 6.4. Some of these differences are indicated by the coloured arrows. For example, the bottom red arrow is used to indicate that there is a special form of causation between the controlling factors (RNAs and proteins working together with lipids and metabolites) and DNA itself. DNA can be affected by Top-down causation in two separate ways. One is the control of gene expression by epigenetic factors, the other is actual change in DNA sequence by the organism. The second form of causation was forbidden by strict interpretations of the Central Dogma of molecular Biology. We now know that such genome reorganisation (natural genetic engineering (Shapiro 2011) is common. All organisms use it, particularly when under environmental stress. This is one of the ways in which Lamarckian forms of development are being brought back into theories of evolution (Smith and Spadafora 2005). The ability of organisms to alter their genetic code is of immense importance in the rapidly growing field of intergenerational inheritance of acquired characteristics (Tollefsbol 2014). A further set of differences in forms of causation occur at the highest level, represented by the blue arrow. These are the social constraints that arise through the interactions of organisms with other organisms and the environment. As we

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Fig. 6.4 Left: The Bottom-up and Top-down forms of causation are now represented by doubleheaded arrows. The precise details of the forms of causation between different levels are not the same. Some of these differences are indicated by the coloured arrows. Right: the co-existence of different forms of causation, up or down, is illustrated by the expanded causation arrows. The effects are co-simultaneous, but the forms of causation can be multiple. Further explanation in the text and in the original article (Noble et al. 2019)

made clear in the discussion of our article (Noble et al. 2019), these forms of causation require more analysis since they include the impact of rationality, ethics and traditions. These are deep philosophical, not just empirical, issues. They lie at the heart of the conflict between empiricist and rationalist interpretations of the world. This is the issue I have recently tackled in collaboration with my brother, Raymond Noble. We propose that this conflict can be resolved by adding the harnessing of stochasticity to the principle of biological relativity. Chance variations, in DNA, in neural electrical fluctuations, and in social interactions with other organisms, are not just experienced. They are used by organisms precisely to seek new ways of resolving the challenges they face in maintaining their integrity. I first described the huge significance of the harnessing of chance in organisms in an article in Interface

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Focus in 2017 (Noble 2017). Raymond and I then showed how the harnessing processes lead to directionality in evolution (Noble and Noble 2017), the ability of organisms to make genuine choices in their behaviour (Noble and Noble 2018), and the ways in which reasons and values can influence physiological activity at all levels or biological organisation, including molecular levels (Noble and Noble 2020). I see these developments as a kind of ‘coming of age’ of the principle of biological relativity. One of its uses is to stimulate deeper thought about the nature of the different forms of causation. The standard molecular level approaches would not have stimulated these developments. That mind-set actually inhibits the formulation of the relevant questions. To complete my earlier quote from James Watson: “It’s all molecules, the rest is sociology.” Even molecules have a ‘sociology’. Once we understand that, its ‘sociology’ all the way down. Even a protein molecule cannot fold correctly and function correctly without the correct cellular environment in which to do so. This is a suitable point at which to emphasise that only some of the boundaries between levels in organisms are discrete membranous structures, such as cell membranes and organism integuments. Some of the boundaries between levels in Fig. 6.4 are fuzzy. The three lowest levels of organisation have no fixed membranous structure separating them. This fact does not pose a problem for physiology. For many years before Hodgkin & Huxley’s 1952 work there was an alternative theory of the nervous impulse, according to which the membrane potential is simply a Gibbs-Donnan equilibrium diffusion potential that would not even require a cell membrane. It would still have been true that the structures maintaining the equilibrium diffusion potential required cellular level organisation to function. Specifically, fixed charge structures would be required whether or not they are constrained by a membrane or simply by the structure of the organism.

6.6 Use of the Principle in Empirical and Theoretical Research I now turn to the question: what use is the principle in practical investigations? This kind of question is a recurring theme in the history of science. Famously, Michael Faraday in the nineteenth century demonstrated his experiment on electro-magnetic induction at a meeting of the Royal Society. It is said that the then Chancellor of the Exchequer, William Gladstone (later to become Prime Minister), asked the question: “Mr Faraday, what is the use of your experiment?” He is said to have replied “One day, Sir, you will put a tax on it”. Over a century later, another Prime Minister, Margaret Thatcher, gave a speech to the Royal Society in which she explained that

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“the value of Faraday’s work today must be higher than the capitalisation of all the shares on the Stock Exchange!”2 Well, I don’t know about value to the stock exchange, but by one of the standard indicators of impact in academic research the principle of biological relativity is doing well. The 2012 article in Interface Focus now has more than 250 citations and has been downloaded nearly 20,000 times. Together with George Ellis’s own article in the same issue of the journal (Ellis 2012), it is amongst the top articles for citation statistics. But citations and downloads alone do not reveal the nature of impact of an idea or experiment. Much more important is the sheer range of the fields in which the principle of biological relativity has been found to be of use. It is impossible to review all the 200 citations. I will just reference a selection from 2014 to 2017 to indicate the range of fields. After 2017 the citations became far too numerous. Over that period they include: Cancer genetics: (Kashkin et al. 2015; Sigston and Williams 2017), Philosophy of the organism: (Nicholson 2014), Self Organisation: (Gouschka et al. 2014), Phenotype complexity: (Annila and Baverstock 2014), Systems Medicine: (Vogt et al. 2014; Boissel et al. 2015; Simeonov and Ehresmann 2017), Microclimate diversity: (Woods et al. 2014), Liver complexity: (D’Alessandro et al. 2015), Immunology: (Cappuccio et al. 2016), Homeostasis: (Torday 2015), Subcellular organisation: (Witzany and Baluska 2015), Infectious diseases: (Leitner et al. 2015) (Garira 2017), Pattern regulation: (Friston et al. 2015), Ant behaviour: (Hunt et al. 2015), Colorectal tumors: (Soto et al. 2016), Bioinspired materials: (Green et al. 2016), Aging: (van Beek et al. 2015), Bioengineering: (Pezzulo and Levin 2016), Vascular physiology: (Hoekstra et al. 2016), Oriental philosophy: (Torday and Miller 2017; Nakajima 2017), Neuroscience: (Krakauer et al. 2017; Fregnac 2017), Atherosclerosis: (Louridas and Lourida 2017), Myocardiac dynamics: (NiellesVallespin et al. 2017), Gravity and phenotype: (Bizzarri et al. 2017), Mesenchymal stem cells: (Green et al. 2017), Evolution: (Baedke 2017), Multi-omics integration: (Tini et al. 2017), Vocal development: (Teramoto et al. 2017), Plant physiology: (do Amaral and Souza 2017). Clearly the formulation of the principle has hit a nerve in science that was waiting to be excited!

6.7 Scales or Levels? Finally, I return to James Watson’s quip “There are only molecules”. I wrote earlier in this paper that a purely molecular model is necessarily conceivable. I also explained that it could always be achieved simply by expanding the scale of the model, eventually to include all the relevant molecules. Such a model

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would be restricted to just one level. All other levels are not considered. After all, the aim of the statement “there are only molecules” is precisely that the other levels are not real and have no causal efficacy. We have also to assume that the modeller has effectively limitless computing capacity because as we expand the scale we will otherwise rapidly run out of computer capacity. That is the problem facing any completely reductionist account (Laughlin and Pines 2000; Noble 2020). Assuming all of this, would he get the same result as a multilevel model, and if so why? Surely, if the other levels really exist then to ignore them must produce a wrong result? How then could the laborious purely molecular level model give the right result? And, on the “there are only molecules” view, wouldn’t it have to be the really right result? Everything else, surely, must be just an approximation to what the molecular model produces. To respond well to these questions, we need to understand the difference between scales and levels. Scale is a relatively neutral concept, involving the Cartesian concept of continuous three-dimensional space. Every molecular interaction within a particular scale must be computed in an almost blind manner. As Spinoza correctly realised, each molecule just ‘knows’ about and interacts with its immediate neighbours. At the molecular level there is no knowledge of the overall situation. Importantly, that even includes the boundaries. They also must be regarded as just yet another group of molecules. And that is the problem. Because, in fact, the molecules at the boundaries have a special function. Boundaries constrain. The molecules at each boundary don’t know that. Only the system as a whole can know that and can control what happens. But, as soon as the molecular level modeller has to start giving special properties to the boundaries, such as cell membranes, he automatically abandons a purely molecular explanation. What else could explain why those particular molecules have a special function? They do so only in the context of constraining global properties. Imagine a nano-observer again. But also imagine that he can move with the focus of our enquiry. So, as we approach a cell membrane, he will know that he suddenly encounters lipids, instead of water and water-soluble chemicals. To him they will be just more molecules, admittedly of a different type from the water, proteins and metabolites he would have encountered so far. But molecules nonetheless. How could he possibly know from his molecular level knowledge alone that these are the molecules that make it possible to constrain the activity of molecules far away from his present position. To him it would look like mysterious action at a distance. Recall that, on a molecular scale a cell is vast. Yet, once we realise that the membrane is the boundary between two levels, we know that all the molecules within the boundary are constrained. That is what we mean by saying that the result is concentrations, pressures, temperatures, pH, and many other global properties. Those properties are smooth functions in the calculations precisely because the stochasticity at the molecular level is smoothed by the presence of very large numbers of molecules (the law of large numbers). As soon as the concept of constraining spatial levels of organisation is admitted, the principle of biological relativity kicks in. There is no alternative. The exercise of that constraint is the necessary and sole causal basis of the principle.

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We can now answer the earlier question: “would the purely molecular-level modeller get the same result as a multilevel model, and if so why?” The answer is, in principle, yes he would get the same answer. The reason is that all the organisational features of higher levels will have corresponding molecular features. Thus, the lipids forming a cell membrane must also be present and functioning in the molecular-level model. The differences would be that the molecular-level model would take far more computer resources to calculate and might even be more inaccurate for that reason. Computational errors accumulate the longer a calculation takes.

6.8 Boundaries Between Organisational Levels Similar considerations apply to boundaries between organisational levels, but within the same spatial scale. As an example, consider the boundary highlighted in red in Fig. 6.4, and specifically when hypermutation happens. At the molecular level of DNA itself, it will be evident that, normally, cellular error correction machinery will be operating to ensure highly accurate copying of DNA from one cell generation to the next. Sometimes though, that machinery will be switched off. But it will not be evident why that is happening. That will be evident only at the level of the complete immune system, where it will be apparent that hypermutation in a highly localised section of the DNA (specifically the variable part of the immunoglobulin sequence) has been triggered in large numbers of cells by detecting the presence of a new invader. The ability to achieve this will depend on receptors at or near the external surface of the cells and on the ability to use cellular microfilament pathways to communicate with the genome (as in, e.g. (Deisseroth et al. 2003; Kar et al. 2016)). To explain what is happening the molecular modeller would once again have to acknowledge the existence of organisation at the level of the whole immune system. Consider also the example of exercise life styles. In (Noble et al. 2019) two examples were given where the choice of exercise life style has been shown to change the relevant RNA levels controlling the production of muscle proteins and the control of heart rate. The triggers here are conscious decisions by the organisms (in this case humans) to adopt a specific life style. The top-down causation in such cases involves a rational decision on the part of the agent. This example raises the hard issue of the dichotomy between rationalist and empiricist explanations of the world. I finish this tribute to George Ellis by noting that this dichotomy still needs to be resolved. However, it is already clear that it cannot be resolved at a purely molecular level. The resolution depends on choice processes at high levels using the harnessing of stochasticity to generate multiple behavioural options from which ones that may instantiate a rational response may be selected. This is precisely what the immune system does unconsciously in us all the time. There is every reason to think that the same kind of process can operate in conscious intentional behaviour (Noble and Noble 2020).

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Acknowledgements This article for the George Ellis Festschrift would have been impossible without the deep digging into the concepts of boundaries and causation in physiology to be found in (Noble et al. 2019). I wish therefore to thank especially the co-authors of that paper: my brother Raymond, who has worked with me on the foundations of modern biology ever since he came to a debate with Richard Dawkins at the Graduate Centre of Balliol College immediately following the publication of The Selfish Gene in 1976. His expertise as zoologist, neuroscientist and philosopher has been seminal. Kazuyo (Maria) Tasaki who came from the Oxford Humanities Division (Oriental and European medieval literature) to join me in a successful project to apply multi-level physiology to research on a traditional oriental medication for the treatment of muscle disease. The role of potassium in mediating a particular form of boundary causation forms part of that project, which has now been published in the new IUPS journal Physiome (Noble et al. 2020; Tasaki et al. 2020). My daughter, Penelope, who has extended many boundaries while working with Physiome-style modelling for many years, as the Oxford expert on COR (Garny et al. 2002b, 2009), OpenCOR (Garny and Hunter 2015) and CellML (Garny et al. 2008).

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Chapter 7

A Macro Agent and Its Actions Larissa Albantakis, Francesco Massari, Maggie Beheler-Amass, and Giulio Tononi

Abstract In science, macro level descriptions of the causal interactions within complex, dynamical systems are typically deemed convenient, but ultimately reducible to a complete causal account of the underlying micro constituents. Yet, such a reductionist perspective is hard to square with several issues related to autonomy and agency: (1) agents require (causal) borders that separate them from the environment, (2) at least in a biological context, agents are associated with macroscopic systems, and (3) agents are supposed to act upon their environment. Integrated information theory (IIT) offers a quantitative account of causation based on a set of causal principles, including notions such as causal specificity, composition, and irreducibility, that challenges the reductionist perspective in multiple ways. First, the IIT formalism provides a complete account of a system’s causal structure, including irreducible higher-order mechanisms constituted of multiple system elements. Second, a system’s amount of integrated information () measures the causal constraints a system exerts onto itself and can peak at a macro level of description. Finally, the causal principles of IIT can also be employed to identify and quantify the actual causes of events (“what caused what”), such as an agent’s actions. Here, we demonstrate this framework by example of a simulated agent, equipped with a small neural network, that forms a maximum of  at a macro scale.

Authors Francesco Massari and Maggie Beheler-Amass have equally contributed to this chapter. L. Albantakis () · M. Beheler-Amass · G. Tononi Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI, USA e-mail: [email protected] F. Massari Swarthmore College, Swarthmore, PA, USA © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_7

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7.1 Introduction What is an agent? To date, there is no single, agreed-upon definition of an agent that captures all relevant intuitions behind the concept. As a minimal property, an agent must be an open system that dynamically and informationally interacts with an environment. This simple requirement, however, immediately poses a methodological problem: When subsystems within a larger system are characterized by biological or informational properties, their boundaries are typically taken for granted and assumed as given (Krakauer et al. 2014; Oizumi et al. 2014; Albantakis 2018; Kolchinsky and Wolpert 2018). Moreover, at least in a biological context, the notion of agency is typically associated with macroscopic spatio-temporal scales (Moreno and Mossio 2015). For example, the causally relevant information that organisms pick up from their environment is generally not dependent on microscopic details; the cognitive abilities of an animal are related to the interactions of their neurons, rather than the underlying molecules, atoms or quarks; and the goal-directed actions performed by humans and other animals, and even life itself, have been characterized as instances of top-down causation (Ellis 2009, 2016; Walker and Davies 2013). This brings us to the last point: that agents are supposed to act upon their environment. Yet, as many have argued, the fact that physical events are either determined by previous (micro-physical) events, or emerge from (quantum) randomness, seems to be at odds with the notion of an autonomous agent with intrinsic causal power. Originally developed as a theory of consciousness (Tononi 2015; Tononi et al. 2016), IIT offers a quantitative framework to characterize the causal structure of discrete dynamical systems (Oizumi et al. 2014). The main quantity, , measures to what extent the causal constraints that a system exerts onto itself are irreducible to those of its parts. A system with  > 0, forms a unitary whole, as all of its subsets constrain and are being constrained by other subsets within the system above a background of external influences (Maturana and Varela 1980; Juarrero 1998; Tononi 2013; Marshall et al. 2017; Aguilera and Di Paolo 2018; Albantakis 2018; Farnsworth 2018). In this way, IIT provides the tools to identify whether a set of elements forms an entity with causal borders that separate it from its environment – a maximum of  (Oizumi et al. 2014; Marshall et al. 2017). The IIT formalism can also be applied across micro and macro spatiotemporal scales in order to identify those organizational levels at which the system exhibits strong causal constraints onto itself. As shown in previous work (Hoel et al. 2016; Marshall et al. 2018), it is indeed possible for a system to have higher  at a macro level than at the micro level. According to IIT principles, the particular spatiotemporal scale that specifies a maximum of integrated information (max ) defines the spatio-temporal scale at which the system specifies itself in causal terms. Finally, the causal principles of IIT, including notions such as causal specificity, composition, and irreducibility, can be employed to identify and quantify the actual causes and effects of events (“what caused what”) within a transition between subsequent states of discrete dynamical system (Albantakis et al. 2019). Such a

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Fig. 7.1 Artificial agent (“animat”) capable of performing a perceptual categorization task. (a) The animat is placed in a 16 by 36 unit environment. The animat itself is three units wide and can move to the right and left one unit at a time. Its two sensors are positioned on each side with one unit between them and switch ‘on’ (1) whenever a block is directly above them irrespective of its distance. Per trial one block is falling to the right or left at one unit per time step. (b) The task is to catch blocks of size 3 and 6 and to avoid blocks of size 4 and 5 (Task 4 in Albantakis et al. 2014). (c) The animat is equipped with a binary, deterministic Markov Brain (Hintze et al. 2017) constituted—at the macro level—of two sensors, three hidden elements, and two motors. The update function is fully described by the animat’s deterministic state transition probability matrix. The sensor states are determined by the environment. The motor elements do not have feedback connections to the rest of the system

principled account of actual causation makes it possible to identify the causes of an agent’s actions and to trace them back in time (“causes of causes”) (Juel et al. 2019). Our goal here is to demonstrate how various aspects of the IIT formalism can be combined to provide an account of (macro) agents and their actions in silico, through the example of a simulated agent (“animat”) equipped with a small neural network that is able to perform a simple perceptual categorization task (Fig. 7.1) (Beer 2003; Albantakis et al. 2014; Hintze et al. 2017). We will first describe the animat as a macro system of interacting “neurons” (black boxes) (Marshall et al. 2018), before zooming in on its micro constituents (Fig. 7.2). As we will show, the animat exhibits higher values of integrated information () at the macro level than at the micro level. Next, we will trace the causes of the animat’s actions back in time. While each action is necessarily preceded by a chain of micro events, these can only account for parts of the action. In our example, a cause for the action as a higherorder event constituted of multiple micro occurrences can only be found at the macro spatio-temporal scale. More broadly, our example analysis serves to demonstrate that IIT’s causal framework provides a consistent, quantitative account of causation that challenges the wide-spread reductionist perspective—that only individual micro constituents ultimately have causal power.

7.2 The Simulated Animat: Macro and Micro The animat we will analyze in the following is capable of performing an active perceptual categorization task (Beer 2003; Marstaller et al. 2013) with high accuracy

Fig. 7.2 Looking inside the macro level black-boxing at the animat’s micro level constituents. Each macro element A, B, C, M1 , M2 is constituted of several (10–17) micro elements (simple logic gates: COPY, AND, OR, XOR, NOT, NOR, and MAJ as indicated). Within each black box, micro elements are connected in a largely feed-forward manner (except for one loop in each motor black box). Every four micro updates correspond to one macro update. The macro state, here S1 S2 ABCM1 M2 = (0, 0, 1, 0, 1, 1, 0), corresponds to the state of the black-box output nodes at the time of each macro update and is thus multiply realizable.

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(97.7% correct). In the simulated environment, blocks of different sizes are falling to the right or left, one at a time, and the animat has to catch or avoid them depending on their size (Fig. 7.1). To that end, the animat is equipped with two sensors that turn ‘on’ (1) if a block is positioned directly above them at any distance, and two motors that enable the animat to move to the right or left (M1 M2 = (0, 1): move right; M1 M2 = (1, 0): move left; M1 M2 = {(0, 0), (1, 1)}: stand still). The animat’s behavior is determined by a “Markov Brain” (Hintze et al. 2017), a small neural network which, in our specific case, is constituted of binary elements with deterministic input-output functions. In Albantakis et al. (2014), we have used a genetic algorithm to evolve a population of this type of Markov Brains for high fitness in the block-catching task. Both the connectivity structure and update function of the Markov Brains were encoded in a genome (string of integers) and adapted through fitness selection and mutation. Macro Level Network At the macro level (Fig. 7.1c), the Markov Brain of our example animat is equivalent to that of the best performing animat in Albantakis et al. (2014) (Task 4), with three hidden nodes (A, B, C) that are connected in an allto-all manner, while connections from the sensors and to the motors are feedforward only. The update function of the animat’s Markov Brain can be represented by its state transition probability matrix (TPM), which specifies the output state of the hidden nodes and motors given the prior state of the sensors and the hidden nodes (the state of the sensors is fully determined by the environment). The macro elements, nodes A, B, C and motors M1 , M2 , update at the same rate as the environment. By construction, each macro element of our example animat corresponds to a “black box” (Marshall et al. 2018), constituted of a set of micro elements that interact and update at a finer spatial and temporal scale. In Fig. 7.2 we zoom in on the micro constituents of the macro-level animat displayed in Fig. 7.1c. Within the IIT framework, the macro level strictly supervenes upon its micro constituents. The macro level corresponds to a mapping that groups disjoint subsets of micro elements into non-overlapping macro elements (Hoel et al. 2013, 2016; Marshall et al. 2018). Likewise, the state of a macro element is always determined by a surjective mapping of the micro states of its underlying micro constituents. Micro Level Network The animat’s micro level is constituted of 72 simple logic gates (COPY, AND, OR, XOR, NOT, and NOR gates, as well as one Majority (MAJ) gate that turns ‘on’ if more than half of its inputs are ‘on’). As shown in  Fig. 7.2 (continued) Shown here is one possible realization corresponding to the last state in the time series shown below. The states of the other micro elements are ignored at the macro level (as they are hidden within the black boxes). Likewise, the state of the other micro timesteps are not taken into account in the mapping (Marshall et al. 2018). Given the particular implementation of the motor black boxes, the animat may only move on those micro time steps that correspond to the macro updates

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Fig. 7.2, the sensors consist of the same two elements at the macro and micro level. However, the macro elements A, B, C, M1 , M2 each correspond to a “black box” (Marshall et al. 2018) constituted of several (10–17) micro elements. The micro elements within these black boxes are connected in a largely feed-forward manner (except for one loop in each motor black box, which “clocks” its motor response (see below) and collectively emulate the logic function of their respective macro node over four micro time steps (updates). Each black box has one output node, but may receive inputs from the other black boxes or the sensors via multiple input nodes. The output nodes of the motor black boxes determine the animat’s movements but do not feedback into the network. In this way, the connectivity between the black boxes mirrors the connectivity of the macro-level animat shown in Fig. 7.1c. State-Mapping As each black-box has four layers (including inputs and the output node), four micro updates correspond to one macro update. The environment updates at the same rate as the macro elements. This means that, when viewed at the micro level, the sensors receive and output the same environmental input for four micro time steps. The mapping from micro-level states to macro-level states is accomplished as proposed by Marshall et al. (2018). The macro state of a black box corresponds to the state of its output node at the time of the macro update (here, every four micro updates) (Fig. 7.2, bottom). The states of all non-output elements are ignored at the macro level, as they are hidden within the black boxes. As a consequence, each macro state is realizable by multiple micro states. Figure 7.2 shows one possible micro state corresponding to the macro state S1 S2 ABCM1 M2 = (0, 0, 1, 0, 1, 1, 0). Similarly, the states between the macro updates are ignored for determining the macro update function. Due to the specific implementation of the motor black boxes, their outputs remain in state (0, 0) between macro updates, if the Markov Brain is initialized correctly at the beginning of each trial (e.g., in state “all off”). This means that the animat may only perform actions on those micro time steps that correspond to the macro update. This guarantees that our example animat behaves in exactly the same way as an animat that, at the micro level, is implemented as in Fig. 7.1c without further subconstituents. In the following we will apply IIT’s causal analysis to our example animat, at both the macro and the micro level. To that end, we will first evaluate the causal constraints the system exerts onto itself—its cause-effect structure—at both levels. Second, we will assess to what extent the constraints specified by the cause-effect structure are irreducible under a partition of the system, as measured by .

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7.3 The Compositional Cause-Effect Structure of a System in a State The IIT formalism evaluates five causal principles: intrinsicality, composition, information, integration, and exclusion (Oizumi et al. 2014; Tononi 2015). We will briefly outline these principles underlying IIT’s causal analysis by example of the macro animat shown in Fig. 7.1c and its corresponding transition probability matrix (TPM). For details and formal definitions of the relevant quantities we refer to the original publications (Oizumi et al. 2014; Tononi 2015). All IIT quantities can be computed from a given TPM using PyPhi, IIT’s python toolbox (Mayner et al. 2018). Here, we used the standard configuration corresponding to “IIT 3.0” (Oizumi et al. 2014). In general, the IIT analysis starts from a discrete dynamical system S, constituted of n interacting elements Si with i = 1, . . . , n. Each element must have at least two internal states, which can be observed and manipulated, and is equipped with a Markovian input-output function fi that determines the element’s output state si, t depending only on the previous system state st − 1 : si, t = fi (St − 1 = st − 1 ). This means that all elements are conditionally independent given the past state st − 1 of the system. S is fully described by its state transition probabilities: pˆ (St = st |St−1 = st−1 ) =

n i=1

  pˆ Si,t = si,t | St−1 = st−1 ,

∀st , st−1 . (7.1)

Note that Eq. 7.1 includes system states that may not be observed during the dynamical evolution of the system, but require system interventions (Pearl 2000; Ay and Polani 2008). The notation pˆ emphasizes that all probabilities herein correspond to interventions, not mere observations: pˆ (St = st |St−1 = st−1 ) = p (St = st |do (St−1 = st−1 )) (Pearl 2000). Intrinsicality Our goal is to evaluate the causal constraints specified by the set of elements S onto itself, above the background of external influences (Juarrero 1998; Albantakis 2018). If S is a subset of elements within a larger system, all elements outside of S are held fixed in their current state throughout the causal analysis and thus act as background conditions (causal conditioning). From its intrinsic perspective, the system is always in one particular state at any given moment. Accordingly, IIT’s causal analysis is state-dependent—it characterizes the system in its current state—and we take all previous system states st − 1 to be a priori equally probable (maximum entropy). State-averaged system properties, such as its stationary distribution, or an observed time-series, are extrinsic, available to an external observer but not the system itself.1

1 While

the IIT analysis depends on a system’s TPM, which specifies its dynamical properties completely, constraints are evaluated in a state-dependent, momentary manner. For an autonomous entity to persist over time, its borders (determined by maxima of , see below) should be stable

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For illustration, we choose the macro candidate set ABC in state ABC = (1, 0, 1) (Fig. 7.3a). In that case, the sensors and motors S1 S2 M1 M2 = (0, 0, 1, 0) act as fixed background conditions. The transition probabilities of ABC can be obtained from the full TPM (Fig. 7.1c) by conditioning on S1 S2 M1 M2 = (0, 0, 1, 0) and are shown in Fig. 7.3b. While the macro level TPM supervenes upon the micro level TPM, we ignore the underlying micro updates here and only take the macro TPM into account when we assess the animat’s macro cause-effect structure. From the intrinsic perspective of the system at the macro level, the micro elements and their updates are hidden inside the black boxes. Only the constraints between the macro elements should be taken into account. Composition In contrast with reductionist accounts that only consider how individual system elements update and interact, and holistic approaches that describe the dynamical evolution of the system as a whole based on its global state transitions, IIT takes a compositional perspective on causation (Albantakis and Tononi 2019). Not only single elements (here A, B, and C), but also combinations of elements may specify their own constraints about other system subsets as long as they are irreducible (see below). Within our candidate set ABC = (1, 0, 1) we thus evaluate the integrated information ϕ(xt ) of all subsets X = xt of ABC = (1, 0, 1) (Fig. 7.3c). A subset X with ϕ(xt ) > 0 is termed a mechanism within the system in its current state S = st . Mechanisms constituted of single elements are termed “first-order mechanisms”, while those constituted of multiple elements are termed “higher-order mechanisms” and are occasionally labeled by their specific order, e.g., “secondorder mechanism” for AC = (1, 1). Information The IIT formalism employs a counterfactual, interventionist notion of causation (Lewis 1973; Pearl 2000) to evaluate the causal constraints that a set of elements in its current state specifies about its causes and effects within the system. However, rather than testing for a counterfactual relation based on a single alternative, IIT considers all possible system states in its causal analysis, which can thus be expressed in probabilistic, informational terms (Albantakis et al. 2019). For clarity we add a time subscript to indicate a system subset at a specific point in time. The constraints that a system subset Xt ⊆ S in its current state xt ⊆ st specifies about the prior or next state of another subset Zt ± 1 ⊆ S are captured by its cause or effect repertoire. Specifically, the effect repertoire of xt over the subset Zt + 1 is defined as: π (Zt+1 |xt ) =

   pˆ Zi,t+1 |xt .

(7.2)

i

The symbol π indicates that the repertoire is a product distribution over the individual elements Zi, t + 1 ∈ Zt + 1 rather than simply the conditional distribution

over multiple time-steps. In this way, IIT’s approach is distinct from other dynamical systems approaches to agency and autonomy that typically evaluate a system’s temporal evolution toward dynamical attractors and thus its convergent (long-term) behavior (Juarrero 2000; Friston 2013).

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Fig. 7.3 Compositional cause and effect information of subsystem ABC. (a) The goal is to evaluate the causal information that ABC in its current state specifies about itself, treating the other elements as fixed background conditions. (b) The TPM for subsystem ABC can be obtained from the system’s TPM (Fig. 7.1c) by conditioning the full TPM on the current state of S1 S2 M1 M2 = (0, 0, 1, 0). Since the elements are binary, we can write the TPM in state-by-node format where each column specifies the probability of A, B, or C to be ‘on’ (1) given the respective input row. (c) Every subset of ABCt = (1, 0, 1) may form a separate mechanism in ABC and thus specify information about its possible causes and effects within the system in a compositional manner. Here, the information that subset ABt = (1, 0) specifies about its causes is reducible to a partition of ABt into At × Bt . Likewise, the information that ABCt = (1, 0, 1) specifies about its effects is reducible to a partition of ABCt into At × BCt . The cause-effect structure (CES) of ABC in state (1, 0, 1) is thus constituted of five irreducible mechanisms and the information they specify

over Zt + 1 . In this way, all Zi, t + 1 are conditioned on xt but receive independent “random” inputs from variables in St \Xt which are marginalized (causal marginalization). The cause repertoire of xt over the subset Zt − 1 is defined as: π (Zt−1 |xt ) =

 1   pˆ Zt−1 |xi,t K i

with

K=

   pˆ Zt−1 = z|xi,t . z∈Z i

(7.3)

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Here the product is over the elements in xt , which discounts biases from common inputs from St − 1 \Zt − 1 that are marginalized. A subset xt specifies information about Zt − 1 and Zt + 1 to the extent that conditioning on xt constrains the state of Zt − 1 and Zt + 1 compared to its unconstrained probability π (Zt ± 1 ) (see Oizumi et al. 2014; Tononi 2015; Albantakis and Tononi 2019 for details). By constraining a subset Zt − 1 , xt specifies information about its possible cause within the system. Likewise, by constraining a subset Zt + 1 , xt specifies information about its possible effect within the system.2 Integration All subsets xt ⊆ st may specify their own information about other subsets Zt ± 1 (see composition). However, a subset only contributes to the intrinsic information of the system if this information is irreducible (ϕ(xt ) > 0). This is tested by partitioning the cause/effect repertoire π (Zt ± 1 | xt ) into two parts π (Z1, t ± 1 | x1, t ) × π (Z2, t ± 1 | x2, t ) and measuring the difference between the intact and partitioned distributions (see Oizumi et al. 2014 for details). Of all such partitions ψ, the one that makes the least difference to the cause/effect repertoire (termed “MIP” for minimum information partition) determines the integrated information ϕ(xt , Zt ± 1 ) specified by xt over the subset Zt ± 1 . Moreover, to be a mechanisms within the system the subset xt must specify information about its causes and effects, requiring that min (ϕ (xt , Zt±1 )) > 0. t±1

Within system ABC in state (1, 0, 1), the information that subset ABt = (1, 0) specifies about its causes is reducible, as its cause repertoire π (ACt − 1 | ABt = (1, 0)) can be partitioned into π (Ct − 1 | At = 1) × π (At − 1 | Bt = 0). Likewise, the information that ABCt = (1, 0, 1) specifies about its effects is reducible, as its effect repertoire π (ABCt + 1 | ABCt = (1, 0, 1)) can be partitioned into π (Ct − 1 | At = 1) × π (ACt − 1 | BCt = (0, 1)). Exclusion Finally, xt may specify integrated information ϕ(xt , Zt ± 1 ) about various subsets Zt ± 1 within a system. The causal role it plays within the system is ∗ ∗ determined by the subsets Zt−1 and Zt+1 over which xt specifies the maximal ∗ ∗ are respectively termed the cause amount of integrated information. Zt−1 and Zt+1 and effect purview of xt . In summary, the amount of integrated information ϕ(xt ) specified by the subset xt can be expressed as: 





ϕ (xt ) = min max min D t±1

2 Within

Z

ψ



π (Zt±1 |xt ) ψ (π (Zt±1 |xt ))

.

(7.4)

the cause and effect repertoire, we can identify the specific state that is maximally constrained by xt , which then corresponds to the specific cause or effect of xt within the system from the intrinsic perspective of the system (Haun and Tononi 2019), (Barbosa et al. 2021).

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The set of all irreducible mechanisms within the system, their cause and effect purviews, and their integrated information ϕ(xt ) compose the intrinsic cause-effect structure of a system in a state C (st ).3

7.4 Comparing the Macro and Micro Cause-Effect Structures As shown in Fig. 7.3c, the macro cause-effect structure of ABCt = (1, 0, 1) is composed of five mechanisms with ϕ(xt ) > 0, all first order mechanisms and two higher order mechanisms. The information specified by these mechanisms corresponds to the compositional intrinsic information that the system ABC in state (1, 0, 1) specifies about itself from the intrinsic perspective. For example, Element At = 1 specifies that Bt + 1 = 1. Likewise, Bt = 0 specifies that Ct + 1 = 1, but only with p = 0.75. Together, ABt = 10 specify BCt + 1 = 11 with certainty (p = 1.0). ABt = 10 thus specifies irreducible information about the next state of BCt + 1 that cannot be accounted for by At = 1 and Bt = 0 taken independently. Nevertheless, some of the information specified by the mechanisms within the system may seem redundant from the extrinsic perspective. In our example, ACt = 11 specifies the next state of the system ABCt + 1 with certainty. As outside investigators, we can thus infer the state of every subset of ABCt + 1 . Note, however, that such an inference requires a mechanism to be performed. The system itself only has information about subsets of ABCt + 1 if other mechanisms exist, such as At = 1 or BCt = 01, that specify that particular information (Albantakis and Tononi 2019). The corresponding set of micro elements consists of the 43 elements included in the black boxes A, B, and C. All other micro elements are taken to be background conditions. The micro system state is the one shown in Fig. 7.2. The micro causeeffect structure is computed based on the micro TPM of the system. All of the 43 micro elements specify first order mechanisms in their current state. In principle, the ϕ values of all subsets of the 43 micro elements would have to be evaluated for higher order mechanisms. However, a set of elements xt can only form a higher order mechanism if each of the elements shares inputs and outputs with other elements in the set. Otherwise, ϕ(xt ) is necessarily 0 as either the cause or effect repertoire can be partitioned without loss (Oizumi et al. 2014; Mayner et al. 2018). As the connectivity at the micro level is rather sparse, modular, and feedforward, only a few layers of nodes may give rise to higher order mechanisms. We identified 12 higher order mechanisms, one in the input layer of black box C, the other 11 are specified by four elements in black box B (second layer, 2–5). On average, the ϕ value of the micro mechanisms is lower than that of the macro mechanisms:

3 In addition, it is possible to evaluate relations between the cause and effect purviews of the various

mechanisms, which specify the causes and effects specified by multiple mechanisms (see Haun and Tononi 2019).

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ϕmicro = 0.16 < ϕmacro = 0.27, which means that the macro mechanisms constrain their respective inputs and outputs more than the micro mechanisms.

7.5 Micro and Macro System-Level Integrated Information  The cause-effect structure C (st ) contains all the intrinsic information the system specifies about itself at the respective level of description. However, the notion of intrinsic information requires that there is a system in the first place, meaning one “whole” as opposed to multiple separate sets (Oizumi et al. 2014; Albantakis 2018; Albantakis and Tononi 2019). The next step in IIT’s causal analysis is thus to evaluate whether and to what extent C (st ) is integrated, i.e., irreducible under a partition of the system. This is quantified by (st ), the integrated information of the system as a whole S in a particular state st : Φ (st ) = min (D (C (st ) ; C (Ψ (st )))) . Ψ

(7.5)

Again, we search for the system partition that makes the least difference to the cause-effect structure C (st ), the MIP (minimum information partition). As defined in Oizumi et al. (2014) and Tononi (2015), system partitions are unidirectional, rendering the connections from one part of the system X ⊂ S to the rest ineffective. If the system does not form a unified whole and can be partitioned into two or more parts without loss,  = 0. Also systems in which two or more parts of the system are connected in a feedforward manner cannot be integrated ( = 0). In a system with  > 0, all parts of the system constrain and are being constrained by the rest of the system above a background of external influences.  can thus be viewed as a measure of how much a system exists for itself, in causal terms. Feedback between a system’s constituents and, in fact, a strongly connected architecture are thus prerequisites for integrated information. Many have argued that an autonomous system must form a unified whole in causal, informational, or dynamical terms, referring to self-maintenance, autopoiesis, and organizational closure (Maturana and Varela 1980; Juarrero 2000; Tononi 2013; Moreno and Mossio 2015; Aguilera and Di Paolo 2018; Farnsworth 2018). In this context, (Moreno et al. 2008) distinguish between constitutive and interactive processes. The architecture for action generation analyzed here corresponds to interactive processes within the agent (see also Bertschinger et al. 2008). In principle, the IIT formalism can be applied to any type of causal network model, representing physical, chemical, or neural interactions (Marshall et al. 2017). (Mossio and Moreno 2010) also distinguish between “organizational closure”, which requires constraints enabling the emergence of other constraints (for instance, in auto-catalytic systems) and the more basic notion of causal cycles, which is sufficient for  > 0.

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Fig. 7.4 Comparing the integrated information of the micro and macro level. The same minimal partition (indicated by the scissors cutting the connection in bold) affects the cause-effect information at the micro level less than at the macro level. While in (a) only the two micro elements directly connected by the partitioned arrow are affected, in (b) the partition also has secondary effects on the constraints of macro node A and C on macro node B (as indicated by the dashed, bold arrows). This explains the higher  value at the macro level

For  to be high, every possible partition must affect the integrated information ϕ specified by many mechanisms within the system. At the micro level, we identified the MIP as indicated in Fig. 7.4a between the fourth input element of black box B and its one output, the first AND gate in the second layer.4 As only two first   order mechanisms are affected, this cut leads to a comparatively low value of Φ stm = 0.032 (the ‘m’ superscript indicates the micro level, below ‘M’ stands for macro level). While the cause-effect structure at the macro level is based entirely on the  macro TPM, the system level integrated information Φ stM is still evaluated by partitioning between micro elements (Marshall et al. 2018). This means that the same set of partitions is tested and can be compared at the macro and micro level. In this way it becomes impossible to trivially increase the system’s integration at certain macro levels by “hiding” weak connections inside the macro elements. The macro TPM of the partitioned system is obtained by black-boxing the partitioned

4 Note

that the IIT python package Pyphi cannot, at the moment, compute   the  value of a 43 element system exhaustively. To identify the micro MIP and assess Φ stm , we took advantage of the modularity of the micro system and identified a separate MIP for each black box using Pyphi. The system MIP then corresponds to the minimum across black boxes. Partitions between black boxes all have larger effects on the micro cause-effect structure, as the output nodes of each black box are connected to many micro elements within the system.

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micro system using the same element and state mapping as for the unpartitioned system. Compared to the micro level, the same partition has more substantial effects on the macro cause-effect structure, affecting the effect information specified by At = 1 and also the cause information specified by ABt = 10 and BCt = 01. For this reason, the integrated information   specified by the system at the macro level amounts to the higher value of Φ stM = 0.213 (Fig. 7.4b). According to IIT, maxima of integrated information  define causal entities having causal borders with their environment (Oizumi et al. 2014; Marshall et al. 2017, 2018). To identify whether a particular set of elements specifies a maximum of , in principle, requires evaluating many other candidate systems. In our example, all systems larger than the set of elements that constitute A, B, and C (within the dashed rectangle in Fig. 7.4) necessarily have  = 0 because the sensors and all elements in M1 and M2 are only connected to ABC in a unidirectional manner). As explained above, systems in which one part is connected to the rest in a feedforward manner cannot form an integrated system according to IIT. Consequently, only sets of elements that are strongly connected (for which a directed path exists from each element to every other element) can have a value of  > 0. Using this short-cut, we can establish that the system ABC, as well as the set of its constituting 43 micro elements analyzed in Fig. 7.4a, b form a maximum of integrated information  in their current state. This means that removing or adding any element from the set would lead to a lower  value.5 In this way, ABC and its set of constituents define a causal border that separate the internal constraints within the animat from its environment, both at the micro and macro level (Marshall et al. 2017, 2018).6 As  measures the irreducible intrinsic constraints of a set of elements onto itself over a background of external influences, the macro system ABC can be said to be more autonomous than the set of its micro constituents.

5 Our

focus here lies on autonomy and the notion of self-defined causal borders that separate the internal mechanisms of the agent from its environment. According to IIT, a physical substrate of consciousness must specify a global maximum of  across all overlapping sets of elements and spatio-temporal scales. In other words, any particular micro element can only contribute its causal power to one physical substrate of consciousness by IIT’s exclusion postulate. Given the size of the animat’s micro implementation, an exhaustive analysis across all possible sets of elements and spatio-temporal mappings was not feasible. Thus, it is possible that smaller subsets within the 43 micro elements may specify even higher values of  within the system. Likewise, other spatiotemporal mappings may reveal additional “meso” levels of description with higher values of  than ABCt . 6 This also means that the animat’s sensors and motors technically form part of the environment, while the causally autonomous entity is defined as the integrated core of the animat.

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7.6 Tracing Back the Causal Chain Leading up to the Animat’s Actions So far, we have focused on the causal information that the system’s elements specify about each other, alone and in combination, at a micro and macro level of description (Fig. 7.3), and its integration as measured by . As we have demonstrated, the macro level description, while supervening on the micro constituents, specifies more integrated information. In particular, the output nodes of the black boxes A, B, and C, play a crucial role in integrating the network over longer time scales. The causal principles of IIT (such as composition, information, integration, and exclusion), can also be employed to identify and quantify the actual causes and effects of an occurrence (“what caused what”), such as an agent’s actions (Albantakis et al. 2019; Juel et al. 2019). An “occurrence” here simply denotes a set of elements in a particular state: xt . As described above, from the intrinsic perspective, the causal role that an occurrence xt plays within the system is determined by the causal information ∗ and Z ∗ , which are the system xt specifies about its cause and effect purviews, Zt−1 t+1 subsets over which the amount of integrated information ϕ(xt ) is maximized (Eq. ∗ ∗ , however, is 7.4). The actual state of the cause or effect purviews Zt−1 and Zt+1 unknown from the intrinsic perspective of the system in its current state. ∗ To identify the actual cause zt−1 of an occurrence xt , instead, we take the perspective of an extrinsic observer of the system with access to the system’s time ∗ series {st − k , . . . , st − 1 , st } (Fig. 7.5a). In parallel to ϕ(xt ), the actual cause zt−1 is then identified as the sub-state zt − 1 ⊆ st − 1 over which xt specifies the most irreducible causal information:    π (zt−1 |xt ) α (xt ) = max min log2 . (7.6) z ψ ψ (π (zt−1 |xt )) π (zt − 1 | xt ) here denotes the probability of the specific state zt − 1 in the cause repertoire π (Zt − 1 | xt ). The goal is to identify what caused xt ⊆ st given a particular state transition st − 1 st . We refer to the original publication (Albantakis et al. 2019) for further details on the measure α(xt ) and the set of permissible partitions ∗ typically corresponds {ψ}. In deterministic systems, the identified actual cause zt−1 to an occurrence at t − 1 that is minimally sufficient for xt to occur, at least in the case where xt is a first-order occurrence (a single element in its particular state).7

7 In non-deterministic systems Eq. 7.6 would generally identify the minimal occurrence at t − 1 that raises the probability of xt the most. Introducing a “specification factor” π(zt − 1 | xt ) in front of   π z |x in Eq. 7.6 effectively implements a tradeoff between an increase in probability log2 ψ π( zt−1 |xt ) ( ( t−1 t )) of xt and the cost of setting additional elements into a particular state, which allows identifying the ∗ part of zt−1 that was particularly relevant for the occurrence of xt .

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Fig. 7.5 Tracing back the causes of action M1 M2 = 10. (a) Micro level time series specifying the state of all 72 micro constituents of our example animat over 32 time steps. (b) Starting from the current micro state of the agent (here t = 31), the actual causes of the occurrences E62 = 1, E72 = 0, and E62 E72 = 10 are identified in the preceding micro time-step t = 30 (proximal causes). The micro elements E62 and E72 here correspond to the output elements of the motor black boxes M1 and M2 . Iteratively, the backtracking analysis then identifies the causes of the set of elements involved in the proximal causes of the previous time step (causes of causes). At each time step we determine the strength α of the causal link between an occurrence and its actual cause (Eq. 7.6) and assign each micro element its summed contribution to α (right panel). The histogram on the left shows the summed contribution across elements. After an initial transient, maxima of causal strength can be observed at every macro time step for the micro elements that correspond to the black box outputs which highlights the special causal role that these output elements play within the system

The actions of our example agent are defined by the state of both of its motor units, the output nodes of M1 and M2 . As indicated by the micro time series displayed in Fig. 7.5a, the agent’s actions are necessarily preceded by a chain of micro events. In the particular state evaluated above M1 M2 = 10, which means that the animat is moving to the left. In the following we will use “E62 ” and “E72 ” to denote the micro output elements of the black boxes M1 and M2 . Both, E62 and E72 are AND logic-gates and receive direct inputs from two micro elements each, here labeled E59 , E61 and E67 , E69 (from left to right). At time t − 1, these micro elements were in state E59 E61 E67 E69 = 1101. Applied to the transition {(E59 E61 E67 E69 )t − 1 = 1101} {(E62 E72 )t = 10}, the actual causation analysis here provides the intuitive result that the actual cause of the occurrence E62, t = 1 was (E59 E61 )t − 1 = 11 with α = 2.0 bits (both inputs had to be ‘on’ in order to switch the AND-gate M1 ‘on’) and the actual cause of E72, t = 0 was E67, t − 1 = 0 with α = 0.415 bits (which prevented E72, t to be ‘on’). In principle, we also evaluate if any higher order occurrences specify their own irreducible causes (applying the composition principle). However, in this particular case the occurrence (E62 E72 )t = 10 is reducible, as the elements do not share common inputs at the micro level. (E59 E61 )t − 1 = 11 and E67, t = 0 are the direct (or proximal) micro causes of the individual outputs E62, t = 1 and E72, t = 0. Yet, the animat’s action (“move left”) here corresponds to the higher-order occurrence (E62 E72 )t = 10, and the proximal micro causes do not provide a causal explanation for why E62, t = 1 and E72, t = 0 occurred together. With respect to an agent’s action, the direct micro-level cause is rarely considered the cause with the greatest explanatory power (Woodward 1989). For example,

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while a motor neuron in the spinal cord may directly initiate a movement, we are typically more interested in identifying the cortical events or external stimuli that triggered the action. To that end, we can employ the actual causation analysis to trace the causal chain of micro occurrences back in time, identifying the “causes of the causes” of the animat’s action (Juel et al. 2019). Specifically, we now start with (E59 E61 E67 )t − 1 = 110, the union of the actual causes of (E62 E72 )t = 10 and identify the actual causes of all occurrences xt − 1 ⊆ (E59 E61 E67 )t − 1 = 110 at time t − 2, and so on. As a measure of the causal relevance of a particular micro element, we sum its relative contribution to the α values of all actual causes it participates in within a given time step (see Juel et al. 2019 for details). Figure 7.5b shows the results of tracing the causes of {(E62 E72 )t = 10} back to the beginning of the trial (t = 0). The histogram on the right shows the summed causal strength across elements. After an initial transient through the micro elements that make up the motor black boxes and the micro elements constituting the internal black boxes A, B, and C (t = 31 to t = 24, moving upwards from the bottom), a first peak of the overall causal strength can be observed at t = 23, when the backtracking reaches the output elements of the black boxes A, B, and C for the second time. This shows that these micro elements play a special causal role, not only with respect to the constraints the system poses onto itself, but also regarding the causes of its actions. Going back further in time, we find additional peaks in correspondence with the spatiotemporal scale that matches the black-box macro level. The reason for these peaks is that the black box outputs act as causal bottlenecks within the system, with many incoming and outgoing connections. Each output element thus contributes to the causes of many occurrences at the next micro time step (setting the states of the many black box input elements). In sum, tracing back the causal chain of events at the micro level of description provides an independent way of identifying nodes within the system that act as “causal bottlenecks”. In this way, the actual causation analysis can inform the search for relevant spatiotemporal scales and black boxings that may form maxima of integrated information. Finally, we can apply the actual causation analysis directly to the macro-level transition {(S1 S2 ABC)T − 1 = 00001} {(M1 M2 )T = 10}. In doing so, we find the macro occurrence (S1 AC)T − 1 = 001 (or equivalently (S1 BC)T − 1 = 001) to be the cause of M1, T = 1 with α = 1.30 bits, and AT − 1 = 0 to be the cause of M2, T = 0 with α = 0.25 bits.8 In addition, the higher-order occurrence (M1 M2 )T = 10 specifies its own irreducible cause (S1 AC)T − 1 = 001 at the macro level with α = 0.35 bits. This can be interpreted as causal information that the joint occurrence of (M1 M2 )T = 10 specifies about the particular state of S1 AC that actually happened at T − 1 which is not specified by its parts taken independently. In other words, there

8 The

α values at the macro level are somewhat smaller than those of the proximal causes at the micro level, as we average over all possible initial states of the motor black-boxes when we evaluate the strength of the causal links in the macro transition, which introduces a certain level of indeterminacy (see Marshall et al. 2018).

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is a causal explanation for the action “move left”, corresponding to (M1 M2 )T = 10 at the macro level, beyond the independent occurrences of M1, T = 1 and M2, T = 0. As we have seen above, such an explanation does not exist at the micro level.

7.7 Discussion In science, macro-level descriptions of the causal interactions within complex, dynamical systems are typically deemed convenient, but ultimately reducible to a complete causal account at the level of the underlying micro constituents. Yet, such a reductionist perspective is hard to square with several properties associated with autonomy and agency that depend on a system’s causal structure beyond its individual micro constituents (Juarrero 1998; Ellis 2016; Albantakis 2018; Marshall et al. 2018; Albantakis and Tononi 2019). For example, the notion of an agent as an autonomous entity that interacts with its environment requires, to begin with, a subdivision of a larger system into agent and environment which cannot be properly formulated using a reductionist account of the system’s causal properties (Albantakis and Tononi 2019). Moreover, while any action performed by an agent is necessarily preceded by a chain of micro events, a dynamical account of “what happened” at the micro level does not equal a causal account of “what caused what” (Albantakis et al. 2019). Nevertheless, the fact that macro-level descriptions of a system supervene upon the dynamics of their microlevel constituents seems to leave no room for genuine macro-level causes and effects (Kim 1993). Here we argue that much of the appeal of the reductionist perspective stems from an inadequate notion of causation that is incoherent, fails to account for causal structure, and does not distinguish causation from prediction (see also Juarrero 2000). By contrast, Integrated information theory (IIT) (Oizumi et al. 2014) offers a consistent, quantitative account of causation based on a set of causal principles, including notions such as causal specificity, composition, and irreducibility, that challenges the reductionist perspective in multiple ways (see also Moreno and Mossio 2015). First, the IIT formalism provides a complete account of a system’s causal structure, including irreducible higher-order mechanisms constituted of multiple system elements (Albantakis and Tononi 2019). IIT’s quantitative notion of irreducibility here supplants the reductionist assumption that mechanisms— irreducible causal units—are ultimately restricted to micro elements (Grasso et al. in press). Second, a system’s amount of integrated information () measures the causal constraints a system exerts onto itself and can peak at a macro level of description (Hoel et al. 2016; Marshall et al. 2018). Finally, the causal principles of IIT can also be employed to identify and quantify the actual causes of (higherorder) events (“what caused what”), such as an agent’s actions (Albantakis et al. 2019; Juel et al. 2019). In this chapter, we have demonstrated IIT’s causal framework by example of a simulated agent, equipped with a small neural network, that forms a maximum of 

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at a macro scale. Our particular example agent is constituted of 72 deterministic logic-gates at the micro level, which are grouped into seven non-overlapping black boxes (including the sensors) at the macro level. The macro-level dynamics supervene upon the micro level and we have full knowledge about the input-output functions of the micro elements and their connectivity. Nevertheless, the agent is an open system, receiving inputs from the environment, which means that its internal dynamics are context dependent and can only be predicted within the larger agent-environment system (Albantakis and Tononi 2019; Bishop and Ellis 2020). By construction, in our example the environment updates at the same temporal scale as the black-boxed macro-level. In future work, we plan to investigate which environmental conditions may facilitate the evolution of animats with a hierarchical causal structure, such as environments that update at a slower rate than the animats’ micro constituents and other forms or macroscopic constraints (Moreno and Mossio 2015; Bishop and Ellis 2020). As our example agent is deterministic, the observed increase in intrinsic causal power () at the macro level is due to the particular causal structure of the system, including higher-order mechanisms and strong constraints across multiple time steps. While the constraints that the system exerts onto itself at the macro level supervene on the micro level, they are intrinsic to the macro level and only become apparent when the system is analyzed as the set of interacting black boxes. In other words, these constraints only exist at the macro level of description. As argued in Ellis (2009, 2016), Hoel et al. (2013) and Bishop and Ellis (2020), indeterminism at the micro level may provide additional “causal slack” at the bottom that allows for the macro level to be causally efficacious over the lower levels. In Hoel et al. (2013, 2016), we have demonstrated that coarse-graining sets of micro elements and their states into macro elements may also increase the causal specificity and integrated information () at the macro level. In any case, while the macro constraints are not necessary to simulate or predict the future state of the system, they are necessary to explain the stability of the system across multiple time-steps in causal terms. The same reasoning applies to the agent’s actions. The output of the animat’s motor units can be simulated, and thus predicted, based on the animat’s micro constituents. Nevertheless, the micro level does not offer a causal account of why the animat performed this particular action. In our simple example, the micro level, for instance, does not provide a cause for the action as a higher-order occurrence of (E62 E72 )t = 10. By contrast, an irreducible causal explanation exists at the macro spatio-temporal scale. More generally, the question “why an agent chose a particular action over another?” cannot be addressed in purely reductionist terms if the action, the choice, and the agent itself correspond to macroscopic causal structures constituted of many micro occurrences or elements. A principled treatment of notions such as causal autonomy, agency, and free will instead require a quantitative, non-reductionist account of causation. Acknowledgments This project was made possible through the support of a grant from Templeton World Charity Foundation, Inc. (#TWCF0196). The opinions expressed in this publication are

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those of the authors and do not necessarily reflect the views of Templeton World Charity Foundation, Inc. In addition, this work was supported by the Tiny Blue Dot Foundation (UW 133AAG3451) and a grant awarded through the Foundational Questions Institute and Fetzer Franklin Fund (FQXi-RFP-IPW-1909). F.M. received divisional funding from Swarthmore College (Wallach Fellowship).

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Chapter 8

Physics, Determinism, and the Brain George F. R. Ellis

Abstract This chapter responds to claims that causal closure of the underlying microphysics determines brain outcomes as a matter of principle, even if we cannot hope to ever carry out the needed calculations in practice. The reductionist position is that microphysics alone determines all, specifically the functioning of the brain. Here I respond to that claim in depth, claiming that if one firstly takes into account the difference between synchronic and diachronic emergence, and secondly takes seriously the well established nature of biology in general and neuroscience in particular, downward causation enables genuine causal powers to occur at higher emergent levels in biology (and hence in the brain) and that causal closure is in reality an interlevel affair involving even social levels.

8.1 Emergence and the Brain The basic issue for this book is a joint set of issues: the alleged overdetermination of the physical level if downward causation takes place, given the assumed causal closure of the physical, and whether reduction is impossible in principle or merely in fact. In this chapter, I give arguments for strong emergence in the case of the brain, based in the nature of causation in biology. It rests on three things. First, taking seriously the nature of biology in general (Campbell and Reece 2008) and neuroscience (Kandel 2012; Kandel et al. 2013) in particular, demanding that whatever overall theory we propose must respect that nature. Second, requiring that individual events and outcomes are what need to be accounted for, not just statistics. Third, noting the key difference between synchronic and diachronic emergence. The answer is very different in these two cases. The latter is the real issue; there is no

G. F. R. Ellis () Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_8

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overdetermination, causal closure is an interlevel affair, and strong emergence is indeed possible. Synchronic and Diachronic Emergence Carlo Rovelli1 argues that the physical microstate of the brain uniquely determines macro level outcomes, hence strong emergence of brain outcomes cannot take place. This is correct when we consider synchronic emergence. That is what a lot of neuroscience is about. It is not valid however when one considers diachronic emergence. The issue here is one of timescales. Synchronic emergence is when the timescale δt := tb − ta of the considered microdynamic outcomes is very short relative to the timescale δT of change of structures at the micro scale: δT  δt. It is the issue of emergent dynamics when parameters are constant and constraints unchanging. In the case of the brain this would for example be the flow of electrons in axons leading to mental outcomes at that time, with this micro structure taken as unchanging. Electrons and ions flow in a given set of neural connections. Diachronic emergence is when the timescale of micro dynamic outcomes considered δt is of the same order or larger than the timescale δT of change of structure at the micro scale: δT ≤ δt, so microdynamics contexts alters significantly during this time. It is the case when parameters or constraints change because of interactions that are taking place. In the case of the brain this would for example be when something new is learned so that strengths of neural connections are altered. Consider First a Single Brain Dynamic outcomes at the molecular scale are due to the specific structures at the cellular scale, neural connectivity for example, and the way that they in turn constrain electron and ion activity. Three points arise. • First, the brain is an open system. It is not possible for the initial physical state to determine later states because of the flood of data incoming all the time. The last round of microlevel data does not determine the initial data that applies at the next round of synchronic emergence. The brain has evolved a set of mechanisms that enable it to cope with the stream of new data flowing in all the time by perceiving its meaning, predicting futures, and planning how to respond. This is what determines outcomes rather than evolution from the last round of initial data. • Second, the brain is a plastic brain that changes over time as it learns. Neural connections are altered as learning takes place in response to the incoming stream of data. This change in constraints alters future patterns of electron and ion flows. This learning involves higher level variables and understandings such as “A global Coronavirus pandemic is taking place”, that cannot be characterised at lower levels and cannot be predicted from the initial brain microdata. • Third, there is a great deal of stochasticity at the molecular level that breaks the ideal of Laplacian determinism at that level. Molecular machines have been

1 Private

communication.

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evolved that take advantage of that stochasticity to extract order from chaos. From a higher level perspective, this stochasticity enables organisms to select lower level outcomes that are advantageous to higher level needs. From a systems perspective, this enables higher level organising principles such as existence of dynamical system basins of attraction to determine outcomes. This argument applies to all biology, as all biological systems are by their nature open systems (Peacocke 1989). The initial physics data for any organism by itself cannot in principle determine specific later outcomes because of this openness. The fundamental physical laws are not altered or overwritten when this happens; rather the context in which they operate—for example opening or closing of ion channels in axons—determine what the specific outcomes of generic physical laws will be as alter configuration. From a physics viewpoint this is represented by time dependent constraint terms or potentials in the underlying Hamiltonian (Ellis and Kopel 2019). The Whole Universe Gambit The ultimate physicalist response is “Yes the brain may be an open system but the whole universe is not; and the brain is just part of the universe, which is causally complete. Hence brain dynamics is controlled by the microphysics alone when one takes this into account, because it determines all the incoming information to the brain”. However this argument fails for the following reasons: • Firstly there is irreducible quantum uncertainty in outcomes, which implies the lower physics levels are in fact not causally complete. This can get amplified to macroscales by mechanisms that change mental outcomes, such as altered gene expression due to damage by high energy photons. • Secondly, this downward process—inflow of outside information to individual brains—does not uniquely determine brain how microstructures change through memory processes because of multiple realisability. But such uniqueness is required to sustain a claim that the causal closedness of microphysics determines specific brain outcomes over time. • Thirdly, chaotic dynamics associated with strange attractors occurs, which means the emergent dynamics of weather patterns is not in fact predictable even in principle over sufficiently long timescales. This affects decisions such as whether to take an umbrella when going to the shops or not. • Fourthly, microbiome dynamics in the external world affects brain outcomes in unpredictable ways, for example when a global pandemic occurs • Fifthly, this all takes place in a social context where social interactions take place between many brains, each of which is itself an open system. Irreducible uncertainty influences such contexts due to the real butterfly effect (weather) and the impossibility, due to the molecular storm, of predicting specific microbiome mutations that occur (e.g. COVID-19), leading to social policy decisions, that are high level variables influencing macro level brain states. The outcomes then influence details of synaptic connections and hence shape future electron and ion flows.

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This downward causation from the social/psychological level to action potential spike chains and synapse activation is essential to the specific outcomes that occur at the physical level of electron and ion flows in individual brains. Causal closure only follows when we include those higher level variables in the dynamics.

8.1.1 The Argument That Follows Section 8.2 sets the scene by discussing the foundations for what follows, in particular the fact that life is an ongoing adaptive process. In the following sections I discuss the key issues that support my view. Firstly, an individual brain is an open system, and has been adapted to handle the problems this represents in successfully navigating the world (Sect. 8.3). This rather than the initial brain micro data determines outcomes. Secondly, the brain learns: it is plastic at both macro and micro levels, which continually changes the context within which the lower level physics operates (Sect. 8.4). Third, the kind of Laplacian view of determinism underlying Carlo’s position is broken at the molecular level because of the huge degree of stochasticity that happens at that level (Sect. 8.5). Biological processes—such as Darwinian evolution, action choices, and the brain pursuing a line of logical argumentation—are what in fact determine outcomes, taking advantage of that stochasticity. Biological causation occurs selects preferred outcomes from the molecular storm, and the brain selects from action options. In Sect. 8.6 I counter the whole universe gambit by claiming that this will not work because of quantum wave function collapse, macro level chaotic dynamics, multiple realisability of macro brain states, and unpredictable microbiome interactions that affect brain dynamics both directly and via their social outcomes. Section 8.7 consider how higher level organising principles—the effective laws that operate at higher levels—are in fact what shapes outcomes. This is what enables causal closure—an interlevel affair—in practice. I also comment on the issue of freewill (Sect. 8.7.2).

8.2 Foundations As stated above, the premise of this paper is that when relating physics to life, one should take seriously the nature of biology as well as that of physics. I assume the standard underlying microphysics for everyday life, based in the Lagrangian for electrons, protons, and nuclei, see (Laughlin and Pines 2000) and (Bishop 2005). This section sets the foundation for what follows by discussing the nature of biology and of causation.

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Section 8.2.1 discusses the basic nature of biology. Section 8.2.2 outlines the biological hierarchy of structure and function. Section 8.2.3 discusses the nature of Effective Theories at each emergent level L. Section 8.2.4 discusses the equal validity of each level in causal terms. Section 8.2.5 discusses the various types of downward causation, and Aristotle’s four types of causes as well as Tinbergen’s ‘Why’ questions. Section 8.2.6 discusses the important issue of multiple realisability of higher level structure and function at lower levels. Finally Sect. 8.2.7 discusses the key role of Higher Level Organising Principles.

8.2.1 The Basic Nature of Biology All life (Campbell and Reece 2008) is based in the interplay between structure (that is, physiology Hall 2016; Rhoades and Pflanzer 1989) and function. For good functional, developmental, and evolutionary reasons, it is composed (Table 8.1: Sect. 8.2.2) of Adaptive Modular Hierarchical Structures (Simon 2019; Booch 2006) based in the underlying physics. It comes into being via the interaction between evolutionary and developmental (Evo-Devo) processes (Carroll 2005, 2008), and has three key aspects.2 1. Teleonomy: Function/Purpose Life has a teleonomic nature, where Jacques Monod defines teleonomy as the characteristic of being “endowed with a purpose or project” (Monod 1971, 9) He points out the extreme efficiency of the teleonomic apparatus in accomplishing the preservation and reproduction of the structure. As summarised by Nobel Prizewinner Leland Hartwell and colleagues (Hartwell et al. 1999), Although living systems obey the laws of physics and chemistry, the notion of function or purpose differentiates biology from other natural sciences. Organisms exist to reproduce, whereas, outside religious belief, rocks and stars have no purpose. Selection for function has produced the living cell, with a unique set of properties that distinguish it from inanimate systems of interacting molecules. Cells exist far from thermal equilibrium by harvesting energy from their environment. They are composed of thousands of different types of molecule. They contain information for their survival and reproduction, in the form of their DNA.

Function and purpose emerge at the cell level. Francois Jacob says Jacob (1974)3 At each level of organisation novelties appear in both properties and logic. To reproduce is not within the power of any single molecule by itself. This faculty appears only within the power of the simplest integron4 deserving to be called a living organism, that is, the cell. But thereafter the rules of the game change. At the higher level integron, the cell

2 An

excellent introduction to the relevant mechanisms is given in Noble (2016). in Peacocke (1989, 275). 4 An ‘Integron’ is each of the units in a hierarchy of discontinuous units formed by integration of sub-units of the level below (Jacob 1974, 302). 3 Quoted

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population, natural selection imposes new constraints and offers new possibilities. In this way, and without ceasing to obey the principles that govern inanimate systems, living systems become subject to phenomena that have no meaning at the lower level. Biology can neither be reduced to physics, nor do without it.

2. Life Is a Process Being alive is not a physical thing made of any specific elements. It is a process that occurs at macro levels, in an interconnected way. In the case of human beings it involves all levels5 from L4 (the cellular level) to Level L6 (individual human beings), allowing causal closure (Mossio 2013; Mossio and Moreno 2010) and hence self-causation (Juarrero 2002; Murphy and Brown 2007). Life is an ongoing adaptive process involving metabolism, homeostasis, defence, and learning in the short term, reproduction, growth, and development in the medium term, and evolution in the long term. It uses energy, disposes of waste heat and products, and uses contextual information to attain its purposes.

The claim I make is that this process of living has causal power, making things happen in an ongoing way. High level processes take place via an interlevel dialogue between levels (Noble 2008), higher levels continually altering the context of the underlying physical levels in order to carry out these functions (Ellis and Kopel 2019). Yes of course the resulting physical processes can be traced out at the physics level. But my claim will be that biological imperatives (Campbell and Reece 2008) enabled by physiological systems (Rhoades and Pflanzer 1989; Hall 2016) shape what happens. Evolutionary processes (Mayr 2001; Carroll 2008) have enabled this synergy to occur (Noble 2016). 3. Basic Biological Needs and Functions In the case of animal life,6 the basic biological functions are, B1: B2: B3: B4: B5:

Metabolism (acquiring energy and matter, getting rid of waste), Homeostasis and defence, Reproduction and subsequent development, Mobility and the ability to act, Information acquisition and processing.

They serve as attractors when variation takes places (Ginsburg and Jablonka 2019, 245). They are the higher level organising principles that evolution discovers and then embodies in hierarchically structured physiological systems, where the macro functions are supported at the micro level by metabolic networks, gene regulatory networks, and cell signalling networks, selected from an abstract space of possibilities and realised through specific proteins (Wagner 2014). Information is central to what happens (Nurse 2008; Davies 2019). These principles cannot be described or identified at the underlying microphysical levels not just because the relevant variables are not available at that level, but because their multiple realisability at lower levels means they do not correspond to

5 See

Table 8.1, Sect. 8.2.2. forms of life share B1-3.

6 Other

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specific patterns of interactions at the ion and electron level. They correspond to a whole equivalence class of such patterns of interactions (Sect. 8.2.6). 4. Interaction Networks These processes are realised by means of immensely complex interaction networks at the molecular level (Buchanan et al. 2010; Junker and Schreiber 2011): N1: N2: N3: N4:

Metabolic Networks (Wagner 2014, §3) and (Noble 2016) Gene Regulatory Networks (Wagner 2014, §5) Signalling Networks (Junker and Schreiber 2011; Buchanan et al. 2010) Protein Interaction Networks (Junker and Schreiber 2011)

based in very complex molecular interactions (Berridge 2014) and with higher level design principles shaping their structure (Alon 2006), and at the cellular level, N5: Neural Networks (Kandel et al. 2013; Churchland and Sejnowski 2016) These networks compute in the sense of (Churchland and Sejnowski 2016, 69–74) 5. Branching Causal Logic In order to meet these needs, the dynamics followed at each level of biological hierarchies is based on contextually informed dynamical branching L that support the functions α of a trait T in a specific environmental context E (Ellis and Kopel 2019). Thus biological dynamics can be functionallydirected rather than driven by inevitability or chance: Biological dynamics tends to further the function α of a trait T through contextually informed branching dynamics L

(8.1)

where the dynamics L in its simplest form is branching logic of the form Hoffmann (2012) L: given context C, IF T (X) THEN F 1(Y), ELSE F 2(Z)

(8.2)

(a default unstated “ELSE” is always to leave the status quo). Here X is a contextual variable which can have many dimensions, Y and Z are variables that may be the same variables as X or not. T (X) is the truth value of arbitrary evaluative statements depending on X. It can be any combination of Boolean logical operations (NOT, AND, OR, NOR, etc.) and mathematical operations, while F 1(Y) and F 2(Z) are outcomes tending to further the function α. Thus they might be the homeostatic response “If blood sugar levels are too high, release insulin”, or the conscious dynamic “If the weather forecast says it will rain, take an umbrella”. At the molecular level, these operations are based in the lock and key molecular recognition mechanism (Noble 2016, 71) and (Berridge 2014). This mechanism is how information (Nurse 2008; Davies 2019) gets to shape physical outcomes. 6. Brain Function The human brain supports all these activities by a series of higher level processes and functions. These are (Purves et al. 2008; Gray and Bjorklund 2018)

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Sensation, perception, classification Prediction, planning, making decisions, and action Experimenting, learning, and remembering Experiencing and responding to emotions Interacting socially, communicating by symbols and language Metacognition, analysis, and reflection, ‘off-line’ exploration of possibilities.

It does so via its complex adaptive modular hierarchical structure (Kandel et al. 2013; Scott 2002). Brains compute (Marr 2010; Churchland and Sejnowski 2016), but they are not digital computers (Piccinini and Shagrir 2014).

8.2.2 The Hierarchy The framework for the following is the hierarchy of structure and function for the biological sciences shown in (Table 8.1), based in the underlying physics. Living organisms are multi-level open stochastic systems in which the behaviour at any level depends on higher and lower levels and cannot be fully understood in isolation The first level where the processes of life occur is L4, the level of cells. At level L6 one finds the integrated processes of an individual organism. At level L7 one finds sociology, economics, politics, and legal systems.

8.2.3 Effective Theories I am assuming that each of these levels exists as a matter of fact—they exist ontologically. They are what Wimsatt (1976) characterizes as privileged “directions of explanatory priority” or “levels of analysis”. The key issue is, if we propose

Table 8.1 The hierarchy of structure for biology (left) and corresponding processes (right). L2 is the relevant physics level of emergence, L4 the fundamental biological level, made possible by L3 (in particular proteins, RNA, DNA), in turn made possible by L2 and so L1 Level 8 (L8) Level 7 (L7) Level 6 (L6) Level 5 (L5) Level 4 (L4) Level 3 (L3) Level 2 (L2) Level 1 (L1)

Biology levels Environment Society Individuals Physiological systems Cells Biomolecules Atom, ion, electron Physics Particle and Nuclear Physics

Processes Ecological, environmental processes Social processes Psychological processes, actions Homeostasis, emergent functions Basic processes of life Gene regulation, metabolism Atomic, ionic, electron interactions Quark, lepton interactions

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a specific level L exists ontologically, there should be a valid Effective Theory ETL applicable at that level which characterizes that level. ‘Valid’ means it either makes testable predictions that have been confirmed, or at least characterizes the variables that would enter such a relation.7 Here following (Ellis 2020a,b), one can characterise an Effective Theory ETL (aL ) valid at some level L as follows: An Effective Theory ETL (aL ) at an emergent level L is a reliable relation between initial conditions described by effective variables vL ∈ L and outcomes oL ∈ L: ETL (aL ) : vL ∈ L → ETL (aL )[vL ] = oL ∈ L

(8.3)

where aL are parameters of the relation, and ETL (aL ) may be an exact or statistical law. The parameters aL may be vectorial or tensorial

Thus I will define a meaningful level to exist if there is such a relation. Determining that relation is in effect epistemology, but what it indicates is the underlying ontology. The effective theory ETL (aL ) is well posed if for specific choices of the parameters aL it provides a unique mapping (8.3) from vL to oL . This is the concept one should use instead or referring to the theory as being causally complete. That is a misnomer because firstly, the idea of causality does not apply to the physics laws per se (although effective theories do), and secondly because causal completion— the set of conditions that actually determine what outcomes will occur in real-world contexts—is always an interlevel affair, no single level L by itself is causally complete (Sect. 8.6.6). Effective Theories represent verifiable patterns of causation at the relevant level, not causal closure (Ellis 2020b). Effective Theory Examples It is useful to give some examples of effective theories at different levels. It is my contention, in agreement with (Noble 2012, 2016), that real causal processes are going on at each of these levels, even though this is enabled by underlying levels, including the physics ones. The relevant effective theories are more than just useful descriptions of high level processes. In all but the last two cases this is demonstrated by the fact that evolution has selected genomes that result in them happening. Their causal effectiveness is a driver of evolutionary selection. 1. Gene regulation The kind of gene regulatory processes discovered by Jacob and Monod (Jacob and Monod 1961; Monod 1971) represent real causal processes at the cellular level (they require the relevant molecular processes, but can only take place in the context of a functioning cell (Hofmeyer 2018)). Their importance is that they underlie the Evo-Devo processes discussed in (Carroll 2005, 2008). 2. Action potential propagation Brain processes are supported at the micro level by propagation of action potential spikes according to the Hodgkin-Huxley Equations (Hodgkin and Huxley 1952). This is an emergent phenomenon that cannot 7 The cautionary note reflects the difficulty in establishing reliable relations at levels L6-L8. The theories may have to be described in terms of propensities rather than mathematical laws. They are nevertheless well established fields of study, for example (Gray and Bjorklund 2018) at Level L6, (Berger 1963) at Level L7, and (Houghton 2009) at Level L8.

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be deduced from the underlying physics per se because they involve constants that are not fundamental physical constants. (Woodward 2018) defends the view that the explanation the equations provide are causal in the interventionist sense. 3. The brain The way the brain works overall (Kandel 2012) (Gray and Bjorklund 2018) is based in the underlying neuroscience (Kandel et al. 2013). It has been arrived at by an evolutionary process based in the advantages its specific functioning provides. Two key issues are the ability to function under uncertainty (Clark 2013, 2016; Hohwy 2013, 2014) and the existence of a symbolic ability (Deacon 1997) that allows language, culture, and technology to arise (Ginsburg and Jablonka 2019). 4. Natural Selection Natural selection (Mayr 2001) is a meta-principle: it is a process of downward causation (Campbell 1974) that allows the others listed above to come into being. Because the biological needs listed above are attractor states in the adaptive landscape (McGhee 2011), evolutionary convergence takes place (McGhee 2006): that is, there are multiple ways they can be met. Any physiological implementation in the equivalence class that satisfies the need will do. Thus this is an example of multiple realisability (Sect. 8.2.6), which characterizes topdown causation (Ellis 2016). 5. Smoking, lung cancer, and death The relation between smoking and lung cancer is an established causal link, as discussed in depth in (Pearl and Mackenzie 2018). It can certainly be redescribed at the physics level, but the key concepts in the correlation—smoking, cancer—cannot. Therefore, starting off with an initial state described at the microphysics level, one cannot even in principle determine the probabilities of cancer occurring on the basis of those variables alone, let alone when death will occur as a result of the cancer, because death also cannot be described at that level. Once cancer occurs (at the genetic/cellular levels L3/L4) leading to death (at the whole organism level L6) this will alter physical outcomes at the ion/electron level L2 because the process of life (see above) has ceased. This is a real causal chain, not just a handy redescription of micro physics: smoking causes cancer and then death as a matter of fact. The physics allows this of course, but the actual physical trajectories and outcomes follows from the essential higher level dynamics of the cessation of being alive.

8.2.4 Equal Validity of Levels There is a valid Effective Theory ETL at each level L, each of them represents a causally valid theory holding at its level (Wimsatt 1976), none more fundamental than the others (Noble 2012). This is expressed nicely in (Schweber 1993), commenting on Phil Anderson’s views: Anderson believes in emergent laws. He holds the view that each level has its own “fundamental” laws and its own ontology. Translated into the language of particle physicists, Anderson would say each level has its effective Lagrangian and its set of quasistable

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particles. In each level the effective Lagrangian - the “fundamental” description at that level - is the best we can do.

None of them can be deemed to be more fundamental than any other, inter alia because none of them is the fundamental level, i.e. none is the hoped for Theory of Everything (TOE). This has to be the case because we don’t know the underlying TOE, if there is one, and so don’t—and can’t—use it in real applications. So all the physics laws we use in applications are effective theories in the sense of (Castellani 2002), applicable at the appropriate level. Similarly, there are very well tested effective theories at levels L3-L5 in biology: the molecular level, the cellular level, the physiological systems level for example. Whenever there are well established laws at the higher levels (for example the laws of perception at Level L6) the same applies to them too. More fundamentally, this equal causal validity occurs because higher levels are linked to lower levels by a combination of upwards and downwards causation (Noble 2012, 2016; Ellis 2016) so no level by itself is causally complete. They interact with each other with each level playing a role in causal completeness. Hence (Noble 2016, 160), The Principle of Biological Relativity: There is no privileged level of causation in biology: in Aristotelian terms, Effective Causation takes place at each emergent level L.

This is because of circular causality which for example necessarily involves downward causation from the whole cell to influence the behaviour of its molecules just as much as upward causation form the molecular level to the cellular level (Noble 2016, 163–164). This applies to all levels in Table 8.1, i.e. it includes the underlying physics levels as well (Ellis and Kopel 2019; Ellis 2020b), as has to be the case for physical consistency. In the case of the brain, after having set out in depth the hierarchical structure of the brain (Churchland and Sejnowski 2016, 11, 27–48), Churchland and Sejnowski state (Churchland and Sejnowski 2016, 415) An explanation of higher level phenomena in terms of lower level phenomena is usually referred to as a reduction, though not in the perjorative sense that implies the higher levels are unreal, explanatorily dismissable, or somehow empirically dubious,

which agrees with the view put here. Brain computational processes have real causal power (Marr 2010; Scott 2002; Churchland and Sejnowski 2016).

8.2.5 Types of Causation Causation can be characterised either in an interventionist or a counterfactual sense, either indicating when causation takes place (Pearl 2009; Pearl and Mackenzie 2018). The first key claim I make is that as well as upward causation, downward causation takes place (Noble 2012; Ellis 2016). The second one is that as well as

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efficient causation, Aristotle’s other forms of causation play a key role in real world outcomes. Downward Causation Physicists take for granted upward causation, leading to emergence through aggregation effects such as coarse graining. However one can claim there is also downward causation that occurs via various mechanisms (Noble 2008; Ellis 2012, 2016), allowing strong emergence (Chalmers 2006) to occur. Carlo agrees downward causation takes place, but believes it can be rewritten purely in terms of low level physics, and hence does not represent strong emergence. Downwards effects in a biological system occur because of physiological processes (Noble 2008, 2012). These processes (Hall 2016) are mediated at the molecular level by developmental systems (Oyama et al. 2001) operating through metabolic and gene regulator networks (Wagner 2014) and cell signalling networks (Berridge 2014), guided by higher level physiological needs. They reach down to the underlying physical level L2 via time dependent constraints (Ellis and Kopel 2019). The set of interactions between elements at that level is uniquely characterised by the laws of physics L, but their specific outcomes are determined by the biological context in which they operate. An example is determination of heart rate. Pacemaker activity of the heart is via cells in the sinoatrial node that create an action potential and so alter ion channel outcomes. This pacemaking circuit is an integrative characteristic of the system as a whole (Fink and Noble 2008)—that is, it is an essentially higher level variable— that acts down to the molecular level (Noble 2012, 2016). In the synchronic case— nothing changes at either macro or micro levels—it is correct that one can predict the lower level and hence the higher level dynamics purely from the lower level initial state. However if the higher level state changes—an athlete starts running— the higher level state changes, and this alters lower level conditions. Nothing about the initial molecular level state of the heart or the underlying physics state could predict this happening. Neither could initial knowledge of both the athletes heart and brain micro states determine this outcome, because it depended on an external event—the firing of the starting gun, another macro level event which the athlete’s initial states cannot determine. Considering the individual athlete, causation at the macro level is real: the firing of the starting gun led to her leaving the starting post. Downward causation that alters motion of ATP molecules in her muscles via metabolic networks is real: that is a well established physiological process (Rhoades and Pflanzer 1989). The result is altered electron flows in the muscles, in a way consistent with the laws of physics but unpredictable from her initial microphysical state. Regression to include the brain state of the person firing the gun will not save the situation, as one then has to include all the influences on his brain state (Noble et al. 2019) as well as all the stochastic elements in his brain (Sect. 8.5.3). A similar example of a rhythmic pattern determined by a network as a whole is the stomatogastric ganglion of the spiny lobster (Churchland and Sejnowski 2016, 4–5):

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The network in question contains about 28 neurons and serves to drive the muscles controlling the teeth of the gastric mill so that food can be ground up for digestion. The output of the network is rhythmic, and hence the muscular action and the grinders movements are correspondingly rhythmic. The basic electrophysiological and anatomical features of the neurons have been catalogued, so that the microlevel vitae for each cell in the network is impressively detailed. What is not understood is how the cells in the network interact to constitute a circuit that produces the rhythmic pattern. No one cell is a repository for the cells rhythmic output; no one cell is itself the repository for the properties displayed by the network as a whole. Where then does the rhythmicity come from? Very roughly speaking, from the patterns of interactions among cells and the intrinsic properties of the component cells.

The network produces rhythmic patterns in the cells, which produce rhythmic activity in the constitutive electrons and ions. This is a classic example of higher level order controlling both macro and micro level outcomes. Types of Downward Causation The basic type of downward causation are as follows (developed from (Ellis 2012; Noble 2012, 2016; Ellis 2016)): TD1A

TD1B

TD2A

TD2B

8 Carlo’s

Boundary conditions are constraints on particles in a system arising from the environment8 as in the case of a cylinder determining pressure and temperature of the enclosed gas, or the shape of tongue and lips determining air vibrations and so spoken words. Structural Constraints are fairly rigid structures that determine possible micro states of particles that make up the structure, as in the case of a cylinder constraining the motion of a piston, or a skeleton that supports a body. Channeling and Containing constraints are key forms of contextual causation shaping microbiological and neural outcomes. Channeling constraints determine where reactants or electrical currents can flow, as in blood capillaries in a body, wires in a computer, or neural axons and dendrites in a brain. Containing constraints confine reactants to a limited region, so preventing them from diffusing away and providing the context for reaction networks to function. A key case is a cell wall. Gating and signalling constraints Gating constraints control ingress and egress to a container, as in the case of voltage gated ion channels in axons, or ligand gated ion channels in synapses. They function via conformational changes controlled by voltage differential in the former case, and molecular recognition of ligands in the latter case, thus underlying cell signalling processes (Berridge 2014). Feedback control to attain goals is a cybernetic process where the difference between a goal and the actual state of a system generates an error signal that is fed back to a controller and causes corrective action, as in thermostats and engine governors (Wiener 1948). In biology this is homeostasis, a crucial feature of physiology at all levels (Hall 2016).

example of Jupiter causing tides on Earth fits here: Jupiter is part of the Earth’s environment, causing a detectable gravitational field at Marseilles.

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Because of this closed causal loop, goals determine outcomes. Changing the goals changes both macro and micro outcomes, as in altering the setting on a thermostat. In biology, multilevel homeostatic systems are continually responding to internal changes and external perturbations (Billman 2020). Creation of New Elements takes place in two ways. Creation of new lower level elements occurs in physics when crystal level conditions create quasiparticles such as phonons that play a key role in dynamics at the electron level (Ellis 2020a). This is what (Gillett 2019) calls a Downward Constitutive relation. It occurs in biology when genes are read to create proteins, a contextual process (Gilbert and Epel 2009) controlled by gene regulatory networks according to higher level needs (Noble 2016). Creation of new higher level elements restructures lower level relations and so alters lower level dynamics. In engineering this takes place by manufacturing processes such as making a transistor. In biology this occurs when cell division takes place at the cellular level, and when an organism gives birth to progeny at the organism level. The context of lower level dynamics changes completely in both cases. In the latter case, as Darwin already recognised, sexual selection takes place and determines outcomes, involving very complex social and psychological interactions that alter outcomes at the genetic and physical levels. Deleting or Altering Lower Level elements is the complementary process that is crucial in biology. In developmental biology, apoptosis (programmed cell death) plays a key role for example in digit formation (separating fingers and thumbs), while in neural development, synaptic connections are pruned as development takes place (Wolpert et al. 2002). Cell are specialised to perform specific functions as growth takes place, altering their nature and behaviour. A fundamental biological process is Adaptive selection due to selection criteria which alters either the set of lower level elements by deletion as in Darwinian selection (Campbell 1974) and the functioning of the immune system, or selecting optimal configurations, as in neural network plasticity involved in learning.

The higher level types of downward causation: TD4 (Adaptive selection of goals) and TD5 (Adaptive selection of selection criteria) build on these ones (Ellis 2012, 2016). The first ones (TD1A, TD1B, and TD2A with TD2B a special case) can be characterised as downward causation due to constraints (Juarrero 2002). By contrast, TD3A and TD3B alter the very elements interacting at the lower level— a key form of downward causation. The latter case usually involves massive stochasticity in the creation of the ensemble from which selection takes place, which is a key reason why causal closure does not occur at the physical level. The molecular storm and associated collisions (Hoffmann 2012) washes out any detailed information as to particle position and movement because initial positions cannot be

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specified to infinite precision (Del Santo and Gisin 2019). Higher level principles can thereby select preferred outcomes at the lower level. The key issue is whether any of these types of downward causation are really causally effective, or just redescriptions in convenient form of microphysical causation. Aristotle’s Kinds of Causation There is an important further point as regards causation. As Aristotle pointed out (Bodnar 2018), there are four kinds of causation that occur in the real world. This is discussed by Juarrero (2002, 2, 125–128, 143), Noble (2016, 176–179), and Scott (2002, 298–300). They are • Material Cause: the physical stuff that is needed for an outcome; the stuff out of which it is made, e.g., the bronze of a statue. In biology this is the physical stuff, the chemical elements as characterised by the periodic table, that make biology possible. In the above classification, TD3A and TD3B are cases of material causation, because they concern the entities that interact at a level L. • Formal Cause: which makes anything what it is and no other; the material cause necessary for some outcome must be given the appropriate form through the way in which the material is arranged e.g., the shape of a statue. In biology, this is the structure at each level that underlies function at that level: physiological systems (Hall 2016) and the underlying biomolecules such as proteins (Petsko and Ringe 2009). In the above classification, TD1A, TD1B, TD2A, and TD2B are cases of formal causation. • Efficient Cause: The primary source of the change or rest, the force that brings an action into being; nowadays in the Newtonian case taken to be the effect of forces on inert matter, in the quantum chemistry case, Schrödinger’s equation. In the above classification, Efficient Causation occurs at each level L through the Effective Theory EFL at that level. • Final Cause: the goal or purpose towards which something aims: “that for the sake of which a thing is done”. This occurs whenever conscious decisions are taken by intelligent beings, and then can be claimed to be a privileged level of causation (Ellis and Noble 2021) because it shapes all lower level effects. Physics usually only considers efficient causes (Juarrero 2002). Biology however needs material, formal, and efficient causes. (Hofmeyer 2018) gives a careful analysis of how the relation between them can be represented and how they are realised in biology, giving as an example an enzyme that catalyses a reaction. He explains that a set of rules, a convention or code, forms an interface between formal and efficient cause. All four kinds of causation are needed to determine specific outcomes in social contexts, which is the context within which brains function. Without taking them all into account, one cannot even account for existence of a teapot (Ellis 2005). A network of causation is always in action when any specific outcomes occurs. When we refer to ‘The Cause’, we are taking all the others for granted—the

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existence of the Universe, of laws of physics of a specific nature, and of the Earth for example. Tinbergen’s ‘Why’ Questions In biology, an alternative view on causation is provided by Tinbergen’s four ‘Why’ questions. (Bateson and Laland 2013) summarise thus: Tinbergen pointed out that four fundamentally different types of problem are raised in biology, which he listed as ‘survival value’, ‘ontogeny’, ‘evolution’, and ‘causation’. These problems can be expressed as four questions about any feature of an organism: What is it for? How did it develop during the lifetime of the individual? How did it evolve over the history of the species? And, how does it work?

That is, he raises functional, developmental, evolutionary, and mechanistic issues that all have to be answered in order to give a full explanation of existence, structure, and behaviour of an organism.

8.2.6 Multiple Realisability A key point is that multiple realisability plays a fundamental role in strong emergence (Menzies 2003). Any particular higher level state can be realised in a multiplicity of ways in terms of lower level states. In engineering or biological cases, a high level need determines the high level function and thus a high level structure that fulfills it. This higher structure is realised by suitable lower level structures, but there are billions of ways this can happen. It does not matter which of the equivalence class of lower level realisations is used to fulfill the higher level need, as long as it is indeed fulfilled. Consequently you cannot even express the dynamics driving what is happening in a sensible way at a lower level. Consider for example the statements The piston is moving because hot gas on one side is driving it and A mouse is growing because the cells that make up its body are dividing. They cannot sensibly be described at any lower level not just because of the billions of lower level particles involved in each case, but because there are so many billions of different ways this could happen at the lower level, this cannot be expressed sensibly at the proton and electron level. The point is the huge number of different combinations of lower level entities can represent a single higher level variable. Any one of the entire equivalence class at the lower level will do. Thus it is not the individual variables at the lower level that are the key to what is going on: it is the equivalence class to which they belong. But that whole equivalence class can be describer by a single variable at the macro level, so that is the real effective variable in the dynamics. This is a kind of interlevel duality: {vL ∈ L} ⇔ {vi : vi ∈ EL−1 (vL−1 ) ∈ (L − 1)}

(8.4)

where EL−1 (vL−1 ) is the equivalence class of variables vL−1 at Level L − 1 corresponding to the one variable vL at Level L. The effective law EFL at Level

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L for the variables vL at that level is equivalent to a law for an entire equivalence class EL−1 (vL−1 ) of variables at Level L-1. It does not translate into an Effective Law for natural variables vL−1 per se at Level L-1. The importance of multiple realisability is discussed in Menzies (2003), Ellis (2019) and Bishop and Ellis (2020). It is as follows: Essentially higher level variables and dynamics. The higher level concepts are indispensible when multiple realisability occurs, firstly because they define the space of data dL relevant at Level L, and secondly because of (8.4), variables in this space cannot be represented as natural kinds at the lower level. Effective Laws EFL at level L can only be expressed at level L-1 in terms of an entire equivalence class at that level. One can only define that equivalence class by using concepts defined at level L.

To inject reality into this fact, remember that the equivalence class at the lower level is typically characterised by Avagadro’s number.

8.2.7 Higher Level Organising Principles A key issue in the discussion is the degree to which higher level dynamics depends on the lower level dynamics. As can be seen from the previous subsections, the nature of biological causation is quite unlike the nature of causation at the underlying physical levels. What determines these outcomes then? Higher Level Organising Principles The key idea here is that higher level biological Organising Principles exist that are independent of the underlying lower level dynamics, and shape higher level outcomes. The specific lower level realisation is immaterial, as long as it is in the right equivalence class (Sect. 8.2.6). Generically they form attractors that shape higher level outcomes (Juarrero 2002, 152–162) the lower level components come along for the ride, with many biological oscillators being examples (Noble 2016, 76–86, 179). Protectorates This is parallel to the claim by (Laughlin and Pines 2000) of existence of classical and quantum protectorates, governed by dynamical rules that characterise emergent systems as such. They state There are higher organising principles in physics, such as localization and the principle of continuous symmetry breaking, that cannot be deduced from microscopics even in principle. . . . The crystalline state is the simplest known example of a quantum protectorate, a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. . . they are transcendent in that they would continue to be true and lead to exact results even if the underlying Theory of Everything was changed.

As an example, (Haken 1996) states that profound analogies between different systems become apparent at the order parameter level, and suggest that the occurrence of order parameters in open systems is a general law of nature. He

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characterizes this in terms of a slaving principle9 (Haken and Wunderlin 1988). Green and Batterman (2020) develop this further, citing the universality of critical phenomena as a physics case. The Renormalisation Group explanation extracts structural features that stabilize macroscopic phenomena irrespective of changes in microscopic details Biology In biology, such organising principles can be claimed to govern microbiology, physiology, and neuroscience (Sects. 8.2.1 and 8.4). The idea is that once life exists and evolutionary processes have started, they are what shape outcomes, rather than the underlying physical laws, because they express essential biological needs (Kauffman 1995) and can only be met in certain ways (Vogel 2000). Physical laws of course allow the outcomes to occur: they lie within the Possibility Space L of outcomes allowed by the physical laws L, for instance the proteins enabling all this to occur are characterised by a possibility space of huge dimension, as are the metabolic networks and gene regulatory networks that lead to specific outcomes (Wagner 2014). But as emergence takes place through developmental processes repeated many times over evolutionary timescales, it is these principles that determine biological success. Hence (Ginsburg and Jablonka 2019) it is they that determine evolutionary outcomes in an ongoing Evo-Devo process (Carroll 2005, 2008). They act as attractors for both evolution and for ongoing brain dynamics. This proposal is supported in multiple ways. In functional terms, homeostasis is a central organising principle in all physiology at multiple scales: “It is important to note that homeostatic regulation is not merely the product of a single negative feedback cycle but reflects the complex interaction of multiple feedback systems that can be modified by higher control centers” (Billman 2020). Also physiological functions acting as dynamical systems have attractors (Arnold 1989) that organise outcomes. For example, this happens in the neural dynamics of cell assemblies (Scott 2002, 244–248): In Hopfield’s formulation, each attractor is viewed as a pattern stored non-locally by the net. Each such pattern will have a basin of attraction into which the system can be forced by sensory inputs.

Thus cell assemblies form attractors (Scott 2002, 287). Also Hopfield neural networks converge to attractors in an energy landscape (Churchland and Sejnowski 2016, 88–89) and attractor networks are implemented by recurrent collaterals (Rolls 2016, 75–98). In developmental terms it can be expressed in terms of Waddington’s epigenetic landscape (Gilbert 1991) and Noble (2016, 169, 259) which presents much the same idea via cell fate bifurcation diagrams. This is how developmental processes converge on outcomes based in the same higher level organising principles.

9I

thank Karl Friston for this comment.

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In evolutionary terms, it can be expressed in terms of the adaptive landscape of Sewell Wright (Wright 1932; McGhee 2006), showing how evolution converges to adaptive peaks where these principles are supported to a greater or lesser degree. This viewpoint is supported by much evidence for convergent evolution (McGhee 2011). Neuroscience There is a huge amount written about neuroscience and biological psychology, with a vast amount of detail: (Scott 2002; Purves et al. 2008; Kandel et al. 2013; Churchland and Sejnowski 2016; Clark 2016; Gray and Bjorklund 2018) for example. The issue is, Can one extract higher level organising principles for the brain from them? I believe one can, examples being hierarchical predictive coding (Clark 2013) and the Free Energy Principle (Friston 2010). I collect them together in the following three sections, looking at how the brain handles the constant influx of new data (Sect. 8.3), the issue of constantly adjusting to the environment (Sect. 8.4), and how the brain uses micro level stochasticity to allow macro level agency (Sect. 8.5). I suggest that it is these principles at the macro level that are the real determinants of what happens, solving the puzzle of how ordered outcomes can emerge in the context of an open system, where the microdynamic states of an individual brain cannot in principle determine future outcomes because they do not have the data necessary to do so. If that is correct, these principles reach down to determine micro level outcomes via the various mechanisms outlined in Sect. 8.2.5. Furthermore they are themselves attractors in evolutionary space: they will tend to come into existence because they enhance prospects of reproductive success (Ginsburg and Jablonka 2019).

8.3 The Predictive Brain: Brains as Open Systems Each human body, and each brain, is an open system. This is where the difference between synchronic and diachronic emergence is crucial. It has two aspects: our brains are not made of the same matter as time progresses (Sect. 8.3.1), and new information is coming in all the time and altering our brain states (Sect. 8.3.2). The way this is interpreted depends on the fact that our brain is an emotional brain (Sect. 8.3.3) and a social brain (Sect. 8.3.4). Language and symbolism enables abstract and social variables to affect outcomes (Sect. 8.3.5). Consequently the microphysical state of a specific person’s brain is unable as a matter of principle to predict their future brain states (Sect. 8.3.6) Predictive brains that can handle this situation are attractor states for brain evolutionary development.

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8.3.1 Matter and Metabolism: We Are not the Same Molecules Because we are open systems (Peacocke 1989), the human body at time t2 > t1 is not made of the same material particles as it was at time t1 . Thus what happens in life is like the case of a candle (Scott 2002, 303): As a simple example of an open system, consider the flame of a candle. .. Because the flame is an open system, a relation P1 → P2 cannot be written - even “in principle”- for the physical substrate. This follows from the fact that the physical substrate is continually changing. The molecules of air and wax vapour comprising the flame at time t2 are entirely different from those at time t1 . Thus the detailed speeds and positions of the molecules present at time t2 are unrelated to those at time t1 . What remains constant is the flame itself - a process.

Body Maintenance A balance between protein synthesis and protein degradation is required for good health and normal protein metabolism. Protein turnover is the replacement of older proteins as they are broken down within the cell, so the atoms and elementary particles making up the cell change too. Over time, the human body is not even made up of the same particles: they turn over completely on a timescale of 7 years (Eden et al. 2011; Toyama and Hetzer 2013). The Brain Neuroscientist Terence Sejnowski states:10 Patterns of neural activity can indeed modify a lot of molecular machinery inside a neuron. I have been puzzled by my ability to remember my childhood, despite the fact that most of the molecules in my body today are not the same ones I had as a child; in particular, the molecules that make up my brain are constantly turning over, being replaced with newly minted molecules.

Metabolic networks ensure the needed replacements take place on a continuous basis, despite stochasticity at the molecular level (Sect. 8.5). This is where multiple realisability plays a key role (Sect. 8.2.6). Conclusion Initial data for the specific set of particles making up a specific brain at time t1 cannot determine emergent outcomes uniquely for that brain over time, for it is not made of the same set of particles at time t2  t1 .

8.3.2 Dealing with New Information: The Predictive Brain That effect of course takes time. The very significant immediate ongoing effect of being an open system is that incoming sensory information conveys masses of new data on an ongoing basis. This new data may contain surprises, for example a ball smashes a window. The brain has to have mechanisms to deal with such

10 https://www.edge.org/response-detail/10451.

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unpredictability: the previously stored data at the microphysics level cannot do so, as it does not take this event into account. Hierarchical Predictive Processing Indeed, the brain has developed mechanisms to make sense of the unpredictable inflow of data and best way react to it (Clark 2013, 2016; Hohwy 2013, 2014; Szafron 2019). Andy Clark explains (Clark 2013): Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to adaptive success. This ‘hierarchical prediction machine’ approach offers the best clue yet to the shape of a unified science of mind and action.

In brief, following up Ross Ashby’s notion that “the whole function of the brain is summed up in error correction,” the following takes place in an ongoing cycle: PB1

PB2

PB3

Hierarchical generative model The cortex uses a hierarchical model to generate predictions of internal and external conditions at time t2 on the basis of data available at time t1 . Prediction error and attention During the interval [t1 , t2 ] sensory systems (vision, hearing, somatosensory) receive new information on external conditions and internal states At time t2 , nuclei in the thalamus compare the predictions with the incoming data. If it exceeds a threshold, an error signal (‘surprisal’) is sent to the cortex to update its model of the internal and external situation (Bayesian updating), and focus attention on the discrepancy. Action and outcomes The updated model is used to plan and implement action. The impact of that action on the external world provides new data that can be used to further update the model of the external world (active intervention).

This is an interlevel information exchange as described by Rao and Ballard (1999, 80): Prediction and error-correction cycles occur concurrently throughout the hierarchy, so topdown information influences lower-level estimates, and bottomup information influences higher-level estimates of the input signal.

The outcome (Hohwy 2007) is (as quoted in Clark 2013), The generative model providing the “top-down”predictions is here doing much of the more traditionally “perceptual” work, with the bottom up driving signals really providing a kind of ongoing feedback on their activity (by fitting, or failing to fit, the cascade of downwardflowing predictions). This procedure combines“top-down” and “bottom-up” influences in an especially delicate and potent fashion, and it leads to the development of neurons that exhibit a “selectivity that is not intrinsic to the area but depends on interactions across levels of a processing hierarchy” (Friston 2003, p. 1349). Hierarchical predictive coding delivers, that is to say, a processing regime in which context-sensitivity is fundamental and pervasive.

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Perception Consequently, perception is a predictive affair (Purves 2010). Helmholz’s inverse problem (how to uniquely determine a 3-d world from a 2-d projection) is solved by filling in missing information on the basis of our expectations. (Kandel 2012, 202–204) gives a overview of how this understanding originated with Helmholz, who called this top-down process of hypothesis testing unconscious inference, and was developed by Gombrich in his book Art and Illusion (Gombrich 1961). (Kandel 2012, pp. 304–321) emphasizes the top-down aspect of this process, and its relation to memory. (Purves 2010, pp. 120–124) describes how he came to the same understanding (see also page 221). Action The relation to action is given by Friston (2003), Friston et al. (2009), and Clark (2013). It is described thus by (Hawkins and Blakeslee 2007, 158) As strange as it sounds, when your own behaviour is involved, your predictions not only precede sensation, they determine sensation. Thinking of going to the next pattern in a sequence causes a cascading prediction of what you should experience next. As the cascading prediction unfolds, it generates the motor commands necessary to fulfill the prediction. Thinking, predicting, and doing are all part of the same unfolding of sequences moving down the cortical hierarchy.

(Seth 2013) summarised the whole interaction thus: The concept of Predictive Coding (PC) overturns classical notions of perception as a largely ‘bottom-up’ process of evidence accumulation or feature detection, proposing instead that perceptual content is specified by top-down predictive signals that emerge from hierarchically organized generative models of the causes of sensory signals. According to PC, the brain is continuously attempting to minimize the discrepancy or ‘prediction error’ between its inputs and its emerging models of the causes of these inputs via neural computations approximating Bayesian inference. Prediction errors can be minimized either by updating generative models (perceptual inference and learning; changing the model to fit the world) or by performing actions to bring about sensory states in line with predictions (active inference; changing the world to fit the model)

This is a very brief sketch of a very complex program, summarised in Andy Clark’s book Surfing Uncertainty (Clark 2016) and in Miller and Clark (2018). Nothing here contradicts the mechanisms discussed in depth in texts such as Purves et al. (2008) and Kandel et al. (2013), and Churchland and Sejnowski (2016). Those texts set the foundations for what is proposed above, but do not develop these aspects in depth. For example (Kandel et al. 2013) has just one relevant section: “Visual perception is a creative process” (page 492). Thus the viewpoint put here accepts the mechanisms discussed in those books (and the underlying physics), and puts them in a larger context that emphasizes overall organising features that are crucial in enabling the brain to function in the face of uncertainty. However there are three further important aspects to be taken into account.

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8.3.3 The Emotional Brain A first further crucial aspect of our brains is that they are emotional brains. The understandings and actions enabled by the predictive mechanisms mentioned above are crucially affected and shaped by affective (emotional) states. The cognitive science paradigm of purely rational choice is not the way the real brain works. Emotion has key effects on cognition (Damasio 2006) and behaviour (Panksepp 2009; Purves et al. 2008; Panksepp and Biven 2012; Gray and Bjorklund 2018). EB1

The emotional brain Both primary (innate) and secondary (social) emotions play a key role in guiding cognition and focusing attention.

The predictive coding paradigm can be extended (Clark 2016, 231–237) to include this case. Seth (2013) says the following The concept of the brain as a prediction machine has enjoyed a resurgence in the context of the Bayesian brain and predictive coding approaches within cognitive science. To date, this perspective has been applied primarily to exteroceptive perception (e.g., vision, audition), and action. Here, I describe a predictive, inferential perspective on interoception: ‘interoceptive inference’ conceives of subjective feeling states (emotions) as arising from actively-inferred generative (predictive) models of the causes of interoceptive afferents. The model generalizes ‘appraisal’ theories that view emotions as emerging from cognitive evaluations of physiological changes . . . interoceptive inference involves hierarchically cascading top-down interoceptive predictions that counterflow with bottom-up interoceptive prediction errors. Subjective feeling states - experienced emotions - are hypothesized to depend on the integrated content of these predictive representations across multiple levels

Miller and Clark (2018) develop this crucial emotional relationship to cortical activity in depth, using the predictive coding framework: But how, if at all, do emotions and sub-cortical contributions fit into this emerging picture? The fit, we shall argue, is both profound and potentially transformative. In the picture we develop, online cognitive function cannot be assigned to either the cortical or the sub-cortical component, but instead emerges from their tight co-ordination. This tight coordination involves processes of continuous reciprocal causation that weave together bodily information and ‘top-down’ predictions, generating a unified sense of what’s out there and why it matters. The upshot is a more truly ‘embodied’ vision of the predictive brain in action.

As well as influencing immediate functioning of the brain, affect relates crucially to brain plasticity and so to changes in brain micro structure (Sect. 8.5.4).

8.3.4 The Social Brain Second, a crucial aspect of our brains is that they are social brains: we are evolved to live in a social context, which has key influences on our lives and minds as the brain receives data and responds to the situation around. Sociality appears to be a main driver for human brain evolution (Dunbar 1998, 2003) and results in social

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cognition (Purves et al. 2008, 359–392) and cognitive neuroscience (Cacioppo et al. 2002). This again crucially affects how we handle the incoming information. The Advantage of Social Brains Living in cooperative groups greatly enhanced our ancestors survival prospects (Harari 2014) enabling the rise of cooperative farming, culture, and technology, which then was the key to the emergence of civilisation that enabled our dominance over the planet (Bronowski 2011). A social brain was needed for social cohesion to emerge: the cognitive demands of living in complexly bonded social groups selected increasing executive brain (neocortical) size (Dunbar 1998a) (Dunbar 2014). The Nature of the Social Brain: Theory of Mind It is not just a matter of being cooperative and able to communicate: central to the social brain is the ability known as “theory of mind” (ToM) (Dunbar 1998a). It is very important that we can read other peoples minds (understanding their intentions)—which we do on an ongoing basis (Frith 2013). We all have a theory of mind (Frith and Frith 2005). Its cortical basis is discussed by Frith (2007), but additionally it has a key precortical base related to the primary emotional systems identified by Panksepp (2009), namely the very strong emotional need to belong to a group (Panksepp and Biven 2012; Ellis and Toronchuk 2013; Stevens and Price 2015). Its evolutionary basis is discussed by Donald (1991), Tomasello (2009), and Dunbar (2014). It is summed up by (Donald 2001, 86–87) as follows: Our normal focus is social, and social awareness is highly conscious, that is, it heavily engages our conscious capacity. . . Conscious updating is vital to social life . . . One might even make the case that consciousness- especially our lightning fast, up-to-date, socially attuned human consciousness - is the evolutionary requirement for both constructing and navigating human culture. It remains the basis, the sine qua non, for all complex human interactions.

Michael Tomasello agrees, as is evident in the title of his book The Cultural Origin of Human Cognition (Tomasello 2009). Relation to Predictive Processing The description of the social brain in terms of the predictive processing paradigm is presented by Constant et al. (2019) through the concept of the extended mind:11 Cognitive niche construction is construed as a form of instrumental intelligence, whereby organisms create and maintain cause-effect models of their niche as guides for fitness influencing behavior. Extended mind theory claims that cognitive processes extend beyond the brain to include predictable states of the world that function as cognitive extensions to support the performance of certain cognitive tasks. Predictive processing in cognitive science assumes that organisms (and their brains) embody predictive models of the world that are leveraged to guide adaptive behavior. On that view, standard cognitive functions - such as action, perception and learning - are geared towards the optimization of the organism’s predictive (i.e., generative) models of the world. Recent developments in

11 See

also Kirchhoff et al. (2018) and Hesp et al. (2019).

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predictive processing - known as active inference - suggest that niche construction is an emergent strategy for optimizing generative models.

Those models include models of social context and of other minds, characterised via cultural affordances (Ramstead et al. 2016). Veissiére et al. (2020) state We argue that human agents learn the shared habits, norms, and expectations of their culture through immersive participation in patterned cultural practices that selectively pattern attention and behaviour. We call this process“Thinking Through Other Mind” (TTOM) in effect, the process of inferring other agents’ expectations about the world and how to behave in social context.

Then downward causation from the social environment changes the brain: The brain only has direct access to the way its sensory states fluctuate (i.e., sensory input), and not the causes of those inputs, which it must learn to guide adaptive action - where ‘adaptive’ action solicits familiar, unsurprising (interoceptive and exteroceptive) sensations from the world. The brain overcomes this problematic seclusion by matching the statistical organization of its states to the statistical structure of causal regularities in the world. To do so, the brain needs to re-shape itself, self-organizing so as to expect, and be ready to respond with effective action to patterned changes in its sensory states that correspond to adaptively relevant changes ‘out there’ in the world

The sociology of this all is discussed by Berger (1963) and Berger and Luckmann (1991). Overall, one can summarise as follows: SB1

The social brain Because we live in a social world we are very socially aware. We have a social brain which shapes our responses to incoming data in crucial ways on the basis of social understandings, which are continually changing over time.

Theory of mind is based in prediction, and is a routine part of everyday life (Frith 2013).

8.3.5 The Symbolic Brain Third, a key feature of the social brain is its ability to engage in spoken and written language, and more generally to engage in symbolism. This adds in a whole new category of incoming information that the brain has to take into account and respond to. Language A key step in evolution of mind is developing language. Dunbar (1998a) suggests its prime function is to enable exchange of information regarding bonding in the social group. It is a product of a mind-culture symbiosis (Donald 2001, 11, 202) and forms the basis of culture (Donald 2001, 274), symbolic technologies (Donald 2001, 305), as well as cultural learning (Tomasello 2009, 6) and inheritance (Tomasello 2009, 13). Ginsburg and Jablonka (2019) state that language enables sharing ideas and information over time and distance, and enables the social and psychological power of stories (Gottschall 2012).

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Abstract and Social Variables In evolutionary terms, the transition to the symbolic species (Deacon 1997) enabled abstract causation (Ellis and Kopel 2019) to occur, which inter alia involves social interactions and abstract concepts such as the amount of money in my bank account and the concept of a closed corporation (Harari 2014). Thus not all the relevant variables are physical variables; some are abstract variables resulting from social interactions (Berger 1963; Berger and Luckmann 1991) which are causally effective. Higher Order Predictability Symbolism and abstract reasoning greatly increases our power of prediction: we can simulate situations offline, rather than having to enact them to see what the consequences are. It also greatly increases the complexity of our responses to incoming social data, which are interpreted in the light of the social context (Berger 1963; Berger and Luckmann 1991; Donald 2001; Frith 2013) SB2

The symbolic brain Human social interaction is based in language, in turn based in our symbolic ability. This ability transforms the way our minds interpret much incoming data, as well as allowing internal cognitive processes that are a major causal factor in our individual and social lives.

This is the fundamental mechanism by which the brain operates at a macro level, for which there is much evidence. Again one can claim that this is the way the brain operates as a matter of fact, it is not just the way we think it operates. Causation at this level is real: the whole of society depends on it. This will play an important role in Sect. 8.6 because it relates to the interaction of the brain to the outside world.

8.3.6 The Dynamics of the Open Brain An individual brain considered as an entity on its own is an open system, and has been adapted to handle the problems this represents in successfully navigating the world. This rather than initial brain micro data determines it specific outcomes as time progresses. Microphysics Data for Brain States Consider a specific individual brain at time t1 . During a time interval [t1 , t2 ], the initial brain microphysics data D(t1 ) is added to by new data Dext (t) coming from the environment after t1 . The data D(t2 ) at a later time t2 > t1 is not predictable even in principle from D(t1 ). Hence the microphysics evolution is undetermined by data D(t1 ), even in principle. You may for example see a car crash at a time t3 > t1 that alters all the future brain states; but your brain did not know that was going to happen. Thus the brain as an open system receives unexpected information and handles it in a predictive way. The initial state of the brain obviously cannot determine these

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outcomes as it has no control over what the incoming data will be. This is the key outcome of the difference between synchronic and diachronic emergence. The brain is an open system. Initial micro data of a brain state at one moment cannot possibly determine what it will do at a later time, not just because new matter comes in and replaces old, but also because new information comes in from outside and alters outcomes. The initial data at time t1 cannot know what the initial data at time t2 will be and hence cannot determine specific later brain outcomes. The brain handles this uncertainty via the predictive brain mechanisms PB1-PB3, EB1, SB1-SB2 outlined above.

The physicalist gambit is to say ah yes, but microphysics determines uniquely the evolution of all the other systems the brain is interacting, so the system as a whole is determined by the microphysics dynamics alone. I respond to that proposal in Sect. 8.6. Predictive Brain Mechanisms as Attractor States Evolutionary processes will hone in on these predictive brain mechanisms as attractor states. This occurs via the mechanism of exploration and selective stabilisation recognised independently by Changeaux and by Edelman (Ginsburg and Jablonka 2019, 119–123, 247–248). Thus these mechanisms can be claimed to be Higher Order Principles (see Sect. 8.2.7) for brain structure and function. It is their remarkable properties that shape brain structure, and its functioning in the face of the unpredictable flow of incoming data.

8.4 The Learning Brain: Plasticity and Adaptation In carrying out these responses to incoming information, remembering and learning takes place; indeed this is a pre-requisite for functioning of predictive brain mechanisms. This adds a new dimension to the effects just discussed: not only is the new data unpredictable, but also brain structure is changed in ways affected by that inflow of new data. Thus the context for microphysics outcomes—the specific set of constraints determining electron and ion flow possibilities—is also different at the later time. Plasticity at the macro level as the brain adapts to its environment, remembers, and learns (Gray and Bjorklund 2018) is enabled by corresponding changes at the micro level as neural networks weights change (Kandel et al. 2013; Churchland and Sejnowski 2016). Thus changes take place at the micro level (Sect. 8.4.1) driven by incoming data at the macro level, and resulting in plasticity at the macro level (Sect. 8.4.2). Because brain neural nets are changing all the time, the context for outcomes of the underlying physics is also changing all the time (Sect. 8.4.3) and is not predictable from the initial brain physical microstate.

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8.4.1 Plasticity at the Micro Level Learning takes place by change of connectivity and weights in neural networks at the neuronal level (Kandel et al. 2013; Churchland and Sejnowski 2016), taking place via gene regulation at the cellular level (Kandel 2001). This alters the context within which electron and ion flows take place in neural networks and in particular at synapses, thereby shaping outcomes of the underlying universal physical laws. Developmental Processes This plasticity occurs particularly when brain development is taking place. Random initial connections are refined (Wolpert et al. 2002, §11) and new experiences can modify the original set of neuronal connections (Gilbert 1991, 642) while the brain is responding to the surrounding environment (Purves 2010, §2–§5, 229). Learning Processes Erik Kandel explored the mechanism of learning in depth. He identified gene regulatory process related to learning (Kandel 2001) Serotonin acts on specific receptors in the presynaptic terminals of the sensory neuron to enhance transmitter release. . . . during long-term memory storage, a tightly controlled cascade of gene activation is switched on, with memory-suppressor genes providing a threshold or checkpoint for memory storage . . . With both implicit and explicit memory there are stages in memory that are encoded as changes in synaptic strength and that correlate with the behavioral phases of short- and long-term memory

The Relation to Physics These changes alter the context within which the underlying physics operates. Changing constraints at the microphysics level is the mechanism of downward causation to that level (Ellis and Kopel 2019). This determines what dynamics actually takes place at the ion/electron level, which of course the fundamental laws by themselves cannot do. The outcomes are determined by biological context in this way. LB1

The Developing and Learning Brain The brain is plastic at the micro level, as development and learning takes place. Neural network connections and weights are altered via gene regulatory processes.

Thus neural network learning (Churchland and Sejnowski 2016)—a real causal process at each network level—alters electron outcomes and so later psychological level dynamics.

8.4.2 Plasticity at the Macro Level Eric Kandel states “One of the most remarkable aspects of an animal’s behavior is the ability to modify that behavior by learning” (Kandel 2001), and emphasizes that social factors affect this learning. (Kandel 1998) gives five principles for

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psychotherapy that make this clear. For those who are skeptical of psychotherapy, replace that word with ‘teaching’ or ‘coaching’ in the following, and its crucial meaning still comes through. Kandel Principle 1 All mental processes, even the most complex psychological processes, derive from operations of the brain. The central tenet of this view is that what we commonly call mind is a range of functions carried out by the brain. The actions of the brain underlie not only relatively simple motor behaviors, such as walking and eating, but all of the complex cognitive actions, conscious and unconscious, that we associate with specifically human behavior, such as thinking, speaking, and creating works of literature, music, and art. Kandel Principle 2 Genes and their protein products are important determinants of the pattern of interconnections between neurons in the brain and the details of their functioning. Genes, and specifically combinations of genes, therefore exert a significant control over behavior. . . . the transcriptional function of a gene—the ability of a given gene to direct the manufacture of specific proteins in any given cell—is, in fact, highly regulated, and this regulation is responsive to environmental factors . . . the regulation of gene expression by social factors makes all bodily functions, including all functions of the brain, susceptible to social influences. Kandel Principle 3 Behavior itself can also modify gene expression. Altered genes do not, by themselves, explain all of the variance of a given major mental illness. Social or developmental factors also contribute very importantly. Just as combinations of genes contribute to behavior, including social behavior, so can behavior and social factors exert actions on the brain by feeding back upon it to modify the expression of genes and thus the function of nerve cells. Learning . . .produces alterations in gene expression. Kandel Principles 4/5 How does altered gene expression lead to the stable alterations of a mental process? Alterations in gene expression induced by learning give rise to changes in patterns of neuronal connections. These changes not only contribute to the biological basis of individuality but strengthen the effectiveness of existing patterns of connections, also changing cortical connections to accommodate new patterns of actions. . .. resulting in long-lasting effect on the the anatomical pattern of interconnections between nerve cells of the brain. The Hierarchical Predictive Coding View The way this all fits into the predictive coding viewpoint discussed in the last section is explained by Rao and Ballard (1999). Overall the outcomes can be summarised thus: LB2

The Learning Brain The brain is plastic at the macro level as learning takes place, supported by plasticity at the micro level. Learning at the macrolevel responds to social and psychological variables.

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8.4.3 The Ever Adapting Brain The previous section emphasized, in the case of a single brain, that because of incoming data, the microstate at time t2 cannot be predicted from initial data at time t1 < t2 because it does not include this incoming data. This section emphasizes that in addition, the micro level constraints are changed because neural network wiring or weights will have changed as the brain adapts at both macro and micro levels to ongoing environmental events and changes. So not only is the data different than expected because the brain is an open system, but the dynamical context for the underlying physics is different too. The brain is an adaptive system. Individual brain structure changes in response to incoming data. As new information comes in, neural network weights are continually changed via gene regulation. This change of context alters constraints in the underlying Lagrangian, and so changes the context for future physical interactions. None of this can be determined by the initial brain micro data at time t1 , as these changes are shaped by data that has come in since then.

This is a further reason why diachronic emergence is crucially different from synchronic. Adapting and Learning Brains as Attractor States Evolutionary processes will hone also in on these learning brain mechanisms as attractor states, via the mechanism of exploration and selective stabilisation recognised independently by Changeaux and by Edelman (Ginsburg and Jablonka 2019, 119–123, 247–248).

8.5 The Stochastic Brain and Agency A key feature undermining physicalist determinism of brain states is the stochasticity that occurs in biology at the molecular level, which uncouples biology from detailed Laplacian determinism. Section 8.5.1 discusses this stochasticity, and Sect. 8.5.2 how this opens up the way for selecting desired low level outcomes that will fulfill higher level purposes—one of the key forms of downward causation. Section 8.5.3 discusses how this applies specifically to the brain. A key way that randomness is used in shaping the brain is Neural Darwinism (Sect. 8.5.4). The issue of how agency is possible arises, and this is essentially via multi level causal closure that takes advantage of this selective process (Sect. 8.5.5). This shows how biological stochasticity opens up the way to higher level biological needs acting as attractors that shape brain dynamics, rather than brain outcomes being the result purely of deterministic or statistical lower level physical dynamics. All of this can again be traced out at the underlying physics level, but it is the biology that is the essential causal factor through setting the context for physical outcomes.

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8.5.1 Biology and Stochasticity There is massive stochasticity at the molecular level in biology. This undoes Laplacian determinism at the micro level: it decouples molecular outcomes from details of initial data at the molecular level. How then does order emerge? By biology harnessing this stochasticity to produce desirable higher level results, as happens for example in the case of molecular machines (Hoffmann 2012) and the adaptive immune system (Noble and Noble 2018). Stochasticity and Molecular Machines As described in Hoffman’s book Life’s ratchet: how molecular machines extract order from chaos (Hoffmann 2012) biomolecules live in a cell where a molecular storm occurs. Every molecular machine in our cells is hit by a fast-moving water molecule about every 10−13 s. He states At the nanoscale, not only is the molecular storm an overwhelming force, but it is also completely random.

The details of the initial data molecular positions and momenta are simply lost. To extract order from this chaos, “one must make a machine that could ‘harvest’ favorable pushes from the random hits it receives.” That is how biology works at this level. Stochasticity in Gene Expression Variation occurs in the expression levels of proteins (Chang et al. 2008). This is a property of the population as a whole not of single cells, so the distribution curve showing the number of cells displaying various levels of expression is an attractor created by the population (Noble 2016, 175– 176). Promoter architecture is an ancient mechanism to control expression variation (Sigalova et al. 2020). Thus one must use stochastic modeling of biochemical and genetic networks (Ingalls 2013, 280–295) when determining their outcomes. This affects the detailed physical outcomes of memory processes based in gene regulation (Kandel 2001). Stochasticity in Genetic Variation The processes of genetic variation before selection are mutation and recombination (Alberts et al. 2007), drift (Masel 2011), and migration. They all are subject to stochastic fluctuations. Mutations arise spontaneously at low frequency owing to the chemical instability of purine and pyrimidine bases and to errors during DNA replication (Lodish et al. 2000). Because evolution is a random walk in a state space with dimension given by the number of the different strategies present (Geritz et al. 1997) this shapes evolutionary outcomes in a way that is unpredictable on the basis of microphysics data. This has key present day outcomes in terms of ongoing mutations of microbes and viruses on the one hand, and of immune system responses on the other, both of which are based in taking advantage of stochasticity (Noble and Noble 2018). The statistics of outcomes however can be studied in terms of evolution over a rugged fitness landscape (Gillespie 1984; Kauffman and Levin 1987; Felsenstein 1988; Orr 2005). Small fluctuations can end up in a different attractor basin or adaptive peak.

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The Microbiome A key factor in physiology is that our bodies contain many billions of microbes that affect bodily functioning and health. This is being studied in depth by the Human Microbiome Project (Peterson et al. 2009) and the Integrative Human Microbiome Project (Integrative H. M. P. 2014, 2019). Thousands of microbial species, possessing millions of genes, live within humans: in the gastrointestinal and urogenital tracts, in the mouth: 1018 , in the nose, in the lungs: 109 /ml, on the skin: 1012 . This leads to infectious diseases (rheumatic fever, hepatitis, measles, mumps, TB, AIDS, inflammatory bowel disease) and allergic/autoimmune diseases (Asthma, diabetes, multiple sclerosis, Croon’s disease). Because of the stochasticity in gene mutation, recombination, and horizontal gene transfer, and the huge numbers involved, together with the impossibility of setting data to infinite precision (Sect. 8.6.1), evolution of specific outcomes is unpredictable in principle, but has major macro level outcomes for individuals.

8.5.2 Stochasticity and Selection in Biology This level of stochasticity raises a real problem: how could reliable higher levels of biological order, such as functioning of metabolic and gene regulatory networks and consequent reliable development of an embryo (Wolpert et al. 2002), emerge from this layer of chaos? The answer is that evolutionary processes have selected for biological structures that can successfully extract order from the chaos. These structures in turn use the same mechanism: they select for biologically desirable outcomes from an ensemble of physical possibilities presented by this underlying randomness. Higher level biological needs may be satisfied this way. As stated by (Noble and Noble 2018): Organisms can harness stochasticity through which they can generate many possible solutions to environmental challenges. They must then employ a comparator to find the solution that fits the challenge. What therefore is unpredictable in prospect can become comprehensible in retrospect. Harnessing stochastic and/or chaotic processes is essential to the ability of organisms to have agency and to make choices.

This is the opposite of the Laplacian dream of the physical interactions of the underlying particles leading to emergent outcomes purely on the basis of the nature of those interactions. It is the detailed structure of molecular machines, together with the lock and key molecular recognition mechanism used in molecular signalling (Berridge 2014), that enables the logic of biological processes to emerge as effective theories governing dynamics at the molecular level. They exist in the form they do because of the higher level organising principles that take over. The emergent levels of order appear because they are based in higher level organising principles characterising emergent protectorates as described by (Laughlin and Pines 2000) (see Sect. 8.2.7). For example Friston’s Free Energy Principle (Friston 2010, 2012) is such a higher level organising principle. It does not follow from the microphysical

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laws. In fact all the higher level Effective Theories ETL (Sect. 8.2.4) characterise such Higher Level Organising principles. STB1

Variation leads to a variety of states, from which outcomes are selected; States that fulfill biological functions are attractor states for function and hence for evolution and development.

This agrees with (Ginsburg and Jablonka 2019, 245) Biological attractors are usually functional - the mechanisms enabling them to be reached reliably, in spite of different starting conditions, evolved by natural selection.

This is the process of exploration and selective stabilisation mechanism that is described in Ginsburg and Jablonka (2019)[119–123, 247–248]. The driving of the process by biological needs is the reason that convergent evolution occurs (McGhee 2011).

8.5.3 The Brain and Stochasticity There are various kinds of stochasticity in brain function, apart from the fact that it involves necessarily the stochasticity in molecular dynamics just discussed. Stochasticity in Neural Activity The neural code is spike chains (Rieke et al. 1999) where (Shadlen and Newsoms 1994) the timing of successive action potentials is highly irregular. Also fluctuations in cortical excitability occur (Stephani et al. 2020). This results in stochasticity in neural outcomes (Glimcher 2005) in contrast to deterministic dynamics, suggesting an organising principle (Stephani et al. 2020): Brain responses vary considerably from moment to moment, even to identical sensory stimuli. This has been attributed to changes in instantaneous neuronal states determining the system’s excitability. Yet the spatio-temporal organization of these dynamics remains poorly understood. . . .. criticality may represent a parsimonious organizing principle of variability in stimulus-related brain processes on a cortical level, possibly reflecting a delicate equilibrium between robustness and flexibility of neural responses to external stimuli.

This stochasticity allows higher level organising principles such as attractors to shape neural outcomes in decision making in the brain (Rolls and Deco 2010; Deco et al. 2009). The higher level structure of attractor networks (Rolls 2016, 95–134) determines outcomes. A particular case where a randomisation and selection process is used is Boltzmann machines and annealing (Churchland and Sejnowski 2016, 89– 91). This demonstrates the principle that stochasticity greatly enhances efficiency in reaching attractor states (Palmer 2020). Creativity A key feature of mental life is creativity, which has transformed human life both through inventiveness in science (Maxwell, Turing, Bardeen, Townes, Cormack, and so on) and in commerce (Gates, Jobs, Zuckerberg, Bezos, and so

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on). It has been proposed (Rolls 2016, 137) that the possibility of creativity is an outcome of stochasticity due to random spiking of neurons, resulting in a brain state being able to switch from one basin of attraction to another. Indeed harnessing stochasticity can be the basis of creative agency (Noble 2020; Noble and Noble 2020). The Gut-Brain Axis The body microbiome (Sect. 8.5.1) has a key influence on the brain. Effects are as follows (Cryan et al. 2019) The microbiota and the brain communicate with each other via various routes including the immune system, tryptophan metabolism, the vagus nerve and the enteric nervous system, involving microbial metabolites such as short-chain fatty acids, branched chain amino acids, and peptidoglycans. Many factors can influence microbiota composition in early life, including infection, mode of birth delivery, use of antibiotic medications, the nature of nutritional provision, environmental factors, and host genetics. At the other extreme of life, microbial diversity diminishes with aging. Stress, in particular, can significantly impact the microbiota-gut-brain axis at all stages of life. Much recent work has implicated the gut microbiota in many conditions including autism, anxiety, obesity, schizophrenia, Parkinson’s disease, and Alzheimer’s disease.

It is also involved in neurodegenerative disease (Rosario et al. 2020). Because of the unpredictability of how the microbiome will develop, both due to the stochasticity of its genetic mutation and the randomness of the microbes imported from the environment, the specific outcomes of these interactions are unpredictable from initial micro biological data in an individual body, and hence a fortiori from knowledge of the details of the underlying physical level. One can however study the statistics of molecular evolution over the mutational landscape (Gillespie 1984; Kauffman and Levin 1987). Note that not all the key factors determining outcomes are purely microbiological or physiological: stress, a mental state, is a key factor in its dynamics.

8.5.4 Neural Plasticity and Neural Darwinism As well as changing neural network weights (Churchland and Sejnowski 2016) via gene regulatory networks (Kandel 2001), neural plasticity during development involves pruning connections that were initially made randomly (Wolpert et al. 2002) as learning takes place. An important way variation and selection happens is via Neural Darwinism (or Neuronal Group Selection) (Edelman 1987, 1993). This is a process where neural connections are altered by neuromodulators such as dopamine and serotonin that are diffusely spread from precortical nuclei to cortical areas via ‘ascending systems’. They then modify weights of all neurons that are active at that time, thus at one shot strengthening or weakening an entire pattern of activation—a vary powerful mechanism. This mechanism (Ginsburg and Jablonka 2019, 119–123, 247–248) was

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also discovered by Changeux and Danchin (1976). Seth and Baars (2005) describe these processes thus: In the brain, selectionism applies both to neural development and to moment-to-moment functioning. Edelman postulates two overlapping phases of developmental and experiential variation and selection. The first is the formation during development of a primary repertoire of many neuronal groups by cell division, migration, selective cell death, and the growth of axons and dendrites. This primary repertoire of neurons is epigenetically constructed through a suite of genetic and environmental influences, and generates a high level of diversity in the nascent nervous system. The second, experiential, phase involves the dynamic formation from this primary repertoire of a secondary repertoire of functional neuronal groups, by the strengthening and weakening of synapses through experience and behavior. This phase involves the selective amplification of functional connectivities among the neurons produced in the first phase, with which it overlaps. In this manner, an enormous diversity of anatomical and functional circuits is produced

This provides a key mechanism for experientially based selection of connectivity patterns. Primary Emotions An important feature of Edelman’s theory is that the subcortical nuclei involved, as well as the neuromodulators, are precisely the same as are involved in Jaak Panksepp’s primary emotional systems (Panksepp 2009) (Sect. 8.3.3). Hence the theory is in fact a theory of Affective Neural Darwinism (Ellis and Toronchuk 2005, 2013), making clear the importance of affect (emotion) for brain plasticity and learning. STB2

Stochasticity and Neural Darwinism Brain plasticity is affected by neuromodulators diffusely projected to the cortex from nuclei in subcortical arousal system via ascending systems, selecting neuronal groups for strengthening or weakening. In this way emotions affect neural plasticity.

This is a key way that interactions at the social level reach down to alter brain connections and hence the context of physical interactions in the brain. It is a specific example of the ‘vary and select’ topdown process (Sect. 8.2.5: TD3B) that plays a key role in all biology.

8.5.5 Agency, Self-Causation, and Causal Closure Agency clearly takes place at the psychological level. People plan and, with greater or lesser success, carry out those plans (Gray and Bjorklund 2018), thus altering features of the physical world. In this way, technological developments such as farming and metallurgy and abstract ideas such as the design of an aircraft or a digital computer have causal power (Ellis 2016) and alter history (Bronowski 2011). The emergent psychological dynamics of the brain demonstrably has real causal powers. So how does such agency occur? Self-Causing Systems Agency is centrally related to the idea of a self-causing system. The idea of a system is crucial, “an integration of parts into an orderly

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whole that functions as an organic unity” (Juarrero 2002, 108–111). This enables self-causation (Juarrero 2002, 252): Complex adaptive systems exhibit true self-cause: parts interact to produce novel, emergent wholes; in turn these distributed wholes as wholes regulate and constrain the parts that make them up.

(Murphy and Brown 2007, 85–104) develop the theme further, emphasizing firstly how a complex adaptive system represents the emergence of a system with a capacity to control itself. Secondly, agency is related to the variation and selection process emphasized here: the dynamical organisation of a complex adaptive system functions as an internal selection process, established by the system itself, that operates top-down to preserve and enhance itself. This process is an example of the interlevel causal closure that is central to biology (Mossio 2013; Ellis 2020b). It leads to the circularity of the embodied mind (Fuchs 2020): From an embodied and enactive point of view, the mind-body problem has been reformulated as the relation between the lived or subject body on the one hand and the physiological or object body on the other. The aim of the paper is to explore the concept of circularity as a means of explaining the relation between the phenomenology of lived experience and the dynamics of organism-environment interactions. .. It will be developed in a threefold way: (1) As the circular structure of embodiment, which manifests itself (a) in the homeostatic cycles between the brain and body and (b) in the sensorimotor cycles between the brain, body, and environment. This includes the interdependence of an organism’s dispositions of sense-making and the affordances of the environment. (2) As the circular causality, which characterizes the relation between parts and whole within the living organism as well as within the organism-environment system. (3) As the circularity of process and structure in development and learning. Here, it will be argued that subjective experience constitutes a process of sense-making that implies (neuro-)physiological processes so as to form modified neuronal structures, which in turn enable altered future interactions. On this basis, embodied experience may ultimately be conceived as the integration of brain-body and body-environment interactions, which has a top-down, formative, or ordering effect on physiological processes.”

This is also related to the Information Closure theory of consciousness (Chang et al. 2020).: “We hypothesize that conscious processes are processes which form non-trivial informational closure (NTIC) with respect to the environment at certain coarse-grained scales. This hypothesis implies that conscious experience is confined due to informational closure from conscious processing to other coarse-grained scales.” The Predictive Processing View Intentional action is a process of an agent selecting from various possibilities. This possibility of agency is congruent with the predictive coding view, as three examples will demonstrate. Firstly (Seth et al. 2012) state, We describe a theoretical model of the neurocognitive mechanisms underlying conscious presence and its disturbances. The model is based on interoceptive prediction error and is informed by predictive models of agency, general models of hierarchical predictive coding

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and dopamine signaling in cortex . . .The model associates presence with successful suppression by top-down predictions of informative interoceptive signals evoked by autonomic control signals and, indirectly, by visceral responses to afferent sensory signals. The model connects presence to agency by allowing that predicted interoceptive signals will depend on whether afferent sensory signals are determined, by a parallel predictive-coding mechanism, to be self-generated or externally caused.

Secondly (Negru 2018) puts it this way: The aim of this paper is to extend the discussion on the free-energy principle (FEP), from the predictive coding theory, which is an explanatory theory of the brain, to the problem of autonomy of self-organizing living systems. From the point of view of self-organization of living systems, FEP implies that biological organisms, due to the systemic coupling with the world, are characterized by an ongoing flow of exchanging information and energy with the environment, which has to be controlled in order to maintain the integrity of the organism. In terms of dynamical system theory, this means that living systems have a dynamic state space, which can be configured by the way they control the free-energy. In the process of controlling their free-energy and modeling of the state space, an important role is played by the anticipatory structures of the organisms, which would reduce the external surprises and adjust the behavior of the organism by anticipating the changes in the environment. In this way, in the dynamic state space of a living system new behavioral patterns emerge enabling new degrees of freedom at the level of the whole.

Finally (Szafron 2019) characterizes it thus: Using the Free Energy Principle and Active Inference framework, I describe a particular mechanism for intentional action selection via consciously imagined goal realization, where contrasts between desired and present states influence ongoing neural activity/policy selection via predictive coding mechanisms and backward-chained imaginings (as self-realizing predictions). A radically embodied developmental legacy suggests that these imaginings may be intentionally shaped by (internalized) partially-expressed motor predictions and mental simulations, so providing a means for agentic control of attention, working memory, and behavior.

The overall result is a final higher level organising principle that acts as an attractor state during evolution: STB3

Stochasticity and Agency Stochasticity at the micro level allows macro level dynamics to select preferred micro outcomes, thus freeing higher levels from the tyranny of domination by lower levels. By this mechanism, downward selection of preferred micro outcomes enables self-causation and agency.

The big picture is that randomness is rife in biology. Evolutionary processes have adapted biological systems to take advantage of this (Hoffmann 2012), with higher level processes selecting preferred outcomes from a variety of possibilities at the lower levels, thereby enabling the higher level organising principles characterised in the previous two sections to shape physical outcomes (Noble and Noble 2018). The underlying physics enables this, but does not by itself determine the particular outcomes that occur, for they are contextually determined via time dependent dynamical constraints (Juarrero 2002, 131–162). It is crucial to agency (Noble and Noble 2020; Noble 2020).

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8.6 The Whole Universe Gambit and Causal Closure The hardcore reductionist responds to the previous sections by saying yes the brain is an open system, but the universe as a whole is not. Extend your micro data to include all the particles in the universe—well, in the region of the universe that is causally connected to us (i.e inside the particle horizon Hawking and Ellis 1973)— and it is then causally closed. All the data incoming to the brain is determined by causally complete microphysical processes in this extended domain, hence brain outcomes are determined by them too. The response, denying that this can work, has many levels. Please note that as stated before I am concerned with the possibility of physics determining specific outcomes, such as the words in emails to me from Carlo Rovelli, not just statistical outcomes. His emails did not contain a statistical jumble of letters or words: they contained rational arguments stated coherently. This is what has to be explained. The question is how the underlying physics relates to such specific rational outcomes. In order of increasing practical importance the issues are as follows. First, Sect. 8.6.1 denies that the micro physical level is in fact causally complete, because of irreducible quantum indeterminism. While this can indeed have an effect on the brain, its primary importance is to deny that physics at the micro level is in principle causally complete. Second, Sect. 8.6.2 makes the case that even if the incoming data was determined uniquely by microphysics everywhere in the surroundings, they would not determine a unique brain micro state in any individual because of the multiple realisability of macro states by microstates (Sect. 8.2.6). Third, Sect. 8.6.3 makes the case that important aspects of macro physics are in practice indeterminate because of the combination of chaotic dynamics and the impossibility of specifying initial data to infinite precision. This has neural outcomes inter alia because it applies to weather patterns and forest fires. Fourth, Sect. 8.6.4 points out that there is considerable randomness in the external world biology that the mind interacts with at both micro and macro levels. These biological outcomes are not precisely predictable from their micro physics initial data. It has key impacts on the mind related in particular to the relations between humans and viruses. Fifth, Sect. 8.6.5 points out that because the brain is a social brain (Sect. 8.3.4), its macro level responses to incoming data are not purely mechanical: they are highly sophisticated responses at the psychological level to social interactions. These are affected by unpredictable effects such as weather and pandemics. By the mechanisms discussed in Sect. 8.4, these understandings reach down to structure the neural context of brain microphysics. Finally Sect. 8.6.6 makes the case that the larger environment interacts with the brain by providing the setting for interlevel circular causation. This can be claimed to be the real nature of causal closure. It is what is involved in order to have the data, constraints, and boundary conditions needed to determine specific outcomes in real

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world contexts, enabling self-causation. This is the opposite of being determined by microphysics alone.

8.6.1 Is Micro Physics Causally Complete? Carlo’s argument is that micro data dependence of all outcomes undermines the possibility of strong emergence. To summarise, suppose I am given the initial positions ri and momenta pi of all particles in the set P everywhere,12 where P := (protons, neutron, electrons)

(8.5)

at a foundational level L1. At a higher level L2 this constitute an emergent structure S, such as a neural network. The details of S are determined by the microdata, even though its nature cannot be recognised or described at level L1. The forces between the particles at level L1 completely determine the dynamics at level L1. Hence the emergent outcomes at level L2 are fully determined by the data at level L1, so the emergence of dynamical properties and outcomes at level L2 must be weak emergence and be predictable, at least in principle, from the state (8.5) of level L1, even if carrying out the relevant computations is not possible in practice. This would apply equally to physical, engineering, and biological emergent systems. It is in effect a restatement of the argument from supervenience. There are problems with the argument just stated as regards both microphysics and macrophysics. Quantum Physics Uncertainty Relation The Heisenberg uncertainty relations undermine this Laplacian dream because initial data cannot be specified with arbitrary accuracy (Heisenberg 1949). The standard deviations of position σx and momentum σp obeys σx σp ≥ h/2 ¯

(8.6)

(Kennard 1927), so one cannot in principle set initial data precisely at level L1. Consequently, outcomes based on standard Lagrangians dependent on x and p are uncertain in principle. Essentially the same issue arise in the case of classical physics (Del Santo and Gisin 2019) because data cannot be prescribed to infinite accuracy (Ellis et al. 2018). Further in the quasi-classical approximation, it will be subject to the uncertainty (8.6), reinforcing that conclusion (Del Santo 2020). This affects outcomes of chaotic dynamics (Sect. 8.6.3).

12 “Everywhere”

means within the particle horizon (Hawking and Ellis 1973).

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Irreducible Uncertainty in Quantum Outcomes There is irreducible uncertainty of quantum outcomes when wave function collapse to an eigenstate takes place, with outcomes only predictable statistically via the Born rule (Isham 2001; Ghirardi 2007). One cannot for example predict when an excited atom will emit a high energy photon, one can only predict the probability of such an event This unpredictability has consequences that can get amplified to macrolevels, for example causing errors in computer memories due to cosmic rays (Ziegler and Lanford 1979; Gorman et al. 1996; Physics World 2020). The specific errors that occur are not determined by physics, because quantum physics is foundationally causally incomplete. Biological Damage Due to Cosmic Rays Cosmic rays can alter genes significantly enough to cause cancer. In particular, galactic cosmic rays lead to significant fatality risks for long-term space missions. This is discussed in (Cucinotta and Cacao 2017; Cucinotta et al. 2017; Cekanaviciute et al. 2018) This shows both the contextual dependence of local outcomes in this case, and their unpredictability in principle. Unpredictable Brain Effects This obviously can affect the mental processes of those undertaking space travel. The brain can be affected crucially by distant events that are in principle unpredictable because they result from quantum decay of excited atoms. The statistics of outcomes is strictly predicted by quantum theory. But in terms of causal completeness of biological events, we wish to know which specific person gets affected at what specific time, thereby changing individual thought patterns. Detailed microphysical initial data everywhere cannot tell us that. This is a situation that only affects a small number of people, but it is important because it establishes that in principle the physicalist whole world gambit does not work (after all, that argument is an in principle argument: no one argues that it can work in practice in terms of allowing actual predictions of unique biological outcomes).

8.6.2 Mental States and Multiple Realisability Incoming sensory data in a real world context affects brain macrostates which then shape micro level connections via learning. But they do not do so in a unique way: incoming sensory data does not determine unique brain microstates because of the multiple realisability of higher level states at the physical level. Mental States and Multiple Realisability A given set of incoming data does not result in a unique brain physical microstate because of multiple realisability of the higher level state at the lower level (Sect. 8.2.6). This is a key property of brain function. (Silberstein and McGeever 1999) state Functionalists (and others) claim that mental states are radically multi-realizable, i.e., that mental states like believing that p and desiring that p can be multiply realized within individual across time, across individuals of the same species, across species themselves,

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and across physical kinds such as robots. If this is true, it raises crucial question: why do these states always have the same behavioural effects? In general we expect physically similar states to have similar effects and different ones to have different effects. So some explanation is required of why physically disparate systems produce the same behavioural effects. If there is nothing physically common to the ‘realizations’ of a given mental state, then there is no possibility of any uniform naturalistic explanation of why the states give rise to the same mental and physical outcomes.

The brain responds to incoming data via the predictive processing mechanisms discussed in Sect. 8.3.2 , with updating of the relevant expectations taking place all the time on the basis of experience. The macro psychological processes that occur in this way reach down to shape neural network connections and weights (Kandel 2001, 1998) in ways that are not unique. These then change constraints at the electron/ion level, realising any one of the billions of possible changes at that level that are in the right equivalence class. Unpredictable Brain Effects Unique micro level physical conditions in the brain (the specific details of constraints in the electron/ion Lagrangian that will determine the ongoing brain dynamics) cannot in principle be determined by incoming data from the external world because of multiple realisability. Ordered outcomes appear at the brain macro level according to the predictive coding logic outlined in Sect. 8.5.3, which then activates any one of the microstates in the corresponding equivalence class at the micro level (Sect. 8.2.6). All of this can of course be traced at the microphysical level, both internal to the brain and externally. But what is driving it is psychological level understandings.

8.6.3 Is Macro Physics Causally Complete? The atmosphere is an open system dynamically driven by the Sun’s radiation, and with vary complex interactions taking place between the atmosphere, subject to winds and convection, water (the seas and lakes and clouds and ice), and land (Ghil and Lucarini 2020). These are unpredictable in detail because of chaotic dynamics. Convection Patterns Consider a higher physical level L3 in the context of a fluid where convection patterns take place. Because of the associated chaotic dynamics together with the impossibility (8.6) of setting initial data to infinite precision (Sect. 8.6.1), macroscopic outcomes are unpredictable in principle from micro data (8.5) . Convection patterns are an example (Bishop 2008): an extremely small perturbation in a fluid trapped between two levels where a heat differential is maintained can influence the particular kind of convection that arises. (Anderson 2001) puts it this way: A fluid dynamicist when studying the chaotic outcome of convection in a Benard cell knows to a gnat’s eyelash the equations of motion of this fluid but also knows, through the operation of those equations of motion, that the details of the outcome are fundamentally unpredictable, although he hopes to get to understand the gross behaviour. This aspect is

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an example of a very general reality: the existence of universal law does not, in general, produce deterministic, cause-and-effect behaviour.

The outcome is an emergent layer of unpredictability at both local scales (thunderstorms, tornados, typhoons, and so on) and globally (large scale weather outcomes). The latter are famously characterised by strange attractors (Lorenz 1963), involving instability and fractals, but much more importantly interactions between different length scales that make prediction impossible in principle (Lorenz 1969), as discussed in depth by (Palmer et al. 2014). Downward constraints then entrains lower level dynamics to follow, as stated by Bishop (2012): “Large-scale structures arise out of fluid molecules, but they also dynamically condition or constrain the contributions the fluid molecules can make, namely by modifying or selecting which states of motion are accessible to the fluid molecules”. The Butterfly Effect Lorenz intended the phrase ‘the butterfly effect’ to describe the existence of an absolute finite-time predictability barrier in certain multi-scale fluid systems, implying a breakdown of continuous dependence on initial conditions for large enough forecast lead times (Palmer et al. 2014). Lorenz (1969) states It is proposed that certain formally deterministic fluid systems which possess many scales of motion are observationally indistinguishable from indeterministic systems. Specifically, that two states of the system differing initially by a small observational error will evolve into two states differing as greatly as randomly chosen states of the system within a finite time interval, which cannot be lengthened by reducing the amplitude of the initial error.

This happens because of the interactions between the different length scales involved. Palmer’s illuminating paper (Palmer et al. 2014) concludes that this real butterfly effect13 does indeed occur—but only for some particular sets of initial data. Nevertheless occurring from time to time denies causal closure of physics on this scale in practice. That clearly means the underlying physics at the particle level cannot have been causally closed either. The multiscale weather dynamics studied by Lorenz (1969) reaches down to influence atomic and electron motions (think thunderstorms) at the lower physics level. But this is the crucial point: you cannot predict when those cases will occur. Forest Fires are an example of self-organised critical behaviour (Malamud et al. 1998) affected by local atmospheric convection activity in that firstly many forest fires are cased by lightning,14 and secondly the spread of the fire is determined by local winds which are changed by local convection effects due to the fire. The detailed dynamics of the fire are unpredictable because of these links; even probabilities are tricky (Mata et al. 2010).

13 See https://www.youtube.com/watch?v=vkQEqXAz44I for an enlightening lecture on the common and real butterfly effects. The implication is that you need ensemble forecasts. 14 Dry Thunderstorms Could Accelerate the California Wildfires.

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The Gravitational n-Body Problem Essentially the same unpredictability applies to gravitating systems with more than two interacting bodies. This is vividly indicated in an Aeon video on Newton’s 3-body problem (Pacucci 2020). Unpredictable Brain Effects In terms of the effect on the brain, these random outcomes shape decisions from whether to open an umbrella on a trip to the shops, to farmers’ decisions as to when to harvest crops, aircraft pilots decisions about en route flight planning, and homeowners decisions about whether or not to flee a forest fire. It causes an essential unpredictability in mental outcomes. This is a first reason the external world has an ongoing unpredictable key effect on individual brains.

8.6.4 Biological Randomness: The Microbiome Biological dynamics in the external world are subject to unavoidable uncertainty because of the random nature of molecular level events, already alluded to in Sect. 8.5.1.

Interacting Microbiomes and Viruses The immense complexity of each individual person’s microbiome (Sect. 8.5.1) interacts, through social events, with other people’s microbiomes, as do their viruses. Genetic variability is central to the mutation of microbes and viruses in the external world. Detailed physical microstates everywhere determine the statistics of such variations, but not the specific ones that actually occur, which are due inter alia to mutation and recombination and horizontal gene transfer in the case of microbes, mistakes by RNA or DNA polymerases, radiation- or chemical- or host cell defences-induced mutation, and re-assortment in the case of viruses. Predicting mutations is essentially impossible, even for viruses with 10,000 bases like HIV. All you CAN say is that the known mutation rate for that organism predicts that every single copy of the HIV genome (for example) will have at least one mutation (10−4 rate).15 Unpredictable Brain Effects This has crucial effects in our brains that are completely unpredictable because firstly of the randomness of the genetic mutations leading to these specific microbes and viruses, and secondly of the details of the events that lead to their spread through animal and human populations; this can all be expressed in terms of rugged adaptive landscapes (Orr 2005). This firstly directly affects human health and brain dynamics in each of the set of interacting brains (Sect. 8.6.5) via the gut brain axis (Cryan et al. 2019), and then plays a key role in individual associated mental events such as individual planning of what do to about

15 I

thank Ed Rybicki for this comment.

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anxiety, obesity, schizophrenia, Parkinson’s disease, and Alzheimer’s disease, or flu, AIDS or COVID-19. This is a second reason the external world has an important unpredictable key effect on individual brains.

8.6.5 Social Understandings and Individual Brains Our brain is a social brain (Sect. 8.3.4). Information from the external world affects mental states via ongoing complex social interactions, which have real causal powers. They structure our mental activities in everyday life. Social Understandings There is an intricate relation between the individual and society (Berger 1963; Longres 1990; Berger and Luckmann 1991; Donald 2001) and between individuals and institutions in a society (Elder-Vass 2010, 2012). The downward effect of the social context on an individual brain is mediated by social interactions and understandings (Sect. 8.3.4). In this social context, a complex interaction takes place involving mind reading, prediction, filling in of missing data, taking social context into account (Longres 1990; Donald 2001; Frith 2009). This nature of the interactions of a many brains, each a self causing open system (Sect. 8.5.5), is the main practical day to day reason that microphysics everywhere cannot determine unique outcomes in each of the brains involved. Downward causation from the social level interactions to individual brains to the underlying molecular biology and thence physical levels is the causal chain. Abstract Variables Have Causal Powers This is all enabled by our symbolic ability (Deacon 1997), resulting in our use of spoken and written language, which is the key factor enabling this to happen (Ginsburg and Jablonka 2019) (Sect. 8.3.5). This affects our individual brain operations as we consider the continually changing detailed implications of money, closed corporations, laws, passports, and so on in our lives. Policy Decisions Have Causal Powers Given this context, social variables have causal power (Longres 1990; Harari 2014) and affect brain states; in particular, this applies to policy decisions. The interaction outcomes are shaped at the social level, which is where the real causal power resides, and then affect individual brain states in a downward way. Complex interpretative processes take place shaping psychological level reactions, which then shape neural network and synapse level changes in a contextual way on an ongoing basis as studied by social neuroscience (Cacioppo et al. 2002). Unpredictable Brain Effects Policy decisions are sometimes based in unpredictable events such as cyclones or forest fires (Sect. 8.6.3) or a global pandemic or local infectious outbreak (Sect. 8.6.4). Mandatory evacuating of towns in the face

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of a cyclone or wild fire,16 going into shelters in the case of a tornado, or policy decisions such as lockdowns in the face of a pandemic will all be unpredictable because their cause is unpredictable, and so will cause unpredictable outcomes in individual brains at macro and micro levels. The causal chain is an unpredictable trigger event, followed by a social policy choice that then changes outcomes in individual brains. Detailed physical data everywhere enables this to happen by providing the basis for stochastic outcomes that cannot be determined uniquely from that data be because of the real butterfly effect in the case of weather, and its analogue in the case of microbe and viral mutations. Carlo’s view that microphysics determines all brain dynamics in this extended context could hold if it were not for the random nature of the trigger events.

8.6.6 Real Causal Closure Carlo’s move of bringing into focus the larger context is certainly correct in the following sense: the way that causal closure takes place in reality involves the whole environment. But that means it is an interlevel affair, for the environment involves all scales. The Real Nature of Causal Closure • From my viewpoint, what is meant by the phrase “causal closure” as used by Carlo and other physicists is in fact that one is talking about existence of a wellposed effective theory EFL that holds at some emergent level L. This means data dL for variables vL at that level L specifies unique outcomes, or the statistics of such outcomes, at that level. • However existence of such a theory does by itself not determine any specific physical outcomes. It implies that if the right data and boundary conditions are present, and all constraints that hold are specified, then a unique or statistical outcome is predicted by the physics at that level. • It does not attempt to say where that data, boundary conditions, and constraints come from. But without them you do not have causal closure in what should be taken to be the real meaning of the term: sufficient conditions are present to causally determine real world outcomes that happen. For example social dynamics are active causal factors that reach down to affect physics outcomes, as is abundantly clear in the COVID-19 crisis: policies about face masks affect physical outcomes. • My use of the term, as developed in full in (Ellis 2020b), regards causal closure as interlevel affair, such as is vital to biological emergence (Mossio 2013). The conjunction of upward and downward effects must self-consistently determine the boundary conditions, constraints, and initial data at a sufficient set of levels 16 For

a typical context see https://www.nytimes.com/2020/08/20/us/ca-fires.html.

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that unique or statistical outcomes are in fact determined by the interlocking whole. • When that happens you can of course trace what is happening at whatever physics level you choose as a base level L0. But over time, the later initial data, boundary conditions, and constraints at that level are dynamically affected by the downward mechanisms outlined in Sect. 8.2.5. Because causation is equally real at each level, the higher levels are just as much key factors in the causal nexus as is level L0, as time proceeds. Higher Level Organising Principles, independent of the lower level physics, shape physical outcomes. The state of variables at level L0 at time t0 uniquely determines the higher levels at that time, but not at a later time t1 > t0 . • The freedom for higher levels to select preferred lower level outcomes exists because of the stochastic nature of biological processes at the cellular level (Sect. 8.5.2). • The illusion of the effective theory at a physical level L0 being causally complete is because physicists neglect to take into account their own role in the experiments that establish the validity of the effective theory that holds at that level. When you take that role into account, those experiments involve causal closure of all levels from L0 to the psychological level L6 where experiments are planned and the social level L7 which enables the experimental apparatus to come into being. Another term used for causal closure in this sense is operational closure: the organisational form of the processes that enable autopoietic self-production and conservation of system boundaries (Di Paolo and Thompson 2014; Ramstead et al. 2019). The Predictive Processing/Free Energy Viewpoint My view agrees with the growing predictive coding consensus, as presented in previous sections. Karl Friston (private communication) says the following: I imagine that downward causation is an integral part of the free energy formalism; particularly, its predication on Markov blankets. I say this in the sense that I have grown up with a commitment to the circular causality implicit in synergetics and the slaving principle (c.f., the Centre Manifold Theorem in dynamical systems). As such, it would be difficult to articulate any mechanics without the downward causation which completes the requisite circular causality. Practically, this becomes explicit when deriving a renormalisation group for Markov blankets. We use exactly the same formalism that Herman Haken uses in his treatments of the slaving principle (Haken 1996; Haken and Wunderlin 1988) to show that Markov blankets of Markov blankets constitute a renormalisation group. If existence entails a Markov blanket, then downward causation (in the sense of the slaving principle) must be an existential imperative.

The final conclusion of this section is the following Unique causal outcomes in individual microphysical brain states do not occur when one includes causal effects of the external world. This does not work (i) because microphysics is not in fact causally closed due to quantum wave function collapse, (ii) external information cannot uniquely determine microphysical states in the brain - multiple realisability makes this impossible, (iii) unpredictable macro level chaotic dynamics occurs, (iv) microbiome

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dynamics that affect brain states is unpredictable, and (v) the way external states influence brain states is strongly socially determined and can include events that are in principle unpredictable.

However it certainly is true that such downward causal effects on individual brains occur. They just do not do so in a way that is uniquely determined by physical effects alone.

8.7 Microphysics Enables But Does Not Determine In this section I summarise my response (Sect. 8.7.1), and comment on the relation of all the above to the issue of free will (Sect. 8.7.2).

8.7.1 The Basic Response There are a series of key issues that shape my response. • I am concerned with what determines the specific outcomes that occur in real world contexts, not just with statistical prediction of outcomes. How does physics underlie the existence of a Ming dynasty teapot? Of the particular digital computer on which I am typing this response? Of Einstein’s publication of his paper on General Relativity? Of the election of Donald Trump as President of the United States of America? • Consider a specific individual brain at a particular time. The difference between synchronic and diachronic emergence is key. Carlo’s view can be defended in the synchronic emergence case, but cannot be correct in the diachronic case, because individual brains are open systems. The initial microphysical state of the brain simply does not include all the data that determine its outcomes at later times. This is what is discussed in depth in Sects. 8.3–8.5. The Whole Universe Context Claiming that this problem is solved by going to a larger scale where causal closure does indeed hold (the cosmological scale), which therefore implies that the specific evolution of all subsystems such as individual brains is also uniquely determined, does not work for a series of reasons. I list them now with the theoretically most important issues first. This is the inverse of the order that matters in terms of determining outcomes in practical terms. As far as that is concerned, the most important issues are the later ones. It does not work because of, 1. Irreducible quantum uncertainty at the micro level which affects macro outcomes; this demonstrates that the claim is wrong in principle. It can indeed have macro effects on the brain, but this is not so important at present times because of

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the shielding effect of the earth’s atmosphere. However it has played important role in evolutionary history (Percival 1991), as discussed by Todd (1994) and Scalo and Wheeler (2002) The fact that downward effects from that larger context to the brain, which certainly occur via neural plasticity and learning, cannot in principle determine a unique brain microstate, because of multiple realisability of those detailed physical states when this occurs. Unique brain microstates cannot occur in this way. Uncertainty in principle at the ecosystem level due to chaotic dynamics and the real butterfly effect plus the inability to set initial molecular conditions precisely. This has major unpredictable effects on individual brains due to forest fires, thunderstorms, tornadoes, and tropical cyclones. Microbiome dynamics that is in principle unpredictable because of the molecular storm and huge number of molecules involved, plus the inability to set initial molecular conditions precisely. This affects individual and social outcomes as evolution takes place on a rugged adaptive landscape that keeps changing as all the interacting species evolve. This crucially affects brain dynamics through the gut-brain axis. Social understandings that shape how external signals are interpreted by the brain, when social level policies and choices (which may involve unpredictable events such as thunderstorm details or pandemic outbreaks) chain down to influence flows of electrons in axons. It simply is not a purely physics interaction.

The vision of the external world as a whole evolving uniquely and thereby determining unique brain states because they are a part of the whole, may work in some contexts where irreducible uncertainty 1. and effective uncertainty 3. and 4. do not occur. It cannot however work when any of these effects come into play, which certainly happens in the real world. This demonstrates that as a matter of principle, it is the higher level effects—psychological and social variables—that are sometimes calling the tune. But that means they are always effectively doing so in the social context which is the habitat of minds. Causal Closure Real world causal closure is an interlevel affair, with microphysical outcomes determined by features ranging from global warming and tropical cyclones to COVID-19 policy decisions. It simply cannot occur at the microphysics level alone. Some of the effective variables which have changed human history are abstract concepts such as the invention of arithmetic, the concept of money, and the idea of a closed corporation. These have all crucially affected microphysical outcomes, as have abstract theories such as the theory of the laser and the concepts of algorithms, compilers, and the internet. Overall, as stated by (Bishop 2012), the situation is that Whatever necessity the laws of physics carry, it is always conditioned by the context into which the laws come to expression.

Completely new kinds of behaviour emerge in the biological domain. The kind of causation that emerges is simply different than the kind of statistically determinist

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relation between data and outcomes that holds at the microphysical level. The microphysics allows this emergence: it lies within the space of possibilities determined by that physics. In that sense the higher level outcomes lie within the domain of validity of the microphysics. But the microphysics by itself does not determine the macro level outcomes (see the listed points above). Occam’s razor does not work. As Aristotle pointed out (Bodnar 2018), efficient causation, which is what physicists study is only one of the four kinds of causation that occur in the real world (Sect. 8.2.5). In the real world the other kinds of causation play a key role in determining outcomes. All four are needed to determine specific outcomes.

8.7.2 What About Free Will? The implication of Carlo’s argument is that the causal power of microphysics prevents the existence of free will. This touches on a vast and complex debate. My arguments above deny that the underlying physics can disprove existence of free will in a meaningful sense. But that does not dispose of the debate. Does neurobiology/neuroscience deny free will? Incomplete Reductionism: Neurobiology Francis Crick gives a neuroscience based reductionist argument regarding the brain in The astonishing hypothesis (Crick 1994): You, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules.

Now the interesting point is that this a denial of Carlo’s arguments. Crick is assuming that the real level of causation is at the cellular and molecular biology levels: that is where the action is, it is at that level that physical outcomes are determined. The implication is that this is what determines what specific dynamical outcomes take place at the underlying physical level—which is my position (Ellis and Kopel 2019). Free Will and Neurobiology As to free will itself, does neurobiology and neuroscience deny its existence? That is a long and fraught debate related to intentionality and agency. Amongst the deeply considered books that argue for meaningful free will are Donald (2001), Dupré (2001), Murphy and Brown (2007), Murphy et al. (2009), and Baggini (2015). Frith (2013) has a nuanced discussion on agency and free will. Murphy and Brown (2007) conclude (page 305) that “free will should be understood as being the primary cause of one’s own actions; this is a holistic capacity of mature, self-reflective human organisms acting within suitable social

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contexts”. This is essentially the consensus of the authors just named, Libet’s experiments notwithstanding. Chris Frith17 expresses it this way (Frith 2009): I suggest that the physiological basis of free will, the spontaneous and intrinsic selection of one action rather than another, might be identified with mechanisms of top-down control. Top-down control is needed when, rather than responding to the most salient stimulus, we concentrate on the stimuli and actions relevant to the task we have chosen to perform. Topdown control is particularly relevant when we make our own decisions rather than following the instructions of an experimenter. Cognitive neuroscientists have studied top-down control extensively and have demonstrated an important role for dorsolateral prefrontal cortex and anterior cingulate cortex. If we consider the individual in isolation, then these regions are the likely location of will in the brain. However, individuals do not typically operate in isolation. The demonstration of will even in the simplest laboratory task depends upon an implicit agreement between the subject of the experiment and the experimenter. The top of top-down control is not to be found in the individual brain, but in the culture that is the human brain’s environmental niche

This is a good description of both topdown effects in the brain (Ellis 2018) and interlevel causal closure (Ellis 2020b). It is also expressed well by Baggini (2015). At the micro level, it is enabled by stochasticity (Noble and Noble 2020). Free Will Denialists Don’t Really Believe It The physicist Anton Zeilinger told me the following story. He was once being harassed by someone who strongly argued that we do not have free will. Anton eventually in frustration reached out and slapped him in the face. He indignantly shouted, “Why did you do that?”, to which Anton responded “Why do you ask me that question? You have just been explaining to me at length that I am not responsible for my actions. According to you, it’s not a legitimate question.” If you have an academic theory about the nature of causation and free will, it must apply in real life too, not just when you are engaged in academic argumentation. If not, there is no reason whatever for anyone else to take it seriously—for you yourself do not. Free Will and the Possibility of Science The ultimate point is that if we don’t have meaningful free will, in the sense of the possibility of making rational choices between different possible understandings on the basis of coherence and evidence, then science as an enterprise is impossible. You then cannot in a meaningful way be responsible for assessing theories anyone proposes. The theory that free will does not exist causes the demise of any process of scientific investigation that is alleged to lead to that theory. We had better find a better theory—such as those in the books cited above. Denial of Consciousness or Qualia Finally one should note that many pursuing the view that free will does not exist also deny that consciousness and/or qualia exist and play any role in brain function. But neuroscience simply does not know how to solve the hard problem of consciousness (Chalmers 1995). As stated in Tallis (2016), neuroscience helps define the necessary conditions for the existence 17 One

of the topmost cited neuroscientists in the world: he had 203,843 citations on 2020/08/01.

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of human consciousness and behaviour, but not the sufficient conditions. The self-defeating philosophical move of denying that consciousness and/or qualia exist (“what one canot explain does not exist” (Tallis 2016)) does not succeed in explanatory terms: how can you deny something if you have no consciousness? In that case, you do not satisfy the necessary conditions to deny anything: you do not exist in any meaningful sense (Donald 2001). For more on this see also (Gabriel 2017; Dennett and Strawson 2018). Acknowledgments I thank Carlo Rovelli for his patient dialogue with me regarding this issue. It is a pleasant contrast with the arrogant dismissive comments and ad hominem contemptuous personal attacks that are common in some reductionist circles and writings. I thank Karl Friston, Tim Palmer, and Ed Rybicki for helpful comments.

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Part IV

The Debate on Top-Down Causation and Emergence

Chapter 9

Downward Causation Defended James Woodward

Abstract This paper defends the notion of downward causation. I will seek to elucidate this notion, explain why it is a useful way of thinking, and respond to criticisms attacking its intelligibility. My account of downward causation will be in many respects similar to the account recently advanced by Ellis. The overall framework I will adopt is the interventionist treatment of causation I have defended elsewhere: X causes Y when Y changes under a suitable manipulation of (intervention on) X. When X is at a higher “level” than Y this allows for the possibility of downward causation from X to Y. True claims of downward causation must meet certain additional conditions, some of which have already been discussed by Ellis. These include (1) the condition that X must have a homogenous effect on Y in the sense that the effect of X on Y must be the same regardless of how X is “realized” at lower levels. In addition, (2) the most plausible examples of downward causation will involve causes X, that in a sense that I will try to specify, are capable of being manipulated by macro-level interventions that have a coordinated or organized impact on them, as when one manipulates the temperature of a gas by placing it in a heat bath. Three common criticisms of the notion of downward causation that I will consider are: (1) the claim that this involves a whole acting downward on its parts which is an objectionable idea because wholes and parts are not sufficiently distinct to stand in causal relationships, that (2) downward causation commits us to the existence of causal cycles in which X causes Y which in turn causes X and that the asymmetric nature of the causal relation rules out such cycles, and (3) causal exclusion type worries, according to which all of the causal action occurs among “low level” variables, so that upper level variables are deprived of causal efficacy.

Thanks to Jan Voosholz and Max Kistler for helpful comments on an earlier draft. Thanks also to Bob Batterman and Sara Green for helpful discussion and stimulation from several recent papers. J. Woodward () HPS, University of Pittsburgh, Pittsburgh, PA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_9

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In response I will argue that (1*) plausible examples of downward causation in the scientific literature do not involve whole to part causation, (2*) there is nothing wrong with causal cycles, which are common in, for example, biological contexts, (3*) exclusion type worries do not arise within the interventionist framework that I favor.

9.1 Introduction It is an honor and a pleasure to contribute to this festschrift for George Ellis. I first became interested in the topic of downward causation as a result of conversations that I had many years ago with Roger Sperry when I was a postdoc at Caltech. I’ve always thought that there was something right in the basic idea but it has only been recently, partly as a consequence of reading work by Ellis (and others such as Denis Noble) as well as some philosophical criticisms of downward causation that struck me as misguided that I have thought that I might have something to say on this subject. The ideas that follow reflect the influence of Ellis and Noble as well as some recent developments in machine learning and computer science concerning forming macro-variables from more fine-grained realizing micro-variables (e.g. Chalupka et al. 2017).1 I begin, though, with some stage setting and methodological remarks. I’m a philosopher of science with an interest in methodology and in causal reasoning. I approach the issues around downward causation from that perspective, not that of metaphysician. Although I address some metaphysical arguments against the possibility of downward causation, my primary concerns are methodological: my goal is to try to understand what it is about certain systems that inclines a number of scientists to characterize their behavior in terms of downward causation, whether such characterizations are ever correct, and if so, in what circumstances. I thus proceed on the assumption that the metaphysical issues are not the only ones that deserve philosophical attention.2 I also approach this subject from what I have elsewhere described as a functional perspective (Woodward 2014, forthcoming): we should think about causal claims in terms of the goals and functions that we want to such claims to serve—in terms of what we want to do with such claims. The interventionist account of causation I describe below embodies this functionalist picture: the idea is that one important function of causal claims is to describe the results of manipulations or interventions. This leads to the way in which I frame the issues around downwards causation: these have to do roughly with whether interventions on upper- level variables can

1 For

additional relevant work in machine learning and computer science on forming macrovariables from underlying micro-variables see Beckers and Halpern 2019, Rubenstein et al. 2017. 2 Contrary to the anonymous referee for this chapter, who claims that the metaphysical issues are the only ones that “count”. For the role that this rhetorical strategy of dismissal of the non-metaphysical plays in contemporary philosophical discussion, see Woodward (2017)

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systematically change lower-level variables and if so, under what conditions this is possible. As I note in Sect. 9.3, there are many cases, both drawn from various sciences and from common-sense causal thinking that seem to be naturally described in terms of downward causation, understood as described above. I do not claim that such descriptions are correct merely because they seem natural or prima-facie plausible or fit with what various scientists have said about the examples. As I said above, I’m very aware that there are in-principle metaphysical objections (based on causal exclusion arguments, worries about violations of the causal closure of the physical and so on) to the very possibility of downward causation. At the same time, as a philosopher of science, I think that it is very much in order to explore what it is about these examples that has led many to think of them in terms of downward causation. (In other words, I assume that if there are any plausible cases of downward causation, these are the sorts of examples we should be looking at.) This functional orientation leads me to explore such questions as what the use might be of a notion of downward causation, why we might find it fruitful to operate with such a notion, what kind of evidence might persuade us that downward causation is present and so on. Of course if the notion is incoherent for metaphysical reasons, then the fact that we might like to think in terms of downward causation cannot show that that the notion is legitimate. But if the metaphysical objections can be disarmed and if we can provide a coherent account of what downward causation involves, why such a notion is a useful one and what sorts of situations are appropriately described in terms of this notion, this can provide a vindication of the notion. In any event this will be my strategy. Metaphysicians sometimes accuse philosophers of science like me of conflating epistemology/methodology with metaphysics or illegitimately arguing from the former from the latter. They acknowledge that we have methods that may be interpreted as providing evidence for downward causation and that it may be “pragmatically useful” to think in terms of this notion, but insist that this shows nothing about whether downward causation is “real”, ontologically or metaphysically speaking. This line of argument raises issues that I cannot fully address in this paper. I will say, however, that on the functional approach to causation (and to methodology more generally) that I favor, we should not expect methodology/epistemology and metaphysics/ontology (insofar as the latter has to do with what is “really out there”) to come apart in this way. On a functional notion of causation—one that we can use—the causal relations that are out there—must be such that, at least in some range of cases, we can know whether they are present are not. Our account of the methodology/epistemology of causal reasoning should to this extent fit with the worldly structures associated with such relationships. Consider, in this light, someone who holds that what causation “really is”,3 metaphysically speaking, has nothing to do with what is disclosed by controlled experiments (the experiments being “merely of epistemological significance”) so

3 For

more on this theme, see Woodward, forthcoming.

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that even if there if are experiments in which upper-level variables are manipulated with associated changes in lower variables this tells us nothing about whether downward causation is “real”. I can envision two possible defenses for such a claim. The first is simply that the experiments in question don’t really show the presence of downward causation, because when so interpreted they are defective in some way— e.g., they fail to control for confounders which should be controlled for (which is one way of interpreting causal exclusion arguments). I claim that the defender of downward causation has a good response to this sort of objection. (Sect. 9.7). The other possible response is that even if the experiments I interpret as showing downward causation are unimpeachable from the point of view of experimental design, showing that “downward causation is “real” present requires some more – that is, there is some thicker notion of causation (“real causation”) that fails to be present in apparent downward causation cases, even in the presence of experimental results like those described above . Here I would challenge those inclined to this view to explain what this “something more” involves, how to detect when it is present, why it is a useful or appropriate to have a conception of causation that incorporates it, and how this conception excludes downward causation. One would also like an explanation of why experimentation fails to detect causal relations in cases involving relations between upper and lower level variables but (presumably) succeeds in other cases. It is not obvious how such an account might proceed.

9.2 Causation and Intervention in the Presence of Realizing Relations To develop an account of downward causation (or, more generally, causal claims in which the candidate causes are upper-level variables and the effects either lower or upper level) we first need to specify what we mean by “causation”. I adopt the following version of an interventionist or manipulationist account defended in Woodward 2003: (M) Where X and Y are variables, X causes Y iff there are some possible interventions that would change the value of X and if were such intervention to occur, a regular change in the value of Y would occur.4

4A

couple of additional remarks: First, in order to avoid needless verbiage, I will usually describe causal relata as “variables” but of course readers should understand this as shorthand for “whatever in the world corresponds to variables or to variables taking certain values”. Thus causal relata are features like mass and charge that may be possessed by systems in the world. Also, in order to simplify the discussion, I will confine myself to cases in which the causal relationships in which we are interested are deterministic. In my view, nothing fundamental changes when we consider indeterministic causal relations, except that “regular change” needs to be interpreted as something like “regular change in the probability distribution of Y”. Finally, the “regular change” requirement in M, which is imposed in Woodward 2003, pp. 41–2, means simply that there must be some values of X such interventions that set those values are followed by regular or uniform responses in Y. This is fully compatible with there being other values of X for which this is not true. In other

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Woodward 2003 provides a technically precise characterization of “intervention” and similar notions are characterized in Pearl 2000 and Spirtes et al. 2000. However it is important to understand that these characterizations were intended to apply to cases in which only causal relations among variables and not supervenience relations are present. Further clarification is required when we apply the notion of an intervention to cases in which supervenience relations are present—see below. As long as we are restricted to cases in which no supervenience relations are present, we may think of an intervention I on X with respect to Y as causing a change in the value of X that is of such a character that any change in Y, should it occur, occurs only “through” X. Expressed slightly differently, an intervention I on X with respect to Y is an unconfounded change in X—unconfounded in the sense that I does not affect Y via any causal route5 that does not go through X. Manipulations of putative effect variables in well-designed experiments, including those achieved in randomized controlled trials, are paradigm cases of interventions. The intention behind M is to capture the common sense idea that the mark of a causal relationship is that causes are potential “handles” for changing effects; causal relationships are those relationships that can be exploited “in principle” for manipulation and control, in the sense that if manipulating X would be in principle a way of manipulating Y, then X causes Y, and conversely. My conception of downward causation simply applies this interventionist picture to the case in which X is at a “higher level”6 than Y. In such a case when (and only when) Y changes in a regular manner under interventions on X, X is a downward cause of Y. It is worth emphasizing that this is a “thin” notion of causation, both metaphysically and otherwise. For X to cause Y it is not required that there be a continuous process running from X to Y, that X “transmit” energy or “biff” or “umph” to Y (or anything similar). Nor is it required that X and Y are variables that occur in some “fundamental” theory drawn from physics. Readers should thus keep in mind that when I talk about downward causation all that I mean by causation is a relationship that satisfies M (suitably elaborated to apply to cases in which

words the condition in M that there must be “some” (not necessarily all) values of X associated under interventions with changes in Y should be understood as requiring that for those values there should be a uniform response in Y. 5 “Causal route” here is intended to contrast with routes or paths corresponding to supervenience relations. Again, we need a somewhat different account of how interventions behave when supervenience relations are present. 6 The notion of “level” is used in many different and not entirely consistent ways in both science and philosophy. In my view it is doubtful that there is any single characterization of this notion that will fit all these uses. Rather than getting bogged down in trying to provide such a characterization I will rely instead on generally accepted judgments in the scientific literature about particular cases as well as some defeasible criteria. For example, I will assume that variables are often legitimately regarded as at different levels when one is a coarse-graining of the other and that variables used to characterize wholes are often legitimately regarded as at a different level than variables that characterize their parts). For additional discussion, see Woodward 2020.

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supervenience relations are present in the manner applied below)—nothing fancier or richer.7 The conception just described is very close (perhaps identical) to the understanding of downward causation advocated in Ellis (2016). One demonstrates the existence of top-down causation whenever manipulating a higherlevel variable can be shown to reliably change lower-level variables

Although this is the basic idea, as I have said, some additional explication is required to specify how it is to be understood in contexts in which variables at different levels are present. To fix our ideas, let us assume that we have two sets of variables Ui (for upper) and Lj (for lower). Assume that a full specification of the values of the lower-level variables determines the values of the upper-level variables, so that the latter “supervene” on the former. We also assume that different values of the Ljs can “realize” the same value of a U variable, so that “multiple realization” is present. For reasons described in footnote 8 in most cases of this sort the relationship between the Us and the Ls will not be one of identity, either of types or tokens, but will instead amount (in the case in which the Ls are low- level physical variables) to a version of non-reductive physicalism.8 In what follows I will assume that such “realization” takes a very specific form: for each upper level variable Ui there is a many to one surjective9 function that maps a number of different values of the Ljs into each value of Ui. We can think of this function as taking one of two possible forms. One possibility is that a number of different values of the same Li variable are mapped into (realize) a single value of a Ui variable. As a standard example, think of the values of Lj as very high dimensional specifications (profiles) of the possible combinations of kinetic energy that might be assumed by the molecules making up a gas. That is, a single value of Lj specifies a possible kinetic energy for molecule 1, a possible kinetic energy for molecule 2 and so on. A different value of Lj specifies a different n-tuple of kinetic energies for the individual molecules. A given value of the upper level variable Ui (e.g., Ui might be temperature T) then can

7I

stress this point because, as noted earlier, I think that some of the opposition to the idea that there can be downward causation or causation involving upper-level variables depends on the (often tacit) assumption of a richer or thicker notion of causation and the thought that this sort of causation is not present in relations involving upper-level variables. We should separate the question of whether there are downward causal relations that are causal in the sense of M from whether there can be downward causal relations according to some alternative conception of causation. I’m concerned only with the former issue in this essay. 8 A common assumption (which I endorse) is that when the relation between upper and lower-level variables is one of identity there is no particular puzzle about how downward causation and causal relations among upper-level variables are possible: the upper-level variables stand in exactly the same causal relations as the lower-level variables with which they are identical. The issues around downward causation become less trivial when non-identity and multiple realization is assumed 9 We assume that this function is surjective to capture the standard assumption that every value of each of the Uis is realized by some value (typically many values) of the Ljs. For example, any possible value of temperature of a dilute gas is realized by some (typically many) profile(s) of molecular kinetic energies.

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be realized by a very large number of different values of Li. Another possibility is that values of several different lower-level variables are mapped into the same value of an upper-level variable. For example, the upper-level variable total cholesterol (TC) is the sum of the values of two lower-level variables, low density cholesterol (LDL) and high density cholesterol (HDL). Different combinations of values of HDL and LDL can realize the same value of TC. For the purposes that follow, there are no deep differences between these two possibilities and because it will simplify the exposition I will often just talk about the relationship between an upper level variable U and a single realizing variable L, assuming that it is obvious how to generalize this to cases in which the realizers of U are functions from values of several different L variables.10 In any case, the realization relation is understood as an “unbreakable” constraint relation rather than a causal relationship. It is unbreakable in the sense that the relationship cannot be disrupted by any combination of interventions. For example, although one can manipulate the temperature of a dilute gas (and in doing so will also manipulate the average kinetic energy of its component molecules), one cannot through interventions alter the relationship between temperature and average kinetic energy – this is treated as fixed. To anticipate discussion below, when L and U

10 I

acknowledge that the possibility just described it a very simple one – I assume it because it is simple, because it is one way of making “realization” precise, and because it is in many ways one of least friendly assumptions for the possibility of downward causation. (That is, if downward causation makes sense in such contexts, it is plausible that it will also make sense in contexts in which realization relations that cannot be represented in the simple way I have described.) In this connection I want to explicitly note that there are many other sorts of cases in science in which inter-level relations are described (at least by philosophers) by means of words like “realization”, “constitution” and so on which involve more complex relationships between upper and lower-level variables. For an instructive illustration of some of these complexities in the case of neuronal modeling at different levels, see Herz et al. 2006. In such more complex cases, the variables of the upper level theory may not “line up” in any simple or well-behaved way with the variables of the lower level theory, the mathematics employed at different levels may be quite different (ordinary versus partial differential equations versus black box Bayesian models etc.), and as a result the relations between different levels may be mathematically very complex. Moreover, in many cases, a fully adequate characterization of an upper-level variable will involve reference to what looks like upper-level information as well as information about its lower-level realizers. For example, in the illustration above, I neglected the fact that the notion of temperature of a gas, as usually understood, is only well-defined if the gas is at equilibrium, which is an “upper-level” feature of the whole gas. One consequence of this complexity is that a good deal of work is often required to connect information at one level to information at different levels—there may not be anything like the simple functional relations I assume above. I will ignore/abstract away from this in what follows. Finally, let me add that the complexity of the relation between upper and lower level variables is one of several reasons why it is often wrong to take this relationship to be one of identity (and, as claimed above, why some form of non-reductive physicalism seems like a more plausible account of this relationship). An additional consideration is that the most plausible understanding of the notion of identity within the interventionist framework requires a notion of identity between variables and between values of variables. In both cases, a plausible necessary condition is that identical variables (or values) should have the same dimensionality— this of course is violated when there is coarse-graining or dimension reduction of the sort described above.

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stand in a realization relation the nature of this relationship is such that they are not sufficiently “distinct” to stand in a causal relationship. Thus an upper-level variable U does not cause its realizers L11 and similarly L does not cause U. However, U may cause some other variable lower-level L* that it distinct from U’s realizer L. When this is the case, there is downward causation from U to L. Consider an intervention on an upper-level variable U in a context of the sort just described—e.g., the temperature T of a gas in a container is manipulated by placing it in a heat bath. Different interventions each of which sets T to some value t will be realized by different combinations of values of the lower-level molecular variables Kj on different occasions (for that matter, the molecular realization of T will vary from moment to moment for the same gas).12 The experimenter thus controls the value of T via the heat bath (that is why it is appropriate to think of the intervention as an intervention on T) in the sense that the experimenter possesses a procedure that can reliably and repeatedly impose that temperature. However, the experimenter does not control in this sense which particular values of the molecular kinetic energies that realize that value of T – putting the gas in a heat bath is not a procedure that reliably imposes any particular molecular realization of T = t. Instead this realization varies from occasion to occasion or over time in a way that is unknown to the experimenter and effectively random from the point of view of what the experimenter can influence.13

11 As

noted below, some prominent discussions (e.g., Craver and Bechtel 2007) proceed on the assumption that if there is such a thing as downward causation it involves an upper-level variable causing its realizer. I agree that upper-level variables do not cause their realizers but argue (Sect. 9.4) that this is not what downward causation involves. 12 Thus if one wants to represent such an intervention within a directed graph framework, the appropriate way to do this, as suggested in Woodward 2015, is by means of a single intervention I that sets T = t and at the same time “selects” some value from the equivalence class of lower level realizers of T = t. There are not two different interventions, one that sets T = t and distinct from this a separate, independent intervention the intervention that sets the value of the lower level realizer of T = t. It is a also mistake to represent such an intervention as a common cause of both T and the realizing variable or variables Kj, as, for example, Baumgartner 2018 does —that is to represent the intervention as Kj← I → T. It follows from standard assumptions made about causal representation in directed graphs (including, for example, the condition of independent fixability (IF) described below), that such a common cause representation would only be appropriate if it were possible to intervene to carry out independent interventions on T and the Kj, changing each independently of the other. The realization relationship between T and Kj rules out this possibility. This is not a pedantic point because the common cause representation is used by Baumgartner and others to motivate the claim that one needs to control for Kj in assessing the causal effect of T and hence immediately to a causal exclusion argument according to which T is causally inert—again see below. 13 In some cases, including the case of temperature discussed above, it may be reasonable to assume that for each value of the upper level variable, there is a single stable probability distribution over the values of the lower-level realizers of the upper-level variable that applies whenever there is an intervention on the upper-level variable. However, in many other cases, this will not be a plausible assumption and I do not adopt it in what follows. The requirement described below that the realizers of each value of the upper-level variable have a uniform effect on the effect variable of interest amounts to the assumption that such uniformity holds for all probability

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As Ellis suggests, we may think of the values of the variables Kj that realize the same value of T as in the same equivalence class, yielding a partition of the different values of Kj based on this equivalence relation. Of course because of the nature of the realization relationship between T and the Kjs any intervention that changes the value of T, from, say T = t1 to T = t2 must at the same time change the values of the lower-level realizing variables Kj from values that realize T = t1 to different values that realize T = t2—that is, to a different equivalence class. Contrary to the arguments of a number of philosophers (e.g., Baumgartner 2010), we thus do not build into the notion of an intervention the requirement that an intervention on U change the value of U while leaving values of the lower variables Lj that realize that value of U unchanged. Such interventions are impossible (because the realization relation is an unbreakable constraint); adopting such a requirement would have the consequence that interventions on upper-level variables are never possible and would render this notion useless for purposes of understanding upperlevel causation.14 (Recall that M requires that for a variable X to have a causal effect, interventions on X must be possible.) In order to apply M to contexts in which different levels are present, we must also impose the following requirement (called realization independence in Woodward 2008): when values of U are realized by a number of different values of Ls, an intervention on U with respect to some second variable Y that sets U = u must have a uniform (or approximately uniform) effect on Y for all lower level realizations of the value U = u. In other words, an intervention that sets U = u, must result in the same response for Y (Y = y), regardless of how U = u is realized at the lower level.15

distributions over the values of the realizing variables. However, there are various ways of relaxing this requirement, one of which is simply to require that uniformity hold only for all “reasonable” probability distributions, where “reasonable” might mean, e.g., “absolutely continuous with respect to the Lebesgue measure.” Other possibilities for relaxing the uniformity requirement are described below. 14 More technically, in contexts in which a realization relation between U and L (or some set of Ls) is present, the requirement in Woodward 2003 that an intervention I on U with respect to a second variable Y not affect Y via variables on paths that do not go through U (“off path variables”) should be understood in such a way that the variable L which realizes U is not treated as such an “off-path” variable. This corresponds to the idea that Ls should not be treated as potential confounders for the U→ Y relationship which we have to “control for” to see the effect of U on Y. Some additional justification for this (which seems to me a common sense requirement) is provided in Woodward 2015 and also below (Sect. 9.7). 15 As several writers note (e.g. Butterfield 2012, Rubenstein et al. 2017, we can think of this uniformity requirement as amounting to a kind of coherence or consistency requirement between the causal relations involving upper and lower-level variables. Given some natural additional assumptions (described in Rubenstein, et al. 2017), it is equivalent to the following “commutivity” requirement: Suppose F describes the lower-level functional relationship between L1 and L2, g1 describes the realizing relation that maps L1 to U1, g2 the realizing relation between L2 and U2 and H describes the upper-level causal relation between U1 and U2. Then for U1 to cause U2 and for consistency across levels, the result of beginning with some value of L1, applying F to it to yield L2 and then coarse graining L2 via g2 to yield some value for U2 = u2 should be the same

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Here again Ellis imposes a closely related requirement: “the same top level state must lead to the same top level outcome, independent of which lower level state instantiates the higher level state”. (2016, 121). The effect of this requirement of realization independence is to exclude so called “ambiguous manipulations” (Spirtes and Scheines 2004) in which the result of setting U = u on some second variable Y depends on how U = u is realized. To illustrate, suppose that the lower level variables are HDL and LDL (as discussed above) with HDL having a favorable effect on heart health and LDL an unfavorable effect. The upper-level variable TC (total cholesterol) which is the arithmetic sum of HDL and LDL will fail the realization independence requirement with respect to heart health since the impact of TC = tc on heart health will depend upon the particular combination of values of HDL and LDL that realize TC = tc. One way of motivating this requirement is to note that it is needed for the effect on Y of an intervention on U to be well-defined: this requires, as Ellis, says, that there be a “regular” or “same” response of Y to the intervention on U. This implies that to the extent that we are interested in effects on heart health, TC is not a “good” upperlevel variable—not a good candidate for an upper-level cause. It should be replaced by variables that have unambiguous (or at least less ambiguous) effects on heart health. Note that the requirement of realization independence, like the notion of an intervention itself is always defined relative to a candidate effect variable. It common for an intervention on U that satisfies the realization independence with respect to Y to fail to satisfy this requirement with respect to some distinct variable Y*. The conditions described are, I believe, necessary for downward causation but I do not claim they are jointly sufficient.16 However, I believe it is plausible that

as beginning with the same value of L1, coarsening it via g1 to yield a value of U1, and applying H to U1—this should yield the same value of U2 = u2 as before. 16 Why might one think that the conditions described above are not sufficient? My doubts arise from the following consideration. It looks as though an upper level variables U1 might meet those conditions and yet be (at least from our perspective) highly gerry-mandered, non- compactly distributed and difficult to recognize, measure or manipulate. Consider tosses of a fair coin. We might form the equivalence class of all those initial conditions of the coin and the tossing apparatus that lead to heads – take all these to have the value h– and the equivalence class of those conditions leading to tails (these have the value t). We might then form the upper level variable C which takes the values h and t. By construction the values of C have a uniform effect on the final position of the coin. But whether or not C is an “in principle” legitimate upper -level variable or candidate cause, it is certainly not a useful variable, assuming that we have no way of telling, apart from the final position of the coin, which value of C is realized in any particular toss, no way of manipulating C and so on. A natural thought which is suggested in passing by Ellis, is that at least in many cases in which we find it natural to talk of upper level or top-down causation, we expect some additional condition to be satisfied that excludes cases of the sort just described: we want the candidate upperlevel variable to correspond to something we can measure with relatively macroscopic (upper-level) measurement procedures and manipulate by means of macroscopic interventions, where we require such interventions to have coordinated or orderly effects on lower-level variables. This expectation is fairly well satisfied in connection with thermodynamic variables—we have straightforward procedures for measuring and manipulating these – e.g., by putting the gas in a heat bath or by

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whatever additional conditions may be required for sufficiency are satisfied for the examples of downward causation I will discuss below—or so I will assume. Finally, there are two other conditions on causation in general (and not just downward causation) that will play a role in my discussion. The first is the requirement that the relata that figure in causal relations must be variables (which, I remind the reader, is my shorthand for what in the world is represented by variables). This is also a requirement that Elllis imposes, as reflected in the passages quoted above. Variables represent quantities or magnitudes (e.g., mass, charge, income) or, as a limiting case, whether some property is present or absent (represented by a binary variable taking the values 1 and 0.) As this suggests, one mark of a variable is that must be capable of taking at least two distinct values. This requirement might seem trivial but as we shall see, neglect of it (or failure to specify just what the relevant variables are) undermines some well - known criticisms of downward causation. A second generally accepted requirement on causation is that variables standing in causal relationships must be “distinct”—the intent here is to rule out cases in which variables stand in logical, conceptual or state-space relationships that exclude causation. For example (Lewis 2000), although whether or not I say “hello loudly” depends in some sense on whether or not I say “hello”, this dependence is not causal dependence. I will provide a characterization of the kind of distinctness that is necessary for causation below—condition IF, Sect. 9.5. The relevance of this consideration to our discussion is that critics of downward causation frequently claim that this involves wholes acting downward on their parts and that wholes and parts are not sufficiently distinct to stand in causal relationships. (See e. g. Craver and Bechtel 2007) I agree that at least in many cases wholes and their parts are not sufficiently distinct to stand in causal relationships but, as argued below, in other respects this criticism misfires. Scientifically plausible examples of downward causation do not involve wholes acting on parts but rather involve variables (as all causal relations do) and these need not stand in part/whole relationships, even when entities of which they are predicated do.

9.3 Some Examples Recent papers and books by Ellis and co-authors and by others such as Denis Noble provide many prima-facie plausible examples of downward causation. (See also

compressing it with a piston. When we do this we think of ourselves as imposing a co-ordinated change in the behavior of the constituents of the gas. This goes along with the more general thought that talk of upper-level causation seems most appropriate when there is a kind of order or coordination or coherence in the behavior of the lower-level constituents that realize the upper-level variables, with the loss of such order corresponding to cases in which causation resides more exclusively at lower levels, as the example involving energy cascades in Sect. 9.3 illustrates. There are connections here with the distinction between work and heat.

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Clark and Lancaster 2017.) Here are a few such examples, with some additions of my own. (Again, in saying that these are “prima-facie plausible” examples I do not mean that I’m going to simply assume that these are genuine cases of downward causation. Rather, following the methodology outlined earlier, these are the kinds of cases that count as downward causation if any cases do and hence the kinds of cases on which we need to focus.) 3.1) The use of mean field theories in which the combined action of many atoms on a single atom is represented by means of an effective potential V rather than by means of a representation of each individual atom and their interaction. Intuitively, V is a higher level than the atom on which it acts. (Ellis 2016, Clark and Lancaster 2017). 3.2) The influence of environmental variables including social relations between animals on gene expression as when manipulating the position of a monkey within a status hierarchy changes gene expression which controls serotonin levels within individual monkeys. Here position within a social hierarchy is thought of (perhaps on the basis of compositional considerations) at a higher level than gene expression. 3.3) A red hot sword is plunged into cold water and this alters the meso -level structure of the steel in the sword— cracks, dislocations, and grains that it contains. The treatment of the sword—heating and cooling—is at a higher level than these mesoscopic changes17 and the former downward causes the latter. (Example due to Bob Batterman.) 3.4) Energy cascades. When a fluid is stirred in such a way that it exhibits largescale turbulent motion this motion is gradually transferred to motion at smaller scales– from large scale eddies to much smaller scale eddies. The large-scale motion may be on the scale of many meters, the small-scale motions on the scale of a millimeter where they are eventually dissipated as heat. Viscosity related effects dominate at this smaller scale but are less important at larger scales. The stirring is an upper-level cause of the subsequent behavior of the fluid. (Example due to Mark Wilson.) 3.5) According to the Hodgkin- Huxley (HH) model, a neuron generating an action potential may be represented by a circuit in parallel, in which there is a potential difference V across the neuronal membrane which functions as a capacitor. Embedded in the membrane are various sodium and potassium ion channels with time and voltage dependent conductances gNa , gK which influence ionic currents through the membrane. V causally influences these conductances and currents which seem intuitively at a lower level than V. (Example discussed by Denis Noble 2006.)

17 The

heating and cooling affect the whole sword, not just components of it.

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In each of these cases the conditions for an intervention on the upper-level variable seem to be satisfied.18 First, the manipulations of the upper-level variables are not confounded by other variables that might affect the dependent variable independently of the intervention in a way that undermines the reliability of causal inferences. (Some writers – e.g., Baumgartner, 2010—hold that all manipulations of upper-level variables are “confounded” by their lower level realizers but this is a tendentious and unmotivated notion of confounding—see Sect. 9.7.) Second, the upper-level variables are multiply realized but it is plausible that their effects on the dependent variables are realization independent in the sense described in Sect. 9.2. For example, there are a variety of different ways of intervening on the mean field to set it to a particular value (with these corresponding to different arrangements of the many atoms making up this field) but as long as the value of the mean field is the same, the effect on the individual atom will be the same. In the case of 3.5, interventions on the membrane potential can be carried out by means of a voltage clamp (the device actually employed by Hodgkin and Huxley in carrying out their original experiment) which exogenously imposes a stable potential difference across the membrane. A particular value for this potential difference can be realized at a lower level by various combinations of charge carrying individual atoms and molecules in the membrane but to the extent that the HH model is empirically correct, these different realizations will have the same uniform impact on lowerlevel variables such as the channel conductances. Although examples of the sort just described appear to be prima-facie plausible examples of downward causation, a number of scientists and philosophers have advanced objections to this concept. In the next several Sects. 9.4, 9.5, 9.6 and 9.7 I review and respond to several of these objections.

9.4 Wholes and Parts A very common criticism of the idea of downward causation is that this requires that “wholes” act downward on their “parts” and that the relation between a whole and its parts cannot be a causal relation of any kind. Two reasons (e.g., Craver and Bechtel 2007) cited in support of this last claim are that (i) wholes and parts are not sufficiently distinct to stand in causal relations and (ii) the relation between wholes and parts is “synchronous” while causal relationships are always “diachronic”, where this is understood as meaning that effects must occur temporally after their causes. For example, Craver and Bechtel 2007 consider, as a putative example of 18 Recall

that according to M for causal claims to be true the interventionist account does not require that interventions actually occur but rather the truth of the appropriate counterfactuals describing what would happen if interventions were to occur. However, in the examples described above, interventions are actually carried out to demonstrate downward causation—for example, position of a monkey within a status hierarchy is manipulated and the effect on its serotonin level observed.

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top-down causation, the claim that the overall process of visual signal transduction (from light falling on the retina to visual object recognition) causes changes in the components or parts of the transduction process such as rod depolarization—i.e., that this whole temporally extended process causes the occurrence of its temporal components. They object that because rod depolarization is part of the overall transduction process, the latter cannot cause the former. More generally, they think of claims of downward causation as claims that the overall state or activity of a mechanism has instantaneous or synchronic causal effects on components of the mechanism—a notion that they find objectionable. A basic problem with this line of argument is that plausible cases of downward causation, including the examples described in Sect. 9.3, do not take this whole to part form. One reason for this is that parts and wholes are (at least on the most natural interpretation of these notions) things or thing-like (where included in the latter category are temporally extended processes or, as some philosophers call them, “activities”). By contrast, as emphasized above, causal claims relate variables and at least in many cases these variables do not stand in part/ whole or containment or constitutive relationships. This is so even if it is true that the things of which these variables are predicated stand in part/whole relationships. For example, in the case of the HH model, the putative top-down cause is not the whole process of the generation of the action potential. Rather the top-down cause is changes in the membrane potential V, a variable (more pedantically a magnitude represented by a variable), and among its effects are changes in the voltage-gated channel conductances, represented by the variables gna , gk . The ion channels, the conductances of which are described by gna , gk are indeed parts of neuronal membrane but it does not follow (indeed it is unclear what it would mean to say) that the conductances are themselves parts of the membrane potential difference.19 More importantly, even if we think that there is a way of making sense of this parthood claim, it does not follow, for reasons described below, that the membrane potential

19 Craver

(2007) does provide a test for whether some activity or behavior is a “part” of another. This appeals to what Craver calls mutual manipulability (MM): when X and S are related as part and whole and F is an behavior of X and J a behavior of S, then F is a constituent or part of J iff (i) there is an intervention on X’s F-ing with respect to S’s J-ing that changes S’s J-ing; (ii) there is intervention on S’s J-ing with respect to X’s F-ing that changes X’s F-ing (Craver 2007, p. 153). This is a test for whether activities/ behaviors rather than variables are parts of others, but putting this aside, MM is inadequate because it fails to distinguish genuine parthood relations from cyclic causal relations. For example if having a certain potential is a behavior then both (i) and (ii) are satisfied with respect to the relations between the potential and the behavior of the channel conductances gna , gk . However, both the V to gna , gk relation and the gna , gk to V relations are causal rather than whole/part relations. (See Sect. 9.6 for remarks defending the claim that causal relations can be cyclic.) As argued in Sect. 9.5, the feature of a part/whole relation that precludes causation is a failure of independent fixability. This is present in Lewis example of the relation between saying “hello” and saying hello “loudly” but not in the case of the relation between V and gna , gk .

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and conductances fail to be distinct in a way that precludes their standing in a causal relationship. Similarly, when a heated sword is plunged into cold water, it is true that the mesostructures affected are parts of the sword, but the relevant causal claim is not that the sword or its overall state causes these meso- structures to change instantaneously or that the temporally extended process consisting of plunging the sword followed by lower-level structural changes causes the temporal part consisting of the latter changes. Instead, the top-down cause in this case is the act of plunging the hot sword into the cold water which might be represented by a binary variable P which takes the values 1 or 0 depending on whether the sword is or is not plunged. Again, the meso-structure of the sword is not plausibly regarded as “part” of the variable P. Similarly, monkey 1 is (let us suppose) a “part” of the monkey band, and monkey 1’s serotonin level is part of monkey 1 but the putative top down cause (and what is experimentally manipulated) is the hierarchical structure of the band and the putative effect (monkey 1’s serotonin level) is not (at least in any obvious sense) part of that. These distinctions (between things or processes which have parts and variables which at least in the cases under discussion do not stand in part/whole relations) would not matter if whenever P is a part of whole W, variables predicated of P and W fail to be distinct in a way (or have some other property) that precludes their standing in causal relationships. However, as I shall now argue, this is not the case: as the examples in 3.5 illustrate, even if P is a part of W, it does not follow that variables predicated of P and W cannot stand in causal relationships.

9.5 Independent Fixability The following condition is commonly assumed, often only implicitly, in the causal modeling literature for when variables are sufficiently distinct to stand in causal relationships. I call it IF (for Independent Fixability) since it embodies the idea that variables are distinct if all of their values are independently fixable via interventions: (IF) Variables in set S are distinct in a way that permits their standing in causal relationships if and only it is “possible” to intervene on each variable independently, holding it fixed at each of its possible values (for the units or systems those values characterize) while intervening to hold the other variables to each of their other possible values. In other words, all possible combinations of values of different variables in the set must be “compossible”.20 Here “possible” includes settings of values of variables that are possible in terms of the assumed logical, mathematical, or semantic relations among the variables as well as certain structural or space-state relationships.

20 On

the other hand, different values of the same variable are not compossible for the same object or system, in the sense that such different values cannot hold for the same object —e.g., the same object cannot have a mass of both 5 and 10 kg. Of course different objects can have different masses, and the velocity of any object can be set independently of its mass.

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As an illustration, consider an example from Lewis (1986) concerning of the relationship between N’s saying “hello” and saying “hello” loudly. Let H be a variable that takes the values 0 or 1 depending on whether or not N says “hello”. Let L be a variable that takes values 0, 1 or 2 depending on whether N does not say “hello”, says “hello” but not loudly, or says “hello” loudly. Then certain combinations of these variables such as H = 0 (N does not say “hello”) and L = 2 are impossible for conceptual reasons and IF is violated. Thus, as Lewis claims, the relationship between H and L is not a causal relationship. As another illustration, the variables in {HDL, LDL and TC} are conceptually connected and fail the independent fixability condition: Given, e.g., values for HDL and LDL, there are values for TC that are ruled out for mathematical or conceptual reasons, since TC is defined as the sum of HDL and LDL. This is reflected in the fact that it would be misguided to claim that HDL and LDL cause TC For similar reasons, IF is violated for upper and lower level variables that stand in realization relations—a variable (with n-tuples as values) representing the kinetic energies of all of the individual molecules in a gas cannot cause its temperature (or conversely.) Fortunately to apply IF to the putative examples of downward causation in 3.5, we do not need to make problematic judgments about logical or conceptual possibility. In each case, the possibility of independent fixability is shown by the fact that experiments have actually been performed (or might readily be performed) that set the values of the variables claimed to be causally related independently of each other. For example, in the experiments which provided the basis for the HH model, the newly invented voltage clamp allowed the experimenters to set the value of V exogenously in a way that was independent of the channel conductances. Similarly, the channel conductances can be manipulated independently of V by molecular agents. In the case of 3.2, the status position of a monkey can be changed by placing him in a new band and observing whether there are changes in his serotonin level. Also the serotonin level of the monkey can be manipulated independently by pharmacological means. These possible experiments reflect the fact that the variables in the relationships 3.1–3.5 do not seem to be logically or conceptually connected in a way that precludes their standing in causal relationships. Another concern expressed by Craver and Bechtel 2007, as well as other writers, is that putative relationships of downward causation are synchronic while legitimate causal relations are diachronic, with the cause temporally preceding the effect. Again this concern seems to derive from the mistaken assumption that downward causal relationships are whole to part relationships, where these are understood as obtaining instantaneously or at single moment. In fact the general claim causes must always temporally precede their effects is far from obviously correct but it is not necessary to argue for this here, since the examples 3.1–3.5 all seem to involve diachronic causation, although this fact may not be represented in the way those relationships are modeled or described. For example, as an empirical matter, there is presumably a very short temporal delay between the momentary value of the membrane potential or its time derivative and the response of the ion channels, although this fact is not represented in the HH model, since it does not matter to the effects that the model is intended to explain. Similarly the response of the

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monkey’s serotonin levels to a change in status presumably also does not occur instantaneously but rather takes time. If, like Craver and Bechtel, one understands part/whole relationships as those that obtain at a given instant, such relations are indeed “synchronous” but this is just further reason to think that examples involving such relations are very different from the relationships described in 3.1–3.5 and not plausible candidates for causal relations of any kind.21

9.6 Cycles Another concern about downward causation that appears in Craver and Bechtel 2007 is this: it appears that countenancing downward causation in a system leads, in many cases, to countenancing causal cycles in that system, in the sense that at some level of representation we have X causing Y which in turn causes X (perhaps via some intermediate variables). Craver and Bechtel claim that such cycles are problematic— because (among other considerations) they are inconsistent with the “asymmetry” of casual relationships.22 The claim that in a number of cases23 systems in which downward causation is present will also be systems in which cycles are present seems correct. For example, as we have noted, in the case of the HH model, the membrane potential causally influences the channel conductances but it is also the case that those conductances, by influencing ion flow, in turn influence the membrane potential. Similarly, although status position influences serotonin levels, it is also the case that serotonin levels influence status, as is shown when the former is exogenously manipulated.

21 It

is worth noting that the examples Craver and Bechtel discuss appear to be ones they have made up—they don’t cite anyone in the scientific literature who treats their examples as cases of downward causation. 22 An anonymous referee suggests this may be a misunderstanding on my part since in subsequent papers (e.g. 2017) Bechtel does discuss causal cycles. But in their (2007) Craver and Bechtel are unambiguous that they think that downward causation as they conceive it is problematic because it seems to involve causal cycles: . . . the possibility of bottom-up and top-down influence ‘propagated’ simultaneously across levels results in problematic causal circles. For example, one might believe that if an object, X, has its causal powers in virtue of possessing a property, P, then if X is to exercise its powers at time t, X must possess P at t. And one might believe further that if something causes X to acquire P at t, then X does not already possess P at t until that something has acted. If X’s acquiring P at t is a cause of S’s having w at t, and S’s having w at t is a cause of X’s having P at t, then it appears that X’s acquiring P at t cannot cause S to have w until S’s having w causes X to acquire P. In that case, it is little wonder that talk of interlevel causation strikes us as mysterious. (552-3). I will not speculate about how to reconcile these remarks with Bechtel’s later remarks regarding causal cycles in mechanisms. 23 This is not true for all examples involving downward causation as shown by 3.3 and 3.5.

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Causal representations involving cycles raise a number of subtle interpretive issues that I lack the space (and competence) to address. However let me make the following brief points: 6.1. The presence of causal cycles is a real feature of many biological systems and for obvious reasons—such cycles are an unavoidable part of feedback and control mechanisms that are ubiquitous in such systems and are necessary for restoring systems to an equilibrium from which they may have departed, avoiding runaway behavior etc. Cycles are also a common feature of many social and economic systems. We don’t want conditions on causation that have the consequence that such cycles are impossible. 6.2. One possible strategy for avoiding cycles is to distinguish variables by assigning them different temporal indices: the membrane potential at time t (Vt ) causally influences the conductances at time t+ d, which in turn influence the membrane potential at time t + 2d represented by a distinct variable (V t+ 2d ) and so on. I will not pursue the question of whether this strategy is always appropriate but it is one way of replacing cycles with non-cyclic systems. 6.3. Representations involving causal cycles (that is, that do not employ the indexing strategy described under 6.2) are common in the causal modeling literature (these are so- called non-recursive models) and in disciplines like economics. It is not obvious that there is anything incoherent (or inconsistent with the “nature” of causation) in the use of such models, even if we think that underlying them at some finer-grained level of analysis is an acyclic model. In thinking about representations with cycles, we should distinguish the issue of whether they postulate relations that have a “direction” from whether causal cycles are possible; directionality is arguably a feature of any causal relationship, in the sense that we haven’t specified the relationship until we have specified a direction and that X➔ Y is a different relation from Y➔ X. However, this does not preclude cycles. In a causal graph in which X ➔Y and Y➔ X appears, the graph is directed (rather than undirected, as would be the case if we had instead written X–Y) reflecting the fact that there is a causal relation is from X to Y as well as from Y to X but a cycle is present. In other words, we need to distinguish directedness from acyclicity: there can be directed cyclic graphs as well as directed acyclic graphs. A simple interpretation for such a directed cyclic graph (which will fit some applications but perhaps not all) is this: There is an intervention on X that will change Y and an intervention on Y that will change X. This seems to fit the examples in Sect. 9.3 in which there are apparent causal cycles—intervening on status changes serotonin levels and intervening on serotonin levels changes status and so on. There does not seem to be anything incoherent about such an interpretation.

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9.7 Causal Exclusion Another objection to the notion of downward causation appeals to causal exclusion arguments. Suppose, as before, that U1 and U2 are upper-level variables and L1 and L2 are lower-level variables with L1 realizing U1 and L2 realizing U2. L1 causes L2. An iconic diagram due to Kim (e.g., 2005), represents these realization relations by means of a thick vertical arrow and the causal relation by means of a thin horizontal arrow: The question is then whether there can be (whether it makes sense to suppose that there are) other causal relationships in this structure; for example, between U1 and U2 or between U1 and L1 (the latter being a case of “downward causation”). According to the causal exclusion argument the answer to this question is “no” and thus downward causation (as well as upper- level causation from U1 to U2) is impossible. A number of different but closely related arguments are invoked in support of this conclusion. Here is one: (i) Assume for simplicity that the lowerlevel causal relation is deterministic. Because of the realization relation, a change in the value of U1 must involve a change in the value of L1. Suppose that under this change there is an accompanying change in the value of L2. (If there are no changes in the value of L2 that accompanies changes in the value of U1/L1, then U1 doesn’t cause L2 and it also does not cause U2.) This change in the value of L2 under a change in L1 shows that L1 causes L2. Moreover (according to this version of the exclusion argument) this change in L2 is” entirely due” to the change in L1, so that there is no “causal work left over for U1 to do” when it comes to L2 (or U2). In other words, U1 appears to be causally inert with respect to L2 once the role of L1 is taken into account. A related argument (ii) claims that countenancing downward causation from U1 to L2 commits us to an implausible and unnecessary claim about causal overdetermination: if downward causation was present we would have both U1 and L1 causing L2. Not only does this seem “counterintuitive” according to critics, postulating such overdetermination seems unnecessary, since as we have seen, any effect on L2 seems to be fully accounted for by L1 alone—postulating a causal influence from U1 to L2 is (it is claimed) superfluous or redundant. Finally, (iii) suppose we want to determine whether U1 has a causal impact on L2. To do this, we must, according to advocates of the exclusion argument, “control for” the causal influence of other causes of L2 besides U1—it is only if U1 influences L2 holding fixed (that is conditioning on) or accounting for the influence of these other causes, that we can conclude that U1 causes L2. But among the “other causes” of L2 is L1 and once we control for the influence of L1 on L2, we see that U1 has no further or additional effect on L2 – indeed, given the value of L1, any further variation in U1 (which might be responsible for any additional effect of U1) is impossible (cf. Baumgartner 2010). I have discussed these arguments elsewhere (e.g., Woodward 2015). Here I will be brief: on my view, they rest on misunderstandings about how to think about causal relationships when non-causal determination relationships (like the

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realization relation between L1 and U1) are also present. Let me begin with version (iii) of the exclusion argument, since the mistake here is perhaps most obvious. Suppose that we have a structure S* (Fig. 9.2, with the thin arrows representing causal relations) in which, in contrast to the structure S in Fig. 9.1, L1 causes (and thus does not realize) U1 and in addition L1 causes L2 which causes U2. In this case U1 and L2 will be correlated as will U1 and U2. In cases of this sort in determining whether U1 causes L2 (or U2), it is indeed entirely appropriate to control for the influence of L1 on L2: U1 causes L2 only if, taking into account the influence of L1 on L2, U1 has an additional independent effect on L2. If the correct structure is what is represented in the diagram, when one controls for L1, U1 will not be correlated with L2 or U2, showing the absence of a causal connection. The basic mistake made by defenders of the exclusion argument is to suppose that we are entitled to reason in the same way when the causal relationship between L1 and U1 in Fig. 9.2 is replaced with a non-causal determination relation like realization as in Fig. 9.1, so that the same test for whether U1 causally influences L2 is appropriate in both cases. In fact the two situations, S and S* are fundamentally disanalogous. For one thing, in situation S* the relevant counterfactual has a possibly true antecedent, indeed one that may be experimentally realizable: one holds fixed the value of L1, manipulates U1 independently (it follows from IF that this will be possible in principle if the relationship between L1 and U1 is causal or correlational, as in S*, and not one of non-causal dependence) and then sees whether there is any uniform change in the value of L2—this is the appropriate criterion for whether U1 has a causal influence on L2. (Parallel remarks apply to whether U1 causes U2.) If it turns out that there is no regular association between U1 and L2 in this circumstance, this does indeed allow one to conclude that U1 is causally inert with respect to L2. But in situation S the corresponding counterfactual has, by hypothesis, an “impossible” antecedent: because of the nature of the realization relation, it is impossible to hold fixed the value of L1 while performing interventions that change the value of U1 and seeing what changes may be associated with these. This is an indication that the use of this counterfactual is the wrong test or criterion for whether U1 has a causal influence on L2. Put differently, in situation S* the conclusion that U1 is causally inert follows if it is possible to vary U1 while P1 is fixed and there is no corresponding change in L2. In situation S, the claim of the exclusion argument is, in effect, that the causal inertness of U1 with respect to L2

Fig. 9.1 Structure S

U1

U2

L1

L2

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U1

U2

L1

L2

Fig. 9.2 Causal Structure S*

follows from the impossibility of varying U1 while L1 is held fixed.24 This relies on a condition for causal inertness that is completely different from the condition employed in connection with S*: a condition that is not supported by (is not a reasonable extension of) ordinary considerations about what it is appropriate to control for when only ordinary causal relationships and no relations of non-causal determination are present.25 Note also that the characterization of interventions on upper-level variables when they have lower- level realizers in Sect. 9.2 avoids the problem just described concerning inappropriate control because according to that characterization an intervention that changes an upper-level variable at the same time is accompanied by some change in the lower-level realizer of that variable. That is, when we intervene on U1 the upshot of that very intervention is also some change in L1 that, whatever it may be, is consistent with the change in U1. This ensures that, assuming U1 has a uniform or realization independent effect on some second variable Y (upper or lower level), this must be consistent with any change in Y due to the change in L1. In other words when we intervene on U1 we just let L1 change in whatever way it does consistent with the intervention and this gives us the effect if any on Y. Another, related way of bringing out why it is inappropriate to control for L1 in assessing whether U1 causes L1 or U2 in cases in which L1 and L2 are realizers of L1 and L2 appeals to the underlying rationale for such control – what we are trying to accomplish when we control for potential confounders. Suppose, to take a concrete example, that we are interested in whether administration A of a drug X causes recovery R from an illness. To answer this question it is not enough to observe whether there is a correlation between A and R. It might be the case that the drug was preferentially given to those with very strong immune systems (S) and that this has an effect on recovery that is independent of the drug. To show that A 24 Recall

that the interventionist condition for causation (M) requires that there exist possible interventions on X such that . . . .. Thus cases involving impossible interventions correspond to false causal claims. 25 Another way of putting this point is that a graph like that in Figure 9.1, in which realization relations are represented, is not a causal graph (that is a graph in which all arrows represent causal relationships) in the sense in which such graphs are understood in, e.g., Pearl 2000, Spirtes et al. 2000 and Woodward 2003. Instead it is a “mixed” graph in which both causal relations and non-causal (e.g. supervenience relations) are present. Such mixed graphs require different rules for characterizing the effects of interventions and what needs to be controlled for in order to “see” causal relationships.

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causes R, we need to rule out such possibilities. We can do so either by means of a randomized controlled experiment in which the possible confounding influence of S is eliminated by the experimental design or, if the study is observational, by measuring S and conditionalizing on (controlling for) it. One obvious motivation for doing this is that if the correlation between A and R is entirely due to S, then when we give the drug to those without strong immune systems this correlation will disappear. Thus we will be misled if we attempt to use the drug to promote recovery in a population with this different value of S. Note that this is a real worry because it is entirely possible to give someone the drug without that person having a strong immune system. Call the randomized experiment described above experiment one and suppose that when we do it we do get convincing evidence that A causes R. Now contrast this with the following possibility which I will call scenario two. Professor Exclusion observes that drug X has microstructure Q and objects to experiment one on the following grounds: in assessing the possible causal influence of A, the experimenters failed to control for Q which is also a cause of recovery (or at least of whatever microlevel facts “underlie” recovery.) Professor Exclusion argues that it is plausible that A has no causal influence on R “over and above” the influence of Q, and concludes from this that A does not cause R. I think it is obvious that Professor Exclusion’s worry is completely different from the worry that S might be a confounding influence that is addressed in experiment one. First, unlike experiment one that addresses the possible confounding role of S, there is no possible experiment that consists of controlling for Q while varying A. Second, as noted above if the association between A and R in experiment one is entirely due to S, then that association will disappear when the drug is given to those with weak immune systems—that is, when there is a change in the value of the confounding variable S. In contrast nothing like this is possible under scenario two. The relationship between drug X and its microstructure Q is unbreakable— you don’t have to worry that, you might be in a situation in which although you administer X, its alleged confounder Q is absent. In other words the kind of concern about the consequences of confounding which is addressed in the first experiment just isn’t a concern in the second scenario. This suggests in turn that there is no obvious motivation for treating Q as a potential confounder that needs to be controlled for. To be sure, from Professor Exclusion’s perspective when you fail to conclude that A is causally inert you make a mistake, but the point is that this alleged mistake has no further consequences you should care about—it doesn’t imply that you will be mistaken about which relationships support manipulation and control, what will happen when you manipulate A and so on. On the contrary, from a functionalist perspective you make a mistake when you control for Q since this mistakenly leads you to conclude that A does not cause R, hence that manipulating A is not a way of changing R, when, supposing that interventions are understood along the lines described above, there is a manipulation-supporting relationship between A and R. To this we may add the following consideration: in the argument immediately above I focused on the use of an exclusion argument to criticize downward

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causation. But of course if the considerations in the various versions of the exclusion argument are cogent at all, they appear to apply not just to downward causation claims but to all claims that attribute causal efficacy to upper-level variables as long as these variables are not identical with lower level variables– that is, all claims according to which upper level causes cause upper-level effects (at the same level) turn out to be false to be false as well, under the assumption of nonreductive physicalism. Needless to say, the conclusion that there is no causation at all involving upper-level variables is a difficult one to swallow—it is reasonable to suspect that something may be wrong with premises that lead to this conclusion, which is what I have suggested.26 What about the overdetermination argument? Again this seems to trade on a misleading analogy (or assumption of similarity between) ordinary cases of overdetermination in which the variables involved do not stand in any non-causal determination relations) and a (very different) kind of “overdetermination” which may occur when such non-causal determination relations are present. Consider an ordinary case of overdetermination in which two riflemen both simultaneous shoot (S1, S2) a victim through the heart with each shot being causally sufficient for death (D). In such a case we may assume that the following counterfactuals are true27 : 7.1. If S1 had not occurred but S2 had occurred, D would have occurred 7.2. If S2 had not occurred but S1 had occurred, D would have occurred These counterfactuals capture an important part of what makes this an ordinary case of overdetermination. Note that the antecedents of both counterfactuals are possible—one of the riflemen might have decided not to shoot while the other does. By contrast consider a case like that in Fig. 9.1 in which U1 = u11 is realized by L1 = l11 and we are interested in how U1 and L1 relate causally to L2 which we assume takes value l22. In this second case, the counterfactuals that correspond to (7.1–7.2) are: 7.3. If U1= u11 and L1 = l11, then L2= l22 7.4. If U1 = u11 and L1 = l11, then L2= l22.

26 Put

slightly differently, the defender of the exclusion argument seems to claim that built into our notion of causation is a requirement to control for lower-level realizing variables (or at least that we ought to adopt a notion of causation that has this feature). This in turn has the consequence that, under the assumption of non- reductive physicalism, upper-level variables are always causally inert, thus depriving the notion of causation of much of its usefulness since it follows that there are no true upper-level claims, completely independently of any empirical investigation. An obvious question is why we would have developed (and continue to use) a notion of causation with this perverse feature One obvious response is that our notion does not have this feature. Alternatively, one might think that if it does, it should replaced with a notion that does not have this feature. In fact, recent psychological experiments (Blanchard et al., forthcoming) seem to show that ordinary people do not employ notions of causation that behave in accord with exclusionist assumptions. 27 These counterfactuals should of course be interpreted in an interventionist, non- backtracking manner.

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The antecedent of (7.3) is possible (since U1 is multiply realizable and hence might have been realized by some other value of L1 besides l11). However (7.3) will not be true if there is a realizer of U1 (different from l11) which does not cause L2 = l22. By contrast the antecedent of (7.4) is not possible. These differences between (7.1–2) and (7.3–4) reflect the fact that even if want to describe the case in which L1 realizes U1 as a case of overdetermination, it involves is a very different kind of overdetermination than is present in the riflemen case. Ordinary cases of overdetermination like the riflemen case are relatively rare and involve either “coincidences” or require the operation of some additional (ordinary) causal structure (e.g., an order from the commander to both riflemen to fire) the presence of which is contingent. This is why we don’t think that such ordinary overdetermination is ubiquitous. By contrast the connection between L1 = l11 and U1 = u11 when the former realizes the latter is not a coincidence and not the result of some additional co-ordinating causal structure. This second sort of “overdetermination” is secured by the presence of the realization relation and for that reason it is both common and unmysterious. The argument that there is something puzzling or problematic about this second kind of overdetermination seems to rely on wrongly assimilating it to the first kind of overdetermination.28 Finally, let me comment briefly on the argument that the postulation of downward (or indeed any upper-level causal relation) is superfluous or redundant, given the lower-level causal relationships. (This is in anticipation of some additional discussion in Sect. 9.8.) There is an obvious sense in which this claim of superfluousness is misleading, at least in the context of a situation like that described by Fig. 9.1. The reason for this is that downward causation (or upper-level causation of upper-level effects) requires satisfaction of the conditions in Sect. 9.2 and these (and particularly the uniformity of effect requirement) are highly non-trivial. In particular, if L1 causes L2 and U1 is realized by L1 and U2 by L2, it does not follow that U1 has a homogeneous or uniform effect on L2 (or on U2). Indeed if L1 causes L2, then in the generic case, most ways of constructing upper level variable U1 that involves coarse-graining L1 will not yield variables that have a uniform causal effect on L2 or on some U2 constructed by coarse-graining L2.29 In other words, given a diagram

28 In

thinking about overdetermination and “extra” arrows, it is also important to distinguish the question of which causal relations exist in nature from the question of which causal relations one needs to represent in a particular graph or other representational structure. Consider the usual case in which L1 causes L2 and L1, L2 realize U1 and U2, with U1 having a uniform effect on U2. If what we are interested in is explaining U2, we may legitimately decide to employ a graph in which there are no arrows from U1 to L2 or from L1 to U2 even if the effects are uniform. The reason for this is that the difference-making information in which we are interested is fully absorbed into the arrow from U1 to U2 – see Sect. 9.8. When we omit the arrows from U1 to L2 or from L1 to U2 this need not be interpreted as claims that these causal relations do not exist; instead we have just declined to represent them. 29 Note that even if U1 has a uniform effect on upper - level variable U2 it need not have a uniform effect on some lower-level variable L2 that realizes U2. Suppose that the exact molecular state of a gas at time t, described by L1, causes its exact molecular state L2 at some later time t + d, with L1 realizing some upper level variable U1, e.g., temperature, at t. U1 will not count as a cause of

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like Kim’s, in which L1 causes L2, it is wrong to think that if one countenances causation by upper-level variables at all, it follows automatically from the fact that L1 realizes U1 and L2 realizes U2 that one should draw additional arrows indicating causal relationships from U1 to L2 or from U1 to U2. Again, one is entitled to do this only if the conditions described in Sect. 9.2 are met for these relationships. Thus when these conditions are met and on this basis we add arrows from U1 to L1 and/or from U1 to U2, we are adding information to Fig. 9.1 that does not follow just from the information in the lower half of the diagram — thus information that is not superfluous or redundant.

9.8 Conditional Causal Independence30 So far I have characterized a notion of downward causation, described some examples that I claim illustrate downward causation, and attempted to respond to several objections. However, an adequate defense of downward causation needs to do more than this; in particular, it would be desirable to have a more positive account of the work that is done by this notion—why it is a useful and fruitful notion in causal analysis, rather than, as critics claim, a dispensable and potentially confusing one.31 In what follows I attempt to provide such an account, which appeals to a notion that I will call conditional causal independence. This will help us to better understand the worldly information that causal claims involving upperlevel variables track. Suppose, as before, that we have an upper-level variable U the values of which are multiply realized by a lower level variable L (or set of these, but, as before, to simplify things I will assume that there is a single L) so that the L has a higher dimensionality than U. Let us say that L is unconditionally causally relevant to (alternatively, causally irrelevant to or independent of) some effect E if there are some (no) changes in the values of L when produced by interventions that are associated with changes in E. (Thus unconditional causal relevance is what is captured by the interventionist criterion for causation M). Say that L is causally irrelevant to (or independent of) E conditional on U if L is unconditionally causally relevant to E, U is unconditionally causally relevant to E, and conditional on the values of U, changes in the value of the L produced by additional interventions and consistent with these values for U irrelevant to E. In other words, we are to imagine a situation in which in which U and L are causally relevant to E, U is set to some value u1 via an intervention and then L is set via independent

L2 because it does not have a uniform effect on this variable, even though it may have a uniform effect on some upper level thermodynamic variable U2 that is realized by L2. 30 Here I want to acknowledge the influence of very similar ideas in Chalupka et al. 2017. 31 Again, this follows from the idea that we want a “functional” account of causation—an account that shows how it is useful to think about causation in the way we do.

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interventions to various values that are consistent with this value U = u1. If under such variations in L for fixed U, the value of E does not change, L is causally independent of E conditional on U.32 For example, conditional on the setting of the temperature of a dilute gas to some value T = t, further variations in the kinetic energies of the individual molecules of the gas as measured by some variable K when these variations are consistent with T = t will have the same effect (to a very high level of approximation) on other thermodynamic variables E such as pressure. Thus conditional on T, further variations in K are causally independent of such Es. Similarly, consider different lower-level ways L = l1, l2, l3 . . . of realizing the same value of the membrane potential V in the HH model—these might correspond to slightly different distributions of charges in the membrane. Then we can interpret the HH model as claiming that conditional on the value of V (realized by an intervention), further variation in L whether V is realized by l1 or l2 or.. makes no difference to the channel conductances, so L is conditionally independent of these effects, conditional on the value of V. When such a conditional independence relationship holds, U will of course have a uniform effect on E, regardless of how U is realized, and since by hypothesis E changes under some interventions on U, if E is a lower-level variable, U will meet the conditions in Sect. 9.2 for being a downward cause of E. One way of thinking

32 Some

additional clarificatory remarks may be helpful. First, in contrast to the more familiar notion of conditional independence in probability theory, the notion of causal conditional independence is formulated in terms or interventionist counterfactuals—these rather than conditional probabilities provide the appropriate framework for understanding causal notions. Second note that we are not considering counterfactuals of the form: “If L = l1 and U were = u2, where l1 is not a realizer of u2, then . . . .” As noted earlier such counterfactuals have impossible antecedents. Rather we are considering counterfactuals whose antecedents are, so to speak, the other way around, with the value u1 of U fixed and the L- realizers of that value u1 allowed to vary. These counterfactuals do have possible antecedents. Third, researchers who adopt the Stalnaker-Lewis closeness of possible world framework for evaluating counterfactuals sometimes argue as follows: Suppose that in the actual world, U takes the value u1, which is realized by L = l1, one of many possible realizers of U (the others being l2, l3 . . . ). Suppose we then consider a counterfactual whose antecedent is (1) “If L did not take the value l1, then . . . ” It is then claimed that the possible world which is closest to the actual world in which the antecedent of (1) holds is one in which some other realizer of U = u1 obtains (that is, a world in which one of L = l2 or L = l3 etc. holds instead) and the counterfactual is evaluated accordingly. (Something like this idea is adopted in List and Menzies 2009 to argue that true upper-level causal claims can exclude causal claims involving their lower-level realizers — so called downward exclusion.) The framework described above does not rest on any such assumptions about closeness of worlds dictating which values of L would occur if l1 did not occur. Instead, we consider counterfactuals whose antecedents correspond to combinations of interventions where we specify exactly what is realized by those interventions rather than relying on closeness considerations to dictate what happens under those antecedents. (For a recent account of counterfactuals that exhibits these features see Briggs 2012.) Thus when we consider counterfactuals like: if (i) we were to set U = u1 and independently of this (ii) set L to some other value (e.g. l2), different from l1 where l1 is the actual realizer of u1 but l2 is also a realizer of u1, we are not supposing that l2 would have been realized if l1 hadn’t been. We are instead thinking in terms of a counterfactual the antecedent of which describes two separate operations, one of which sets U = u1 and the other of which sets L = l2.

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about this is that under these conditions all of the information in the lower-level variable L that makes a difference for E is absorbed into the upper level variable U so that to the extent that explaining E is a matter of exhibiting those factors that make a difference for E, U does just a good a job in this respect as L. This justifies us in appealing to U as a cause of E. A similar analysis holds when E is an upper level variable. This account has several additional features that are worth underscoring. Note first that we are assuming that L is unconditionally relevant to E as is U. Within the interventionist framework, this means that both U and L cause E so that, as remarked above (see footnote 32), we reject downward exclusion. The resulting “redundancy” is unproblematic, for reasons described in Sect. 9.7. A closely related point is that when a conditional independence relation of the sort described holds (with L being independent of U conditional on E) this by itself does not license the claim that upper-level causal claim provides a “better” explanation than the lower level claim. Rather what is licensed is the weaker claim that the upper-level explanation is just as good as the lower-level explanation as far as E is concerned—just as good because it captures all of the relevant differencemaking information for E that is provided by L. This contrasts with the idea (accepted by many philosophers and some scientist who regard upper-level causal claims as legitimate) that the upper-level explanation in terms of U is superior to the lower-level explanation. This claim may be correct but it requires some additional argument for superiority. Another point to keep in mind is that conditional causal independence relations are always relative to some target explanandum or effect E. That is, L might be conditionally causally independent of E1, given U but L might not be conditionally causally independent of some other explanandum E2 given U. For example, there are many features of neuronal behavior which are dependent on the lower level details of exactly how charge is distributed along the neuronal membrane (again see Herz et al. 2006), even if this is not true for the effects described by the HH model.

9.9 The Role of Epistemic Factors Considerations involving conditional independence of the sort just described can be invoked to explain why it is permissible or legitimate to formulate causal claims in terms of upper-level variables, including causal claims that involve lower-level variables as effects— when conditional causal independence holds we may lose little or nothing, in terms of difference-making information, by doing so. However, there is a crucial additional element to the story about why we actually employ such upper-level variables. This has to do with the various sorts of limitations that we humans (and perhaps all bounded agents) face. Some of these are calculational or computational – we can’t solve the 1023 body problem of calculating bottom up from the behavior of individual molecules to the aggregate behavior of the gas. Nor can we make the kinds of fine-grained measurements that would be required

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for such calculations to reach reliable results. Similarly, in the case of neuronal modeling, although there are more fine-grained models that describe the behavior of small individual “compartments” of the neuron, these cannot be simply “aggregated up” to produce a tractable model of the whole neuron (Again see Herz et al. 2006). We thus find that not only is it permissible to formulate theories in terms of upper level variables if we wish to explain certain explananda but that we have no alternative to doing so if we want models that are tractable or that we can calculate with. Put differently, we are very fortunate that nature presents us with relations of conditional irrelevance/independence of the sort I have been describing that we can exploit because otherwise scientific understanding of much or all of nature would be impossible. When we build models and theories that exploit these opportunities, we have models and theories in which upper level causation appears.

9.10 An Objection The ideas just defended are likely to prompt the following objection among reduction-minded critics. The objection is that on a view like mine top-down causation (and for that matter upper-level causation of upper-level effects) does not turn out to be “really real”—instead use of top-down causal claims just reflects shortcuts, approximations, idealizations etc. that scientists make for “pragmatic” reasons, like getting numbers out of their models, with genuine causation always occurring at a lower-level. Following this line of argument, it might be observed that in the HH model the neuron itself is composed of atoms and molecules which interact locally, mainly through the electromagnetic force. The membrane potential, the channel conductances and so on is thus the upshot or resultant of complex patterns of interaction among these atomic and molecular constituents. It follows, according to the argument we are considering, that V, the channel conductances and other variables in the HH model do not represent anything “over and above” these atomic constituents and their interactions. Similarly for the other putative examples of downward causation described above. We may be forced to talk in terms of causation by upper-level variables because of our computational and epistemic limitations, but (the objection goes) this just reflects something about us, not anything that is “out there” in the world or anything having to do with “what nature is really like”. There a number of things that might be said in response to this objection, many of which I lack the space to discuss. But one relevant consideration is this: the “world” and “what nature is like” do enter importantly into the account of downward causation that I have presented. That certain variables L are conditionally causally independent (or nearly so) of other variables E, given the values of other variables U is a fact about what the world is like, and not a fact about us or what we are able know or do. I see no reason to hold that facts about conditional independence are somehow unreal or in some way lacking in “objectivity”. The way we should think about their status is not that our interests or limitations (or our willingness to

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employ pragmatic shortcuts) somehow create these facts about conditional causal independence. Rather the obtaining of these facts presents us with opportunities to formulate models and causal claims with certain structures (including those that contain claims of top-down causation) and which allow us to carry out calculations and construct derivations that would otherwise be impossible. Another way of bringing out the role of these facts about conditional independence is to note that they are, so to speak effaced, if we focus only on derivations of particular token explananda from lower-level theory. To illustrate, consider a wildly counterfactual scenario33 in which we are somehow able to deduce, from detailed information about the positions and momentum of each of the individual molecules making up a particular sample of gas and the fundamental laws governing their interactions—call this M1– facts about the temperature and pressure of the gas, E. This deduction – call it D– by itself will not tell us which other microstates of the gas besides M1 would have led to E and which would have led instead to different values for the temperature and pressure. This last is information about conditional independence relationships and it is not apparent if we focus just on D. Of course, if we were somehow also able to derive for each possible set of values for the positions and momenta of the individual molecules, facts about the resulting temperature and pressure (i.e., if we could construct and survey all derivations of form D for all microstates of the gas), then this would tell us which microstates of the gas lead to E and which would lead to other values for the temperature and pressure. In this sense (it might be argued) information about the relevant conditional causal independence relations is “contained in” the representation provided by the lower-level theory, and, to repeat an earlier objection, not something that is “over and above” what is in this theory.34 I accept this last claim, at least as far as the kind of realization relation on which I have focused in this essay is concerned. The defense of downward causation I have provided does not rest on claims about the emergence of novel causal facts that are

33 Here

I indulge a common claim in the philosophical literature: that all true upper-level claims are derivable in principle from information about lower-level variables and the laws governing their behavior. This claim should be treated with skepticism: One problem is that it is unclear, absent a specification of “in principle” and “derivable”. If the derivation would require a computer as big as the solar system would that count as “in principle” derivability? And what counts as a “derivation”? For example, does it include use of limiting and asymptotic relations and perturbation techniques? Given that on many interpretations, quantum mechanics and quantum field theory give us only information about probabilities of outcomes, and that unlikely or unpredictable outcomes will sometimes occur and affect what happens later how does this affect such derivability claims? 34 Even if it is true, as I am conceding for purposes of this essay, that we knew “everything” about the lower level variables and the laws that characterize their behavior and had unlimited computational power we could “derive” all true upper-level causal claims, it does not follow that the upper level claims are “reducible” to the lower-level claims. There are many accounts of reduction on offer but on most reduction requires something stronger than this sort of derivability. For example, many think it requires identities between upper-level and lower-level variables. As claimed previously, there are many cases identity is not the appropriate way to think about the relation between upper and lower.

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somehow independent of all of the causal information (which I assume includes information about conditional causal independence) that follows in principle from the lower-level theory. Conditional independence of upper-level causal claims does not mean that those claims have no connection with lower-level theory. Again, I’m willing to stipulate, for purposes of this essay that these facts about conditional causal independence are in some way “contained in” the lower level theory. In this respect the account that I have provided respects what is sometimes called the causal closure of the physical—there is no invocation of causal facts that are not present in some form in the underlying physics. However, leaving matters with just this observation leaves out some considerations of great importance, which have to do with epistemology of upper-level causal claims and methodologies for finding them The basic point is that finding out or “seeing” what information in lower-level causal claims is conditionally causally irrelevant to upper-level causal claims and what information is conditionally relevant and finding upper-level variables that capture conditional irrelevance relations is a highly non-trivial task. There are many other important issues concerning the relation between upper and lower-level causal claims besides the metaphysical ones reflected in denials or affirmations of “over and above” claims. The notion of conditional causal independence helps in thinking about these “other” issues. In an influential essay Anderson 1972 notes there that even if it is true that all of the information that is relevant to some set of upper-level phenomena (such as superconductivity) is in some sense contained in an underlying theory, it may be as a practical matter difficult or impossible to extract the relevant variables for explaining these upper-level phenomena merely from an examination of the lower-level theory. One reason for this is that there are many different ways of forming upper-level variables from the variables of the lower-level theory and most of these will not lead to the successful formulation of conditional causal independence relations. The lower-level theory is not organized around (and doesn’t care about) conditional causal independence facts involving upper-level variables, so that both upper-level information (e.g., empirically discovered regularities about superconductivity) and in some cases imaginative mathematical developments are required to find conditional causal dependence relations concerning upperlevel variables. Reductivist minded philosophers sometimes neglect this because they think that the only relevant issue is whether various particular upper-level explananda are derivable in principle from lower-level facts. But as illustrated above, such derivations at least when considered individually, are not going to disclose the conditional independence relations and variables needed for the formulation of upper-level causal claims. And even putting this point aside, the fact of in-principle derivability tells us nothing about how to find the appropriate upper-level variables.

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9.11 Autonomy The notion of “autonomy” is closely associated with issues having to do with the status of upper-level causal claims. What might it mean to claim that a set of upper-level causal claims are autonomous with respect to causal claims involving their lower-level realizers? One possibility is that upper-level causal claims are (in some sense) completely independent of the lower level causal facts—the upperlevel is “novel” (and perhaps unexplainable even in principle) with respect to the lower level. I rejected this idea above. Another (in my view more reasonable) possibility is that autonomy has to do with the extent to which one can discover and formulate “good” upper level causal relationships without reference to information about their underlying realizers and the laws and causal relations governing these realizers. On this understanding of autonomy, the continuum mechanics of fluids is autonomous to the extent that one can formulate stable continuum level relationships with uniform effects of upper-level variables (e.g., as in the NavierStokes equations) without reference to underlying molecular details. Similarly, psychological generalizations are autonomous with respect to neurobiology to the extent that there are true psychological generalizations specifying uniform effects on other psychological variables, so that psychology can proceed independently of neurobiology. Of course the extent to which this sort of autonomy holds is an empirical matter. This notion of autonomy is closely bound up with the extent to which various conditional independence relations hold, thus providing an additional illustration of the usefulness of the latter concept. When some causal claim featuring psychological variables is autonomous with respect to neurobiology, then given the values of some psychological variables, further variation in the values of neurobiological variables will be causally irrelevant to other psychological variables, so that a conditional causal independence relation holds. When this is the case, we can ignore the neurobiology to the extent that we are interested in psychological effects.35 Note again that this does not mean that the psychological claims are causally independent of the underlying neurobiology– instead what is claimed is that the neurobiology is conditionally irrelevant to certain psychological variables, given other psychological variables.36 Although I don’t have the space to argue for this claim in detail here, I believe that it is only to the extent that such conditional causal independence relations hold that we have the possibility of upper-level or special sciences. This then is my answer to Fodor’s well-known question, “why is there anything but physics?”: The special sciences exist because or to the extent that

35 Remember

that this is a claim about what needs to be case for psychology to be autonomous from neurobiology and not an empirical claim about the extent to which such autonomy holds. 36 It is also not claimed that if the causal relations among psychological variables are real, there must not be causal relationships among the underlying neurobiological variables which is what downward exclusion arguments claim.

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the physics encodes conditional causal independence relations among variables that pertain to the sciences in question.

9.12 Is Conditional Causal Independence Common? Can we Make Sense of Closeness to Conditional Causal Independence?37 Several philosophers with whom I have discussed this issue have claimed that causal conditional independence relations of the sort described (or even approximations to them), at least when they involve substantial reductions in degrees of freedom are very rare or perhaps non-existent and similarly for satisfaction for the conditions I have imposed on downward causation. Instead, their idea is that lower-level variables will always have a substantial causal impact on other variables, even conditional on the value of suitably chosen upper level variables. There are several things to be said about this. First, I emphasize again that whether conditional causal independence holds for various Ls, Us and Es is always an empirical matter. It is plausible for some lower-level variables L, there may exist no Us with a substantial smaller dimensionality than the Ls, conditional on which the Ls become independent of explananda of interest. (Maybe some systems studied in the social sciences are like this.) Moreover, it is true, as noted above, that for most arbitrary sets of Us, Ls and Es causal conditional independence, or even approximate causal conditional independence will fail. This does not in itself indicate anything about the usefulness of the conditional independence notion. It merely reflects that the fact that “good” upper level-variables are hard to find – indeed, as noted above, they can be hard to find even given a lower-level ground truth from which the upper- level variables can be constructed. Despite this I claim that in a number of cases, for Ls that figure in an empirically well supported lower-level theory, there will exist upper-level variables U that render the Ls conditionally causally independent of various explananda Es of interest. In other words, conditional causal independence or a close approximation to it sometimes holds, with the interesting scientific problem being to identify the variables for which it holds. I have already mentioned some examples (Sect. 9.3) but here are some more general observations:

37 For

a number of additional examples illustrating the ideas of conditional causal independence and relative autonomy see Green and Batterman (this volume).

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9.12.1 Physics A number of physical systems exhibit universality in the sense of irrelevance of various sorts of lower-level detail to some aspects of the system’s behavior, given certain upper level variables. For example, conditional on certain very generic or coarse-grained variables having to do with the symmetry of the system, its dimensionality, and the extent to which interactions are local, the lower-level details of many very different substances (different gas/liquid systems, ferromagnets etc.) are irrelevant to certain aspects of their behavior near their critical points. Explaining why this is so and identifying the relevant upper-level variables is one of the triumphs of the renormalization group analysis of such systems.

9.12.2 Biology In many cases, organisms are constructed in such a way that certain variations in lower-level detail are conditionally irrelevant to more upper-level variables, given other upper-level variables to which the organism is responsive. This is so for a variety of reasons including selective pressures that reflect the desirability of eliminating the influence of various sorts of low-level noise, computational limitations which make it optimal for the organism to respond to coarse-grained variables and the fact that the coarse-grained variables can sometimes capture all that is ecologically significant. For example, it would make little sense for bodily responses of medium-sized organism like ourselves to dangerous stimuli to vary depending on the exact details of, say, the molecular realization of those stimuli—it is the fact that the stimulus is dangerous or perhaps that it involves a particular kind of danger (large predator) that is relevant. In such cases and for most of sensory processing we have screening off (conditional causal independence) of lower-level detail by ecologically relevant upper- level variables with respect to behavioral responses. Thus to the extent that organisms are only sensitive to coarse-grained variables rather the details of their realizers, good theories of the behavior of these organisms also may only have to keep track of coarse-grained variables. In general, there are many examples of biological systems in which some transducing system is sensitive only to lower dimensional patterns in some continuous lower-level variable with down-stream variables being influenced only by the information in the transduced pattern. Again in such cases one has conditional causal independence. That is, such systems operate by finding upper-level coarse grained variables that satisfy conditional independence relations with respect to lower level variables.

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9.12.3 Relaxing Conditional Causal Independence So far I have focused on cases in which complete conditional causal independence or something close to it holds. However, it is also worth exploring whether there are principled ways of relaxing that requirement.38 One possibility is that although there may be rare or exceptional values of L that are conditionally relevant to E, even given the values of U, this may not be true for most or “almost all” values of L —for most or almost all such values, L is conditionally independent of E, given U even if there are a few values of L for which this is not true. Or perhaps conditional independence holds for all values of L and U within a certain large interval, including those values most likely to occur (at least around here right now). Or conditional irrelevance or near conditional irrelevance may hold on some scales (typically coarser ones) but not on others. Yet another possibility is that when we consider possible probability distributions for the values of L that realize various values of U we find that conditional independence relations hold with respect to some E for most “well-behaved” probability distributions—e.g., those that satisfy some continuity condition. Finally in cases in which we don’t have complete conditional causal independence, a natural question to ask is how much explanatorily or causally relevant information about E do we “lose” if we employ U instead of L? (Here relevant information is information about difference-making variables, understood along interventionist lines.) One possible way of doing this employs a notion of conditional mutual information interpreted causally along the lines described in Ay and Polani 2008: the information loss if we employ U instead of L (or gain if we employ L instead of U) is measured by I (E: L) |U) the mutual information between U and E conditional on L where U and L are set by independent interventions in the manner described above.39 Complete conditional causal independence then corresponds to the case in which I (E: L) |U) = 0.

References Anderson, P. W. (1972). More is Different. Science, 177, 393–396. Ay, N., & Polani, D. (2008). Information flows in causal networks. Advances in Complex Systems, 11, 17–41. Baumgartner, M. (2010). Interventionism and epiphenomenalism. Canadian Journal of Philosophy, 40, 359–383.

38 Of course this needs to be done in such a way that “highly” ambiguous interventions are avoided. 39 Ay

and Polani 2008 employ this expression to measure what they call “information flow” between variables in an ordinary causal network with no realization relations present. I suggest that the same measure can be used to measure conditional information when realization relations are present.

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Baumgartner, M. (2018). The inherent empirical Underdetermination of mental causation. Australasian Journal of Philosophy, 96, 335–350. Beckers S. and Halpern, J. (2019) Abstracting causal models. Blanchard, T., Murray, D. and Lombrozo, T. (Forthcoming). Experiments on causal exclusion. Mind and Language. Briggs, R. (2012). Interventionist counterfactuals. Philosophical Studies, 160, 139–166. Butterfield, J. (2012). Laws, causation and dynamics at different levels. Interface Focus, 2, 101– 114. Chalupka, K., Eberhardt, F., & Perona, P. (2017). Causal feature learning: An overview. Behaviormetrika, 44, 137–164. Clark, S., & Lancaster, T. (2017). The use of downward causation in condensed matter physics. In M. Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 42–53). New York: Routledge. Craver, C., & Bechtel, W. (2007). Top-Down causation without top-down causes. Biology and Philosophy, 22, 547–563. Ellis, G. (2016). How can physics underlie the mind? Top-down causation in the human context. Berlin: Springer. Green, S., & Batterman, R. (this volume). Making sense of top-down causation: Universality and functional equivalence in physics and biology. Herz, A., Gollisch, T., Machens, C., & Jaeger, D. (2006). Modeling single-neuron dynamics and computation: A balance of detail and abstraction. Science, 314, 80–85. Kim, J. (2005). Physicalism or something near enough. Princeton: Princeton University Press. Lewis, D. (1986). Philosophical papers, volume II. Oxford: Oxford Univeristy Press. Lewis, D. (2000). Causation as influence. In J. Collins, N. Hall, & L. Paul (Eds.), Causation and counterfactuals. Cambridge: MIT Press. List, C., & Menzies, P. (2009). Nonreductive physicalism and the limits of the exclusion principle. Journal of Philosophy, 106, 475–502. Noble, D. (2006). The music of life. Oxford: Oxford University Press. Pearl, J. (2000). Causality. Cambridge: Cambridge University Press. Rubenstein, P. , Weichwald, S.; Bongers, S.; Mooij, J. Janzing, D.; Grosse-Wentrup, M., & Scholkopf, B. (2017). Causal Consistency of Structural Equation Models. In Proc. 33rd Conference on Uncertainty in Artificial Intelligence (UAI 2017). Spirtes, P., & Scheines, R. (2004). Causal inference of ambiguous manipulations. Philosophy of Science, 71, 833–845. Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction and search. Cambridge: MIT Press. Woodward, J. (2003). Making things happen. New York: Oxford University Press. Woodward, J. (2008). Mental causation and neural mechanisms. In J. Howhy & J. Kallestrup (Eds.), Being reduced: New essays on reduction, explanation and causation (pp. 218–262). Oxford: Oxford University Press. Woodward, J. (2014). A functional account of causation. Philosophy of Science, 81, 691–713. Woodward, J. (2015). Interventionism and causal exclusion. Philosophy and Phenomenological Research, 91, 303–347. Woodward, J. (2017) Interventionism and the Missing Metaphysics. In Metaphysics and the Philosophy of Science (ed. Mathew Slater and Zanja Yudell), pp 193–227. Woodward, J. (2020). Levels: What are they and what work do they do? In Kendler & Parnas (Eds.), Philosophical issues in psychiatry V: The problems of multiple levels, explanatory pluralism, reduction and emergence. Cambridge: Cambridge University Press. Woodward, J. (Forthcoming). Causation with a human face: Normative theory and descriptive psychology. New York: Oxford University Press.

Chapter 10

A Pragmatist Perspective on Causation, Laws and Explanation Richard Healey

Abstract I offer a pragmatist understanding of causation, laws and explanation that traces the features of these notions to their functions in our practical as well as theoretical projects. Laws derive their importance from their epistemic and methodological functions, while the primary role of causal concepts is in guiding action. Contemporary interventionist accounts of causation and causal modeling appeal to and clarify this practical role while downplaying the causal significance of laws. They also explain how causation in one science or at one level of complexity may be either related to or independent of causation in other sciences or at other levels. In this way they can demystify the notion of top-down causation by showing how, and when, it is possible.

10.1 Introduction The subtitle of George Ellis’s (2016) book How Can Physics Underlie the Mind? flags top-down causation as the key notion needed to answer the question posed by its title. This notion is in tension with the Laplacean vision of causation as the playing out of laws governing the global evolution of the world by determining the motion of its basic physical parts. Some physicists and philosophers still think of causation as ultimately physical, even if the fundamental laws are not deterministic. But causation plays a vital role through all of science and human life in ways that may be understood locally, and without reference to physical (or even any) laws. I will offer a pragmatist understanding of causation, laws and explanation that traces the features of these notions to their functions in our practical as well as theoretical projects. Laws derive their importance from their epistemic and methodological functions, while the primary role of causal concepts is in guiding action. Contemporary interventionist accounts of causation and causal modeling appeal to and clarify this practical role while downplaying the causal significance of

R. Healey () University of Arizona, Tucson, AZ, USA © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_10

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laws. They also explain how causation in one science or at one level of complexity may be either related to or independent of causation in other sciences or at other levels. In this way they can demystify the notion of top-down causation by showing how, and when, it is possible. At the most general level, explanation leads to understanding: but this can take different forms. Consequently, explanation serves different functions in science and comes in many varieties. Some scientific explanations are causal, but others are not: many scientific explanations appeal to laws, but many do not. Unifying explanations serve the epistemic function of connecting otherwise separate items or branches of scientific knowledge. This promotes an economy of thought but can also strengthen the evidence supporting one or more hypotheses by adding links to newly relevant data. Causal explanations can be especially satisfying when they lead to the kind of practical understanding that permits control over the phenomena explained. I will illustrate these general points by means of specific examples, including smoke detectors, measurements of the Hubble constant, and the game of Life. Finally I will comment on how far this pragmatist perspective helps one to see how physics can underlie the mind.

10.2 Causation I follow most philosophers in calling the relation a cause bears to its effect causation. The alternative term ‘causality’ has associations it is best to avoid. These emerge in a famous passage from Laplace (1820): We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

Known for his successful application of Newtonian mechanics to the solar system, Laplace here contemplates its application to all bodies of the universe. His second sentence has been understood to imply a thesis of universal determinism, to the effect that the entire history of the universe is determined by its present state. The first sentence may be read as a proposed analysis of the causal relation that would make it both global and deterministic, thereby supporting a “principle of causality” according to which every event has a preceding cause that determines its occurrence. Indeed, causality has sometimes been confused, if not identified, with determinism. In fact, causal relations are typically neither global nor deterministic: the lightning caused the fire, the fire made the alarm go off, the sound of the alarm brought out the fire department, etc. To reconcile such examples with the Laplacean vision one would have to take the lightning, fire and sound each to be determined by a localized part of some global event and to appeal to exceptionless laws of

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time-evolution relating these global events. But with no access to such global events and no knowledge of the required laws we are nevertheless somehow in a position confidently to make such causal claims about the fire. In fact basic physics gives us reason to believe there are no exceptionless laws of time-evolution relating the state of the universe when the fire breaks out to its state when the fire alarm sounds. A fire alarm is typically triggered by an ionization smoke-detector whose operation relies on the radioactive decay of a small sample of the Americium 241 isotope by emission of alpha-particles. These ionize enough of the air in a thin gap between metal plates to produce a small electric current in a circuit as the ions are collected on these electrodes. As the gap fills with smoke from a fire, some of the ions are removed by adhesion to smoke particles, the current decreases, and a switch in the circuit sets off the alarm. But radioactive decay is believed to be an indeterministic process: it is entirely possible for the current flow to be maintained because enough Americium nuclei randomly decay while the smoke particles are in the gap to keep the current flowing at the original rate, so the alarm fails to go off. An ionization smoke detector works not because there are laws that relate the global state of the universe at different times, but because there is a robust regularity relating the current through its circuit to the presence of smoke in the gap in that circuit. Robustness here means that the regularity is preserved under a wide range of variations in other features of the detector and its environment, including the temperature of the air, the amount and composition of the smoke, and how long the detector has been in place. The regularity is not robust against other variations, including draining of its battery, placement under water or in a sealed container, and overenthusiastic frying. This regularity is not accidental, but nor is it an instance of any law of nature, fundamental or otherwise (though its holding does depend on a stochastic physical law of radioactive decay). Underlying it is a functional relation between two magnitudes: an inverse relation between the amount of smoke in the gap between the electrodes and the current in the circuit. Contemporary interventionist approaches to causation represent these magnitudes as nodes in a Directed Acyclic causal Graph (DAG) (see Pearl 2009; Woodward 2003). The direction of the graph corresponds to the direction of causation, so one can represent the fact that the smoke causes the sound of the alarm (not vice versa) by the orientation of the arrow linking their nodes on the graph. The orientation of a link in a DAG may be checked by controlled interventions on the nodes it connects. To test a fire alarm one can intervene by increasing the amount of smoke between its electrodes and look for a corresponding variation in the current through its circuit. Changing the current through the circuit by increasing the voltage across it will not change the amount of smoke in the gap in the circuit. Such causal modeling techniques do not yield an analysis of causation insofar as the notion of an intervention is itself causal. Woodward (2003) gives a more precise account of an intervention in causal terms while insisting that this does not rely on any appeal to human agency. Price (2017), by contrast, locates the origins of the concept of an intervention within the perspective of a hypothetical agent able to

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contemplate the alternative possible consequences of his or her own decisions—a perspective that may itself depend on how the agent is physically situated. Either way, one can offer a non-reductive account of the causal relation between events c and e of types C, E, respectively in terms of counterfactual statements about the effects of an intervention on c that replaces it by an event c* of type C*, where this different type of event corresponds to the same magnitude taking on a different value. Interventions may or may not be understood as natural occurrences independent of the perspective of any agent. But they are certainly just what one needs to attain goals by manipulating elements of the environment. In this way an interventionist approach to causation explains the practical function of causal concepts for agents like us—physically situated as we are in a small part of a much bigger and longer lasting universe, to which we have very limited direct epistemic access though our senses. This makes an interventionist approach to causation very attractive to a pragmatist whose first question when confronted by a problematic concept is to ask what function is served by possession and use of that concept. As we’ll see in §6, it will also help to explain the nature and possibility of downward causation.

10.3 Explanation I begin with a rapid and selective review of recent history of philosophical thought about scientific explanation, emphasizing changing views on the roles of laws and causation. Logical positivist philosophers and their logical empiricist heirs maintained that any fully satisfactory scientific explanation must include at least one scientific law (see Carnap (1966/1995, chapter 1), Hempel (1965)). Critics exhibited cases in which, they argued, laws sufficient to effectively guarantee the occurrence of the phenomenon in question nevertheless failed to explain it: what was missing in these cases, allegedly, was any claim about the cause of the phenomenon (Bromberger (1966), Salmon (1984)). Lewis (1986) argued that to explain the occurrence of an event was just to provide information about its causal history, and backed up this proposal with an influential analysis of causation (1973/1986) in terms of counterfactuals—statements of the form If a had not happened then b would not have happened. Following these developments, philosophers came to emphasize the importance of causation in understanding what it is to explain something in science without reference to laws. Some (such as Strevens (2008)) maintained that all scientific explanation is causal, while others (including Woodward (2003)) took their accounts of causal explanation as models to be extended to accounts of other kinds of scientific explanation. But Maudlin (2007) argued, against this trend, that causation and counterfactuals are best understood by appeal to laws of evolution, whether fundamental (in physics) or derivative (as in special sciences). And more recent work by philosophers (Lange

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(2017), Reutlinger and Saatsi (2018) has explored a variety of different kinds of non-causal explanation in science. Those with a jaundiced eye may see the fluctuating fortunes during this period of appeals to law and to causation as a glaring example of philosophy’s failure to progress as a discipline. As a pragmatist I see here a case in which explanation has multiple roles in science that may be played by different actors. If this is right, we should not seek a unified theory of scientific explanation, but an account of a variety of explanatory tasks and a corresponding variety of kinds of scientific explanation best suited to accomplish these. Some scientific explanations are prized because of their unifying power. In biology these include explanations that locate a species or other taxon on a single tree of terrestrial life, explanations in terms of natural selection, and explanations that appeal to a small stock of biochemical ingredients (such as nucleic acids and their bases) and processes (such as protein synthesis). In physics they include the explanation of heat as molecular motion and of light (as well as radio waves, X-rays, ...) as electromagnetic radiation within a certain range of wavelengths, as well as the common pattern of mechanical explanation that Newton used to unify celestial and terrestrial phenomena. A unifying explanation need not be causal, and will not be if what it unifies are laws, theories or branches of science rather than natural phenomena. Unifying explanations serve methodological needs within science by helping to organize and simplify the structure of scientific knowledge. Causal explanations are valued because they contribute to our practical knowledge. Some do so directly by showing how we may achieve practical goals of manipulation and control by appropriate interventions. But a causal explanation may yield understanding even of phenomena in which we cannot intervene. It can enable us to represent these phenomena within our perspective as agents situated in a world on which we can act, rather than as passive observers of events that play out in that world.

10.4 Laws While laws play several roles in science—especially physical science—it is fruitful to think of these as all related to a function pointed out long ago by Gilbert Ryle (1949, p. 121): Law-statements are true or false but they do not state truths or falsehoods of the same type as those asserted by the statements of fact to which they apply or are supposed to apply. They have different jobs. At least part of the point of trying to establish laws is to find out how to infer from particular matters of fact to other particular matters of fact . . . . A law is used as, so to speak, an inference-ticket (a season ticket) which licenses its possessors to move from asserting factual statements to asserting other factual statements.

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Ryle’s distinction between two types of truth (statements of fact and the true law statements to which they apply) is murky. But his emphasis on the distinctive job of law-statements in licensing scientific inference is important and worth salvaging. There is a lively debate in contemporary philosophy about an issue in the metaphysics of scientific laws: Do laws govern the construction of the physical world, or is the framework of scientific law a metaphysical superstructure supported by what actually happens in it? For a pragmatist this is the wrong question to ask: laws provide science with an epistemic infrastructure, not a metaphysical superstructure. Law statements do this by licensing reliable inferences that connect not only singular statements but also other law statements and, through them, different theories and branches of science. To play this role a law statement need be neither universal nor even true. But endorsement of a law-statement commits one to its general reliability in an acknowledged domain of applicability (its scope). Astrophysics and cosmology provide some of the most impressive examples of the epistemic function of scientific laws in gaining new knowledge. Without their aid we would know very little about the solar system and next to nothing about what lies beyond it. Of course instruments such as telescopes have also played a vital role in acquiring knowledge of what lies beyond our physical reach. But scientists rely heavily on inferences warranted by scientific laws in their construction, calibration and deployment, and especially in the interpretation of the data they provide. Here are some examples. We know a great deal about the atomic composition of stars and other celestial objects by telescopic observation of the light they emit or absorb. Such knowledge depends on inferences licensed by laws of spectroscopy. This is how helium was discovered on the sun 27 years before any was found here on the earth. In combination with laws of the Doppler shift (and subsequently general relativity) laws of spectroscopy license the inference to the conclusion that (on a sufficiently large scale) the universe is expanding in accordance with Hubble’s law that recession velocity is proportional to distance. But justification for belief in Hubble’s law also depends on knowledge of the distance to the receding body—knowledge that is come by only through inferences crucially involving additional scientific laws (such as the initially crude empirical generalization known as the Leavitt-Shapley law relating the period and absolute luminosity of Cepheid variable stars). The exact value of the proportionality constant in Hubble’s law is currently a matter of intense investigation because apparently reliable observational techniques that require inferences using different scientific laws lead to significantly different values. To extend the metaphor of epistemic infrastructure, it is as if engineers digging a tunnel under a mountain from different sides to connect a road or rail network had trouble precisely aligning their tunnels where they met under the mountain. The investigation will be successfully concluded when consensus is reached on which techniques and laws are to be relied on in determining the exact value of the Hubble constant at different epochs. Scientific laws also license inferences that serve the function of standardizing and applying existing scientific knowledge. The 2019 redefinition of basic units in the metric system of units provides an interesting example. Four units were then

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redefined in terms of so-called constants of nature: the kilogram, kelvin, ampere and mole were defined by setting Planck’s constant h, the speed of light in a vacuum c, the charge on the electron e, Boltzmann’s constant k equal to specific numerical values when represented in these units. The assumption that each of these magnitudes is indeed constant is justified by inferences from basic physical laws into which they enter. Prior to the redefinition various techniques had been used to measure the value of each constant. This is no longer necessary since their values have been fixed by definition. Instead, these same techniques are used to measure the mass, temperature, current, or amount of a sample in the relevant units. Each such measurement technique itself relies on a variety of scientific laws. For example, a watt or Kibble balance may be used to very accurately measure the mass of an object. A large number of physical effects are involved in the operation of the balance, some electromagnetic, others mechanical. Two effects are explicitly quantum mechanical, in the sense that laws of quantum theory are needed to use these effects to infer the values of relevant magnitudes: the Josephson effect and the quantum Hall effect together permit very accurate measurements of current and voltage, and hence electric power. Laws of classical mechanics, gravity, the Doppler effect, and elementary electric circuit theory are all also used to infer the mass of the measured object from the observed behavior of the balance as well as other devices in and outside the laboratory in which the balance is located. These laws have very different pedigrees. Few, if any, are now regarded as fundamental: some long predate the twentieth century relativity and quantum revolutions. Many are known not to hold in certain situations: they are neither true nor universal. The laws justifying an inference to the mass of the measured object may even be collectively inconsistent. But that inference is nevertheless licensed because each law is applied only where inferences based on it can be relied upon in reaching conclusions that are accurate within assessable error bounds. I noted in the previous section that some scientific explanations appeal to laws while others appeal to causes. A good explanation of the operation of a Kibble balance would advert to many of the laws used to infer the mass of the measured object. But laws used to infer the value of the Hubble constant would not explain why the Hubble law holds: that calls for a causal explanation of why the universe is expanding in accordance with the law.

10.5 Emergence and the Life World Downward causation is sometimes thought of as a phenomenon in which emergent, higher-level properties causally effect lower-level properties out of which they emerge. But both emergence and downward causation are problematic concepts. In discussing them it will be helpful to have in mind a model that is simpler than the actual world but still rich enough to provide illustrations of potential analogs to emergence and downward causation. This is John Conway’s game of Life.

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Life is not so much a game as a kind of cellular automaton. Events in a Lifeworld occur within a two-dimensional grid of congruent square cells in which each cell touches eight neighboring cells. Events play out in discrete time steps. At each step a cell has one of two properties: it is in a state at which it is said to be either alive or dead. The state of a Lifeworld at step t + 1 is uniquely determined by the distribution of these properties over its cells at step t. Here we assume a criterion for what counts as the same cell at different times. The determination relation is local: the state of each cell at t + 1 is a function of its state and those of its eight nearest neighbors at t, as follows: Any live cell with fewer than two live neighbors dies. Any live cell with more than three live neighbors dies. Any live cell with two or three live neighbors lives, unchanged, to the next generation. Any dead cell with exactly three live neighbors will come to life.

One can think of the cells as micro-objects in a Lifeworld, at each time-step in a micro-state of being alive or being dead. The state of a cell at t constitutes a microevent. One can also regard the local determination relation as specifying micro-laws of time evolution that hold for these micro-events. This micro-structure generates a remarkably rich macro-structure of emergent objects, properties, laws and causation in some (though not all) Lifeworlds that begin in a particular global micro-state and then evolve in conformity to the above conditions. The possibilities are most easily explored by implementing the defining conditions as a computer program and watching how the chosen Lifeworld develops on the screen. Many such implementations are now readily available for download from the Web.1 One basic macro-object is called a glider. At each time-step a glider is a shape made up of five contiguous live cells, each with no other live nearest neighbors. The glider changes at every time-step: the live cells cycle through three different shapes before the glider returns to its original shape. But the cells in that shape at t + 4 are not the same as those that made it up at t: the original pattern has been shifted over diagonally, and is now formed by cells located elsewhere on the grid. A glider constitutes a macro-object that retains its identity despite changes in its shape, location and component micro-parts. It may be taken as an example of an emergent object, and its shape and location as examples of emergent properties of that object. Its behavior is consistent with an emergent macro-law of motion specifying that it moves one cell horizontally and one square vertically every four time-steps. A single glider in an otherwise empty Lifeworld (all other cells are dead) continues to exist and to move in accordance with this law forever. But if there are other live cells its behavior may differ, as we shall see in the next section.

1 Click on the following URLs to access programs implementing, respectively: glider, glidergun, glidergungliderdestruction

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David Chalmers (2006) distinguished two notions of emergence as follows: . . . a high-level phenomenon is strongly emergent with respect to a low-level domain when the high-level phenomenon arises from the low-level domain, but truths concerning that phenomenon are not deducible even in principle from truths in the low-level domain. . . . a high-level phenomenon is weakly emergent with respect to a low-level domain when the high-level phenomenon arises from the low-level domain, but truths concerning that phenomenon are unexpected given the principles governing the low-level domain.

Life presents no examples of strong emergence because all high-level phenomena are determined by the starting micro-state in accordance with the local, algorithmic rules of the “game”. But it will serve as an illuminating example of weak emergence, since a Lifeworld can display quite unexpected high-level behavior. The Lifeworld primer, for example, evolves so as to produce a stream of leftward-moving “space ships” with the spaces between them proportional to those between the prime numbers. Most strikingly, there is a Lifeworld that can be thought to realize a universal Turing machine and so implement any digital computer program. Such examples of weak emergence suggest this playful tweak to the conclusion to Charles Darwin’s Origin of Species: There is grandeur in this view of Life,... from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

Chalmers (2006) takes consciousness to present the only example of strong emergence because he believes that even if consciousness has physical correlates in our world these don’t suffice to deduce their conscious correlates without additional psycho-physical laws that are not themselves consequences of laws like those physicists currently have or seek. His view remains controversial among philosophers of mind and the issue is unlikely to be resolved without taking a stand on the metaphysical status of laws—something that a pragmatist would do well to avoid. Someone might appeal to quantum entanglement as an instance of strong emergence because the physical properties of compound systems are not deducible from those of their component subsystems. But this appeal fails if, as I believe (see my 2016) entanglement is not a physical relation.

10.6 Downward Causation The metaphor of downward causation depends on a conception of the world as stratified into levels ordered from lower to higher, or even bottom to top. In one way of understanding it, the origin of such an order lies in a composition relation that relates objects to the wholes they compose. For example, quarks are often said to compose nucleons that form the nucleus of a carbon atom whose other parts are electrons, while the atom is itself part of a DNA molecule that is part of the nucleus of a neural cell in a human brain. Despite such examples it is not clear how well the composition relation and the levels conception itself stand up to critical scrutiny.

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This is not the place to provide it, so I’ll assume they do and pass on to see how the metaphor of downward causation arises and why it has seemed problematic. The levels conception suggests the possibility of reducing the behavior of an object to that of its component parts, where reduction is thought to permit or even require explanation. The possibility holds out the promise of another kind of order in which facts about objects at different levels are related by an explanatory relation. Steven Weinberg (1992, 2015), for one, sees science as succeeding in its attempt to fulfill this promise. In his (2001) essay, Weinberg himself proposes no well-developed theory of scientific explanation while encouraging philosophers in their attempts to clarify the notion. But he stresses the importance of explaining regularities or principles rather than individual events, and his remarks on deduction hark back to the logical empiricist theories of Hempel while he raises doubts about explanation in terms of causes.2 Strevens (2008), by contrast, gives causal explanation center stage even while agreeing with Weinberg that explanation is located out in the world, not in the communicative acts of scientists. For levels to be asymmetrically ordered by causal explanatory relations these must also be asymmetric: they must explain what goes on at higher levels in terms of underlying lower level causal mechanisms. A relation in which higher level objects or processes cause lower level events or phenomena might threaten the asymmetry inherent in this perspective. Indeed, Jaegwon Kim (e.g. 2005) has formulated so-called causal exclusion arguments intended to rule out the possibility of any downward causal relations. But a pragmatist who adopts the interventionist approach to causation discussed in §2 has a ready reply to such causal exclusion arguments (Woodward, 2015). Consider a case in which the instantiation of a low-level property P1 determines the instantiation of a distinct high-level property M1 and P1 is a sufficient cause of a different low-level property P2 whose instantiation determines that of a distinct high-level property M2 . Here is a causal exclusion argument intended to show that M1 cannot be the cause of P2 . By assumption, P1 caused P2 . If M1 also caused P2 then P2 was overdetermined, since P1 was its sufficient cause and M1 , P1 are not causally related. But this case is quite different from standard cases of overdetermination: all the “causal work” here is done by the lower-level cause P1 . M1 is not an overdetermining cause but a mere epiphenomenon. Since this argument is quite general there can be no downward causation. Roughly, on an interventionist approach M1 is a cause of M2 just in case appropriate interventions that change the property M1 are accompanied by corresponding changes in M2 . This is a crude statement of the view expressed by Woodward (2003) who here supplies the missing details. When it is applied to the case of the previous paragraph this approach may or may not deliver the verdict that M1 is a cause of M2 . As Woodward (2015) points out, it is consistent with the description in that

2 In

a puzzling footnote Weinberg (2001) takes Kitcher to advocate a causal theory of scientific explanation. But Kitcher (1981) sees unification as the key to scientific explanation, apparently in agreement with Weinberg himself.

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paragraph to suppose that M1 and M2 are not even correlated properties. But one can point to cases meeting that description in which the approach will correctly count a high-level property as cause of another even though their instances are determined by instantiation of low-level properties P1 , P2 respectively where P1 is a sufficient cause of P2 . In such case M1 will count as a cause of P2 as well as M2 , so we have an unproblematic example of downward causation. We can find many such cases in the game of Life. In §5 I claimed that some Lifeworlds contain a rich causal macro-structure. Here are some examples. A glider is a persisting macro-object that perdures by constituting a causal process in which each time-stage produces the subsequent stage of the glider. A glidergun is a macroobject that remains at the same macro-location while producing a sequence of gliders. In glidergungliderdestruction five gliders converge on a complex macrostructure and are successively destroyed while destroying that structure. In the third example, consider an early period during which the first glider is destroyed as it encounters a stationary object composed of a block of four live cells that is also destroyed in the process. We may define two macro-properties of the Lifeworld: containing a glider moving south-east across the world, containing a small stationary block of live cells in the path of that glider. Each macro-property is determined at each time-step by the micro-properties “being alive”, “not being alive” of particular individual cells. It is intuitively clear that the first macro-property causes the second not to be possessed as time passes. This agrees with the verdict of the interventionist approach. An intervention that altered the Lifeworld just by giving the glider a north-east trajectory or turning it into a similar stationary block of live cells would ensure continued possession of the second property. That same intervention would also alter those micro-properties of the Lifeworld that determine possession or non-possession of this second macro-property. So this is a case of downward causation in a Lifeworld: a case in which a higher-level property causally influences lower-level properties. The game of Life can provide a powerful intuition pump (to use Daniel Dennett’s term), but we do not live in a Lifeworld. Are there examples of downward causation in the real world? A contemporary LCD computer screen provides some. I am now composing this paper by pressing keys on a keyboard connected to a personal computer. As I press each key a black letter appears on the computer monitor. This is not a coincidence. Pressing the key marked D (as I just did) caused a black mark shaped like an upper case letter d to appear at a specific place on the screen which had previously appeared white. A sequence of such key-pressings caused the previous sentence to appear on the screen. Here we have familiar instances of macro-causation observable in the real world. A black D-shape reliably appears on the screen when the key marked D is pressed thanks to the operation of unobservable micro-processes. Electrical currents produced by depressing the key are input to a word-processing program running on the computer. Its output causes electrical currents to pass through some tiny liquid crystals sandwiched between two crossed layers of polarizing material, all back-lit by white light. Three crystals compose each of the roughly 1 million pixels arranged as a rectangular grid across the screen. Passage of electrical currents through all of

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the three crystals in a pixel allows horizontally polarized light to pass through them, only to be blocked by the second layer of vertically polarized material. So none of the light emerges from that pixel. That’s true of all the pixels making up a Dshape at that place on the screen. So a black D-shape appears on the screen. No similar electrical currents pass through the crystals making up each surrounding pixel. Each of these crystals therefore rotates the plane of polarization of the light as it passes through so that light is now able to pass through the second layer of polarized material. That’s why the surrounding screen looks white. The continued appearance of the black D-shape on the screen is realized microscopically by the continual “refreshing” of the currents through the crystals making up the pixels in that area of the screen, 60 times each second. Every one of those micro-events was caused by my once pressing the key marked D on the keyboard. Together they determine the appearance of the black D-shape on the screen—the macro-event I caused by pressing the key on the keyboard. Here we have an actual example of downward causation. It would be easy to find many similar examples involving the use of contemporary digital computers. If you ran the Life programs referred to earlier you have produced your own examples. Loading each program and pressing the Run key once causes the image on the screen to change in such a way as to represent the evolution of that particular Lifeworld. While a Lifeworld is itself a purely abstract structure, you can intervene in its physical representation by modifying which cells are alive at any particular stage in the evolution. In this way any instance of downward causation in a Lifeworld may be used to provide instances of downward causation in the real world. Some have associated the downward-causal impact of high-level phenomena with the existence of autonomous high-level “configurational” laws (see McLaughlin 1992). “Kicking in” only at a certain level of complexity, such macro-laws would supplement or even trump the operation of low-level laws. So a Laplacean intelligence knowing only initial conditions and micro-laws could not deduce the macro- or even micro-history of the world. The game of Life illustrates the fact that downward causation requires no such laws. Even though it manifests downward causation, its rules suffice completely to specify the evolution of a Lifeworld in terms of the behavior of individual cells. But there is still a sense in which robust macro-laws of Life are autonomous from these basic micro-laws. On an interventionist approach to causation, there are many macro-properties in a Lifeworld that cause other macro-properties. The underlying correlation between their instances is robust against some interventions on the cause macro-property as well as against a range of variations in their environment. One who adopts the pragmatist view of laws promoted in §4 will be ready to call this correlation a macrolaw. But, like all laws, it has a limited domain of applicability. The correlation will fail for interventions and/or environmental variations against which it is not robust. For example, adding a single live cell to a glider can make the glider self-destruct or evolve into a sequence of complex patterns that finally resolves into an alternating pair of nine objects instead of just gliding (try this using add to glider). Such a macro-law is autonomous from micro-laws because there are cases in which it prescribes macro-behavior that cannot be realized if the micro-laws

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hold universally. In that case the macro-law fails to hold. But, though subject to exceptions, the macro-law can remain of great practical benefit if (unlike in Life) you have no way of knowing the micro-state or micro-laws. In a sense, the microlaws constrain the macro-law by determining its scope. If the micro-laws themselves are subject to exceptions in certain circumstances then there is even more room for the autonomy of macro-laws. In a pragmatist view the limited reliability of both laws and causal relations makes room for them to fulfil their theoretical and practical functions at any level and between any levels, whether upward, downward or horizontally.

10.7 Program Explanation Someone might claim that the real cause of a micro- or macro-property of the lifeworld is the program implementing that run. For example, the program primer outputs a line of left-moving “spaceships” representing the successive prime numbers 2,3,5,7,11,13,17,19,23, . . . . But as a set of instructions, a program is an abstract object like a number or string of symbols, and abstract objects have no causal powers. This remains true even when primer is implemented by running it on a physical representation of the required initial configuration of live and dead cells in a Lifeworld. The idea that a program or something like it can be causally relevant to an effect without being causally efficacious in its production has been promoted by Pettit (1993, 2007) in his notion of program explanation. Perhaps a program such as primer can at least be causally relevant to the explanation of the production of a physical representation of a Lifeworld containing a line of left-moving “spaceships” representing the successive prime numbers 2,3,5,7,11,13,17,19,23, . . . . because it programs for this process? If so, one might maintain that the program itself is a downward cause of the micro-events that constitute the physical representation of the Lifeworld process involved. I find this line of thought confused. §3’s pragmatist view of explanation suggests a variety of different kinds of explanation of what happens when primer is run on a computer, and in particular of why the sequence of “spaceships” emerging from the left in a run of Life with initial data implementing that program is isomorphic to the sequence of prime numbers. Here are crude renderings of three kinds of explanation: This follows from the four basic rules of Life and the initial Life-world configuration of live cells. All spaceships corresponding to non-prime numbers have been eaten before they would have appeared in this sequence. The program primer was designed to generate precisely this sequence of spaceships; acting on a physical implementation of the micro-structure of a Lifeworld it physically implements the four rules of Life when the program is run by using a computer mouse to press the “Run” button; and the “Run” button has just been pressed.

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Explanations of these three kinds are not in tension with one another: none is “the real” explanation. The third sketches a causal explanation that begins with a macrocause (masquerading as a teleological explanatory factor) but then proceeds to locate causes at the micro-causal level. The second gives a macro-causal explanation. If the term program explanation is to be used here it is most appropriately applied to the first kind of explanation. But that is not a causal explanation at all. Here, as elsewhere, there may be program explanations, but the program itself is not a causally relevant factor in the explanation: at most it directs attention to the existence of causally relevant factors, though perhaps without specifying what they are (at least at the micro-level). The causal explanation itself does not mention any program, but only properties (in particular, values of magnitudes) and their causal relations, understood in terms of an interventionist model of causation. According to Pettit and Jackson (1990), a little reflection suggests that perhaps most of the explanations we are ever likely to offer will be program explanations, and (they presumed) we only reach potentially efficacious properties in physics at the level of unspecified micro-physical particles. In fact we can and do have plenty of causal explanations in daily life as well as throughout the sciences, few (if any) of which deal with specific micro-physical particles.

10.8 The Mind There is plenty of downward causation, but does it underlie the mind, and if so how? The issue of mental causation has motivated causal exclusion arguments intended to prove that mental properties have no causal powers of their own. By undermining such a causal exclusion argument the interventionist approach to causation reopens the question of downward mental causation—of physical events at the macro- or micro-level by the instantiation of mental properties. There seem to be clear cases of this. A few years ago a driver suffering an epileptic fit ran off the road and destroyed a row of saguaro cactus on the ranch where I live. Many other automobile accidents are caused by the mental states of drivers who are distracted by thoughts about other things. Discussion of mental causation tends to focus instead on cases of intentional action, where a physical event would not have occurred if an agent had not intended its occurrence. But it is not so clear that the relation is causal between an intention and its successful execution, or the consequences of its execution. Even the view that an action is caused by a collection of beliefs and desires has its critics. In his book Ellis (2016) takes plans and theories as causes of physical effects, mediated by the minds of agents who execute or use them. These plans and theories are all consequences of our thought processes. They are the result of top-down effects from abstract ideas to neural excitations and into the world, down to the level of atoms. We are surrounded by proof of the efficacy of mental thought. This effectiveness is based specifically on models and theories. (2016, p. 358)

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This quote leaves the causal direction ambiguous. If a plan or theory is a causal consequence of our thought processes then can it also be a causal result of the plan or theory as an abstract idea? Ellis goes on to reject the (strange) idea that a theory is a single person’s brain state, identifying it instead with an equivalence class of mathematical representations (which may themselves be represented physically— by writing them down, for example). As such, a theory is an abstract object which, as noted earlier, can be neither cause nor effect of any mental state(s) since it cannot be intervened upon. One can certainly appeal to plans, models and theories in an explanation of the existence and features of a physical object like an Airbus (Ellis’s example). But the explanation will not be causal: these abstracta do not cause it to exist, though physical representations of them clearly do play a causal role in the construction of the relevant physical object. They are able to play this role because of their effect on the mental states of the agents who construct them. Those mental states are distal downward causes of the presence and interconnections of the various atomic components of each micro-chip in the Airbus’s control systems. The detailed conceptual model of an Airbus Ellis represents in his Fig. 7.14 might naturally be thought to supply the program for the construction of the aircraft in something like a program explanation.

10.9 Conclusion In order to understand the world, we need to deploy multiple explanatory strategies, each suited to the reliable but not exceptionless regularities that emerge at different scales or in different contexts. Not all of these yield causal explanations. A good explanation will yield understanding by unifying apparently unrelated phenomena. Sometimes we may be lucky enough to unify explanatory strategies at different levels by showing how phenomena at one level are reducible to, determined by, or grounded in phenomena at another level. In any case, we continue to seek explanations wherever we can find them. In theoretical science we treasure unifying explanations, whether or not these are causal. Practical life prioritizes causal explanations. For a naturalist, there are two senses in which physics underlies not only the mind but every phenomenon studied by science. The first sense is just that if there were no physical things there would be no minds: naturalism precludes disembodied spirits. The second sense has to do with the scope of physics. Physics claims the entire natural world as its domain of applicability, unlike other sciences which focus on phenomena that manifest themselves only in special circumstances—chemistry only where in space-time there are atoms and molecules, biology only where there is life, neurophysiology only where there are organisms with brains or at least central nervous systems, psychology only where there are agents with mental states. But each science retains a certain autonomy for its laws and explanations (whether or not these are causal): different specialized concepts prove useful in understanding

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and intervening in the physical world in different domains. Phenomena (weakly) emerge that are best described and understood using these specialized concepts. This is true even within physics. The Standard Model of elementary particle physics does not help us understand high temperature super-conductivity.

References Bromberger, S. (1966). Why-Questions. In R. G. Colodny (Ed.), Mind and Cosmos: Essays in contemporary science and philosophy, volume 3. Pittsburgh: University of Pittsburgh Press. Carnap, R. (1966) Philosophical Foundations of Physics. New York: Basic Books. Reprinted (1995) as An Introduction to the Philosophy of Science. Minneola, New York: Dover. Chalmers, D. (2006). Strong and weak emergence. In P. Clayton & P. Davies (Eds.), The reemergence of emergence (pp. 244–256). Oxford: Oxford University Press. Ellis, G. F. R. (2016). How can physics underlie the mind? Berlin: Springer. Healey, R.A. (2016) A pragmatist view of the metaphysics of entanglement, Synthese. Published first online 21 September 2016. https://doi.org/10.1007/s11229-016-1204-z. Hempel, C. G. (1965). Aspects of scientific explanation. New York: Free Press. Kim, J. (2005). Physicalism, or something near enough. Princeton: Princeton University Press. Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48(4), 507–531. Lange, M. (2017). Because without cause. Oxford: Oxford University Press. Laplace, P. (1820). Philosophical essay on probabilities. Republished 1951, New York: Dover. Lewis, D. K. (1973). Causation. Journal of Philosophy, 70, 556–557. Reprinted with postscripts in Lewis (1986). Lewis, D. K. (1986). Philosophical Papers, Volume 2. New York: Oxford University Press. Maudlin, T. (2007). The metaphysics within physics. New York: Oxford University Press. McLaughlin, B. (1992). The rise and fall of British emergentism. In Beckermann, Flohr, & Kim (Eds.), Emergence or Reduction? Berlin: Walter de Gruyter. Pearl, J. (2009). Causality (2nd ed.). Cambridge: Cambridge University Press. Pettit, P. (1993). The common mind. New York: Oxford University Press. Pettit, P. (2007). Joining the dots. Brennan, Goodin and Smith, eds., Common Minds. Oxford: Oxford University Press. Pettit, P., & Jackson, F. (1990). Program explanation: a general perspective. Analysis, 50(2), 107– 117. Price, H. (2017). Causation, intervention and agency: Woodward on Menzies and Price. In Beebee, Hitchcock, & Price (Eds.), Making a Difference (pp. 73–98). Oxford: Oxford University Press. Reutlinger, A., & Saatsi, J. (2018). Explanation beyond causation. Oxford: Oxford University Press. Ryle, G. (1949). The Concept of Mind. London: Hutchinson’s University Library. Salmon, W. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press. Strevens, M. (2008). Depth. Cambridge, MA: Harvard University Press. Weinberg, S. (1992). Dreams of a final theory. New York: Pantheon. Weinberg, S. (2001) Can science explain everything? Anything?, The New York Review of Books. Weinberg, S. (2015). To explain the world. New York: Harper Collins. Woodward, J. (2003). Making things happen. Oxford: Oxford University Press. Woodward, J. (2015). Interventionism and causal exclusion. Philosophy and Phenomenological Research, 91, 303–347.

Chapter 11

Top-Down Causation Without Levels Jan Voosholz

Abstract The paper addresses a question concerning George Ellis’s theory of top-down causation by considering a challenge to the “level-picture of nature” which he employs as a foundational element in his theory. According to the levelpicture, nature is ordered by distinct and finitely many levels, each characterised by its own types of entities, relations, laws and principles of behavior, and causal relations to their respective neighbouring top- and bottom-level. The branching hierarchy that results from this picture enables Ellis to build his model of modular hierarchical structure for complexity, his account of same-level, bottom-up and topdown causation, of emergence, equivalence-classes and multiple realisability. The three main arguments for the level-picture in Ellis’s works are reconstructed and shown to face serious problems. Finally, the paper presents a possible solution to this challenge by introducing a reformulation of certain fundamental points of Ellis’s theory that does without the level-picture of nature. This allows us to preserve all of his central claims about the model of complexity, the three types of causation, emergence, equivalence-classes and multiple realisability. Any problems pertaining to the level-picture can be remedied in the context of Ellis’s theory of top-down causation.

11.1 Introduction This paper sets out, firstly, to present a challenge to George Ellis’s theory of topdown causation by questioning what will be called the “level-picture of nature”, and, secondly, to argue that Ellis’s theory can answer this challenge if it adapts certain of its ontological premises. The level-picture consists in the claim that nature is ordered by distinct and finitely many levels, each with its own types of entities, relations, laws and principles of behavior, and causal relations to its

J. Voosholz () Institute for Philosophy, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_11

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respective neighbouring top- and bottom-levels. The branching hierarchy that results from this picture enables Ellis to build his model of modular hierarchical structure for complexity, his account of same-level, bottom-up and top-down causation, of emergence, equivalence-classes and multiple realisability. The level-picture is, on the face of it, a cornerstone of Ellis’s account.1 Yet this paper argues for three conclusions: (C1) Ellis’s theory of causation hinges—in its current form—on eight essential assumptions concerning ontologically robust levels of nature. Section 11.2. of this paper assembles these eight crucial points via a reconstruction of key passages of Ellis’s work. This serves to substantiate the notion of the level-picture. (C2) Ellis’s arguments in favour of the level-picture stemming from the debates on reductionism and emergence are not fully convincing—at least in the context of the current set-up of his theory. Upon closer inspection, various counterarguments reveal the level-picture to be questionable. Section 11.3. presents this dialectic, yet argues that a central insight can nevertheless be preserved: Ellis successfully establishes that there are constitutional hierarchies for physical entities and that there is a gradient of complexity of systems and structures in the universe. (C3) Therefore, the apparent failure of the level-picture of nature does not pose a fatal problem for Ellis. My argument for this claim consists in presenting eight alternative foundational hypotheses, which can stand in for the eight assumptions of the level-picture. I further argue that these hypotheses can be reconciled with the critical challenge outlined in the preceding section. Moreover, they can support the key elements of Ellis’s theory of causation, such as his modular hierarchical structure-model of complexity, the three types of top-down, bottom-up and samesystem causation, equivalence-classes and multiple realisability. The paper will also stress that this result ought not to be seen as a setback by proponents of Ellis’s theory: One line of criticism against his theory and other accounts of top-down causation, strong emergence and genuine complexity tries to exploit the gap in the argument stemming from the level-picture in order to suggest, explicitly or implicitly, that such accounts of causation are wrong. These kinds of criticism could be avoided if it were possible to establish either that a weaker epistemic notion of levels in the universe would suffice for Ellis’s position or even that his position remains tenable without any notion of distinct levels at all, instead simply using a gradient of complexity and constitutional hierarchies. I will

1 This

definition applies to many different theories of causation; it is neither limited to Ellis nor meant to imply that his proposal originated the level-picture. The latter can be traced back at least to Anderson (1972), who introduced this kind of formulation into the debates about emergence and causation. Thus defined, the level-picture is a broad concept with a long history in thinking about nature. Yet in every different theory of emergence and causation its defining features change considerably. Any critique has to focus on the particular analysis at issue. George Ellis’s theory is a perfect case in point, not only due to its substantial weight in the debate on causality in the sciences and philosophy, but on account of its clarity regarding the role of levels. For other literature on the level-picture in the aforementioned debates see (Kim 1992, 1999, Emmeche et al. 1997, 2000, Hulswit 2005, Paolini Paoletti and Orilia 2017).

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suggest that the latter is indeed the case. To argue for a complete theory of top-down causation and genuine complexity without distinct levels is a task yet to be achieved.

11.2 The Level-Picture of Nature Before we look at the arguments for and against, we first have to establish what use of “levels of nature”—the level-picture—Ellis makes in the scope of his theory (step 1), how his account of complexity and, in consequence, his different types of causation, rest on modelling physical systems as or within modular hierarchical structures by presupposing the level-picture (step 2), and finally, how his critics see the underlying assumptions about levels of nature at the foundation of his theory (step 3).

11.2.1 Ellis’s Theory of Causation, Complexity and Emergence George Ellis’s account of causation, put forward in his book How Can Physics Underlie the Mind? (Ellis 2016) and elsewhere (Ellis 2013, 2012, 2009, 2008, 2006; Ellis and Gabriel 2021; Ellis and Drossel 2019, 2018; Ellis et al. 2012, 2008), is generating increasing interest in discussions of causation in philosophy and the natural sciences. Ellis’s influential proposal employs the following definition of cause and effect: Causes are separated from effects by searching for correlations between phenomena such that manipulation of one (the cause) can be shown, in a specific context, to reliably result in specific changes in the other (the effect) at a later time. (Ellis 2016, p. 8)

According to the definition, a cause is a factor in the net of dependencies in the world, while an effect is a dependent knot, for if the cause is altered its effects differ too. Ellis’s definition closely resembles Jim Woodward’s so-called manipulability theory of causation (Woodward 2003, 2007, 2021). The basic idea is similar to other counterfactual theories of causation (Paul 2009, p. 166): If the cause were to differ or not obtain at all, the effect would also differ or not obtain at all. Usual problems with counterfactual theories resulting from over-determination, pre-emption and vicious circularity are amended by Woodward through tying causality to the idea that causes are manipulable in principle. He defines total causation as follows: X is a total cause of Y if and only if under an intervention that changes the value of X (with no other intervention occurring) there is an associated change in the value of Y. (Woodward 2007, p. 73)

Woodward offers corresponding definitions for (type-level) direct causes and contributing causes (Woodward 2003, p. 59). Contrary to other notions of intervention (like Price and Menzies 1993), Woodward tries hard to steer clear of human agency and subjectivity in his explication of an intervention, as the intervention by an act

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of free will is seen as just any other natural instance of an intervention from one system on another (Woodward 2003, pp. 94–112). The similarity between Woodward and Ellis is uncanny. The counterfactual, interventionist, non-subjectivist, ontological definitions of cause and effect by Ellis and Woodward are supposed to hold in every case, so it seems to suggest a monistic theory of causation, meaning the concept of causality picks out one single type of relation between entities.2 Yet, according to Ellis, even if we can define causes and effects in Woodward’s and his way, we find different kinds or types of causation at work in nature. Ellis works with three main distinctions: 1. Causation on the same level in nature (for instance, two comets that mutually attract each other in their gravitational fields when they closely pass by one another); 2. bottom-up causation across two neighbouring levels of the natural hierarchy, where the cause is at the lower level and the effect on the higher level (for instance, cell necrosis due to a high lead concentration causes the disfunctioning of an organ); 3. top-down causation across two neighbouring levels of the natural hierarchy, where the cause is at the higher level and the effect on the lower level (for instance, the running program in a digital computer determins the actions of the gates and memory registers). We will revisit these three types of causation later in more detail. First, it is important to note that Ellis uses all three types of causation to present a theory of the emergent complexity of entities on higher levels from lower-level parts or modules. According to Ellis, genuine complexity cannot emerge in a bottom-up way alone. [. . .] Like bottom-up causation, top-down causation should be seen as an inter-level phenomenon between neighbouring levels in the hierarchy. Just as bottom-up causation does not (clearly) imply the existence of a clearly identifiable bottom level, top-down causation does not necessarily imply existence of a clearly identifiable topmost level. (Ellis et al. 2012, p. 2)

If we were to assume that Ellis’s top-down causation is a real phenomenon, which we can find in many different domains of nature, then it exists independently of our scientific practices and of whether or not we register it in our theories. Since Ellis is quite clear that this is indeed the case, he holds a realistic and ontologically robust view of top-down causation. The question of how this is possible in light of his manipulability theory-style definition of cause and effect, is not addressed in Ellis’s works. Similar positions have been defended by Woodward (2008) and Siriwardena (2019) against criticism by Strevens (2007) and Price (2017) respectively. The following analysis does not attempt to pursue this discussion, but aims to show that Ellis’s three basic types of causation are ontologically distinct in so far as

2 There

is an extensive ongoing discussion in the philosophy of causation on the issue of pluralism and monism, see (Longworth 2006; Williamson 2006; Cartwright 2006, 2007; Psillos 2010; de Vreese 2010; Strevens 2013).

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they exhibit categorically different features. We will see that Ellis is able to make this distinction due to the placement of the causes and effects on different levels of nature in the cases of bottom-up and top-down causation. Should we be inclined to follow Ellis’s assessment that top-down causation is a real and ontologically robust phenomenon, we must accept that bottom-up and same-level causation are too. Furthermore, we would then need to concede that there are—in an ontologically robust sense, independently of our registration of them in our theories—different levels in nature. Ellis’s pluralist picture of causation is incomplete until we take his thoughts on the nature of emergence, genuine complexity and the specifics of interlevel causation into account: Ellis compares cases of weak emergence, like gas in a container, in which the complexity is no more than the sum of the effective parts, with instances of genuine complexity, for which strong emergence and top-down causation are necessary: Examples include the interconnected neurons in a brain, which form structures inexplicable by bottom-up causation alone.3 Aside from same-level causation, we also find interlevel causation, naturally subdivided in two types: Firstly, we have bottom-up causation, the cases where lower level parts add up to form, support or effect higher level entities. The parts form or constitute wholes in a hierarchical fashion, and so “each lower level underlies what happens at each higher level in terms of structure and causation” (Ellis 2016, p. 88). Secondly, we find top-down causation, where higher level systems and objects set constraints for lower level causation by providing a context in the form of specific structure.4 We can now see how, according to the theory, the three basic types of causation rest entirely on what I will call the MHS-model of causation and complexity (“MHS” for “modular hierarchical structure”). This in turn utilises the picture of levels of nature, which play the key roles of constituting parallel and intersecting hierarchies and so delivering the structure of nature. Both will be the topics of discussion in the next subsection.

3 “Genuine

complexity can only emerge from interlevel causation (both bottom-up and top-down) in modular hierarchical structures. [. . .] The structure is emergent from lower level entities, but is much more than the parts. It is the patterns of structuring that count. This is a higher level property of the system: its description requires variables that relate to more than just the properties of the components. [. . .] In addition to the properties of the units themselves, it is the set of relations between units [. . .] that is crucial to building up complexity. These aspects cannot be reduced to lower level variables. [. . .] Higher level structural patterns channel causation at lower levels in the system, breaking symmetry and so constraining what happens at those levels” (Ellis 2016, pp. 85–87). 4 Ellis can support this type of causation with any example where the whole determines movements of and changes to its parts, like the changes in the cardiovascular system due to heavy body movements of the whole organism. This seems to suggest that for Ellis a top-cause must always be deterministic for the bottom-effect. On the question of how top-down causation and the question of indeterminism fit together, see (Beebee 2014).

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11.2.2 The MHS-Model and the Levels of Nature Regarding emergence, Ellis states that the basis of complexity is modular hierarchical structures, leading to emergent levels of structure and function based on lower level networks. Each of these aspects (‘modular’, ‘hierarchical’ and ‘structure’) is crucial in the emergence of complexity out of interactions between simpler units. (Ellis 2012, p. 126)

This means any given complex system S can be differentiated into modules based on their function in S. Take the examples from the last subsection: If S is an organ, say a human heart, its parts (modules, subsystems) can be distinguished by their respective function (heart valves, chambers, etc.) and these parts are in turn comprised of cells. This perspective suggests that there is a hierarchy of structures. S is supposed to be more complex than any one of its parts (the modules/subsystems), and those in turn should be more complex than their parts (the module’s parts/sub-subsystems). If this constitutes a hierarchy, this complexity relation is transitive: S is more complex that its sub-subsystems. This means a heart is far more complex than a cell from the papillary muscles. Here, a worry could be raised: Depending on the supposed function of S and our description of the subsystems, one could certainly have a model of the heart with less complexity than that of a model of a single cell. This doubt disappears once we realise that Ellis’s modular hierarchical structures are located within real world ‘target systems’, not in our models of them, because the complexity of a (sub)subsystem of S always adds to the complexity of S: Firstly, due to the transitive nature of the structural hierarchy, if S is comprised of two subsystems (SU 1 , SU 2 ) S is minimally as complex as both subsystems combined (due to the principle of weak emergence). Secondly, according to Ellis, due to the modular structure of these subsystems, we sometimes find the emergence of genuine complexity in S, which is not present at the level of the two subsystems, but results only from their structured contextual interaction (principle of strong emergence). This is crucial: Only because of this emergent genuine complexity, can S possess properties which are not mere effects of a subsystem but uniquely appear where S is concerned as a whole. In this case, the complexity of S is higher than the sum of the complexities of all of its parts. But why must S and its subsystems be on ontologically distinct levels in nature? Up until this point, Ellis’s picture of nature seems only to indicate a gradient of complexity between subsystems and systems. Ellis associates the hierarchy of complexity with a particular hierarchy of sciences. He does this in a simple table: A simplified version of the basic hierarchy of complexity and causality for natural systems (left) and for human beings (right) is given in Table 11.1. [. . .] This figure gives a simplified representation of this hierarchy of levels of reality (as characterised by corresponding academic subjects) for natural systems (left) and human beings (right). Each lower level underlies what happens at each higher level, in terms of causation. There is no correlation between the left- and the right-hand columns above the level of chemistry, as emergence and causation are quite different in the two cases; but the first four levels are identical (life emerges out of physics!) (Ellis 2012, pp. 126–127).

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Table 11.1 The hierarchy of structure and causation Level 10 9 8 7 6 5 4 3 2 1

Discipline Cosmology Astronomy Space science Geology, earth science Materials science Physical chemistry Atomic physics Nuclear physics Particle physics Fundamental theory

Discipline Sociology/economics/politics Psychology Physiology Cell biology Biochemistry Chemistry Atomic physics Nuclear physics Particle physics Fundamental theory

From Ellis (2016, p. 6)

Ellis also has a deeper view on the question regarding the point at which genuine emergence occurs: The way they [the modules; J.V.] interact with each other at a specific level can be characterised by an interaction network showing which modules interact with which other modules through various possible interaction modes (inter-module forces, or matter, energy and information exchange); this is the structure of the system. Emergence of a higher level system from the lower level modules takes place when reliable higher level behaviour arises out of the lower level actions taking place in the context of this structure, with lower level units grouped together to form higher level modules that one can identify as meaningful entities that persist over time and have identifiable laws of behaviour. (Ellis 2012, pp. 126– 127)

The table and the descriptions combined are extremely suggestive: According to Ellis, the main target systems studied by the respective disciplines all seem to be on one distinct level of complexity in the modular hierarchical structure of nature.5 But is the whole of our solar system (as one level studied by solar system sience) more complex than the whole of the planet Earth (conceived as one system on its own level)? A critic could repeat this point time and again. Ellis answer to the

5 Take

solar system science: It studies our solar system. Modular subsystems on the same level of complexity and which causally interact with one another include the planet Earth, the moon Callisto, the dwarf planet Ceres, the Mars trojans, Halley’s Comet and many others. The causal relations form a net with an internal hierarchy (Ceres is part of the asteroid belt, moons orbit their planets, trojans are tied to their planets or moons and so on). Yet even at this one distinct level of nature, there are modular subsystems with greater complexity than others: Jupiter seems to be more complex than Halley’s Comet if we take Jupiter not only to have more functionally distinct parts (an outer and inner atmosphere with sub-parts like cloud layers, possibly a rocky core, etc. (Guillot et al. 2004)) than Halley’s Comet but also, due to the interaction of those parts, more genuine complexity, such as weather events (take the Great Red Spot). According to Ellis’s view, interaction between these two modules, Jupiter and Halley’s Comet, in the whole of the solar system still has to be conceived as same-level causation, even if there can be a difference of complexity between modules.

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question is: The solar system is more complex because it is a natural systems with subsystems, where the complexity of a part can never exceed the complexity of the whole it is part of, due to the relations I have outlined before: The complexity of a system is the sum of the weakly emergent complexity of its parts plus the strongly emergent, genuine complexity resulting from their interactions and relations with one another.6 This is the definition of all complexity according to the MHS-model. Yet, why should there be distinct levels in this ontologically robust way? Why not speak of a gradient of complexity (or rather multiple gradients of complexity) in any direction where natural systems form wholes and parts without clear borders? Each of the different levels of the hierarchy function according to laws of behaviour appropriate to that level, and are describable only in terms of language suited to that level [. . .]. Higher level entities, such as plans and intentions, have causal power in their own right, which partially determine what happens at lower levels in the hierarchy (billions of atoms and molecules move in accord with our intentions when we raise our arm). Here, we characterise a level as ‘higher’ when it can be shown to influence another level (‘a lower’ level) by setting a context that guides the way the lower level actions take place. (Ellis 2012, p. 127)

This does invite another reason to think of these levels as not distinct or not real: If an event, process, state, system, etc. on the higher level sets the context, for instance by setting certain boundary conditions (the orbit of Earth around the sun sets certain boundary conditions for Earth’s climate), it is easy to see gradual differences between individual systems and subsystems. Yet it leaves completely open how one might justify a hard level distinction. Ellis is very clear on this point: Each higher level physical element, created by structured combinations of lower level elements, has different properties from the underlying lower levels—the entities at each level show behaviours characteristic of that level. [. . .] Essential Differences Between Levels. Hierarchical structures have different kinds of order, phenomenological behaviour, and descriptive languages that characterise each level of the hierarchy. It is sometimes queried whether these levels actually exist “out there”, or are rather impositions of the mind. My position is that different kinds of causation do indeed exist at the different levels as characterised here, and the mind recognises these distinctions which actually exist. They are not just inventions of the mind. Atoms are different from molecules, whether characterised as such by a mind or not. (Ellis 2016, p. 89) Existence. The different levels are all real, each existing with causal powers in its own right, because [. . .] they each have determinable effects on the levels above and below them. No level is more real than any other. (Ellis 2016, p. 90)

6 The option to define a natural system by way of analysing whether its complexity actually exceeds

and not only equals the complexity of the sum of its real functional parts (which would supposedly be the case for any mereological sum of the complexity of arbitrary parts, say the planet Mars and the exoplanet TrES-3b regarded as one part) is not further pursued in Ellis’s work as far as I know. If this were possible it would offer a way to search for cases of strong emergence and top-down causation (understood as feedback loops).

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Table 11.2 The hierarchy of structure and causation with example target systems Discipline Level Inanimate matter 10 Cosmology 9

Target systems Universe

7

Galaxies, star clusters Space science Solar systems/ interstellar space Geology, earth science Planets

Cell biology

6

Materials science

Biochemistry

5 4 3

Physical chemistry Atomic physics Nuclear physics

2

Particle physics

1

Fundamental theory

8

Astronomy

Discipline Target systems Living matter Sociology/economics/ Global society politics Psychology Minds

Metals/semiconductors/ceramics/ polymers Molecules Atoms Nuclei/ protons/neutrons Quarks/ leptons/bosons/ quantum fields Strings/etc.

Physiology

Chemistry Atomic physics Nuclear physics Particle physics

Fundamental theory

Human/animal/ plant bodies Cells/cell organelles Biomolecules

Molecules Atoms Nuclei/ protons/neutrons Quarks/ leptons/bosons/ quantum fields Strings/etc.

From Ellis (2016, p. 6), target systems added by J.V.

The apparent reason to assume levels exist in an ontologically robust, real way, independently of their registration, is that the three different forms of causation hinge on the existence of different levels, and we can make empirical discoveries about causation once we accept the Ellis-Woodward definition. The exact arguments for this will be analysed in Sect. 11.3 below. Yet before we come to that, I want to bring out another consequence resulting from the long quote from Ellis above: The scientific disciplines characterising the 10 levels in Table 11.1 are of course practices of human animals on planet Earth, with their respective histories and so on. As all levels exist independently of any registration of them, they exist independently of the respective discipline(s) that researches them. Ellis characterisation seems to be merely instrumental: They are in reality constituted by the entities with causal effects on other entities (on the same or neighbouring levels). In other words, the target systems of the respective sciences are naturally organised in distinct levels. Table 11.2 gives important example target systems for every level of nature. On Table 11.2, we can now see that Ellis employs the level-picture of nature to categorise (“real”) systems as belonging to certain levels depending on their complexity. He then utilises this division to introduce his concepts of emergence and same-level, top-down, and bottom-up causation. Before we turn to the arguments

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for and against the level-picture, it is important to explicate the eight main points that underlie the levels picture on this reading of Ellis’s theory. It will later become apparent that each of these eight points can be appropriately reformulated, even if we abandon the level-picture of nature.

11.2.3 The Eight Points on Levels According to the interpretation given above, Ellis holds the following view of levels, which he exploits within his theory of top-down causation and emergence: L1 Levels are structures in nature and real in the sense of existing independently of our (or any) knowledge of them. L2 Any fully or partly concrete (meaning: existing in spacetime) object or system is situated on a certain level in nature and behaves according to a set of principles and laws effective on this level, which can possibly be discovered by science. L3 Levels are ordered by the degree of complexity of the objects and systems that are found on them. It is unclear whether there is either a top or a bottom level (or which ones they would be). L4 To describe different levels (and the associated objects, systems, structures, laws and principles), we need to deploy different scientific languages and different variables suited to any one level. This results in the disunity of sciences, where for every level we have one (or more) science studying it. L5 For any system S on level n we can identify parts of it either on level n or n−1 . For any object O, located on level n, considered as a whole, there are proper parts of it either on level n or n−1 . L6 Levels are distinct entities with clear boundaries, which are marked by emergent objects and systems with corresponding properties, structures, principles, laws, and variables, which can neither be found at, nor explained by, nor fully accounted for by the next lower or higher level. L7 For any level n (apart from a theoretically existing bottom level) there exists exactly one lower level n−1 , which constitutes the complete set of basic parts for all systems and objects on n. In this sense the lowest physical levels are the basis for everything else in nature. L8 For any level n (apart from a theoretically existing top-level) there exists one higher level n+1 , which might be branched. This means it is possible that different higher levels of complexity are constituted by the same lower level. This is the case for levels 4 and 5, where 4 – the level described by atomic physics – forms the basis for level 5, on which the branch of life departs from the branch of inanimate nature, as represented in the sciences of chemistry and physical chemistry. In the next section, I will critically question L6 and so raise a doubt regarding L1 by first presenting Ellis’s arguments for the level-picture and show that they do not fully support L1 and L6. Following this step, instead of arguing against Ellis’s account of top-down causation, I will propose a reformulation of L1–L8 in order to show that his theory can be stated in terms that do not impose a level-ontology

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onto nature. In particular, the idea of modular hierarchical structures, which can be parallel to or intersect one another, will be preserved. Furthermore, his idea of a plurality of causal modes transecting systems of different complexity and the borders of animate and inanimate parts of nature, minded and non-minded reality or the realm of the concrete and the abstract will be left intact by my criticism of the level-picture of nature.

11.3 Arguments for and against the Level-Picture We can now reconstruct the arguments speaking for and against the level-picture as outlined above (3.1). Though they remain partly implicit, it is possible to distinguish three arguments in Ellis. In a further step (3.2), we consider the possibility of giving up the level-picture. Fortunately, there are good reasons to hope for a superior replacement for the level-picture in antireductionist theories of causation in general and Ellis’s in particular. So even if a critic does manage successfully to argue against the level-picture, she does not thereby refute Ellis.

11.3.1 The Arguments for the Level-Picture We will review Ellis’s three arguments for the level-picture in turn. The first argument rests on Ellis’s account of genuine complexity and laws. We will see how this argument has the disadvantage of being unable to justify the level-picture as such, because it leaves us stranded half way. The second argument hinges on the apparent disunity of science. We can characterise the problem here as a categorical one: If this argument were successful, it would only prove an epistemic notion of levels derivative from contingent languages and scales. But this limited conclusion may also be attacked by the critic in turn, because the argument might beg the question. The third argument is the strongest: It takes the different local ontologies for different contexts in nature and establishes the existence of wholepart-relationships between entities from different local ontologies. Two consecutive counterarguments by a potential critic of Ellis’s third argument point in the direction of an alternative to the level-picture.

11.3.1.1

The Argument from Genuine Complexity, Principles and Laws

Ellis’s first argument tries to individuate distinct levels in nature in light of the facts that, firstly, laws of nature (or—to put it more cautiously—reliable principles of behavior) affect only certain entities at a certain scale (of complexity, mass, length, etc.) and, secondly, there are intrinsically higher level variables of an abstract nature

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and determined by a higher-level logic, which are cases of genuine complexity above the physical laws of nature. Ellis expresses this in the following way: Each of the different levels of the hierarchy function according to laws of behaviour appropriate to that level [. . .]. (Ellis 2012, p. 127) Each higher level, created by structured combinations of lower level elements, has different properties from the underlying lower levels—the entities at each level show behaviours characteristic of that level. (Ellis 2006, p. 80) Specific higher level variables characterise the macroscopic state of the system at a specific level, and occur in effective laws of behaviour at that level. (Ellis 2016, p. 12) Higher level variables [e.g. for properties of systems, J.V.] may be emergent from the lower level variables [. . .]. However, there are some kinds of higher level variables that are not emergent: they are intrinsically higher level variable [which in this paper are called strongly emergent; J.V.]. (Ellis 2016, p. 105) Though they are realised in various lower level physical substrates, they are determined by higher level logic, and so are intrinsically of higher level nature: 1. Algorithms. Examples are quicksort or the Google search algorithm [. . .]. 2. Codified Laws of Physics. Our mental representation of physical interactions, such as Newton’s equations or Maxwell’s equations, the foundation of mechanical and electrical engineering, respectively. 3. Social Agreements. Examples are the rules of football, [. . .] the constitution of an organisation, or exchange rates for money. 4. Conceptual Plans. Examples are the plans for a building, a town, an aircraft, or for a musical concert, a company, or a physics experiment. [. . .] Intrinsically Higher Level Variables. These are not physical variables, and there is no way to obtain them by any kind of coarse-graining process. Rather they are of mental or abstract nature. However, they are certainly causally effective. (Ellis 2016, p. 108)

This argument is twofold, but both lines of reasoning are intertwined: Firstly, there are principles and laws which only hold for a specific context. Examples include the gas laws, which are applicable only to gases, the Friedmann equations, which apply only to expanding space, generalised Lotka–Volterra equations, which apply only to species in competition and trophic relationships in a closed ecosystem. Take the level of statistical mechanics (level 4, inanimate branch in Table 11.2), with target systems such as confined gases in experimental chambers or mesoscopic natural systems of gases: only these systems, gases, can be modelled with the variables behaving according to the gas laws on that particular level of physics. The same holds for the Friedmann equations, which are valid only for the extending space of the universe on the level of cosmology (level 10, inanimate branch in Table 11.2), and for Lotka–Volterra equations, which only describe the behavior of populations of species in direct competition or trophic relationships in one ecosystem over time on the level of ecology (possibly level 10, animate branch in Table 11.2). In all these cases, the subsystems of the three example systems (single molecules in the gas, stars or galaxies within the universe, individual animals or plants) do not show similar behavior. They do not even possess the properties which are important for law-like behavior (a single molecule has no temperature or pressure, etc.). Therefore, the variables of the equations cannot be applied. So, the first step of the argument clearly shows that we have to cross a distinct border of levels in

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nature if we go from subsystem to system in these (and other) cases. Ellis concludes that we here have instances of hierarchical complexity and (what we have called in this paper weak or strong) emergence: New laws, principles and properties arise in the order of nature and, depending on our chosen scale, we have to apply different variables which stand in different relationships with one another. Now we can analyse the next step of the argument: as Ellis’s examples of algorithms, social agreements, etc. indicate, the higher levels of natural organisation somehow allow for cases of genuine complexity in which intrinsically higher-level variables appear: Fully abstract variables which behave according to rules of logic or discourse. Social agreements are reached in historic processes of discourse— rational argumentation, group negotiation, exercise of power, etc.—, algorithms are executed by a local conventional logic (binary code in a digital computer, a formula in a formal language on paper). Neither can be accounted for by physical properties or entities alone, even though both can be realised in physical systems (an actual computer or an actual group of people and so on). Both steps of the argument are intertwined because the first step introduces constitutional hierarchies with distinct levels via level-specific properties and laws of behavior on which the second step is dependent, while the second step places our codified laws of nature and their variables as abstract entities in nature, to allow the first step to take place. With Ellis, we can resist any criticism of this as begging the question: This does not involve a vicious circle, because only our discoveries of and epistemic access to level-specific properties and laws of behavior are dependent on pre-existing discourse and logic (which can be justified and explained with other arguments), and not the entities with said properties or their behavior according to laws or principles. Yet both parts of the argument, if we grant the premises, suffice only to establish that we have particular constitutional hierarchies with weak and strong emergence as well as cases of genuine complexity, and that these constitutional hierarchies have different levels in the sense that (weakly) emergent variables or (strongly emergent) intrinsically higher-level variables for higher-level properties can be found at the level of the complete system, while these properties are absent in all subsystems. It does not prove that these particular constitutional hierarchies can all be integrated into the general branching hierarchy Ellis shows us in Table 11.1 or 11.2, where all systems fall into one of ten levels. Certainly, it does not convince the critic that the outcome of such an integration would be the discovery of real levels, existing in the ontologically robust sense defined by L1/L6 in the last section. This conclusion needs another step, which would take us from constitutional hierarchies with levels of emerging properties and abstract variables to L1 and L6. This first argument has the disadvantage of being unable to justify the level-picture as such, because it leaves us stranded half way.

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J. Voosholz

The Argument from the Disunity of Scientific Language

When Ellis writes about levels, appropriate laws and genuine complexity, he almost always speaks about the different languages of different sciences. Could this help to bring us the rest of the way to the level-picture? Ellis’s second argument seems to pick up the thread right where the first argument left off: Each higher level physical element, created by structured combinations of lower level elements, has different properties from the underlying lower levels [. . .]. Each level is described in terms of concepts relevant to that level of structure (particle physics deals with quarks and gluons, chemistry with atoms and molecules, and so on), so a different descriptive language applies at each level. Different levels of the hierarchy function according to laws of behavior appropriate to that level, and are describable only in terms of language suited to that level. One cannot even describe higher levels in terms of lower level languages because a different phenomenological description of causation is at work at the higher levels, which may be described in terms of different causal entities. Ideas applicable to lower level causation do not by themselves succeed in explaining the higher level behaviors, for the concepts employed are simply not appropriate to the higher level kinds of causation [. . .]. Essential Differences Between Levels. Hierarchical structures have different kinds of order, phenomenological behavior, and descriptive languages that characterise each level of the hierarchy. [. . .] Thus the hierarchy on the life science side is in term of function and causation rather than the scale of physical entities. The hierarchy is determined by finding out what entities—physical or otherwise—exert constraints or set conditions so as to channel interactions between elements which have their own laws of interaction at their own level, for any environment acts in this way on any system it contains. Together with a careful analysis of what more complex elements emerge from simpler ones, this defines which is a higher level and which a lower level in the hierarchy. (Ellis 2016, p. 89)

Here, Ellis takes the constitutional hierarchies with different levels and the intrinsically higher-level variables as granted and adds an observation regarding the apparent disunity of science. We have different sciences exploring different contexts in nature: Sometimes they look at a specific length or energy scale like radioactive atoms, sometimes they focus on a functional context like different ecosystems, sometimes they concentrate on a type of entity like cells. In order to understand these contexts of nature, the scientists develop their own languages suited to their fields. Apart from science-specific notions (“proton; niche; vacuole”) and kinds of description, they often introduce scales with their own units and variables with an associated formal notation. Using these, it is often possible to identify the relevant entities of the context, their properties, relations, laws of behavior, and to explain phenomena and patterns, make predictions, design experiments, control the context and so on. Ellis notes that it is not possible to take the scientific language (with its concepts, scales and variables) of one context and use it to describe another. One cannot use nuclear physics to explore ecosystems or ecology to investigate cells. He associates this contention with the conclusion of his first argument for constitutional hierarchies with different levels and intrinsically higher-level variables, equating these levels with the contexts of nature researched by different special sciences.

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This is the crucial point of this second argument, and it also explains why Ellis uses scientific disciplines to designate ontologically robust levels of nature in his Table 11.1: If the countless constitutional hierarchies of different systems could all be integrated into a single hierarchy formed by (a limited number of) different context of nature, which in turn would comply with the structure of present-day scientific disciplines and their languages, scales and variables (Table 11.1), then the level-picture would be justified. Whilst Ellis is right to acknowledge the disunity of the sciences, the critic may well regard his further step of associating the many constitutional hierarchies of natural systems with the context under investigation by the various sciences as unmotivated and problematic. Take a human body: A physician can study the organisation of the organs and the role the liver plays within it, while a cell biologist can concentrate on liver cells and a biochemist can look into certain sets of molecules in these cells. All three scientists use different languages, and they investigate different levels of the same constitutional hierarchy. Yet this does not prove that all constitutional hierarchies are integrable into one global hierarchy. It shows that the contexts investigated by these scientists overlap insofar as they study three systems standing in a whole-part-sub-part relationship. The overlap is reflected by the language of the disciplines: The concept of “hepatic lobiles” is used in physiology and cell biology alike, the concept of “DNA” in cell biology and biochemistry. There is no hard disunity here, no distinct borders, only a particular constitutional hierarchy. Thus, the one further conclusion we can draw here is that the present-day sciences have different languages, scales and variables suited to contexts of phenomena and that these contexts often overlap because the systems under investigation stand in whole-part relationships. It is neither clear that the contexts of phenomena are necessarily all “naturally distinct” and have sharp borders, nor—even if they were— that these contexts form a single branching hierarchy of distinct levels, which could integrate every constitutional hierarchy of natural systems. Just because we might call the context of the phenomena investigated by ecology the “level of ecology”, it does not follow that it is equivalent to a distinct level within all constitutional hierarchies of natural systems. The only possibility with which the critic leaves us is to show that the merely epistemic and operational level of ecology is equivalent to a distinct context in nature by proving that all the systems in context (all ecosystems) share one similarity in their respective constitutional hierarchies: Having the same general levels of nature as a single meta-structure for all respective levels in the constitutional hierarchies to appear on. But the critic will remark that this would beg the question: We would need to assume general levels in nature to make the argument work in the first place. So even if one could link every science to a distinct context in nature, the argument would still be circular.

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The Local Ontologies Argument

If we concede to the critic that the first two arguments are not able to prove the levelpicture, we can still try to reconstruct an argument that avoids the main problems: We cannot start with differences in scientific languages, and the constitutional hierarchies and their (weakly or strongly emergent) levels do not cut any ice by themselves. But what if we concentrate on the different “local” ontologies of the numerous contexts of nature directly? This is the path taken by the third argument. Albeit more implicit than the first two, it is contained in another explicit argument. Let us therefore consider Ellis’s antireductionist argument, which provides another reason to think of levels as distinct and real: The core of the reductionist view is that everything can be explained by such bottomup mechanisms based on the laws of physics, with no remainder. [. . .] The phenomenon of emergent order is when higher levels display new properties not evident at the lower levels. More is different, as famously stated by Anderson. Emergence of complexity takes place where quite different laws of behavior hold at the higher levels than at the lower levels. These properties are characterised by named higher level variables, and it is the symbolic naming of these variables that enables us to contemplate their nature. (Ellis 2016, pp. 99–100)

Ellis continues this line of thought by considering the example of the structure of a forest (how the trees, rocks, plants, rivers, etc. are grouped in the landscape) as a formal cause (by setting constraints to effective causal agents such as wind or fire) of the type of top-down causation: The structure as a top-down cause is not operative without an effective causal agent, yet it has causal power over lower level entities (such as the movement of animal bodies). The problem for the reductionist is now that on her picture, it seems impossible even for the lower level entities (rocks, rivers, fire etc.) to do any work in explaining what happens, as they are made up of lower level elements and so do not possess real causal power or effectiveness. They do not exist, strictly speaking. In fact nothing does, except vibrations of superstrings, if they exist, which may or may not be the case. Lower level causality vanishes into unknown and untestable regions. The only sensible way to handle this is to take an interlevel view, i.e., forget the bottommost level and assign real causal power to the lower level with respect to its immediate upper level, and to do this for every pair of levels: Interlevel Causation. For every pair of levels (N, N+1), the lower level “does the work”, but the higher level is able to influence what work is to be done by setting constraints on the lower level operations. This is the basis for regarding every level as real: each is able to do real work. If we don’t take this view, then genes and neurons are not able to do real work, as they are not the lowest level [. . .]. (Ellis 2016, p. 112)

The argument is directed at strict reductionism. In Ellis’s view, its conclusion establishes the reality of distinct levels. How? By explicitly delivering a reason for thinking that entities on all levels have real causal power and/or effectiveness and implicitly introducing the premise that every entity depends upon its appearing on one distinct level in nature. If that premise were true, it would follow that the distinct levels were necessary conditions for any entity to “do work”, to cause at all.

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The reason for the premise—every entity depends on its appearing on one distinct level in nature—can be explicated by following the thrust of the overall argument. I will call it the local ontologies argument: The ontologies (and not only the languages) of sociology, cell biology, astronomy and particle physics are radically different (they name different entities which are connected by different laws, principles and relations), yet their respective target systems all do “real work”, i.e., possess causal power and/or can be causally effective. If the ontologies of these sciences devoted to different respective contexts—let us call them local ontologies—are necessary for their entities to stand in (causal) relations to one another and to exhibit law- and principle-guided behavior at all, then they have to constitute a distinct level. As the antecedent is the case—the entities sometimes stand in (causal) relations and exhibit such behavior—distinct levels are real. The critic will of course object that Ellis again fails fully to establish what he purports to, even if we grant all the premises. If we do grant them, the main conclusion is that all the different target systems are real (see Table 11.2) and possess causal power and/or effectiveness. This does represent a partial success; it proves that the different local ontologies of different disciplines are equally correct. What is missing is an argument establishing that if there are (correct) local ontologies with sets of (real) entities, then they necessarily form distinct levels, one level per local ontology. One can think of two arguments against this assumption. The first can be posed as a question: If nature really falls into a limited number of distinct levels, what would follow? The second counterargument states that even if it were possible to operate with a multitude of levels, these levels would not be distinct in the way Ellis seems to believe. Counter 1: Infinite Hierarchies Let us start with a premise Ellis and many others share. For many entities (say, a particular cell) we can find a constitutional hierarchy: It is composed of organelles, which are in turn composed of bio-molecules, etc, all while the cell itself might be a part of an organ, which is part of an animal etc. The levels of this hierarchy (of cell A), running both upwards and downwards, can be very different from the levels of another hierarchy (of cell B, which is a Acidithiobacillia): This other hierarchy has different organelles and is not part of a larger organ or life-form etc. The critic could make a similar argument for two molecules, one a N2 H + -molecule in a gas cloud in the star-forming region ρ Oph A (Liseau et al. 2015, p. 2), the other a molecular iron complex in the steel of a sword. The hierarchies of cell A and B (and the two molecules) seem to involve very different levels. Someone defending Ellis could counter that this is only partially true. Cells A and B might have different upwards hierarchies but the same downwards hierarchy, and it is this fact (the identical downward hierarchy) that identifies two entities as belonging on the same level in nature. This solution seems plausible, since the structurally different cell organelles7 are on one level with the whole cells (see

7 In

cell A we find a cell nucleus and in cell B we do not.

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Table 11.2), yet all the sub-subsystems (bio-molecules) and sub-sub-subsystems (atoms) are on the same lower levels. But why should cells and cell organelles be entities on one level, yet bio-molecules on another level? Since some organelles could be just macro-biomolecule, or (if we exclude this by defining a cell organelle as having at least two molecules as parts) the part-whole relationship between cells and cell organelles holds just as well as that between organelle and bio-molecules. In any case, it is unclear why the distinct level border between cell–organelle–biomolecule should be drawn so as to split the first part-whole relation or the second and not the other. Defending Ellis, we could introduce an extra level (and so a second border) between cell and bio-molecule, namely the newly minted level of organelles. But we have to repeat this manoeuvre for every example where we find part-whole relationships that seem to occur on the same level. Soon, we would have discovered a multitude of distinct levels. The critic might find different constitutional hierarchies for every “natural kind” or type of target system, maybe in fact for every physical entity. This would mean that there are (almost) infinitely many hierarchies, each possessing many more levels in turn. This would not only make the level-picture difficult to manage within the scope of Ellis’s theory; it would also make it impossible to support the missing premise in the local ontologies argument: Even for a small local ontology with a limited set of entities, one has to deal with a vast number of levels. If the local ontology is that of standard-model particle physics, meaning there would be a reason to be concerned only with the downward hierarchies, it might be possible to accommodate all levels. Yet for cell biology or physical chemistry, as the examples above show, it is unfeasible. Certainly, there is no one-to-one correspondence between level and local ontology, yet this is exactly what would be needed to argue for the missing premise. Counter 2: Against Distinctness From the critic’s perspective, another argument is more damning for the levelpicture: Let us, for the sake of the local ontologies argument, assume that a multitude of levels would be manageable—say one hundred levels. Let us further stipulate that we could find a hundred suitable local ontologies, which could be grasped by various disunified sciences. Why should these 100 levels be distinct, with clear cut boundaries, such that for every abstract or physical entity with causal power/effectiveness (electrons, the structure of a forest, the Google search algorithm, Acidithiobacillia cells, a N2 H + -molecule in a gas cloud, the plan to build an aeroplane, to cite just some examples) we would have a corresponding level number from 1 to 100? From the reconstructed argument above, the only answer seems to be that the entities at each level always fall within one (and only one!) level-specific local ontology (which Ellis in fact—for simplicity’s sake, as he writes—associates with twenty-first century scientific disciplines, while the 100-natural-level-hierarchy we are contemplating is associated with the fictitious scientific disciplines of an ideal future). Yet some entities seem to appear simultaneously in different ontologies: Electrons show up in explanations in material science, particle physics,

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and physiology (in explanations of neural activity for instance); N2 H + -molecules are referenced by astronomy and chemistry alike; the Google search algorithm appears in sociology and computer science—and all within Ellis’s simplified model. It will certainly become a lot more intractable if we try to differentiate between 100 levels. One solution could be that the Google search algorithm designates a different entity in sociology and computer science (so would electron, etc.). This is implausible, however, because even if different sciences with different local ontologies investigate the different properties of different target systems, not only does the algorithm preserve key properties (being an abstract entity, giving a probability distribution for links/web-pages, etc.), but its properties in one local ontology are only fully understandable against the background and within the context of the other local ontologies: The development of the algorithm (and any changes that were made) makes sense for a computer scientist only with its social function in mind, while its success as a tool in global society can only be explained by reference to its mathematical qualities which cause its relative reliability. Even if this problem could be resolved, the solution of confining entities to one level would still fail: Ellis’s theory insists that the systems of one level make a reappearance on the next higher level as possible parts. Might this last point hint at a resolution of the puzzle: systems of level 4 reappear on all higher levels as subsystems and sub-subsystems? Unfortunately not. The Google search algorithm is a proper object of study for sociology and computer science alike, as is fear for physiology, psychology and political science, or water in chemistry, geology and solar system science. All of these appear as proper entities in different ontologies, i.e. target systems in different sciences, not only as parts or subsystems. It is also not true that a system appears only in the neighbourhood of a few levels: the electron and water are telling examples. If we apply the 100-naturallevel-hierarchy to these examples (with a hundred levels and sciences) it results in even more problematic cases. Both counterarguments clearly show that the local-hierarchies-argument does not establish the existence of distinct levels of nature. This failure does not harm the main conclusion of Ellis’s argument against reductionism, because this does not require the full-fledged level-picture. All of Ellis’s partially implicit arguments for the level-picture seem to fail; but in all three cases, many of the desired conclusions for which Ellis mainly argues follow anyhow: The argument for constitutional hierarchy and genuine complexity, the argument for the disunity of sciences and different phenomenal contexts, and the argument against strict reductionism all succeed—without proving the level-picture. The failure of the local ontologies argument provides a good reason to think of Ellis’s ten distinct levels as a hypothesis for his theory. It is neither proven empirically in cosmology that all systems of the universe fall into distinct levels, nor do science studies of any kind suggest that all scientific ontologies need to operate with a finite number of distinct levels to account for their respective entities, nor is it a result of fundamental theory. In my view, the level-picture seems to

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be a reductionist premise which was spared by Ellis’s critique and utilised for the threefold distinction of same-level, bottom-up and top-down causation and to grant every emergent natural entity a context in which it can “really” exist with causal powers/effectiveness. If that were true, there could be a possibility for Ellis to drop the level-picture but keep his theory intact nevertheless.

11.3.2 Why We Should Give Up the Level-Picture From our discussion of these arguments, it follows that Ellis’s theory of causation and emergence does not have good reasons to assume the level-picture. Yet the same arguments suggest that it is not so much a cornerstone of the theory as it is a contingent addendum to the theory. Therefore, we can apply Occam’s razor and see if we might dispense with this hypothesis. As will be shown below in section 4. in more detail, we can find alternative, weaker assumptions which can take over the role of the level-picture. The first argument is that it would thus simply be good scientific practice to jettison the level-picture in accordance with the principle of scientific parsimony. Another important reason to abandon the level-picture derives from our considerations of Ellis’s antireductionist argument above. It is not only a bone of contention for reductionists but a possible weakness to be exploited by them in arguments against Ellis. The level-picture works in favour of reductionism. It states that the basic ontological structure of nature is a single branching tree with fundamental physics at its root, only two branches (the animate and the inanimate), and a finite, neat number of distinct steps in complexity from the most basic components to the most elaborate systems, such as the universe, global society or the human mind. And moreover, it invites the idea of total reduction, because so many systems in one distinct level are just weakly emergent from subsystems on the next lower level (Luu and Meißner 2021; Castellani 2002).8

8 Ellis’s argument

stands in a long line of antireductionist arguments that follow Anderson’s classic criticism of the constructionist hypothesis, that is “the ability to start from those [fundamental] laws and reconstruct the universe”, because “at each new level of complexity entirely new properties appear”. (Anderson 1972, p. 393) Many philosophers and scientists with the same agenda follow his lead (see Meyr 1988; Nagel 1998; Castellani 2002; Ellis 2006; Chalmers 2006; Corning 2012). Thomas Nagel’s argument against reductionism, for example, introduces levels in nature as joints in nature (Nagel 1998, pp. 7–12): Our explanations and theories always focus on a specific level, depending on which scale we are looking at. According to Nagel, not all natural kinds and laws can be defined in this reductionist way, functional properties in biology being a case in point. One consequence of his argument is that levels in nature are real because the natural kinds of the higher level of biology cannot even in principle be defined by the fundamental level of physics. So we have at least two distinct levels: The fundamental level of physics without functional properties and the higher level of biology with them. Only an ontological reductionist could claim the absence of distinct levels of nature. Nagel does not find a joint in nature which separates the level of larger entities with functional properties and the level of smaller entities without them. (Though even this

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The third argument for abandoning the level-picture is that multiple parallel and intersecting modular hierarchies of structure and a gradient of complexity are more compatible with the local ontologies of disunified and specialised sciences with overlapping contexts of interest. The transdisciplinary and intersecting structure of different scientific disciplines and sub-disciplines is captured more accurately and easily without the level-picture. A rigorous proof of this would have to venture deep into both the philosophical meta-theory of current science and empirical studies of research programmes, which are tasks for another time. Such a proof would likely constitute a further, positive argument for favouring a picture of nature without levels.

11.4 Top-Down Causation Without Levels In this section, our question is what becomes of Ellis’s theory of (top-down) causation and emergence if we would decide to abandon the level-picture of nature. It will be answered in two steps: Step one revisits the eight fundamental points, as reconstructed from Ellis’s theory in Sect. 11.2.3 above. The aim is to reformulate all eight in light of the criticism of the level-picture, and subsequently prove their value as a foundation for the core concepts of Ellis’s theory. Accordingly, the second step is to sketch this possibility.

11.4.1 The Eight Points Revisited To reformulate all eight points so that they function as a foundation for Ellis’s theory without using the level-picture of nature, we must keep in mind three things: (1) We cannot eliminate the notion of levels completely, because the MHS-model requires the “H”, the numerous hierarchies, the whole-part relationships of natural system. Without hierarchies, there will be no bottom-up or top-down causation, which is perhaps the key feature of Ellis’s account. (2) At the same time, we have to be careful not to reintroduce the level-picture by a sleight-of-hand or by accident. We thus have to, firstly, ensure levels are not construed as necessarily distinct, and secondly, accommodate multiple (possibly infinitely many) hierarchies and therefore levels, and thirdly, secure any other notion which might play the role of levels, by making sure it is not necessarily distinct or only conceived in a finite number either. (3) It would be best if we would not introduce new concepts into Ellis’s theory but employ the conceptual means already at our and his disposal, i.e. concepts used in the reconstruction of his position and arguments.

is debatable; for a definition of every physical property as dispositional and second-order functional property see Yates 2012.)

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I will first present the reformulated eight points, then revisit L1–L8 and compare them with their new counterparts. Here are the alternative (“A” instead of “L”) eight points: A1 Levels are layers in the constitutional hierarchy of fully or partly concrete (meaning existing in spacetime) objects or systems and real in the sense of existing independently of our (or any) knowledge of them. There is an infinite number of parallel and intersecting hierarchies for all such entities and therefore infinitely many levels (from now on designated as CH-levels, for “constitutional hierarchy”). A2 Any fully or partly concrete entity can appear in a context with its own local ontology and behaves according to a set of principles and laws effective in that context, which can potentially be discovered by science. A3 CH-Levels are ordered by the part-whole relationships of the hierarchy to which they belong. It is unclear if there is either a top or a bottom CH-level (or also which ones that would be) in any hierarchy. All fully or partly concrete entities in and across contexts are ordered by their degree of complexity, their properties and their relations with one another, which are all subjects of the local ontology of a context or of an intersectional ontology of an intersection of many contexts. A4 To describe different local or intersectional ontologies (and the associated entities they contain—the types of objects, systems, structures, properties, relations, laws and principles) we need to deploy different scientific languages, scales and variables suited to any one local or intersectional ontology. This results in a disunity of sciences where for every local or intersectional ontology we have one (or more) science studying it. It is important to note that, depending on the local ontology, scales and variables can be structures in SV-levels (for “scale and variable”, they do not have to be structured in this way), which are epistemic and should not be confused with CH-levels. A5 For any system S in context n we can identify parts of it either in context n or an intersection i of different contexts, constituting the next lower level in the constitutional hierarchy of S. For any concrete object O, located in context n, considered as a whole, there are proper parts of it either in context n or contextintersection i. A6 CH-Levels are marked by emergent objects and systems with corresponding properties, structures, principles, laws, and assigned variables which can neither be found at, nor explained by, nor fully accounted for by the next lower or higher CHlevels. A7 For any CH-level l (apart from a theoretically existing bottom-level) in any hierarchy Hs of a physical system S there exists a finite number of neighbouring lower CH-levels l −1a , l −1b , . . . , which constitute the complete set of basic parts for all (sub)systems and objects on l. In this sense, the lowest physical CH-levels in any constitutional hierarchy of concrete objects or systems are the basis for everything else in nature. A8 It is possible that many different lower CH-level states Sl11 , Sl21 , . . . of system S constitute S with exactly the same properties in its context ns . It is important to note that A1–A8 are formulated solely with conceptual resources from Ellis (2016) or my reconstruction of his position and arguments,

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so this step does not introduce any problematic notions replacing the level-picture. In all eight reformulated points, the reference to the level-picture is replaced, and some are slightly changed: A1 preserves the necessary constitutional hierarchies with levels allowing samelevel, top-down and bottom-up causation and Ellis’s realist notion of them. The notion of CH-level is less demanding than that of the level-picture and can be proven by Ellis’s first and third arguments. By contrast, A2 makes no reference to CH-levels but instead uses the notions of context and local ontology to replace the level-picture. This reflects the counterarguments. Otherwise, as with the relation of A1 to L1, A2 is very similar to L2 in all other respects. While L3 presented the order of levels, A3 presents both the order of CH-levels and the order of entities in different contexts. The word “ordered” regarding entities in A3 does not mean ordered into distinct levels, quite the contrary: There are overlaps between different contexts, meaning there is no total distinctness. While some local ontologies might be described as being structured into levels, other contexts can be organised in ways which are radically different. A4 states the reason for the disunity of science (as well as different languages and variables) in the same manner as L4 but more convincingly: The mystery of why one level can have different sciences associated with it disappears; every divergent epistemic grasp of a different context merits a new discipline. Even closer to L5 is A5: it substitutes context for level in the sense of A2. Regarding A5, it is noteworthy what would follow if we were to postulate an absolute bottom level in the hierarchy of an object O, say a level of vibrating one-dimensional strings: Any such string would not be a system or a concrete object composed of elements. It would undoubtedly be some kind of object (because it would possess properties like being one-dimensional), and it would be located in spacetime. Yet A5 does not deny this: It denies the string is a system (because it lacks the internal structural requirements) and identifies the only proper part of the string as identical to the whole string, located in the given context. While for the first five points, the L’s match the A’s relatively closely, this is not true for L6 and A6: One of the key features of the level-picture was that levels are distinct entities with clear boundaries, and this is just not so in all cases of CHlevels. The means of demarcation, on the other hand, has changed only ever so slightly: CH-levels can have more than one higher or one lower neighbouring CHlevel. This last point is also the main difference between L7 and A7, which preserves Ellis’s hypothesis that physics is fundamental for every concrete object in nature.9 L8 and A8 are now completely different: Instead of following L8 and claiming a branching hierarchy of animate and inanimate nature with clear distinctions, based on the underlying idea that two higher levels can rest on one lower level, A8 is more modest, simply stating for CH-levels the key feature of equivalence-classes

9 It

would of course be possible to consider A7*, which would not make this claim, because it neither follows from the first sentence of A7 nor does the first sentence require the second as a premise. But with the second sentence, A7 is closer to L7.

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and multiple-realisability with regard to the context and local ontology of the entity thus constituted. This can function as a good starting point for showing that the key features of Ellis’s theory of causation can be defended without the level-picture, instead using A1–A8. This cannot be carried out in any detail here, but should suffice to assure us that the level-picture is at least not a prerequisite for such a theory per se.

11.4.2 Ellis’s Account Reformulated After revisiting both versions of the eight points regarding levels, CH-levels and contexts, we can see that Ellis’s theory of causation, emergence and complexity can be restated without the level-picture. We can base it on an alternative set of key concepts and see that they will continue to work. To state the theory of Ellis (2016) in these new terms without any reliance on the level-picture is of course an ongoing task. Definition of Cause and Effect The Woodward-Ellis definition of cause and effect is not harmed by the changes: If anything, the notion of context is better defined, and those of variables and intervention/manipulation are as unproblematic as in the level-picture. Three Basic Types of Causation All basic types of causation can be introduced in the alternative picture. Same-level causation occurs on the same CH-level of any constitutional hierarchy of a given entity in a single context. It could also be called same-system causation between any two entities which are not connected by a mutual downward hierarchy. Let us take an example: Jupiter and Halley’s Comet do not share subsystems, so they have separated downward hierarchies. It can remain open whether or not these two entities are causally connected by being modules in the same system on one CH-level (which Jupiter and Halley’s Comet are as parts of our solar system). More often than not, there will be a gradient of complexity between two entities (as is the case for Jupiter and Halley’s Comet): Yet we should not therefore be misled into thinking of this as a case of top-down causation. It is not a difference in complexity between two entities that constitutes their causal relationship as top-down or bottom-up; rather, it is the constitutive role one entity plays for the other entity as one of the modules in its structural hierarchy or their connection in a context or intersection. Top-down causation is accordingly the name for causal relation from a higher to a lower CH-level in a hierarchy, of the context or intersection on an entity, or both, or from a wider to a smaller context. Finally, bottom-up causation is the reverse of the previous case: from a lower to a higher CH-level, from an entity on a context or intersection or both, or from a smaller to a wider context. This also illuminates interesting subdivisions in bottom-up and topdown causation which could be connected to the five different types of top-down causation.

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Genuine Complexity and the MHS-Model All cases of genuine complexity can be preserved and modelled in the alternative picture: Genuine complexity is an effect within the hierarchies of different systems and accords with the MHS-model. The MHS-model itself can be derived from the alternative points: It is modular due to the whole-part relationships and the fact that context can appear within contexts. The hierarchies are the constitutional hierarchies of the systems, and the structure is a result of how the different hierarchies are parallel to or intersect with one another within a single or many intersection contexts. All the further points (basis of physics, disunity of sciences, different laws, variables, scales, etc.) can all be taken more or less directly from the alternative picture. Equivalence-Classes and Multiple Realisability These key features of Ellis’s theory were not presented thus far. Suffice it to say that they can be formulated on the alternative foundations: Multiple Representation. In general, many lower [CH-]level states correspond to a single higher [CH-]level state [. . .], because a higher [CH-]level description H1 is arrived at by ignoring the micro-differences between many lower [CH-]level states Li , and throwing away a vast amount of lower [CH-]level information (coarse-graining). (Ellis 2016, p. 102)

Examples include “numerous microstates of particle positions and velocities correspond[ing] to a single macrostate of nitrogen gas with a pressure of one bar and a temperature of 20 K in a volume of 1 L.” (Ellis 2016, p. 103) The idea is to prove multiple realisability, meaning that a higher-level state or property is realised by different heterogeneous states or properties at a lower level (Green and Batterman 2021), via equivalence-classes of physical systems: Almost infinitely many microstates correspond to a single macro state. In the alternative picture it becomes apparent that these are both hypotheses about CH-levels in a single context. We could continue this list or take this paper as a reason to give a partial reformulation of Ellis’s account on a larger scale. For now, the criticism of the levelpicture and the evident functionality of the alternative must suffice.

11.5 Conclusion: New Realist Ontologies and Top-Down Causation We can now see that how the conclusions presented in the introduction are justified: (C1) Ellis’s theory of causation hinges on eight essential assumptions concerning ontologically robust levels of nature. All eight were reconstructed and their function within his framework explored. Ellis has reasons to employ the level-picture, but: (C2) Ellis’s own arguments in favour of the level-picture fail, at least in the context of Ellis’s theory. We contemplated various counterarguments and revealed the level-picture to be untenable. In doing so, we saw that this might not be all too damaging for Ellis because:

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(C3) The failure of the level-picture of nature is not a fatal problem for Ellis’s theory of (top-down) causation, complexity and emergence. To show this, we presented eight alternative foundational hypotheses that dispense with the levelpicture and went on to sketch how one might use them to arrive at all of the key features of Ellis’s account. Finally, I want to make a suggestion, which cannot be substantiated here: It seems likely that Ellis’s theory of causation can be merged with a pluralist ontology or metaphysics provided the latter (1) were a thorough realism (which includes causal powers of abstract, mental or social objects) and (2) were to accommodate—at least in my alternative interpretation—local hierarchies which cannot be integrated into a global hierarchy or an overarching context. Both seem to be key features of Markus Gabriel’s fields of sense ontology (Gabriel 2015). If Ellis insists on a monist philosophy of nature, which allows the possibility of a global hierarchy and an overarching context—the level-picture—he might be at odds with the general framework of Gabriel and more likely to take up a position like that elaborated by Quentin Meillassoux (Meillassoux 2008).

Appendix I would like to thank Markus Gabriel and Otávio Bueno for the encouragement and opportunity to write this paper and helpful remarks, Alex Englander and Max Kistler for their comments on an earlier version of this paper, and Noemi Stelzig for all her support during the process of writing.

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Chapter 12

Causation as a High-Level Affair Simon Friederich and Sach Mukherjee

Abstract The causal exclusion argument supports the notion that causation should be thought of as a purely low-level affair. Here we argue instead in favour of highlevel causation as a natural and meaningful notion that may even be more useful than causation at more fundamental physical levels. Our argument is framed in terms of a broadly interventionist conception of causation. Its essence is that causal relations at an appropriately high level can in a certain sense be less sensitive than those at a fundamental, microscopic level. This means that in settings where causal relations at the (micro-) physical level are not considered in the context of some suitable macro-level interpretation, statements concerning the low-level relations may be highly sensitive with respect to changes in background conditions. Using an example of accelerator experiments in particle physics, we consider what it means to characterize extremely sensitive low-level events as causal.

12.1 Introduction Identifying cause-effect relations is central to disciplines such as psychology, medicine, biology, sociology and economics that focus on relatively high-level (as opposed to micro-physical) phenomena. According to some philosophers, however, causation is in fact a pure low-level affair, i.e. it is confined to the most fundamental level of elementary physics that exists. This is, notably, the conclusion of the causal exclusion argument, championed by Jaegwon Kim (1998, 2005). It applies on the condition that the plausible doctrine of non-reductive physicalism is correct: the view that higher-level properties supervene on lower-level physical (micro-) properties, but are not identical to

S. Friederich () University College Groningen, University of Groningen, Groningen, The Netherlands e-mail: [email protected] S. Mukherjee Statistics and Machine Learning, DZNE, Bonn, Germany © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_12

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them. Physicalism entails that (micro-) physical properties are not affected by any non- (micro-) physical causes over and above their (micro-) physical causes. And supervenience entails that fixing the (micro-) physical properties of the world fixes all other properties. Accordingly—the argument roughly goes (there are various versions of it in the literature which use somewhat different assumptions)—unless one implausibly accepts that higher-level facts are causally overdetermined by lower- and higher-level facts, only the more fundamental physical properties can be genuinely causally effective. So unless one assumes that higher-level properties are actually themselves identical with lower-level properties, they cannot possibly be causally effective. If the causal exclusion argument is correct, to assume that there is any higher-level causation requires accepting interactionist dualism or austere reductive physicalism. In this contribution, we argue for a quite different position: namely, that causation not only applies at higher levels, but that it can be a more natural notion at higher levels than at the more fundamental physical levels. As the backdrop of our argument we use a broadly interventionist conception of causation such as that invoked by Pearl (2009) and Woodward (2003). We note that our argument does not contradict the physicalist position: rather we focus attention on the interpretation and sensitivity of causal claims at higher and lower levels, but within a framework in which in the end any specific higher-level causal effect operates via some sequence of micro-physical events. The structure of our argument is as follows: in Sect. 12.2, we recapitulate extant interventionist responses to the causal exclusion argument. In doing so, we highlight that, even though these responses assert the existence of causal relations at the (micro-) physical level, we typically have no independent grip on the micro-physical variables between which those relations obtain beyond their playing a role in this argument. Next, in Sect. 12.3, we discuss the notion of sensitivity as it relates to causation and the level of hierarchy at which causation is invoked. We argue that causal statements at an appropriately high level can in a certain sense be less sensitive than those at a micro-physical level. Our argument for the robustness of high-level causal claims focuses on the background conditions with respect to which causal relations obtain. Following Lewis (1986) and Woodward (2006), we call causal relations that obtain for a wide range of background conditions insensitive and those that obtain only for a narrow range sensitive. As pointed out by Woodward, the more sensitive some purportedly causal relation is, the less appropriate it seems to describe it as genuinely “causal”. Finally, in Sect. 12.4, we argue that, where statements concerning causal relations at the (micro-) physical level are not coupled with causal statements at some suitable macro-level—e.g. in accelerator experiments in particle physics—the causal relations tend to be highly sensitive. Our point is a gradual one: we do not deny that it can be perfectly legitimate to apply causal vocabulary at the level of fundamental physics, as persuasively argued by Frisch (2014). Not does our argument presuppose a sharp hierarchy of clearly delineated levels of theories. With those caveats in mind, we argue that causal relations at a fundamental, microscopic level may be highly sensitive to background

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conditions and to that extent may obtain only in a somewhat weak and “boundary” sense. In the example of accelerator experiments in particle physics this sensitivity is to a degree that the experimental setup can be considered essentially a background conditions-controlling machine.

12.2 Intervention and Causation in Complex High-Level Systems: Micro-properties that Realize Macro-properties The interventionist conception of causation (see Pearl 2009 and Woodward 2003) emphasizes the role of external manipulation (“intervention”) on a system and in particular the notion that what is special about a directed causal relationship between variables A and B is that intervention on A can alter B. This view has close links to the experimental sciences, where designed experiments are used to carry out interventions on systems for which the scientist may not have a complete microscopic description or any plausible route to such a description. Interventionist concepts have played a key role in contemporary developments in causal analysis in the field of machine learning (see for example Pearl 2009 and Peters et al. 2017). The interventionist framework can be formalized in terms of random variables (RVs) with a key notion being that the joint probability distribution (over the RVs in the system) can be changed under intervention on the system. Note that the RVs in this formalism need not be at the micro-physical level and indeed the probabilistic interventionist formalism is in a way agnostic to level. A causal graph is a directed graph with vertices corresponding to RVs in the system of interest and edges corresponding to causal relations. There are many variants of causal graphs and their semantics and interpretation are the focus of an active scientific literature (see e.g. Hyttinen et al. 2012 and Kocaoglu et al. 2017), but an important point is that causal edges in such graphs refer to causal relations whose micro-physical details may be left implicit. Thus, in a graph with vertices {smoking, lung cancer, blood pressure}, an edge from smoking to lung cancer (not via blood pressure) would mean that the effect of smoking on lung cancer is causal in an interventionist sense and furthermore direct in the sense of not operating only via its effects on blood pressure, but it would be left implicit that the effect of smoking on lung cancer operates via myriad micro-physical events. Shapiro (2012), partly in joint work with Sober (Shapiro and Sober 2012), as well as Woodward (2015) argue that, in the framework of interventionism about causation, the causal exclusion argument is to be rejected. If M1 and M2 are higherlevel variables such that M1 causes M2, one can think of more fundamental microphysical variables P1 and P2 such that M1 and M2 are coarse-grained versions of them, respectively, where P1 causes P2 just as M1 causes M2. As Shapiro and Sober emphasize, in this case, just as intervening on M1 is a way of (indirectly) intervening on M2, intervening on P1 is a way of (indirectly) intervening on P2. The functional

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dependence between M1 and M2 on the one hand and P1 and P2 on the other may be very different from each other, but the two causal relations in general coexist. We agree with Shapiro and Sober on this point but wish to point out that, for realistic cases of variables M1 and M2 (where, say, M1 is the variable “smoking” and M2 is the variable “cancer”) the variables P1 and P2, when imagined in the language of, say, quantum field theory, are not literally given and may not be even approximately expressible in practice. Moreover, inasmuch as we can characterize the conditions in which “Smoking causes lung cancer obtains”, we do so in higherlevel language. The very idea of variables P1 and P2, as well as the idea of a robust causal relation between them are in this sense “parasitic” on our understanding of a robust higher level causal relation. In the following section we will further explore the distinction between robust (“insensitive”) and sensitive causal relations.

12.3 Sensitive and Insensitive Causation Reviewed The distinction between sensitive and insensitive causation appeals to the background condition with respect to which causal relations obtain. A causal relation is sensitive if even rather small changes in background conditions disrupt it. Otherwise it is insensitive. The distinction is highlighted as of crucial importance stage in an illuminating article by Woodward (2006). Woodward traces the underlying idea back to Lewis (1986) and introduces it as follows: The counterfactual dependence of effects on their causes is such an obvious feature of many examples of causation that it is easy to miss the fact that there is another feature having to do with counterfactual structure that plays an important role in such examples. This feature has to do with the sensitivity of the causal relationship (and, more specifically, the sensitivity of certain of the counterfactuals associated with it) to changes in various other factors. Broadly speaking, a causal claim is sensitive if it holds in the actual circumstances but would not continue to hold in circumstances that depart in various ways from the actual circumstances. A causal claim is insensitive to the extent to which it would continue to hold under various sorts of changes in the actual circumstances. The sensitivity of counterfactuals is understood similarly (Woodward 2006, p. 2).

We note that sensitivity of a causal effect can be thought of in terms of a causal graph on a set of variables V, augmented with additional “background” vertices V for variables not considered to be part of the system under study but which may influence one or more of its variables V. In that case, a causal effect between variables in the system (i.e. members of V) can depend on the configuration of the (background) variables V and the entire system can be studied within a unified probabilistic formalism (see for example Pearl and Bareinboim 2014). Sensitivity then amounts to the strength of this coupling and could be quantified using mathematical tools.

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Woodward illustrates the concept of sensitivity with an example as follows: The sensitivity of the counterfactual (2.1) If the event of the rock thrown by Suzy striking the vase were to occur, the shattering of the vase would occur has to do with whether (2.1) or its analogues would continue to hold under circumstances that differ in various ways from the actual circumstances. Put slightly differently, what we are interested in is whether (and which) counterfactuals of the form (2.2) If the rock thrown by Suzy were to strike the bottle in circumstances Bi different from the actual circumstances, the bottle would (still) shatter are true for various Bi Some of the circumstances Bi for which claims of form (2.2) are true are so obvious that they will seem trivial. If Suzy’s rock strikes the vase in Boston at the moment at which someone sneezes in Chicago, then presumably if that person had not sneezed but the world had remained relevantly similar in other respects, the bottle still would have shattered. Similarly, if we vary the color of Suzy’s blouse or the price of tea in China at the time of the impact (Woodward 2006, p. 5).

Woodward goes on to list other aspects of the background conditions which presumably can be varied without affecting the truth of (2.1), notably, when and where Suzy’s striking and the subsequent vase shattering occur. Here we consider these notions in type-causal contexts. Example: “Exercise causes elevation of heart rate in humans” holds for a wide variety of background conditions. “Being born in August causes better grades than being born in July” may hold in rather specific conditions (societies where children born in August tend to be the oldest ones in their classes etc. etc.) The distinction between sensitive and insensitive causation may be gradual and may not admit a clear classification into “specific” as opposed to more “general” background conditions. Furthermore, inasmuch as background dependence of causal relations can be quantified it is often multi-dimensional, i.e. a causal relation can be sensitive along one dimension and insensitive along another. For example, the causal claim “Being born in August causes better grades than being born in July” might obtain robustly for all children within a school system, independent of the specific school district, say, (and, so, be insensitive with respect to the “dimension” school district), but only be true about specific school systems, where, in any given school class, children born in August are on average older than children being born in July. Two related aspects of sensitive causal relations matter for the present discussion: first, the more sensitive causal relations are, the less useful they tend to be because it is more difficult to exploit them. If some causal relation holds only for very specific background conditions, then, it may be challenging to guarantee that these background conditions indeed obtain or even to verify that they do. In those cases, one may have difficulties to exploit that causal relation in practice because one may not be able to ascertain that the background conditions obtain in which it holds. Second, we tend to view sensitive causal relations—or at least very sensitive ones—as only borderline causal. For example, one may argue that “Being born in August causes better grades than being born in July” does not represent a strong causal statement: it is not really one’s birth month per se that influences one’s success; rather, it is the wider setting, including conventions about deadlines for school entry, which is influential. Note that from a strictly formal, interventionist

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perspective a highly sensitive causal relation remains causal in the sense of describing changes under intervention in the system, albeit under restrictive background conditions. Nevertheless, regarding highly sensitive causal relations as second class (and perhaps not even causal at all) is particularly natural in situations where one has no chance to ascertain whether the background conditions obtains with respect to which a given sensitive causal relation supposedly holds.

12.4 Is Causation in Fundamental Physics (Hyper-) Sensitive? In textbooks of fundamental physics, unlike in those of, say, the social sciences, causal notions are typically not very prominent. As pointed out by Woodward (2006), the typical problem in the social sciences—that one observes certain correlations but finds it difficult to judge whether and, if so, to what degree they are causal—does not prominently arise in fundamental physics. Still, discoveries in fundamental physics involve the tracing of effects to their causes. In accelerator experiments, for example, inferences are made about the causes of certain detection events. Sometimes those events can be linked to decays of more energetic particles such as the Higgs boson, whose existence can then be indirectly inferred. Wüthrich (2017) gives an account of the 2012 discovery of the Higgs boson (ATLAS Collaboration 2012; CMS Collaboration 2012) as such a causal inference. In the meantime, not only the existence, but also the specific properties, of the Higgs boson have been inferred from combining data on detection events of proton pairs (ATLAS Collaboration 2014), lepton quartets (ATLAS Collaboration 2015), and bottom quarks (CMS Collaboration 2018) among others. That decays of Higgs particles can—directly or indirectly—result in the creation of such pairs can relatively straightforwardly be derived from the Standard model of elementary particle physics using the formalism of quantum field theory. In actual physical experiments, however, the inference from detecting such pairs and quartets of particles to such a decay having taken place requires great care. Part of the reason for this is that the background conditions potentially affecting the detection events must be carefully controlled. The decay (assuming that it has indeed happened) must take place in a high quality vacuum so that the trajectories of the decay products are accurately predictable, other potential causes of the detection events can be excluded, the detectors must be carefully setup and calibrated, and the numerical analysis that separates detection events from “noise” must be carefully designed. Because of these complexities, particle accelerator and detector design and construction are now scientific (and engineering) fields in their own right, as is the extraction of genuine particle “signals” from noise in high energy physics experiments.

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One way of understanding these complexities is to regard them as manifestations of the very high sensitivity of causal relations at fundamental physical levels: the decay of a Higgs boson causes the imminent detection of particles at specific angles with specific velocities, but it does so only against a very specific fixed background that must be rigorously controlled, both concerning the spatio-temporal setup (which is predominantly an engineering challenging) and concerning the numerical analysis (which is predominantly a theoretico-computational challenge). This point can be illustrated by highlighting that there are also about 10,000 decays of Higgs particles per day in the atmosphere of the Earth, created by cosmic rays. But apart from the fact that the locations of these decays are impossible to predict, the background conditions against which they occur are not “under control” in that it is impossible to discern particles that result from them from irrelevant statistical noise. Experiments in high energy physics are in a sense “background conditions controlling machines” that enable discoveries about fundamental physical objects. Beyond those experiments, causal reasoning plays at best a limited role in fundamental physics. Generally, types of earlier events and types of later events may be counterfactually linked such that intervening on the former would lead to changes in the latter. But in general, what occurs at the fundamental physical level in a limited spatio-temporal region depends counterfactually on everything that occurs in that region’s backward light cone, and if there is quantum entanglement with objects outside the region, even on space-like separated events. It is no wonder that, outside of highly controlled particle physics experiments, causal notions are usually not much employed in fundamental physics.

References ATLAS Collaboration. (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Physics Letters B, 716, 1–29. ATLAS Collaboration. (2014). Measurements of Higgs boson production and couplings in the diphoton decay channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector. Physical Review D, 90, 112015. ATLAS Collaboration. (2015). Measurements of Higgs boson production and couplings in the four-lepton channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector. Physical Review D, 91, 012006. CMS Collaboration. (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Physics Letters B, 716, 30–61. CMS Collaboration. (2018). Observation of Higgs boson decay to bottom quarks. Physical Review Letters, 121, 121801. Frisch, M. (2014). Causal reasoning in physics. Cambridge: Cambridge University Press. Hyttinen, A., Eberhardt, F., & Hoyer, P. (2012). Learning linear cyclic causal models with latent variables. Journal of Machine Learning Research, 13(1), 3387–3439. Kim, J. (1998). Mind in a physical world. Cambridge: MIT Press. Kim, J. (2005). Physicalism, or something near enough. Princeton: Princeton University Press.

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Kocaoglu, M., Shanmugam, K., & Bareinboim, E. (2017). Experimental design for learning causal graphs with latent variables. Advances in Neural Information Processing Systems, 30, 7018– 7028. Lewis, D. (1986). Postscript C to “Causation”: (Insensitive Causation). In Philosophical papers, (Vol.2, pp. 184–88), Oxford: Oxford University Press. Pearl, J. (2009). Causality: Models, reasoning and inference. Cambridge: Cambridge University Press. Pearl, J., & Bareinboim, E. (2014). External validity: From do-calculus to transportability across populations. Statistical Science, 29(4), 579–595. Peters, J., Janzing, D., & Schölkopf, B. (2017). Elements of causal inference: Foundations and learning algorithms. MIT Press. Shapiro, L. A. (2012). Mental manipulations and the problem of causal exclusion. Australasian Journal of Philosophy, 90, 507–524. Shapiro, L. A., & Sober, E. (2012). Against proportionality. Analysis, 72, 89–93. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press. Woodward, J. (2006). Sensitive and insensitive causation. The Philosophical Review, 115, 1–50. Woodward, J. (2015). Interventionism and causal exclusion. Philosophy and Phenomenological Research, 91, 303–347. Wüthrich, A. (2017). The Higgs discovery as a diagnostic causal inference. Synthese, 194, 461– 476.

Chapter 13

Models of Downward Causation Max Kistler

Abstract Two conceptual frameworks – in terms of phase space and in terms of structural equations – are sketched, in which downward causal influence of higher-level features on lower-level features is possible. The “Exclusion” principle, which is a crucial premise of the argument against the possibility of downward causation, is false in models constructed within both frameworks. Both frameworks can be supplemented with conceptual tools that make it possible to explain why downward causal influence is not only conceivable and compatible with the “Closure” principle, but also why it is often relevant to causally explain facts in terms of downward causal influence. It is briefly shown that (1) the analysis of downward causation in the two frameworks complements Bennett’s (Nous, 37:471– 497, 2003) analysis of overdetermination, (2) the analysis does not entail the failure of the “Closure” principle and (3) it does not require the postulate of synchronic downward causation.

13.1 Introduction The idea that the mind causally influences the physical world is often claimed to be incompatible with physicalism. Physicalism is the doctrine according to which (1) everything is either physical or exclusively composed of physical parts, and (2) all properties of all objects supervene on the physical properties of those objects. There are stronger versions of physicalism, such as reductionism and eliminativism.1 According to the construal of physicalism in terms of supervenience, mental 1 According

to the former, all real properties are reducible to physical properties, and according to the latter, strictly speaking, there are only physical properties. According to these strong forms of physicalism, the question whether the mind influences the physical world does not really arise, either because there is no mind (eliminativism) or because the mind is itself physical (reductionism).

M. Kistler () Université Paris 1 Panthéon-Sorbonne and IHPST, Paris, France e-mail: [email protected]

© Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_13

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properties, events, and processes are distinct from physical properties, events, and processes. Thus the question arises whether mental events, or indeed any kind of higher-level events, in a sense of “higher-level” to be specified shortly, can influence2 physical events. I will address this question within the framework of physicalism construed in terms of supervenience. Kim (1998, 2005) has developed a strong argument according to which downward causation is incompatible with this construal of physicalism: It can never be literally correct that a mental event causes a physical event, because the causes of physical events are always exclusively physical.3 This result is troubling because it seems obvious that its conclusion is wrong and that our minds do influence physical events. Here is a case of such a “downward” influence. My thoughts about the relation of the mind to the body, together with my desire to make my thoughts publicly known, cause my fingers to move over the keyboard and indirectly cause words to appear on the screen of my computer. Downward influence from psychological on physiological features of persons can be studied experimentally. Psychotherapy has been found to influence brain function in many psychiatric disorders (Barsaglini et al. 2014). Obsessive-compulsive disorder (OCD) is correlated with hypermetabolism in, among other regions of the brain, the right caudate nucleus. It has been found (Baxter et al. 1992) that behavioral therapy of patients suffering from OCD results in decreased rates of glucose metabolism in the head of the right caudate nucleus of their brains. There are at least two interpretations of what it means to characterize such influences as being “downward”. The reductionist interpretation uses the hypothesis of a hierarchy among the sciences that is structured by partial and local reduction relations between theories.4 Few philosophers today think that the history of science tends towards unification, in the sense that all sciences tend to get reduced, directly or indirectly, to physics (Dupré 1993; Cartwright 1999). However, it is not controversial that there are cases of successful reductive explanations of certain laws or theories. These successful cases of local reductions can justify the hypothesis that the sciences concerned by those reductions are ordered in a partial hierarchy. Thermodynamics has been (in part) reduced to statistical physics and certain simple 2 When

I speak of influence, I always mean causal influence. I am using “cause” and “influence” as synonymous, the only difference being stylistic. 3 Here I use the term “event” in Kim’s sense, as the instantiation of a property by some object at some time. I shall later express the same question as being (in the model of state spaces, see below) (1) whether mental facts can be causally responsible for physical facts or (in the model of structural equations, see below) (2) whether mental properties can influence physical properties. 4 This reductionist concept of levels corresponds to Craver’s “levels of science” (Craver 2007, p. 172), whereas the mereological concept of levels (see below) corresponds to Craver’s “levels of composition” (Craver 2007, p. 184). For the relevant concept of reduction, see Nagel (1961) and Schaffner (1967).

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forms of learning by classical conditioning have been reduced to neuroscience. By virtue of these reductions, statistical physics lies lower in the hierarchy of the sciences than thermodynamics, and neuroscience lower than psychology. The causal influence of psychotherapy on the glucose metabolism in the caudate nucleus of a patient’s brain is a case of downward causation in this hierarchical sense because psychotherapy modifies the properties of persons at the level of psychology, whereas the features of glucose metabolism in the caudate nucleus belong to neurophysiology, which lies at a lower level than psychology. A second interpretation of the concept of downward causation derives from the distinction between properties of a whole object and properties of the object’s parts. In a mereological sense of levels, the properties of a whole object lie at a higher level than the properties of its parts.5 Levels can be locally defined and structured in local hierarchies by mereology. Levels in the reductionist sense, as defined by partial and local reductions, do not coincide with levels in the mereological sense.6 The mouse’s perceiving the cat approaching it causes the mouse to flee: here, the cause (the mouse’s perceiving) and effect (the mouse’s fleeing) lie at the same level (in both the hierarchical and the mereological sense) because both events are changes in properties of the same object, i.e. the mouse. However, the same perception also causes a given determinate muscle fiber in the mouse’s left rear leg to contract. The perception’s causing the contraction of the fiber in the mouse’s leg is downward causation in the mereological sense, because the muscle fiber is a part of the mouse, and thus, its contraction is a lower-level property compared to the property of perceiving the cat. It is also downward causation in the reductionist sense, because perception belongs to psychology, the contraction of muscle fibers belongs to physiology, and physiology lies at a lower reductionist level than psychology. For lack of space, I will concentrate in what follows on downward causation in the reductionist sense. The levels required to analyze the concepts of same-level, downward, and upward causation are always locally defined, with respect to the objects or systems involved in the causal interactions under enquiry. It is not plausible that locally and partially defined reductionist levels (or, for that matter, mereological levels) can somehow

5 Only

some parts have “constitutive explanatory relevance” (Craver 2007, p. 140) in the context of mechanistic explanation. In an “interlevel experiment” of the “top-down” variety (Craver 2007, p. 145), an experimenter manipulates a property of a system and observes the downward effect of this manipulation at the level of such a constitutively relevant part. However, the meaning of the term “downward” need not be restricted to constitutively relevant parts. Downward causation in the mereological sense exists within physics: Heating (i.e. a modification of a macroscopic property) of piece of Nickel modifies the properties of microscopic parts of that piece of Nickel (Kistler 2017). 6 The two concepts of level do not have the same extension. (1) Many sciences study objects that lie at different mereological levels, in particular because they study, as does neuroscience, whole mechanisms as well as their parts; (2) many objects are studied by sciences that lie at different reductionist levels: Proteins are studied by physics (e.g., in X-ray crystallography), chemistry, and physiology.

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be merged into a unique global hierarchy of levels.7 However, the analysis of local downward causation does not require the existence of such a unique global hierarchy of levels. We have analyzed one part of what it means to say that some influence is a case of downward causation, by explaining what it means to say that the effect lies at a lower level than the cause. It remains to be analyzed what is meant by “cause” or “causal influence”. In what follows, I sketch two models of causation that provide frameworks for making sense of downward causation.8 The first model is based on the notion of phase space. The second model elaborates the framework of structural equations. Within each of these models, we will evaluate the argument against downward causation in the following form.9 (1) (Closure) The causal closure of the physical domain. If a system p has at t1 a physical property R1 , then there is, at each time t0 preceding t1 , a physical property N such that the fact that p has N at t0 is causally responsible for the fact that p has R1 at t1 . (2) (Exclusion) Principle of causal exclusion.10 If the fact that p has N at t0 is causally responsible for the fact that p has R1 at t1 , there cannot be any property M distinct from N, and in particular no property M at some level higher than N, such that p has M at t0 and such that the fact that p has M at t0 is also causally responsible for the fact that p has R1 at t1 .

7 For

reasons against the existence of a unique global hierarchy of levels, see Eronen (2013, 2019) and Voosholz (this volume). 8 In (Kistler 2017), I have explored whether it is possible to make sense of downward causation by modifying the framework of analyzing causal influence in terms of interventions (Woodward 2003) and using it as a complement to the account of causation in terms of transference (Kistler 2006a, 2013). In (Kistler 2017), downward causation is interpreted in terms of the mereological notion of levels, according to which a property P is at a higher level than property Q if and only if Q characterizes a proper part of the object characterized by P. 9 There are many versions of this argument and of its premises “Closure” and “Exclusion”. For an overview, see (Robb and Heil 2018). Kim’s own version of the argument aims at establishing that mental properties are not downward causes by construing them in terms of higher-order predicates (Kim 1998, p. 83). This leaves open the question whether there is downward causation by higher-level properties as defined in this chapter. For critical analyses of Kim’s construal of mental properties in terms of higher-order predicates and his use of the distinction between levels and orders in the context of his argument against downward causation, see (Kistler 2006b) and (Gozzano 2009). 10 This principle has the consequence that one complete causal explanation of the fact that p has R1 at t1 by the fact that p has N at t0 excludes other independent causal explanations of the fact that p has R1 at t1 by other facts about p at t0 . However, our “Exclusion” principle is weaker than Kim’s “principle of explanatory exclusion”: “There can be no more than a single complete and independent explanation of any one event” (Kim 1988, p. 233). He later calls this stronger principle the “principle of determinative/generative exclusion” (Kim 2005, p. 17). This strong principle is not plausible because one fact can have both a causal and a non-causal explanation, which can be independent of each other (Kistler 2006b).

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(3) No downward causation. Therefore, no higher-level level property M is such that the fact that p has M at t0 is causally responsible for the fact that p has R1 at t1 .

13.2 Downward Causation in the Framework of Phase Space The framework of dynamical systems theory provides one way to think about causal influence (Hitchcock 2012).11 The decision of a person to raise her arm causes her arm to rise. This is downward causation both in the reductionist sense, because the cause is psychological and the effect physiological, and in the mereological sense, because the arm is a part of the person taking the decision: Let us assume that a person is identical with her body.12 We can conceive the body of person p as a physical system whose state at time t0 can be represented as a point p0 in the body’s state space. The number of dimensions of this state space equals the number of degrees of freedom the system possesses. Each degree of freedom corresponds to a way in which the system can change. A classical mechanical system of n particles has 6n degrees of freedom, 3 degrees of freedom for the position of each particle and 3 degrees of freedom for the velocity of each particle, in each of the 3 Cartesian dimensions. The space state of a system as complex as a human body in interaction with its environment, has a very large number of dimensions. Here is a way of representing causality in this framework. Take as cause the state p0 of the system at t0 , represented by a point in the system’s state space. The system evolves through time according to the dynamical equations governing the system, following what is called its trajectory, which can be represented by its position in state space as a function of time. A point pi on that trajectory at time ti is a cause of all points pj on the trajectory at later times tj > ti , and an effect of all points pk on the trajectory at earlier times tk < ti .13 The question of what was the cause, at t0 , of p’s raising her arm at time t1 , can be interpreted in at least two ways. On one interpretation, the effect is an event in the sense of something that is identified as the whole content of the region of spacetime where it is happening (Quine 1960, 1985; Kistler 2006a). When we ask for the cause of the state p1 of the person at t1 , the answer can be found by following the trajectory of her body, considered as a physical system, backwards in time, up to t0 . According to this interpretation, the state p0 of the person at time t0 is the cause of her state p1 at the later time t1 . 11 Hitchcock

calls this model of causation “Laplacean causation” (Hitchcock 2012, p. 46). assumption is of course controversial. Cf. Lowe (2000a, chap. 2). 13 We shall see that an analysis of causal relations in the conceptual framework of dynamical systems is compatible with more traditional conceptions of causation as a relation between two events or between facts about substances. Causal statements expressed in the language of points, regions and trajectories of phase space can be translated in the language of events and facts, and vice versa. 12 This

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However, when we ask questions about causes, we are typically interested in answers that give us more information than that. We want to know, not only what, at t0 , was the cause of p1 at t1 , but also what it was about that cause that is responsible for the fact that p1 has a certain property.14 We want to know, not only what was the trajectory of p up to p1 , but also what made her raise her arm at t1 , or, in other words, what fact about p0 was causally responsible for the fact that she raised her arm at t1 ?15 Why would we want to have such additional information? One reason is that it gives us the means to generalize to other similar cases. A second reason, linked to the first, is that such information has counterfactual implications that we can use for planning actions. If what is causally responsible is the fact that p took at t0 the decision to raise her arm at t1 , we know that, in general, had she not taken that decision, her arm would not have risen. We know also that, if she took a similar decision in other circumstances, her arm would probably rise. When we ask what it was about p0 that made it the case that p1 is a state of a person raising her arm, we can interpret this question as the application to this particular case of the more general question: For any person p and any time t0 , what is it about p at t0 that makes it the case that p raises her arm at t1 > t0 ? At this point, the issue arises whether we can make sense of the possibility that psychological properties causally influence the body. Such downward influence is controversial because there always seem to be several complete causes (and therefore causal explanations) of the bodily movements that are parts of actions. Even if we accept that the fact that p raised her arm at t1 is caused by her decision at t0 to raise her arm, the same fact also seems to be the effect of a physiological fact: that the relevant part of her brain showed a specific pattern of activity at t0 . To address the question of how these facts about p at t0 are related to each other in the framework of dynamical systems, we need the conceptual tool of regions of state space. A predicate describing the system determines a whole region of the state space of the system, consisting of all states in which the system satisfies the predicate. If p1 is the point representing p at t1 , the predicate “raises her arm” corresponds to a region R1 that includes p1 . All points in R1 represent possible states of the system in which the person raises her arm. Points outside R1 represent possible states in which she does not raise her arm. Saying what made it the case that p raised her arm at t1 requires finding a feature (or property) of p’s state p0 at t0 such that the fact that p had property P0 at t0 is causally responsible for the fact that p had R1 at t1 . The property P0 must satisfy the

14 On

the distinction between these two questions, the corresponding two sorts of causal information, and the metaphysical and logical relations between causal relations between events and relations of causal responsibility between facts, see Kistler (1999, 2006a, 2014). 15 According to some conceptions of actions, the bodily movement of the arm that rises is only part of the action. According to Dretske (1988), the action consists in the whole process starting with the decision and ending with the bodily movement.

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following requirement: P0 must be such that for all points of the state space within P0 , these points lie on trajectories that lie, at t1 , within R1. 16 Here is a way of representing the search for the causally relevant property P0 . If we trace back in time up to t0 the trajectory of all points within region R1 , we obtain a region R0 , which can be called the projective state of R1 at t0 , or the reverse image of R1 at t0 . R0 contains all and only those points in state space at t0 that represent possible states that evolve towards a state within R1 . The more the system is sensitive to initial conditions, or in other words “chaotic”, the more R0 will be spread out in state space. Let us suppose that there is a predicate P, in science or common sense, whose extension at t0 in the space state of the system is entirely included within R0 . The fact that p has P at t0 is sufficient for p’s trajectory lying within R0 at t0 . R0 is the projective state of R1 , so that the fact that p is P is also sufficient for its having R1 at t1 . In our example, if R0 is the projective state of the fact that p raised her arm (R1 ) at t1 , and P is the predicate “decides to raise her arm”, the fact that p decides at t0 to raise her arm (which is represented by the fact that the trajectory of p lies within P at t0 ) is causally responsible for the fact that she raised her arm at t1 (which is represented by the fact that her state lies within R1 at t1 ). Insofar as P is a psychological predicate and R1 is a region corresponding to a physiological predicate, we have a case of downward causation. Possessing P at t0 is sufficient for possessing R1 at t1 : All points within P lie on trajectories that cross R1 at t1 . However, it is not necessary. Many points within R0 lie outside P. Such points represent states of p at which p does not possess P but nevertheless lie on a trajectory that leads through R1 at t1 . There may also be predicates such as P*, sketched in Fig. 13.1, which is almost necessary and almost sufficient for R1 , in the sense that it comes close to picking out the same region as the projective state R0 . Almost all states that satisfy P* are on trajectories that lead through R1 . This means that P* is almost sufficient for R1 , or is sufficient with exceptions for R1 . And almost all states that lie outside of P*, i.e. that do not have P* are such that their trajectories do not lead through R1 . This means that P* is almost necessary for R1 , or is necessary for R1 with exceptions. We are now in a position to evaluate the argument against the possibility of downward causation. (1) (Closure) The causal closure of the physical domain. If a system p has at t1 a physical property R1 , then there is, at each time t0 preceding t1 , a physical property N such that the fact that p has N at t0 is causally responsible for the fact that p has R1 at t1 . (2) (Exclusion): Principle of causal exclusion. If the fact that p has N at t0 is causally responsible for the fact that p has R1 at t1 , there cannot be any property

16 Knowing

that p has P0 at t0 also provides someone who doesn’t yet know what p will do at t1 with the means to predict that she will do R1 at t1 . It also justifies the counterfactual judgment about a situation at t2 in which p does not have P0 , that if p had had P0 at t2 , she would have had R1 (i.e. raised her hand) a little later.

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R0 P

P* R1 t2

t1

Fig. 13.1 R0 is the projective state of R1 , where R1 represents the region of the state space of a person p corresponding to the extension of the predicate “x raises her arm”. Having P at t0 is a sufficient (but not necessary) condition for having R1 at t1 : all possible states of the system represented by points within P have trajectories that run through R1 . P* is almost necessary and almost sufficient for R1 . The figure is similar to fig. 3 in Hitchcock (2012, p. 49)

M distinct from N, and in particular no property M at some level higher than N, such that p has M at t0 and such that the fact that p has M at t0 is also causally responsible for the fact that p has R1 at t1 . (3) No downward causation. Therefore, no higher-level level property M is such that the fact that p has M at t0 is causally responsible for the fact that p has R1 at t1 . Concerning premise (1), Hitchcock (2012) argues that there seems to be no principled reason for thinking that there will always be a physical property that plays the role of P (or P*, for that matter). “What reason do we have for thinking that P will correspond to some physical property? That is, why think that the similarity shared by all of the states in P will involve the values of some simply specifiable physical parameter – e.g. having a kinetic energy or angular momentum within some specific range?” (Hitchcock 2012, p. 50). However, I think that we can interpret Closure in this framework so as to see why it is generally taken to be true by physicalists. Hitchcock’s point seems plausible only insofar as we mean by “physical property” a property that corresponds to a simple predicate in physical vocabulary.17 However, there is a more charitable interpretation of Closure. The conjunction of the description of the positions and velocities of all atoms constituting system p may be longer than what can possibly be expressed within the limited time and space available to us. However, this is no reason to deny that the corresponding physical property exists, in the sense that it corresponds to a well-defined region within R0 . Let us interpret the condition that N is a physical property of p at t0 as meaning that there is a region including p0 that corresponds to the physical properties of all physical constituents of system p at t0 (even though 17 The

interpretation of Closure according to which there is at each time t0 preceding t1 , a cause N that is a sufficient condition for R1 and that can be described with a short expression in the vocabulary of physics, might be called, with Flanagan (1992, p. 98) “linguistic physicalism”. Such an interpretation is much stronger and less plausible than the metaphysical interpretation suggested in the text.

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R0 P2

R1

P1

Fig. 13.2 R0 is the projective state of R1 , where R1 represents the region of the state space of a person p corresponding to the extension of the predicate “x raises her hand”. P1 and P2 represent two properties of p at t0 such that both are sufficient conditions for having R1 at t1 : all possible states of the system represented by points within both P1 and P2 have trajectories that run through R1 . The figure is similar to fig. 4 in Hitchcock (2012, p. 50)

these properties cannot be actually described given human limitations). In this “metaphysical” interpretation, premise (1) seems plausible and can be accepted. According to Exclusion (premise (2)), there cannot be two different properties M and N such that p has both N and M at t0 , and such that each of the facts that p has N and that p has M is by itself causally responsible for the fact that p has R1 at t1 . The Exclusion principle is often stated with the proviso that there are exceptional cases of “genuine overdetermination”.18 Genuine cases of overdetermination are situations in which “R1 is somehow being caused twice over” (Hitchcock 2012, p. 50). This is not the case here. Say P1 is a physical property and P2 a psychological property, both with extensions contained within R0 , as sketched in Fig. 13.2. There seems to be nothing problematic in allowing that facts involving both P1 and P2 are causally responsible for the fact that p is R1 at t1 . The causal responsibility of the fact that p has P2 at t0 for the physical fact that p has R1 at t1 is downward. Its causal responsibility is not threatened by the existence of physical facts about p at t0 (that p has P1 at t0 ) that are also causally responsible for the fact that p has R1 at t1 . This is enough to show that, in the dynamical systems framework, the existence of downward causation is conceivable and plausible, in the sense that psychological features of a person may causally influence her physiological features. However, the framework also shows that there can be situations where both a physical (or physiological) and a psychological causal explanation is available for some physiological fact, and where the psychological (downward) causal explanation is the more relevant one.19 Here is why. R1 corresponds to a coarse grained predicate, “raising one’s arm”. There are many different ways of performing this act, differing along many dimensions, such as the particular angle of the elbow that is reached at the end of the movement, the speed of the movement, and the exact states of all muscle fibers that are constituents of the movement. It is plausible that the 18 “If

an event e has a sufficient cause c at t, no event at t distinct from c can be a cause of e (unless this is a genuine case of causal overdetermination)” (Kim 2005, p. 17). What Kim calls “event e” is in our terminology the fact that p has property R1 at t1 . For Kim’s notion of event, see Kim (1973). 19 Hitchcock (2012) doesn’t mention this consideration in his discussion of Kim’s argument of causal-explanatory exclusion in the framework of dynamical systems.

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causes of these physiologically different processes will be spread out in state space and that any predicate whose extension comes close to R0 would be a very long disjunction. The extension of some specific detailed description Pk of the cause of one particular type of raising one’s arm will cover a very small subregion within R0 . The corresponding physical property Pk is sufficient but not necessary for R1 . However, the extension of the psychological predicate “decides to raise her arm” might resemble P* in diagram 1 above. It is plausible that most arm raisings are caused by decisions to do so – only few small subregions of R0 lie outside P* – and most decisions to do so lead to arm raisings – only a few small subregions of P* lie outside R0 . If that reflects the situation, P* comes closer to specifying a necessary and sufficient condition for R1 than any predicate Pk in physiological or physical vocabulary. P* comes closer than any such Pk to expressing a difference-maker for arm-raising: A condition X is a difference-maker for condition Y if X is necessary and sufficient for Y, so that the trajectories of all states within X run through Y, and no trajectories of states outside X run through Y. A causal explanation of R1 in terms of the difference-making psychological property P* is more relevant and therefore preferable to a causal explanation in terms of a sufficient but not necessary physiological or physical condition Pk .

13.3 Downward Causation in the Framework of Structural Equations Recent years have seen much work dedicated to developing the method of representing the search for causes by models using structural equations (Pearl 2000; Spirtes et al. 2000). This method constitutes the conceptual basis of algorithms that are successful in the discovery of causal structure, especially in complex systems studied by sciences such as economics or epidemiology. I can here only present the fundamental conceptual structure of the formalism, following Halpern (2000) and limiting myself to deterministic models with a finite number of dimensions. The construction of a structural equations (SE) model requires three steps. In the first step, the system under study is represented by a finite set of variables, which correspond to the predicates characterizing the features of the system. There are two sorts of variables. Endogenous variables are such that their values are determined by other variables within the model, whereas the values of exogenous variables are determined in a way that is independent of other variables of the system. The structural equations describe the functional dependence of the endogenous variables on other (endogenous and exogenous) variables in the model. The first step of construction of the model consists in determining a signature S. S is a triple (U,V,F), where U is the set of exogenous variables, V the set of endogenous variables, and F a set of functions associating with each variable Y a non-empty set F(Y) of values of Y. F(Y) is the range of the values of Y.

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The situation of arm-raising can be represented with the following simple signature: U contains the variable D representing p’s decision to raise her arm, V contains the variable R representing the raising of p’s arm, the function F(D) maps D on (0,1) and F(R) maps R on (0,1). The fact that D takes the value 1 represents the fact that person p takes the decision to raise her arm, whereas D = 0 represents the fact that p doesn’t take that decision. Similarly for R: The fact that R takes the value 1 represents the fact that p raises her arm, whereas R = 0 represents the fact that she doesn’t. The second step introduces the formal means representing the dependence relations among the variables introduced in the first step. A causal model consists in a pair (S,E), whose members are (1) the signature S and (2) a set of structural equations. There is exactly one structural equation for each endogenous variable X ∈ V, expressing the value of X as a function of all other variables in U ∪ V. The simplest model we can build for our example consists in the equation R = D. It expresses the assumption that the question of whether (R = 1) or not (R = 0) p raises her arm is perfectly determined by a single factor, i.e. the value of D. If D = 0, then R = 0, and if D = 1, then R = 1. This model is of course very much oversimplified because it does not represent the many other factors that may influence whether a person raises her arm at a given moment. The decision may be overrun by interference of external or internal factors, so that the arm does not rise although the decision has been taken (D = 1 but R = 0), and the arm may raise for reasons independent of the decision, so that R = 1 although D = 0. A third step consists in an assignment, which represents the application of the causal model to an actual situation. An assignment consists in attributing a value to each of the external variables. In our model, the assignment simply consists in attributing to the exogenous variable D one of its two values, 1 for situations in which the decision is taken and 0 for situations in which it is not taken. The minimal model I have used as an example to introduce the SE formalism already shows, albeit in a rather trivial sense, that downward causation is conceivable in this framework. The equation R = D represents a downward influence because D is a psychological predicate and R a physiological one. In order to evaluate the argument against the possibility of downward causation that relies on the premises of Closure and Exclusion, we need to construct a slightly more complex model. Let N be the only exogenous variable in U, where N = 1 represents one particular state of activity of the neurons in p’s brain at t0 , and N = 0 all other states of activity of the brain. As above, let D = 1 represent the fact that p takes the decision to raise her arm, whereas D = 0 represents the fact that she doesn’t take that decision. Let V contain, as endogenous variables, D and R (R = 0 and R = 1 are interpreted as above). Any adequate model should respect the local supervenience20 20 According

to externalism, the content of some mental states of a person depends on her social (Burge 1979) or physical (Putnam 1975) environment. Such mental states do not locally supervene on the person’s physical state. We can leave such states to one side here. It can be doubted whether mental states that do not supervene locally can play a role in causing behavior. The challenge we are addressing in the present paper is whether one can make sense of the idea that mental states

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N=1

D=1

N=0

D=0

Fig. 13.3 One value of N is mapped on two different values of D: D is not a function of N Fig. 13.4 No value of N is mapped on two different values of D: D is a function of N

N=1 N=2

D=1

N=3

D=0

of psychological variables over neurological variables, so that D must be a function of N. In other words, it must be excluded that one value of N is mapped to different values of D. The simplest structural equation would be D = N. However, in any realistic situation, D as defined will not be a function of N as defined. It is plausible that different values of D will be associated with N = 0. If N = 0, the brain is not in exactly the neurological state represented by N = 1 but it may be in a state that differs from such a state only slightly, maybe by the activity of a single neuron in an area with large redundancy. In that situation, we will have N = 0 and D = 1 because that slight neural difference makes no psychological difference so that a person in that situation would still take decision D. However, there will be other states that are represented by the same value N = 0 which differ a lot from the situation with N = 1, so that no decision is taken, and D = 0. Thus there is no functional dependence of D on N, as sketched in Fig. 13.3. A slightly more complex choice of signature can be used to model the situation in a more realistic way. Let N have 3 values instead of 2. Let N take value N = 1, as before, when the brain of p is in a perfectly specific state of neural activation, which happens to be p’s state at t0 . Let N take value N = 2 when the brain is not in exactly the state corresponding to N = 1 but in some other state that is also in the supervenience base of D, so that D = 1 for both N = 1 and N = 2. Finally, let N take the value N = 3 when the brain is in a state that is not in the supervenience base of D, so that D = 0 whenever N = 3. In this situation we can define the SE for D = F(N) with F(N=1)=F(N=2)=1 and F(N=3)=0, as sketched in (Fig. 13.4) Furthermore, let us suppose as before that D is necessary and sufficient for R, so that R = F(D), with F(D = 0) = 0 and F(D = 1) = 1. This model contains two structural equations: D = F(N) represents the noncausal dependence relation between a psychological property and the underlying

that do locally supervene can influence behavior, although the same behavior is also influenced by underlying physical states of the person.

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neurological property in its supervenience base.21 R = F(D) represents the causal dependence between the decision D and the bodily movement R. There is downward causation in this model, just as in the simpler first model. Indeed, the only SE representing a causal dependence represents a downward influence, of a psychological variable (D) on a variable representing bodily movement (R). However, this second model is rich enough for the challenge of Exclusion to arise. The model respects “Closure”, the first premise of the argument against downward causation sketched above. R depends both directly on D and indirectly on N. R is function of D and D is a function of N. Functional dependence is transitive; therefore R is a function of N. What about “Exclusion”, the second premise? This principle does not hold in the model I have sketched. Remember that the question we address is not about which event, interpreted as what fills a space-time zone, causes which event. This information is taken for granted. The information about the functional dependence of variables characterizing these events corresponds to aspects, features or properties of these events by virtue of which they influence each other. The functional dependencies represented by structural equations correspond to generalizations: The fact that R depends on D means that all events that resemble each other with respect to the variable D give rise to events that resemble each other with respect to the variable R. There is no reason why two such dependencies cannot coexist. No problem is created by the fact – if it is a fact – that R depends both on D and on N, in the sense that R is both a function of D and of N. This double causal dependence is no case of “genuine overdetermination”, which would be a situation in which R = 1 is caused “twice over”. Let me compare the situation with the situation of the firing squad where we have the clear intuition that the death of the victim is “overdetermined” in the sense of having several independent causes. The crucial difference with our model of mental causation is that the death caused by the firing squad is caused “several times”, through several mutually independent paths, by several mutually independent particular events, which are located at different places, i.e. where the different soldiers of the firing squad stand. By contrast, R = 1 is not “genuinely overdetermined” by the variables N = 1 and D = 1, or “caused twice over”, because N and D are variables representing properties that the same person possesses at the same time. In terms

21 It is in general taken for granted that the dependence (and supervenience) of properties of wholes

on properties of parts is a non-causal form of dependence (Kim 1974), insofar as it is a form of dependence without any temporal or spatial distance between the bearers of the two related properties. Some authors have recently argued that such dependence relations should be considered as causal nevertheless (Mumford and Anjum 2011; Leuridan 2012; Wilson 2018). I will leave this issue to one side and stick with the traditional thesis that properties standing in a supervenience relation based on the dependence of the properties of a whole on the properties of its parts do not stand in a causal relation. Schaffer (2016) uses structural equation models for both causal and noncausal grounding relations. However, Schaffer does not explore mixed models with both causal and non-causal dependence relations.

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of events, interpreted as what fills a space-time zone, there are just two particular events, which are related by a single causal relation: one event corresponds to the person at the time t0 when the variables N and D have values N = 1 and D = 1, the other event corresponds to the person a t1 , when R has value R = 1. Our model shows that an event can be causally influenced by two different aspects of some earlier event, or by two properties of that earlier event. This is so in particular when these aspects are not independent of each other: In our model, D is a function of N, which expresses the fact that the decision is nomologically dependent on the state of the person’s brain. However, even if the fact that R = 1 causally depends on more than one factor does not entail that R is “genuinely” causally overdetermined, one might still argue that one of these factors – represented by the value of N – is fundamental, whereas the other – represented by the value of D – is only derivative. In other words, one might hold that a causal explanation of R by N is superior to an explanation of R by D, because the former explanation is in terms of a more fundamental variable. In other words, on might hold that even if R can be causally influenced “in parallel” by both N and D, the causal explanation of R in terms of the most fundamental variable N “excludes” all explanations in terms of less fundamental variables, such as D. One might hold in other words that even if a mental variable D can influence R in parallel to N, D is never explanatorily relevant. This reasoning depends on a principle of “causal-explanatory exclusion”, according to which a causal explanation E1 “excludes” other causal explanations E2 of the same fact (even if both are correct) in the weak sense that E1 is better than E2 because E1 explains the explanandum in terms of more fundamental variables than E2 . Is it plausible that explanations in terms of more fundamental variables are always preferable? Explanations are assessed by two criteria: correctness and utility. The utility of an explanation depends on the interests and background knowledge of the explanation seeker (Bromberger 1966; van Fraassen 1980, pp. 132–4), but it can also be evaluated in general terms of relevance. I would like to suggest that it is often more appropriate to causally explain a fact in terms of higher-level variables than to explain it in terms of more fundamental variables. The model of structural equations provides a straightforward criterion for comparing the relevance of various influences for the causal explanation of a given factor. Each influence on R is expressed by a structural equation expressing a function R = F(X). This function can be injective or not.22 A function Y = F(X) is called injective if there do not exist two different values xi = xj of X that F maps on the

22 The

analysis of specific causation in terms of the concept of an injective function is a variant of Woodward’s (2010, p. 305) analysis, who builds on Yablo’s (1992) notion of proportional causation and Lewis’ (2000) notion of influence. My own use of the term “specificity” differs from Woodward’s in that Woodward calls a function “specific” if it is both injective and surjective, whereas I use a weaker notion that requires only injectivity but not surjectivity. A function Y = f(X) is surjective if and only if, for every value yi of Y there is some value xj of X such that yi = f(xj ). Griffiths et al. (2015) provide a quantitative measure of the specificity of X for Y on terms of the mutual information between variables X and Y. See also Calcott (2017).

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same value of Y, so that f(xi ) = f(xj ). The causal influence of X on Y is specific if and only if Y = F(X) is injective. Here is a criterion of relevance for causal explanations in terms of structural equations. If a variable Y depends on two factors Xi and Xj , and if Y = F(Xi ) is injective whereas Y = F(Xj ) is not injective, it is more relevant to causally explain Y in terms of Xi than in terms of Xj . In the model sketched above, R is a function of both N and D. However, R is an injective function of D, but not of N. The function R = F(N) is not injective, because F(N = 1) = F(N = 2) = R = 1. However, function R = F(D) is injective because F(D = 0) = F(D = 1). In our model, the variable D has not only downward causal influence on R, but it is more relevant to mention this downward causal influence in a causal explanation of R than to mention the parallel same-level cause N, because the downward causal influence is specific whereas the same-level influence is not.23

13.4 Other Accounts of Downward Causation There is downward causation in both models I have sketched. I would like to briefly put this result in the perspective of other proposals for making sense of downward causation. Both of our models provide ways of escaping the conclusion of the argument against downward causation by challenging “Exclusion”. This result can be seen as establishing the cogency of compatibilism: A higher-level variable (or a higher-level feature of a system) D can exercise downward causal influence on a lower-level variable R even if there are also lower-level variables N that exercise low-level causal influence on the same variable R.

13.4.1 A Counterfactual Criterion for Compatibility Karen Bennett (2003) has developed a defense of compatibilism that relies on the fact that a mental sufficient cause m and a physical sufficient cause p of the same effect e can coexist insofar as the former depends on the latter, or in other words, is determined by the latter. In such a situation, m and p are not “overdetermining” e.

23 List

and Menzies (2009) analyze downward causation in terms of the notion of realizationinsensitivity. However, their account leads to what they call “downward exclusion”, according to which the causal influence of a higher-level variable D on a lower-level variable R excludes the existence of a parallel low-level causal influence of N on the same variable R. It would be a mistake to judge, as List and Menzies (2009), but not Woodward (2010, p. 288) do, that all causation is specific (Kistler 2017; McDonnell 2017). My suggestion that the higher-level cause D is more relevant for the causal explanation of R than the lower-level cause N if the function R = F(D) is injective whereas R = F(N) is not injective, seems to be compatible with, and complementary to, Woodward’s (this volume) analysis.

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If m and p did overdetermine their effect e, the following two counterfactuals would both be (non-vacuously) true: O1 : If m had happened without p, e would still have happened. O2 : If p had happened without m, e would still have happened. Given that m is determined by p, O2 is vacuous (Bennett 2003, p. 483–7), and so the compatibilist can deny that both O1 and O2 are non-vacuously true. Our models can be seen as providing a complement to Bennett’s demonstration. Bennett provides a criterion for the conceivability of downward causation: downward causation is conceivable if O2 is vacuous. Our models clarify how O2 can be vacuous in situations in which the issue of downward causation arises.24 The semantic evaluation of O1 and O2 in our models yields the result that O2 is vacuous. Thus, to the extent to which the models are adequate, there is downward causation in the situations represented by the models. The reason for which O2 comes out vacuous is the same in both models: The counterfactual situation described by the antecedent of O2 , in which p is present but m is absent, does not respect the relation between p and m in the actual world: Given the actual laws of nature, p determines m. In the SE model, the antecedent of O2 corresponds to a situation where N = 1 but D = 0. This situation is impossible in the model because it contradicts the functional dependence of D on N: N = 1 is mapped on D = 1. The functional dependence expressed in the SE D = F(N) represents the fact that D is grounded on N, which entails in turn that D supervenes on N, so that there cannot be a change in the value of D, while N is held fixed, which is the content of the antecedent of O2 . Thus, O2 ’s antecedent is false in all worlds that share our actual laws of nature. In terms of dynamical systems, all systems that share the phase space of some actual cognitive system in our world, i.e. all systems that share the actual laws of nature, are such that P ⊂ M. The antecedent describes a system whose position in phase space lies within P but not within M. There is no system of that sort that corresponds to the actual laws of nature. Therefore the antecedent of O2 is nomologically impossible and O2 is vacuous.

13.4.2 Rejection of Closure Orilia and Paolini Paoletti (2017) claim that the acceptance of downward causation leads to “the rejection of causal closure” (Orilia and Paolini Paoletti 2017, 24 Kim

also suggests that the task of establishing the existence of certain causal relations cannot be accomplished simply by making it plausible that certain counterfactuals have certain truth values. “Merely to point to the apparent truth, and acceptability, of certain mind-body counterfactuals as a vindication of mind-body causation is to misconstrue the philosophical task at hand.” (Kim 1998, p. 71) What is needed in addition is providing “an answer as to why these counterfactuals hold, that is to say, to find the relevant truthmakers” (Gozzano 2017, p. 301).

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p. 34). They justify this claim by using Yablo’s (1992) framework of proportional causes. According to Orilia and Paolini Paoletti, the search for an adequate causal explanation of a bodily movement is constrained by the conception of that movement as being of a certain type, which has a certain degree of determination. Let us suppose that John’s decision at t1 to raise his arm causes, at t2 , an event at which his arm raises. That arm-raising event exemplifies a very specific sort of arm-raising, which they call R321 . The same event however also exemplifies a whole series of less and less specific, or more and more abstract types of arm-raising. R32 is the property of raising one’s arm up to a height lying in a certain interval, with a speed lying within a certain interval, etc. but leaving open many more specific details, concerning e.g. the positions of the hand and fingers. R3 might be the even more abstract property of raising one’s arm, in any way whatsoever. The effect of John’s decision corresponds to a particular degree of determination in that hierarchy. Let us suppose it is R32 . Now, they argue, the cause that is proportional to the exemplification of that property is the decision, i.e. a mental cause. By contrast, the exemplification of the underlying physical property of the person’s brain and body is too specific to be proportional to the exemplification of R32 . This results indeed from the application of Yablo’s criteria of proportionality: to be a proportional cause of e, a cause c must be (1) required for e and (2) enough for e. The physical cause underlying the decision is not required for R32 . Different physical events would have caused movements very similar to the actual movement exemplifying R321 : the movements they would have caused would still have belong to the determinable type R32 of arm-raising. Only John’s decision to perform an action of type R32 is proportional to R32 (in the sense of being both required and enough for the exemplification of an event of precisely that type). However, according to Orilia and Paolini Paoletti, the result that there is a downward causal influence from the decision to the arm-raising has been reached in a way that entails “the rejection of Causal Closure in the form suggested by Kim” (Orilia and Paolini, p. 34), according to which25 : “If a physical event has a cause that occurs at t, it has a physical cause that occurs at t” (Kim 2005, p. 43). This result may seem surprising, insofar as it seems to contradict the compatibility of downward causation with the existence of a parallel underlying process of physical causation, which characterizes our two models of downward causation.26 25 Contrary

to the version we have used, this formulation of the closure principle leaves it open (following at this point Lowe 2000b) whether every physical event at t has a physical cause at every instant t* earlier than t. 26 Hendry also judges that “the existence of strong emergence in chemistry is incompatible with the causal closure of the physical” (Hendry 2017, p. 160). Anjum and Mumford (2017) say that downward causation requires “that causal closure should be rejected” (Anjum and Mumford 2017, p. 106). These authors do not explicitly argue against the hypothesis that all cases of downward causation are accompanied by parallel low-level causation. Their reasoning might be this. Given that a higher-level cause has to be postulated to causally explain the effect, there can be no baselevel cause that can explain that effect. Thus, there is no causal closure at the base level. This reasoning relies on an oversimplification. In many cases in which the postulate and use of a higherlevel cause is justified, that higher-level cause is only necessary to “specifically causally explain”

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However, the contradiction is only apparent. It can be overcome by making explicit the different terminological choices underlying the two analyses. Orilia and Paolini Paoletti use the word “cause” only to make reference to proportional causes, in Yablo’s sense of being both required and enough for a given effect. In that terminology there is indeed no physical cause happening at the same time as John’s decision because all physical types of event are too specific to be required for the type of event R32 . In our own terminology, there may well be such a physical cause at the time of the mental cause. Closure can be accepted insofar as a cause is an event of a type that is sufficient for a given type of effect. In our terminology, and in our two models of downward causation, the mental cause of R32 at time t coexists with a physical cause at time t, but only the mental cause is specific (or proportional), which is why it is in general more appropriate to mention the mental cause in a causal explanation of why an event of type R32 has happened.27 Our terminology seems preferable to Orilia and Paolini Paoletti insofar as it makes it possible to say that there are non-specific causes.

13.4.3 Must Downward Causal Relations Necessarily Be Mediated by a Synchronous Top-Down Determination Relation? Carl Gillett (2016, 2017) argues that downward causal relations are necessarily mediated by synchronic top-down determination relations. Gillett’s argument runs as follows. (1) In a first step, Gillett argues that there are numerous scientific examples of strong emergence (“S-emergence”). The instance of a property F in object s is a case of S-emergence if it a) contributes to determining powers of some parts of s and b) contributes to “powers causally resulting in effects at their own level” (Gillett 2017, p. 258). In other words, F is emergent if and only if it (a) is a higher-level property of a composed object s, (b) gives objects that possess it causal powers at its own level, i.e. makes them capable of influencing properties of other objects at the same level, and (c) modifies the causal powers of the

the effect, not to explain the effect, tout court. Thus, it is often justified to introduce a higher-level variable and to use it to causally explain an effect although it is also possible to explain that same effect at a lower level. One reason for which the higher-level explanation may be better is that it is specific whereas the lower-level explanation lacks specificity. 27 Woodward draws a similar distinction between David Lewis’ (2000) terminology and his own, where the notion of specificity is used to “distinguish in a useful way among causal relationships, rather than treating it as a ‘criterion’ of causation” (Woodward 2010, p. 304; italics Woodward’s). Lewis (2000) takes “influence”, which is similar to causal specificity, to be characteristic of causation as such. Woodward’s terminology is preferable to Lewis’ (2000) insofar as it is compatible, whereas Lewis’ is not, with the existence of non-specific causes.

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parts of s. Focusing on condition c), the S-emergence of property F requires that the fact that s has F modifies the causal powers of some of s’s parts, where this modification of the parts by the whole is synchronic, in the sense that s possesses F at the same time t at which s’s parts possess those powers that are modified by s’s possession of F. (2) In a second step, Gillett argues that this top-down determination relation cannot be causation.28 A relation between the instance of a higher-level property P of an object s at t and an instance of a lower-level property Q of a part p of s, at the same time t, cannot be causal. The reason is that (s,P,t) and (p,Q,t) are temporally and spatially co-located, whereas causation requires the localizations of cause and effect to have no spatio-temporal overlap. Gillett dubs such synchronic top-down determination relations of properties of parts of composed objects by properties of those whole objects “machretic” (Gillett 2017, p. 257) determination relations. (3) From (1) and (2), Gillett draws the conclusion that downward causal relations, where an S-emergent property instance G at t influences the instance of some lower-level instance P at some later time t*, can only be indirect: the influence of (s,G,t) (the exemplification of G by s at t) on (p*,P*,t*) (the exemplification of lower-level property P* by lower-level individual p* at t*, where t* is later than t) must be mediated by a synchronous “machretic” top-down determination relation from (s,G,t) on (p,P,t) (the exemplification of lower-level property P by lower-level individual p, which is a part of s, at t). For lack of space, I cannot here do full justice Gillett’s analysis of machretic determination and downward causation. Let me just note that both models we have sketched above make sense of downward causation without positing any synchronous downward determination relation of the sort of Gillett’s machresis. Gillett’s argument shows that (1) the definition of S-emergence seems to entail machresis, (2) there are scientifically plausible cases of S-emergence, (3) machresis is non causal, and (4) given the acceptance of machresis, one can conceive of downward causation as mediated by machresis. However, this argument does not show that there cannot be downward causation that is not mediated by machresis. The postulate of machresis, i.e. of a relation of synchronic top-down determination raises the following worry. If higher-level property G of complex object s at t can be given a “compositional explanation” (Gillett 2017, p. 246), in terms of the bottom-up determination of G by the parts p1 , . . . pn of s and the lowerlevel properties Pi of those parts at the same time t, and if the higher-level property G also determines, at the same time t, in the reverse top-down direction, some lower-level property Pi of part pi , it seems to follow that there can be (non-trivial)

28 This

move makes Gillett’s account escape the objection based on Kim’s (1999/2010, p. 35/6) argument according to which emergence entails that there are situations of “mutual causal interdependence” (Kim 1999/2010, p. 36), in which an object x is caused to acquire P at t although, at that same moment t, x already possesses P and exercises the causal determinative powers inherent in P.

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self-determination: The lower-level property Pi of part pi determines G of s, which itself determines Pi of part pi , all synchronously at t.29 It would seem that models of downward causation that avoid the consequence that there can be non-trivial selfdetermination are preferable to those that do have that consequence.

13.5 Conclusion I have sketched two conceptual frameworks that leave room for downward causation. Downward influence of higher-level features of complex systems on lowerlevel features of these systems can be represented in the framework both of dynamical systems and of structural equations. The “Exclusion” principle, which is a crucial premise of the argument against the possibility of downward causation, is false in both types of models. Furthermore, both frameworks can be completed with conceptual tools that make it possible to justify why downward causal influence is not only conceivable and compatible with the “Closure” principle, but also why it is often relevant to causally explain facts in terms of downward causation.30

References Anjum, R.L. & Mumford, S. (2017). Emergence and Demergence. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 92–109). New York: Routledge. Barsaglini, A., et al. (2014). The effects of psychotherapy on brain function: A systematic and critical review. Progress in Neurobiology, 114, 1–14. Baxter, L. R., Jr., et al. (1992). Caudate glucose metabolic rate changes with both drug and behavior therapy for obsessive-compulsive disorder. Archives of General Psychiatry, 49, 681–689. Bennett, K. (2003). Why the exclusion problem seems intractable, and how, just maybe, to tract it. Nous, 37, 471–497. Bromberger, S. (1966). Why-questions. Reprinted in On what we know we don’t know (pp. 75– 100). Chicago: University of Chicago Press and Stanford, CSLI Press, 1992. Burge, T. (1979). Individualism and the mental. In P. A. French, T. E. Uehling, & H. K. Wettstein (Eds.), Midwest studies in philosophy (Vol. IV). Minneapolis: University of Minnesota Press. Calcott, B. (2017). Causal specificity and the instructive-permissive distinction. Biology and Philosophy, 32, 481–505. Cartwright, N. (1999). The dappled world. A study of the boundaries of science. Cambridge: Cambridge University Press.

29 This

argument, according to which the existence of mutual metaphysical determination entails, via the transitivity of metaphysical determination, the implausible consequence that contingent facts determine themselves, has a similar structure to the argument (Kistler 2013) according to which the interpretation of mutual nomic dependence as causal has the implausible consequence that contingent facts cause themselves. 30 I thank Simone Gozzano and an anonymous referee for this volume for their helpful comments.

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Craver, C. (2007). Explaining the brain. Mechanism and the mosaic unity of neuroscience. Oxford: Oxford University Press. Dretske, F. (1988). Explaining behavior. Cambridge, MA: MIT Press. Dupré, J. (1993). The disorder of things. Metaphysical foundations of the disunity of science. Cambridge, MA: Harvard University Press. Eronen, M. I. (2013). No levels, no problems: Downward causation in neuroscience. Philosophy of Science, 80(5), 1042–1052. Eronen, M. (2019). The levels problem in psychopathology. Psychological Medicine, 1–7. https:// doi.org/10.1017/S0033291719002514. Flanagan, O. (1992). Consciousness reconsidered. Cambridge, MA: MIT Press. Gillett, C. (2016). Reduction and emergence in science and philosophy. Cambridge: Cambridge University Press. Gillett, C. (2017). Scientific emergentism and its move beyond (direct) downward causation. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 242–262). New York: Routledge. Gozzano, S. (2009). Levels, orders and the causal status of mental properties. European Journal of Philosophy, 17(3), 347–362. Gozzano, S. (2017). The compatibility of downward causation and emergence. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 296–312). New York: Routledge. Griffiths, P. E., Pocheville, A., Calcott, B., Stotz, K., Kim, H., & Knight, R. (2015). Measuring causal specificity. Philosophy of Science, 82, 529–555. Halpern, J. (2000). Axiomatizing causal reasoning. Journal of Artificial Intelligence Research, 12, 317–337. Hendry, R. (2017). Prospects for strong emergence in chemistry. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 146–163). New York: Routledge. Hitchcock, C. (2012). Theories of causation and the exclusion argument. Journal of Consciousness Studies, 19, 40–56. Kim, J. (1973). Causation, nomic subsumption, and the concept of event. Journal of Philosophy, 70, 217–236. Reprinted in J. Kim, Supervenience and mind (pp. 3–21), Cambridge: Cambridge University Press, 1993. Kim, J. (1974). Non-causal connections. Reprinted in J. Kim, Supervenience and mind (pp. 22–32). Cambridge: Cambridge University Press, 1993. Kim, J. (1988). Explanatory realism, causal realism, and explanatory exclusion. Midwest Studies in Philosophy, 12, 225–240. Kim, J. (1998). Mind in a physical world. Cambridge, MA: MIT Press. Kim, J. (1999/2010). Making sense of emergence. Reprinted in J. Kim, Essays in the metaphysics of mind (pp. 8–40). Oxford: Oxford University Press, 2010. Kim, J. (2005). Physicalism, or something near enough. Princeton: Princeton University Press. Kistler, M. (1999). Causes as events and facts. Dialectica, 53, 25–46. Kistler, M. (2006a). Causation and laws of nature. Londres: Routledge. Kistler, M. (2006b). The mental, the macroscopic, and their effects. Epistemologia, 29, 79–102. Kistler, M. (2013). The interventionist account of causation and non-causal association laws. Erkenntnis, 78, 65–84. Kistler, M. (2014). Analysing causation in light of intuitions, causal statements, and science. In B. Copley & F. Martin (Eds.), Causation in grammatical structures (pp. 76–99). Oxford: Oxford University Press. Kistler, M. (2017). Higher-level, downward and specific causation. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 54–75). New York: Routledge. Leuridan, B. (2012). Three problems for the mutual manipulability account of constitutive relevance in mechanisms. British Journal for the Philosophy of Science, 63, 399–427. Lewis, D. (2000). Causation as influence. The Journal of Philosophy, 97, 182–197.

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List, C., & Menzies, P. (2009). Non-reductive physicalism and the limits of the exclusion principle. Journal of Philosophy, 106, 475–502. Lowe, E. J. (2000a). An introduction to the philosophy of mind. Cambridge: Cambridge University Press. Lowe, E. J. (2000b). Causal closure principles and emergentism. Philosophy, 75, 571–585. McDonnell, N. (2017). Causal exclusion and the limits of proportionality. Philosophical Studies, 174, 1459–1474. Mumford, S., & Anjum, R. L. (2011). Getting causes from powers. Oxford: Oxford University Press. Nagel, E. (1961). The structure of science. London: Routledge and Kegan Paul. Orilia, F., & Paolini Paoletti, M. (2017). Three grades of downward causation. In M. Paolini Paoletti & F. Orilia (Eds.), Philosophical and scientific perspectives on downward causation (pp. 25–41). New York: Routledge. Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press. Putnam, H. (1975). The meaning of meaning. In H. Putnam (Ed.), Mind, language, and reality: Philosophical papers (Vol. 2). Cambridge: Cambridge University Press. Quine, W. V. O. (1960). Word and object. Cambridge, MA: MIT Press. Quine, W. V. O. (1985). Events and reification. In E. LePore & B. McLaughlin (Eds.), Actions and events: Perspectives on the philosophy of Donald Davidson. Oxford: Basil Blackwell. Robb, D., & Heil, J. (2018). Mental causation. Stanford Encyclopedia of Philosophy. https:// plato.stanford.edu/entries/mental-causation/ Schaffer, J. (2016). Grounding in the image of causation. Philosophical Studies, 173, 49–100. Schaffner, K. (1967). Approaches to reduction. Philosophy of Science, 34, 137–147. Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction and search (2nd ed.). Cambridge, MA: MIT Press. Van Fraassen, B. C. (1980). The scientific image. Oxford: Oxford University Press. Voosholz, J. (this volume). Top-down causation without levels. In M. Gabriel & J. Voosholz (Eds.), Top-down causation and emergence. Cham: Springer. Wilson, A. (2018). Metaphysical causation. Nous, 52, 723–751. Woodward, J. (2003). Making things happen. New York: Oxford University Press. Woodward, J. (2010). Causation in biology: Stability, specificity, and the choice of levels of explanation. Biology and Philosophy, 25, 287–318. Woodward, J. (this volume). Downward causation defended. In M. Gabriel & J. Voosholz (Eds.), Top-down causation and emergence. Cham: Springer. Yablo, S. (1992). Mental Causation. Philosophical Review, 101, 245–280.

Part V

Responses

Chapter 14

Responses to Part I: Applications of George Ellis’s Theory of Causation George F. R. Ellis

Abstract In this response, George Ellis comments on the publications of Part I. He responds first to Sara Green and Robert Batterman, before outlining his thoughts on Otávio Bueno’s piece.

I am grateful to all the authors who have contributed chapters to this book, to the Editors who made it possible, and to Markus Gabriel and Jan Voosholz for arranging the enjoyable and enlightening meeting out of which this book emerges. Most of the chapters are supportive of my proposals regarding downward causation. There is just one that is seriously critical: Chap. 5 by Thomas Luu and Ulf-G. Meißner. I respond to them below in Chap. 15. The chapter by Jan Voosholz is supportive but suggests a substantial rephrasing of some points which are important; I respond to him in Chap. 17. The chapter by Richard Healey also is in effect largely supportive, but I disagree with him on some key points in my response in Chap. 17.

14.1 Making Sense of Top-Down Causation: Universality and Functional Equivalence in Physics and Biology: Sara Green and Robert Batterman I appreciate the supportive nature of this article, and the extension it gives in terms of universality and functional equivalence in physics and biology. It is difficult to say much about an article when I agree with so much in it!

G. F. R. Ellis () Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_14

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14.1.1 Relative Autonomy and Kinds of Upscaling The first issue is “Explanations of phenomena at higher scales or levels are (relatively) autonomous of explanations at lower levels”—indeed, this is the core issue. In the terms of Ellis (2020b), there is an Effective Theory ETL at each level L. This is a generalized form of what Robert Laughlin and David Pines call “Classical and Quantum Protectorates” (Laughlin and Pines 2000). While these emergent layers depend on the lower levels for their existence, their functioning can be largely independent. This is Denis Noble’s Principle of Biological Relativity (Noble 2012) generalised to physics and engineering (Ellis 2020b). The logic of each level has its own autonomy. Types of Upscaling Green and Batterman emphasize that when considering systems with complex microstructures at the mesoscale (such as steel or bone), simple averaging over lower-scale variables would not enable scientists to predict macroscale material properties. This is because physical systems at different scales display distinct physical structures and behaviors, while at the same time that higherlevel behaviors are dependent on some microstructural details (the kind of circular causality I emphasize in Ellis (2020b)). For multiscale systems that are composed of materials with different conductivities or elastic behaviors, the aim of upscaling is to find effective (continuum scale) parameters (like Young’s modulus) that code for microstructural details of the composites. The authors state in particular, “We argue that simple averaging strategies for upscaling only work for simple homogeneous systems (such as an ideal gas), and thus suggest that examples of mechanical top-down causation present an even greater challenge to reductionism than typically recognized.” That is a welcome addition. Black Boxing There is an important point one can add here: namely that in the case of biological or engineering systems, often another kind of upscaling takes place: namely Black Boxing (Ashby 2013), whereby higher level logic emerges from lower level logic. A specific case is given in Ellis and Kopel (2019). This occurs once information processing has come into being and plays a dynamical role in determining outcomes, distinguishing biology from physics (Nurse 2008; Davies 2019). It also occurs in engineering inter alia via the ubiquitous use of digital computers (Ellis and Drossel 2019).

14.1.2 Constraining Relations Green and Batterman say “Top-down causation implies that higher-level features are not just relatively autonomous from lower-level description but also influence the latter through constraining relations”. Indeed. That is central; it is one of the two key ways whereby downwards causation takes place (Salthe 1993, Juarrero 2002,

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Blachowicz 2013 and Chaps. 1 and 8). That is (quoting from Ellis 2020b, §2.3), outcomes P(d) at Level L depend on constraints CLI at the level L arising from conditions at a Level of Influence LI. Thus the Effective Theory ETL at level L depend on these constraints: ETL (CLI ) : vL ∈ L → ETL (CLI )[vL ] = oL ∈ L

(14.1)

The constraints CLI may be time independent: ∂ CLI /∂t = 0 in which case they are structural constraints; or they may be time dependent: CLI = CLI (t), ∂CLI /∂t = 0, in which case they are signalling or controlling constraints, as for example in the case of cell signalling networks (Berridge 2014). This then ties nicely into the discussion by Green and Batterman, who say that that ‘bottom-up reductionism’ can be challenged by examples of mechanical or algorithmic top-down causation in both physics and biology.

14.1.3 Interlevel Loops Green and Batterman then put a conundrum: Top-down causation implies that higher-level features are not just relatively autonomous from lower-level description but also influence the latter through constraining relations. An objection to this view may be that since higher-level features primarily select among possible lower-level states, higher levels are not really autonomous after all. If lower levels define the possibilities, and if emergent features are always realized through materials at lower levels, what does autonomy really consist in?

They then give convincing answers. I’d just add one more: this is the kind of Interlevel Causal Closure that I discuss in Ellis (2020b). The idea comes from biology (Mossio and Moreno 2010; Mossio 2013) but in fact applies also across all real world contexts such as engineering. It is the integral interlevel loop that is the real emergent feature allowing causal closure. None of its constituent levels, including the underlying physics levels, are causally complete by themselves. An example where this is immediately clear is the COVID-19 pandemic, involving all levels from microbiology to political decisions with outcomes reaching down to the particle level (for instance the atoms constituting aircraft which now follow different trajectories than they used to).

14.1.4 Homeostasis and Feedback Control This is a special case of signalling constraints, involving interlevel loops, that is so important that it deserves characterisation in its own right, so I labeled it TD2. This is cybernetics in engineering as defined by Wiener (Wiener 1948) and homeostasis in physiology as defined by Guyton (1977). It is one of the key network

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motifs defined by Uri Alon (Alon 2006). As Green and Batterman state, the same mathematical models can be used to describe feedback control in very different oscillatory systems, from electrical circuits to metabolic regulation in different organisms, and they give many interesting examples such as Integral Feedback Control. In a sense this is an example of the universality classes they discuss (see below): a higher level pattern of dynamics that a great many different lower level systems realise.

14.1.5 Multiple Realisability, Causal Slack, and Universality Green and Batterman state that the most important aspect of multiple realizability is that it supports the explanatory autonomy of more general higher-level models capturing similarity in behaviors of heterogeneous systems. Indeed. In Ellis (2020b) I have found a new way to express it: It is not the individual variables at the lower level that are the key to what is going on: it is the equivalence class to which they belong. But that whole equivalence class can be describer by a single variable at the macro level, so that is the real effective variable in the dynamics that is going on. This is a kind of interlevel duality: {vL ∈ L} ⇔ {vi : vi ∈ EL−1 (vL−1 ) ∈ (L − 1)}

(14.2)

where EL−1 (vL−1 ) is the equivalence class of variables vL−1 at Level L-1 corresponding to the one variable vL at Level L. The effective law EFL at Level L for the (possibly vectorial or matrix) variables vL at that level is equivalent to a law for an entire equivalence class EL−1 (vL−1 ) of variables at Level L-1. It does not translate into an Effective Law for natural variables vL−1 per se at Level L-1. Green and Batterman make the important point that this amounts to use of a highly abstract functional description that is (relatively) independent of molecular details, but also that functional equivalence classes involve information hiding. This is one of the key principles in modular hierarchical structures (Booch 2006). They point out that Functional equivalence classes occur in the case of feedback control TD2, in agreement with (Auletta et al. 2008). Causal Slack The idea of causal slack that Green and Batterman emphasize arises in relation to multiple realisability, and perhaps this is an issue that needs more development. Causal Slack When one has a lower level equivalence class corresponding to a higher level variable or relation, it does not have to be a precise correspondence: there will be some wiggle room at the lower level that still allows the higher level function to be realised.

This is often realised via thresholds that have to be overcome in order to trigger a higher level reaction, as in the case of binding energy in all sorts of contexts, and in the functioning of synapses, or tolerance limits in feedback control systems that correct higher level outcomes within acceptable limits when lower level variation

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takes place. It also occurs via attractors in phase space and in Integral Feedback Control (IFC), where complex networks often converge to a limited set of stable state. is an important theme, as Green and Batterman say. It particularly arises in the highly contested area of neutral selection in evolutionary theory, see Duret (2008). Universality and Multiple Realizability in Physics A very interesting point that Green and Batterman make is that Equivalence Classes are also called universality classes in thermodynamic behavior near critical points, because of the universality of behaviour there. Like the classical and quantum protectorates of Laughlin and Pines (2000), these are cases where higher level behaviour emerges that is an essentially independent phenomenon: “the closer the system is to criticality, the less the macroscopic/continuum properties depend on the dynamical details of the system”. Thus what we seem to have is, Critical Phenomena: Rather than being emergent in an upward fashion, critical phenomena are essentially higher level phenomena which can be realised by a large variety of lower level systems.

A Renormalisation Group explanation extracts these structural features, and this explains why very simple models such as Ising models can be used to explain the behaviours of a variety of real systems such as fluids and magnets. So now the following comes to mind. With Auletta and Jaeger, I have argued in a limited context (Auletta et al. 2008) that existence of equivalence classes characterizes top-down causation. Can it be that existence of universality classes in critical phenomena shows that downward causation is necessarily taking place then, because it involves equivalence classes? I now believe that this may well be the case. It would be good to have this either formally proved, or shown to be wrong. Convergence in Biology Similarly to this emergence of similarity classes, in biology there is much evidence of convergence of structure and function to fulfill higher level biological needs. Many examples are given in McGhee (2006). Many of these convergences arise because of engineering constraints on solutions to biological problems as shown in Catspaws and catapults (Vogel 2000). Even complex networks often converge to a limited set of stable states as Green and Batterman remark. Thus there are attractors in the emergent dynamics that play a strong role in shaping what happens. Multiple Realisability and Identity Robert Rosen makes a key remark (Rosen 1987): One problem is that organisms are open systems; there is turnover (not to mention growth and development), a phenomenon very hard to integrate into the Newtonian picture. In fact, in the strict Newtonian sense, organisms are not even systems. We may be able to describe the motions of the particles which constitute an organism at some instant, but we would clearly very quickly lose, the organism itself if we did so.

That is, multiple realisability enables us—identifiable individual human beings— to be realised by different molecules at the molecular scale (there is a complete turnover about every 7 years) and particles at the underlying physical scale, while

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retaining our identity as individuals. Organisms cannot be identified with the particles out of which they are made at a particular instant. Machines may also experience such a turnover as they are repaired. This raises key issues of identity and system boundaries that I will not pursue further here. But it demonstrates decisively the key importance of multiple realisability. The same issue arises in some natural phenomena, for example a river, and in organisations in terms of which individuals occupy specific organisational roles.

14.1.6 Inherently Higher Level Concepts This is the single most important concept in the paper. Time and again I find in interacting with reductionists that they cannot grasp the idea that higher level effective variables exist that are not derived in an upward way from lower level variables. All examples that makes this clear are very helpful. Green and Batterman give very useful cases, for example material parameters of relevance for modeling of the development of an embryo are inherently higher-level concepts. They emphasize that although parameters such as the cell voltage, or the geometrical and electrical properties of different tissue types are ‘nothing but’ properties of physical structures, they are not reducible to or derivable from lower-scale variables. “In fact, one cannot measure or even conceptualize these variables at lower scales”. Similarly organizing or design principles occur in living systems (Alon 2006; Green 2015), e.g. bacterial chemotaxis. They are related to integrative organ functions that underlie human physiology as effective higher level theories (Rhoades and Pflanzer 1989). This discussion leads to the key idea of Higher Level Organising Principles (HLOPs) that shape system dynamics outcomes, independent of lower revel structures. They state that systems biologists use the term design principles for such features that enable generic types of functions such as sustained oscillations, noise filtering, robust perfect adaptation, signal amplification, etc. It is these higher level principles principles that determine physical outcomes, when they are instantiated in lower level contexts. Similarly attractors in systems dynamics act as such organising principles, where complex networks often converge to a limited set of stable state (Denis Noble makes this point, see Chap. 15). This is in effect what Stuart Kauffman discusses in his book (Kauffman 1995). Intrinsically Higher level Variables Occurrence of such variables is a key feature of such principles. They occur for example where environmental variables that trigger phase transitions are ‘high level’ variables because temperature and pressure cannot be attributed to isolated molecules. “Like order parameters, these point to a collective properties arising in a constrained system, such as a gas container”. Actually temperature is a difficult concept if one tries to base it properly in the underlying physics (Bishop and Ellis 2020).

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Russ Abbott (a computer scientist) gives quite different examples, such as Abbott (2008) Most of what we call emergence is the result of constructive processes. New entities are constructed from existing entities. The new entities have properties that are considered emergent with respect to the existing entities. A typical example is a steel-hulled boat. It floats because of its shape, according to a macro-level theory of buoyancy. Even though the boat supervenes over its steel component elements, its buoyancy is neither reducible to nor predictable from the properties of steel.. The key here is that there are theories that come into play at a higher level that are independent of the properties of the lower level... This is not a matter of derivability. Formally, any theory T that is independent of some theory S is derivable from S. One imply ignores S and derives T. Adding S to the derivation presumably doesn’t hurt as long a S is not in conflict with any of the assumptions used by T. The more important point is that T is autonomous with respect to S.

He then very convincingly gives abstractions in computer science as another example: Computer science studies the conceptualization and implementation of abstractions. We build higher level regularities—we call them abstractions—from lower level regularities. That’s what we do for a living—day after day. Every software application is the implementation of higher level abstractions. Software applications implement abstractions by organizing the lower level abstractions, typically those expressed in a programming language. . . . We know how to make higher level regularities “emerge” from lower level regularities.

The really contentious cases are biology, where information plays a key roles (Nurse 2008; Davies 2019) and logical choices take place (Ellis and Kopel 2019), and the brain, where rational thought occurs and has demonstrable physical outcomes (Ellis 2016). The problem is that when something is so obviously true (these higher level variables are not coarse grained lower level variables but are surely causally effective) it is difficult to prove it! More conceptual work needs to be done. The example of a digital computer, where algorithms are clearly causally effective, is a useful stepping stone (Ellis and Drossel 2019).

14.1.7 Practical Importance Yes indeed, the topic is of practical importance, for example in terms of medicine, as they clearly explain. I love placebos as a pure demonstration of top-down causation from expectations in the mind to outcomes at all biological levels. There is a causal explanation for some of those outcomes via the fact that some immune system molecules are also neuromodulators (Sternberg 2001).

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14.2 Mathematics and Measurement: Causation and the Mind: Otávio Bueno I appreciate the supportive nature of this paper, and the significance of the two issues raised by the author: the causal role of mathematical structures, and the role of topdown causation in measurement (especially in quantum mechanics).

14.2.1 Mathematics and Causation The crucial feature of the causal power of mathematics must take into account the nature of the hierarchy of emergence and causation on the life sciences side, extended to include psychological processes, social processes, and the abstract logical processes that underlie thought (Table 14.1). Note that this is not a purely physical hierarchy: it is one of causation, including all of Aristotle’s kinds of causation (Bodnar 2018), see also Juarrero (2002), 2, 125–128, 143, Noble (2016), 176–179, and Scott (2002), 298–300. There are two separate issues here: the way mathematics relates to the mind (this section), and the way it relates to physics (Sect. 14.2.2). Mathematical Structures In his chapter, Otavio Bueno states Mathematical structures are abstract and, as such, are causally inactive and are not located in spacetime. They do not specify anything directly about the physical world, since physical processes are concrete: they [physical processes] are spatiotemporally located and causally active . . . Rather than describing this process as a form of top-down causation from abstract structures to physical phenomena, processes, and events, it can be accounted for in terms of the inferential role played by mathematics in the representation of the physical world. Mathematical structures provide information about possible (or impossible) configurations in a given abstract domain

Table 14.1 The hierarchy of causation for humans (left) and corresponding processes (right). L2 is the relevant physics level of emergence, L4 the fundamental biological level, made possible by L3 (proteins, RNA, DNA), in turn made possible by L2 and so L1. The topmost level is the level L8 of Platonic spaces which underlie possible thoughts Level 8 (L8) Level 7 (L7) Level 6 (L6) Level 5 (L5) Level 4 (L4) Level 3 (L3) Level 2 (L2) Level 1 (L1)

Levels Platonic Spaces Society Individuals Physiological systems Cells Biomolecules Atom, ion, electron Physics Particle and Nuclear Physics

Processes Logical processes Social processes Psychological processes, actions Homeostasis, emergent functions Basic processes of life Gene regulation, metabolism Atomic, ionic, electron interactions Quark, lepton interactions

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Fig. 14.1 Mandelbrot set

I agree that mathematical structures are abstract, however the phrase “causally inactive” depends on how one defines causation. They become causally active once instantiated in a brain or a digital computer, for example when they are utilised in optimisation procedures while designing an aircraft, or in creating patterns to be printed on paper, as in the case of a Mandelbrot set (Fig. 14.1). Using the counterfactual definition of causation, this is then indeed causation, because the Mandelbrot set is the set of values c in the complex plane for which the orbit of the origin point z = 0 remains bounded when the map zn+1 = zn2 + c

(14.3)

is iterated repeatedly. A different mathematical structure than (14.3) (e.g. add +zn on the right hand side) will result in a different image on paper or a computer screen. But how was that specific mathematical structure chosen? It was selected for realisation by a human brain. Thus the brain is the mechanism whereby abstract mathematical patterns become realised in the physical world, and thereby become causally effective in terms of creating patterns on paper or computer screens, as in Fig. 14.1. Platonic Spaces One way of looking at this is the idea that there exists a Platonic space of mathematical relations that the human brain discovers by a process of exploration (Changeux √ and Connes 1998; Penrose 2000). These relations, for example the fact that (2) is irrational, are timeless and eternal and unchanging: they are true everywhere in the universe at all times, independent of culture or the representation used to express this fact, and have been true since time began. Thus such relations can be thought of as belonging to a Platonic space of mathematical

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relations M , represented in a given society by a mapping Rt into a representation space m : Rt : R ∈ M → r ∈ m .

(14.4)

The key point is that M is timeless, unchanging, and independent of social understanding, whereas Rt depends on time and culture and mathematical understanding. The problems that are supposed to occur with this idea arise from failing to make this distinction. The representation space m and map Rt are time and culturally dependent, whereas M is not. The representation r of R depends on variables, bases, and coordinates used. The Relation to the Brain The way this relates to the brain is developed in depth in the book Plato’s Camera: How the physical brain captures a landscape of abstract universals by Paul Churchland. It is summarised as follows (Churchland 2012): In Plato’s Camera, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation—or “takes a picture”—of the universe’s timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland’s book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level.

The book examines in depth the neural network structures that enable this to happen. Thus the way that abstract mathematical structures are causally efficacious is via the relation Abstract Maths ⇒ Embodied I dea ⇒ P hysical Outcomes (P latonic space)

(Brain)

(14.5)

(P rint/Screen/Electronic)

such occurs in the case of the image of the Mandelbrot set in Fig. 14.1, whether printed on paper or shown as an image on a computer screen. These are alternative physical realisations of this abstract pattern deriving from (14.3). The relation (14.5) is represented in Table 14.1 by the addition of Level L8 as the topmost causal level in human ideas. Possibility Spaces and Constraints Another way of looking at it is to regard the Platonic space of mathematics as a possibility space for mathematical and logical relations. This set of possibilities constrains what valid mathematical relations can exist on combining elementary mathematical and logical operations. This agrees with the last sentence in the quote from Bueno above (but not the second last sentence in that quote, which relates to the next Sect. 14.2.2). Then one can use Juarrero’s concept of constraints as causation (Juarrero 2002) to claim that this

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is indeed a form of causation that is applicable in this context. It can perhaps be added to Aristotle’s four types of causation (Bodnar 2018) to give a fifth: Platonic or Abstract causation (see Ellis and Kopel (2019)).

14.2.2 Mathematics and Physics Whether or not one takes this step of introducing a Platonic space in order to represent what is happening, mathematics is undoubtedly causally effective in the real world in terms of underpinning commerce and science and engineering projects. This further step is due to the possible use of mathematics to represent physical relations. Mathematical structures provide information about possible (or impossible) configurations in a given abstract domain. Once suitably interpreted, as Dirac did when he was trying to connect to the physical world negative energy solutions to the Dirac equation, mathematical results can be used to draw inferences about concrete objects

Indeed so. The first sentence characterizes maths as providing a possibility space for mathematical objects and relations. The second characterizes how these objects and relations can be used to provide descriptions of the physical world. Real World Representations The fact that the same mathematics is compatible with very different physical states in the world seems to question that a direct causal link between the abstract world and physical circumstances can be established. Any such link is mediated by suitable interpretations of the mathematical structures, with the consequence that rather than the mathematics, it is its interpretations, connecting the relevant abstract structures to corresponding physical processes that are playing the crucial role.

The causal link is not direct: the latter is correct, the causal link is via the brain. When interpreted suitably, the some mathematical structures represent the physical world with great fidelity—a remarkable phenomenon. Partial differential equations, groups, fibre bundles, gauge theories, Riemannian geometry represent basic physics very well, and partial differential equations, ordinary differential equations, dynamical systems, adaptive landscapes, networks, directed graphs, and so on represent higher emergent levels of physical reality. Why this works so well is one of the deep mysteries of nature (Penrose 2000). Multiple Realisability and Dualities A key point is Multiple Realisability of such representations. In some cases this is linked to symmetry groups, the Lorentz group or diffeomorphisms for example, allowing use of different bases and coordinate systems for the same geometric objects. In some cases this is rather related to dualities. They can be descriptive, for example the relation between algebra and geometry or between vectors and 1-forms, or between vectors and spinors and quaternions; and can be the duality relations represented by Fourier or Laplace transforms. They can be dynamical, for example the ability to represent classical electromagnetism in terms of 3-dimensional or 4-dimensional Maxwell’s equations,

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or a Lagrangian or Hamiltonian. Similarly one can represent quantum mechanics in Heisenberg of Schrödinger or Dirac form, and quantum field theory via a Lagrangian or the Dirac equation or Feynman diagrams. The implication in each case is that it is the entity being represented that has the real causal power via human brains. The specific representation chosen is just that, a convenient representation whereby the mind can best get a handle on the underlying causal physical relations, and manipulate them so as to design physics experiments and engineering outcomes. Causal Power What is the nature of the causal power of mathematics when applied in physics and engineering? Bueno states [I]t is unclear that abstract mathematical structures per se can be causally efficacious (or have any causal power), despite their undeniable role in the representation of physical phenomena and in the analysis of possibilities involved in the design and construction of buildings and artefacts in the world. Rather than describing this process as a form of top-down causation from abstract structures to physical phenomena, processes, and events, it can be accounted for in terms of the inferential role played by mathematics in the representation of the physical world.

Yes that is right. The causal link is shown in (14.6): Abstract Maths ⇒ (P latonic space)

P hysics (Representation)

⇒ Design I dea ⇒ P hysical Outcomes (Brain)

(P hysics/Engineering)

(14.6) The brain is what enables this to happen. But the point is it does happen: there is a causal link from the very left to the very right of (14.6).

Excess Structure and Infinities Bueno states there is much more mathematics than is realised in physics. Two comments. Firstly, as stated by Hilbert, infinities never occur on physical reality (Ellis et al. 2018). We do not need an isomorphism (14.6)from an entire mathematical structure to physics: a local isomorphism will do. Secondly it is in any case a subset of all mathematical structures that usefully represent physical relations, even taking the dualities mentioned above into account. At any particular time, we have a physical representation Pt of a subset P of M that is useful for physics and engineering by being represented as a physics subset p (t) of known maths m (t): Pt : {R ∈ P ⊂ M } → {r ∈ p (t) ⊂ m (t)}. (P latonic relation)

(14.7)

(Representation)

Both representations continue growing as we learn more about physics and maths. Thus Pt is a function of time.

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14.2.3 Preparation and Measurement I very much like this discussion of classical measurement. It is very helpful, and fills in my own discussion very nicely. As Bueno states, both state vector preparation and providing a context for measurement outcomes are instances of top-down causation. The example of sample preparation in the case of transmission electron microscopes is a great example. Classical Measurement Bueno characterizes a measurement by (a) it is a particular kind of physical interaction, thus, in principle the kind of thing that is able to provide information about the physical world (b) it is a process of collecting relevant information, appropriate for the purpose of measurement This must be interpreted in the light of our understanding of physics: thus {(P hysical world) ⇔ (I nteraction)} ⇒ P ointer reading ⇒ I nterpretation (Apparatus)

(Representation)

(P hysics)

(14.8)

is a context sensitive process of obtaining relevant information. The idea of perspectival drawing as a way of measurement is a very interesting proposal. One has here to solve Helmholz’s inverse problem (Purves 2010; Kandel 2012), and the human brain has developed a predictive processing way of dealing with this issue (Clark 2016) (see Chap. 8 for an in depth discussion). It might be interesting to look at the measurement issue from this perspective: measurement is to do with surprisal, i.e. detecting the unexpected (Friston 2010). This in effect is a form of use of Baye’s Theorem.

14.2.4 Wave Function Collapse, Measurement, Observers Bueno bases his discussion of the quantum measurement issue on my book (Ellis 2016), and I still agree with what is said there. There is one place of disagreement between us: Given the centrality of measurement in quantum theory and the role of observers in topdown causation, it seems that observers are ultimately required in the measurement process after all.

What one needs to do to analyse this further is to distinguish between wave function collapse, and a measurement. Is an Observer Necessary? Bueno states There is no doubt that in order for measurements to yield relevant information, they need to be physical processes of a suitable kind. Without a proper physical interaction, it is unclear that a measurement could take place. However, until an observer decodes the relevant information, the measurement will fail to yield any such result.

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That is, he is emphasizing the last two stages of (14.8). However one should distinguish Wave Function Collapse from a measurement process. The former occurs when a superposition changes to an eigenstate |un  of an operator: |  =



cn |un  → |  = αN |uN 

(14.9)

n

for some value N, with probabilities given by the Born rule (Ghirardi 2007; Ellis 2012). Thus there is a definite outcome: a quantum state changes to a specific classical state when this happens. It is additionally a Measurement if the final state is associated with a pointer reading, as in (14.8). The point then is the a measurement is a process of wave function collapse, but the converse need not be the case. Wave function collapse has the structure {(Superposition) ⇔ (I nteractions)} ⇒ Classical outcome (Context)

(Context depedent)

(14.10)

There is no pointer associated, and no ‘observer’ is needed. An example is nucleosynthesis in the early universe, where a classical mixture of hydrogen and helium is the outcome—not a superposition of possible ratios of hydrogen and helium. There were no observers around at the time to make this collapse to an eigenstate happen. The confusion arises because wave function collapse (14.9) is often referred to as being a ‘measurement’, even though no observer need be involved. The point is that the idea first arose in the context of laboratory experiments such as the twin slit experiment where observers were indeed involved. In that context, wave function collapse and measurement are synonymous, even thought that is not the case in general. The name has stuck. But observers are not needed for (14.9) or (14.10). In summary: A quantum measurement always involves wave function collapse, but the converse need not be true; indeed that is usually not the case, for example it happens every time a photon hits a chlorophyll molecule in a leaf and releases a specific free electron at a specific time and place that is then used in the processes of photosynthesis.

I believe that with this clarification, there should be no disagreement between us. Contextual Wave Function Collapse Since I wrote the book (Ellis 2016), together with Barbara Drossel I have made considerable progress in regard to wave function collapse, as described in the paper (Ellis and Drossel 2018) on Contextual Wavefunction Collapse (CWC). The paper sets this out in depth, forming a nice further step as regards what is discussed in the latter part of Bueno’s paper, and in agreement with Leggett’s views (Leggett 1991). What is still needed is derivation of laboratory experimental tests of this proposal on the one hand, and working out its consequences in such contexts as the transition from quantum to classical perturbations in the context of the inflationary universe scenario in the early universe on the other.

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If such tests were to prove this proposal wrong, we need some other theory of Contextual Wavefunction Collapse that agrees with experiment. This certainly takes place in a contextual way, broadly in agreement with the Copenhagen interpretation where emergent classical entities have causal powers over quantum level events, for example entangling photons or selecting spin states or causing particle collisions in colliders. This is an important foundation of everyday physics and of life.

References Abbott, R. (2008). Constructive emergence: why is emergence still a mystery? academia.edu Alon, U. (2006). An introduction to systems biology: design principles of biological circuits. Boca Raton: CRC Press. Ashby, W. R. (2013). Design for a Brain: The origin of adaptive behaviour New York: Springer. Auletta, G., Ellis, G., & Jaeger, L. (2008). Top-down causation by information control: From a philosophical problem to a scientific research programme. Journal of the Royal Society Interface, 5, 1159–1172. Berridge, M. J. (2014). Cell signalling biology. London: Portland Press. https://doi.org/10.1042/ csb0001001. http://www.cellsignallingbiology.co.uk/csb/ Bishop, R., & Ellis, G. (2020). Contextual emergence of physical properties. Foundations of Physics, 50, 1–30. Blachowicz, J. (2013). The constraint interpretation of physical emergence. Journal for General Philosophy of Science, 44, 21–40. Bodnar, I. (2018). Aristotle’s natural philosophy. In E. N. Zalta (Ed.) The Stanford encyclopedia of philosophy (Spring 2018 edition). https://plato.stanford.edu/archives/spr2018/entries/aristotlenatphil/ Booch, G. (2006). Object oriented analysis and design with application (2nd ed.). Boston: Addison Wesley. Changeux, J.-P., & Connes, A. (1998). Conversations on mind, matter, and mathematics. Princeton: Princeton University Press. Churchland, P. M. (2012). Plato’s camera: How the physical brain captures a landscape of abstract universals. Cambridge: MIT Press. Clark, A. (2016). Whatever next? Predictive brains, situated agents, and the future of cognitive science. Behavioral and Brain Sciences, 36, 181–253. Davies, P. (2019). The demon in the machine: How hidden webs of information are solving the mystery of life. Chicago: University of Chicago Press. Duret, L. (2008). Neutral theory: The null hypothesis of molecular evolution. Nature Education, 1, 218. Ellis, G. (2016) How can physics underlie the mind? Top-down causation in the human context. Heidelberg: Springer-Verlag. Ellis, G., & Drossel, B. (2018). Contextual wavefunction collapse: An integrated theory of quantum measurement. New Journal of Physics, 20, 113025. Ellis, G., & Drossel, B. (2019). How downwards causation occurs in digital computers. Foundations of Physics, 49, 1253–1277. https://arxiv.org/pdf/1908.10186 Ellis, G., & Kopel, J. (2019). The dynamical emergence of biology from physics. Frontiers in Physiology, 9, 1966. Ellis, G. F. R. (2012). On the limits of quantum theory: Contextuality and the quantum? Classical cut. Annals of Physics, 327, 1890–1932. Ellis, G. F. R. (2020a). Emergence in solid state physics and biology. Foundations of Physics, 2020. http://arxiv.org/abs/2004.13591

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Ellis, G. F. R. (2020b). The causal closure of physics in real world contexts. Foundations of Physics, 2020. https://arxiv.org/abs/2006.00972 Ellis, G. F. R., Meissner, K. A., & Nicolai, H. (2018). The physics of infinity. Nature Physics, 14, 770–772. Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11, 127–138. Ghirardi, G. (2007). Sneaking a Look at God’s Cards: Unraveling the mysteries of quantum mechanics. Princeton: Princeton University Press. Green, S. (2015). Revisiting generality in the life sciences: Systems biology and the quest for general principles. Biology and Philosophy, 30, 629–652. Guyton, A. C. (1977). Basic human physiology: Normal functions and mechanisms of disease. Philadelphia: W B Saunders. Juarrero, A. (2002). Dynamics in action: Intentional behavior as a complex system. Cambridge: MIT Press. Kandel, E. R. (2012). Reductionism in art and brain science. New York, Coumbia University Press. Kauffman, S. (1995). At home in the universe: The search for the laws of self-organization and complexity. New York: Penguin. Laughlin, R., & Pines, D. (2000). The theory of everything. Proceedings of the National Academy of Sciences of the United States of America, 97, 28–31. Leggett, A. J. (1991). Reflections on the quantum measurement paradox. In B. J. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in honour of David Bohm (pp. 85–104). London: Routledge. McGhee, G. R. (2006). The geometry of evolution: Adaptive landscapes and theoretical morphospaces. Cambridge: Cambridge University Press. Mossio, M. (2013). Closure, causal. In W. Dubitzky, O. Wolkenhauer, K.-H. Cho, & H. Yokota. (Eds.), Encyclopedia of systems biology (pp.415–418). New York: Springer. Mossio, M., & Moreno, A. (2010). Organisational closure in biological organisms. History and Philosophy of the Life Sciences, 32, 269–288. Noble, D. (2012). A theory of biological relativity: No privileged level of causation. Interface Focus, 2, 55–64. Noble, D. (2016). Dance to the tune of life: Biological relativity. Cambridge: Cambridge University Press. Nurse, P. (2008). Life, logic and information. Nature, 454, 424–426. Penrose, R. (2000). The large, the small and the human mind. Cambridge: Cambridge University Press. Purves, D. (2010). Brains: How they seem to work. Upper Saddle River: FT Press. Rhoades, R., & Pflanzer, R. (1989). Human physiology. Fort Worth: Saunders College Publishing. Rosen, R. (1987). On complex systems. European Journal of Operational Research, 30, 129–134. Salthe, S. (1993). Development and evolution: Complexity and change in biology. Cambridge: MIT Press. Scott, A. (2002). Neuroscience: A mathematical primer. New York: Springer. Sternberg, E. M. (2001). The balance within: The science connecting health and emotions. Stuttgart: Macmillan. Vogel, S. (2000). Cats’ paws and catapults: Mechanical worlds of nature and people. New York: WW Norton and Company. Wiener, N. (1948). Cybernetics or control and communication in the animal and the machine. Cambridge: MIT Press.

Chapter 15

Response to Part II: The View from Physics George F. R. Ellis

Abstract In this response, George Ellis comments on the publications of part II. He responds first to Barbara Drossel, before outlining his thoughts on Thomas Luss’s and Ulf-G. Meißner’s piece.

15.1 Strong Emergence in Condensed Matter Physics: Barbara Drossel I agree with everything in Barbara Drossel’s nicely written paper, so it does not require a lengthy response. Her deep knowledge of statistical physics and condensed matter theory underlie her position. I particularly like the biographical start to her paper. I will just make a few remarks on some issues in her paper. Phil Anderson Anderson’s famous paper “More is Different” (Anderson 1972) and many others (Anderson 1984, 1994) are taken by many to imply he believes in strong emergence, so for example the Festschrift for his 90th Birthday (Piers et al. 2015) was entitled Pwa90: A Lifetime Of Emergence. However, as Drossel says, he is strangely ambivalent: he also claims to be a reductionist, so others have claimed he is not an emergentist (for example Luu and Meißner, Chap. 5). However (Anderson and Stein 1987) cite rigidity as an example of true emergence: We emphasize that this rigidity is a true emergent property: none of the forces between actual particles are capable of action at a distance. It implies that the two ends cannot be decoupled completely without destroying the molecular order over a whole region between them.

Anderson makes similar claims as regards the classical-quantum transition. He strongly wants to defend the reductionist aspect of physics, because it is undoubtedly

G. F. R. Ellis () Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_15

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true, and he understands the emergence side, and indeed gives various examples where strong emergence occurs. However has not clearly defined what he means by reduction and emergence (for example the Nagel versus Chalmers views), so he is caught in an uneasy position. In the end his reductionism in the sense that ‘everything obeys the same fundamental laws’ is fully compatible with strong emergence, see for example (Ellis 2020a), for all the reasons discussed in this book. Statistical Physics and the Concept of Probabilities This section makes very interesting points about statistical physics and the way it is a bridge to calculating properties of systems of 1023 particles. As she says, “The basic concept of statistical mechanics is that of the probability of a state of a system or a subpart of the system”. Clearly that is not a concept that can occur at the micro level. A further key concept is randomness, which also cannot be reduced to a deterministic ‘fundamental’ theory, but it is imposed on initial conditions and hidden there. Developing these considerations, Drossel concludes, developing from ideas presented in Drossel (2017) and in agreement with Leggett, that quantum mechanics is not consistent with physics of macroscopic, finite-temperature objects. This very important result is of course in strong contradiction with what seems to have now become the orthodox view that quantum theory applies to all objects on all scale. for example to cats as a whole. I suggest the real situation is that quantum mechanics applies everywhere all the time on small enough scales (Ellis 2012), where “small enough” is the contextually dependent issue of whether the wave function |  in a domain D can be considered as being governed by a linear (Schrödinger or Dirac) equation in D. This will not be the case for example if feedback control loops are to be represented by | . Strong Arguments for Strong Emergence in Physics This is a key set of points, which Drossel relates to the classical to quantum transition, which can be claimed to be a contextual affair (Ellis and Drossel 2018). Thus she gives a sound basis for strong emergence in both solid state physics and biology (because biology emerges from quantum chemistry), backed up by reference to Chibbaro et al. (2014). The Microscopic World Is not Deterministic This is true both classically because initial data can only be set to finite accuracy (Del Santo and Gisin 2019) and in the quantum case both because of the Heisenberg uncertainty principle and because of wave function collapse (Ghirardi 2007; Ellis 2012). As Drossel says, “In order for full reductionism to hold, the microscopic theory must be deterministic. Only then does the microscopic theory determine everything that happens. Otherwise the microscopic theory can at best give probabilities for the different possible events”. Indeed so. It is tamed by causal slack introduced by thresholds (Section 2.4 in Chapter 13) allowing branching logic to emerge in biology (Hoffmann 2012; Ellis and Kopel 2019) and computers (Ellis and Drossel 2019), together with downward selection in the case of biology, where lower level indeterminism is used as a lever by which to choose favourable higher level outcomes (Hoffmann 2012) (Noble and Noble 2018).

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Emergent Properties Are Insensitive to Microsopic Details This is a strong argument, basically related to multiple realisability, which is discussed in depth by Green and Batterman (see Chapter 2 and Section 2.4 in Chapter 13). Many Systems Are Inseparable from Their Environment This is again spot on. Commenting on dissipative systems in general and life in particular that exist only due to being continually sustained by their environment, “it is completely wrong to think of them merely in terms of their parts and the interactions of their parts. The emergent features of these systems are therefore clear-cut cases of top-down causation.” The ultimate source of this possibility is the high grade radiation arriving at the Earth from the Sun together with the dark night sky that allows low grade energy to be radiated away (Penrose 1990). And that is only possible because of the cosmic context (Sciama 2012) which leads to the existence both of stars and a dark night sky. Fully Reductionist Explanations Exist in Some Cases It is taken by some as an argument against emergence that fully reductionist explanations can be given in some cases, with Statistical mechanics and the Second Law of Thermodynamics in mind. Although this is taken as a paradigmatic case by many, in fact it is fraught with difficulties. To name just two: firstly, the definition of temperature is a key problem (Bishop and Ellis 2020). The usual trick is to identify it macroscopically, and then identify its microscopic correlates. This is a classic example of failure of strictly upwards derivation of unknown emergent variables. Secondly, because of Loschmidt’s paradox, Boltzmann’s derivation of the Second Law of thermodynamics in a bottom up way from kinetic theory, thereby proving that entropy S cannot decrease for an isolated system: dS/dt ≥ 0, is a dismal failure because it works in both directions in time. The arrow of time is in fact determined by the cosmic context of the expanding universe (Penrose 1990; Ellis and Drossel 2020). The Majority of Physicists? Drossel concludes with the remark “Anthony Leggett writes in his above-cited article that the non-reductionist view is a minority view among professional physicists. In fact, I am not so sure about this.” I agree. There is a major split between the views of many particle physicists and condensed matter physicists, as discussed by Schweber (1993), Cat (1998), and Weinberg (2008). Given that the largest group of physicists are in condensed matter theory, the public image of who has what standpoint is probably highly misleading. It may be a selection effect due to the most voluble physicists being in the particle physics and cosmology communities.

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15.2 On the Topic of Emergence from an Effective Field Theory Perspective: Thomas Luu and Ulf-G. Meißner While the other articles in this collection are supportive of my views on emergence and downwards causation, this one is not, indeed it is strongly critical. As there is indeed such a view out there, strongly held by many reductionists, it is important that it be included in the collection, and that I give a detailed response.

15.2.1 Differing Viewpoints, and Cultural Clashes There are fundamentally different views about emergence in different sections of the physics community. On the one side are fundamental particle physicists such as Weinberg and Glashow, nuclear physicists such as Luu and Meißner, and quantum physicists such as Dirac. On the other side are condensed matter physicists such as Anderson, Laughlin, Leggett, Lancaster, and Simon, soft matter physicists such as McLeish, and statistical mechanicists such as Drossel. There have been major clashes between those holding these two viewpoints, as discussed by Schweber (1993) and Cat (1998). Weinberg puts it this way (Weinberg 1994): The claim of elementary-particle physicists to be leading the exploration of the reductionist frontier has at times produced resentment among condensed-matter physicists. (This was not helped by a distinguished particle theorist, who was fond of referring to condensedmatter physics as ‘squalid state physics’.) This resentment surfaced during the debate over the funding of the Superconducting Super Collider (SSC).

That disdainful epithet represents a common view of fundamental particle physicists and string theorists, expressing an assumed scientific and intellectual superiority to fields such as solid state physics. In fact the latter is a fascinating and challenging endeavour (Anderson 1994; Piers et al. 2015), requiring just as much scientific depth, creativity, and technical expertise as the ‘more fundamental’ theories. Indeed Anderson claims they are just as fundamental (Anderson 1972). That is because they are exploring the kinds of Higher Order Principles mentioned in the Chap. 14. I need to comment on an issue that will emerge later in this section. Responses by some reductionists to claims of strong emergence and downward causation sometimes involve ad hominem attacks and ridicule that avoid addressing the intellectual issues at hand in a spirit of rational debate, and instead are aimed at undermining the credibility of an individual as a person. This is sometimes done by the rhetorical trick of using dismissive emotive phrases implying the person making an argument is not worth listening to. It is a way of avoiding dealing with the quality or validity of an argument.

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15.2.2 The Nature of Effective Field Theories (EFTs) Chapter 5 is based on the success of Effective Field Theories in providing a ‘bottom-up’ description of phenomena whose intrinsic (underlying) degrees of freedom occur at length scales far different from their effective degrees of freedom. This Chapter by Luu and Meißner (henceforth LM) concentrates on nuclear physics/particle physics contexts, and cites cases such as the Heisenberg-Euler Theory of photon-photon scattering, Fermi’s Theory of Beta Decay, and many nuclear physics/particle physics examples. They comment that in the case of (lowenergy) nuclear physics, emergent phenomena are always associated with highly complex and highly non-linear behavior, for example “ninety five percent of the mass of the observable universe is generated from interactions between massless particles (gluons). The term holistic might be an understatement in this case.” Thus they deal, via EFTs, with very interesting emergent phenomena. How does an EFT work in practice? The name “EFT” covers a variety of different approaches (Hartmann 2001) (Castellani 2002) (Burgess 2007) (Bain 2013) (Butterfield 2014). LM identify five key elements in constructing an EFT. They are as follows: EFT1: Identification of effective, or active degrees of freedom: “The emergent phenomena (e.g. protons, pions, nuclei, . .) dictate the active (relevant) degrees of freedom, despite the fact that such phenomena can be expressed as collections of more fundamental degrees of freedom (i.e. constituents).

The key issue is whether these degrees of freedom can be deduced in a purely bottom up way from lower level variables. If so, it is weak emergence, if not, the higher level variables must be determined in their own terms,1 and it is strong emergence (Ellis 2020a). EFT2: Separation of length scales: The separation of length (or energy) scales is implicit in all EFTs. Such separation in length scales allows one to express an EFT as an expansion in the ratio of scales.

This is the emergence of hierarchy in physical systems. EFT3: Identification of symmetries: Symmetries play a fundamental role in the construction of any EFT of some emergent process. The symmetries that the emergent phenomenon respects are identical to the symmetries of its constituents and their interactions.

This is a strong restriction on the applicability of the EFTs that LM consider. EFT4: Power counting scheme: One employs the concept of power counting, where the different terms are enumerated in hierarchical importance related to some expansion parameter (usually related to the ratio of some soft momentum scale to a hard scale).

This systematic EFT approach differs from usual approaches to deriving emergent phenomena in other contexts, such as solid state physics (Kaxiras and Joannopoulos 2019) (Snoke 2020) and quantum chemistry (Karplus 2014). 1 As

emphasized in the Leggett quotes given by Drossel in Sect. 4.4 in Chap. 4.

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EFT5: Valid representation of emergent levels This effective field theory (EFT) is not an ad hoc description of the emergent phenomena, however. If developed properly, the EFT represents an equally valid representation of the phenomenon and can be used to predict new phenomena as well as to verify the lower level theory. .

This important remark is essentially a physics version of Denis Noble’s “Principle of Biological Relativity” (Noble 2012), which states that in biology, no emergent level is privileged over any other. Phil Anderson also supported such a view, as described in (Schweber 1993): Anderson believes in emergent laws. He holds the view that each level has its own “fundamental” laws and its own ontology. Translated into the language of particle physicists, Anderson would say each level has its effective Lagrangian and its set of quasistable particles. In each level the effective Lagrangian - the “fundamental” description at that level - is the best we can do.

In other words, an Effective Theory ETL emerges at each level, and indeed is the reason that such levels can be identified as being ontologically real (Chapter 1 and Ellis 2020b). The authors do not here presume, as some do, that there is a specific bottom-most level to which everything in physics can be reduced. They do not for example claim one can use an EFT to derive the Standard Model of Particle physics from String Theory/M Theory, regarded as the foundational theory; rather the Standard Model of Particle Physics is their base level, even though it is not fundamental. They state “Nowadays it is widely accepted that all field theories are effective field theories, which makes the phenomenon of emergence even more natural”. Actually neither Maxwell’s Electromagnetic Theory nor Einstein’s Theory of Gravitation are EFTs in their sense; they are however both field theories, and Effective Theories of the kind mentioned above.

15.2.3 Effective Field Theories and Emergence LM state the following regarding the relation between EFTs and emergence. EM1: The EFT description naturally leads to a bottom-up approach, where upper level emergent phenomena and their associated larger length scales/lower energies are built from lower-level (more) fundamental constituents. The level below the EFT is required to calculate certain properties from more basic constituents, like e.g. the values of the lowenergy constants (LECs).

Certainly the emergent phenomena are built from lower level fundamental constituents (electrons, protons, neutrons for example). The emergence of higher levels depends on this fact. But in solid state physics, some important effective entities at lower levels such as phonons and Cooper pairs are not fundamental constituents of the lower level. Although dynamically important (Singleton 2001), and (Blundell 2019, 244), they themselves are (downwardly) emergent phenomena. They only exist because of the higher level context, e.g. a specific crystal structure (Ellis 2020a). Additionally, as regards the criteria regarding determining emergent

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constants (LECs) from the underlying theory, this is not possible in principle in condensed matter physics in as simple a case as electrical conductivity (Singleton 2001, 117–125), and it is not possible in biology for example in the case of the constants occurring in the Hodgkin-Huxley equations (Hodgkin and Huxley 1952) for action potential propagation (Scott 1999). EM2: (As an example of upward causation): Within the EFT prescription, it is the symmetries of the lower level that dictates the allowed interaction terms at the higher level, but not the other way around

The lower level physics of course determines what specific symmetry breaking higher level structures are possible. But spontaneous symmetry breaking when structures emerge in solid state physics (think crystallizing) results in emergent levels with different symmetry than the underlying physics (the standard model of particle physics) by itself. This is excluded by the LM approach, see EFT3 above (Sect. 15.2.2). Thus the family of EFTs considered by LM does not cover the many cases in condensed matter physics where symmetry breaking is a key to emergence (Anderson 1984, 1994). Hence the EFT approach of LM has nothing to say about whether strong emergence does or does not take place in solid state physics (and chemistry, where symmetry breaking also takes place). Note that one can indeed get EFTs that cover the cases where symmetry breaking takes place. They simply cannot be derived in a purely bottom up way, precisely because of the symmetry breaking that takes place (Ellis 2020a). EM3 It is natural to think then that causation follows this same bottom-up (or upward) direction as well

This philosophical assumption is where I disagree with LM (Ellis 2016). It is the higher level broken symmetries that cause effective interaction terms with broken symmetries, such as phonons and Cooper pairs, to exist at the lower level in condensed matter systems (Ellis 2020a). Such downward effects, called “Foundational Determinative Relations” (FDR) by Gillett (2019), affect interactions at the lower levels. Their EFT approach does not take downward effects into account. However they do occur in nuclear physics (Sect. 15.2.7). EM4: The EFT description . . . is consistent with the laws that govern the lower level constituents. Any prediction it makes, regardless of how ‘disconnected’ or ‘unexpected’ when viewed from the lower level theory, is consistent with the laws that govern the lower level constituents. Such predictions, and the associated causal impacts that accompany them, are in principle deducible from the lower level constituents.

The first part is certainly correct; that fits in completely with my approach (Ellis 2016). Both strong emergence and downward causation do not violate any lower level physical laws. The last sentence, which states that strong emergence cannot take place (“it is in principle possible . . .”), is where the disagreement lies. That this is not correct in the case of condensed matter physics is the burden of (Leggett 1992) and the chapter by Drossel (see Sect. 15.1 above), commenting that one cannot use an EFT to deduce higher level outcomes without first introducing higher level concepts to guide the derivation. This is confirmed by (Rivat and Grinbaum 2020):

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Yet another example is the use of EFTs in condensed matter physics: even when the underlying theory is known, often the only tractable way to compute low-energy observables is to build an effective model as if the underlying theory were unknown.

This is true in many cases: it is derived as an EFT at the emergent level, without trying to derive it from the more fundamental level. Hence in this case it has nothing to say about emergence from the underlying level. One does not derive the emergent phenomenon: one rather explains it in terms of lower level mechanisms, but only by use of higher level concepts. You can get a (reductive) bottom-up description once you know what the answer is, and introduce higher level variables that are not implied by the lower level theory. In contrast to my conclusion that EFTs cannot disprove strong emergence, (Bain 2013) claims they can prove it! He suggests the following interpretation of EFTs: (a) Ontological dependence. Physical systems described by an EFT are ontologically dependent on physical systems described by a high-energy theory. (b) Failure of law-like deducibility. If we understand the laws of a theory encoded in a Lagrangian density to be its Euler-Lagrange equations of motion, then the phenomena described by an EFT are not deducible consequences of the laws of a high-energy theory. (c) Ontological distinctness. The degrees of freedom of an EFT characterize physical systems that are ontologically distinct from physical systems characterized by the degrees of freedom of a high-energy theory. In other words, he believes that EFTs support both epistemological and ontological strong emergence. This is undoubtedly controversial (Rivat and Grinbaum 2020), but it must surely give pause to those who claim EFTs disprove strong emergence. Conclusion: EFTS do not disprove strong emergence. EFTs do not disprove strong emergence in condensed matter physics because (a) claimed such derivations in fact depend on higher level concepts that are not implied by the lower level physics per se, so they fulfill Chalmer’s criterion for strong emergence (Chalmers 2006), (b) they are unable to determine in a purely upwards way the constants in the emergent effective equations. (c) In the particular case of the EFTs considered by LM, they do not allow the symmetry breaking that is essential to most of emergence in solid state physics.2

Additionally, one should note limits on the applicability of EFTS (Adams et al. 2006).

2 In

their article (Luu and Meißner 2020), they misrepresent what I said. I did not say “most of condensed matter and solid-state physics is off-limits to EFTs”; I said it is off limits to their version of EFTs, for this reason (see EFT3 and EM2 above, quoted from their paper). The “egregious error” is theirs.

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15.2.4 Anderson and Emergence In their Section 4, LM criticize the way that I interpret in (Ellis 2016) the paper “More is different” (Anderson 1972) by Phil Anderson as supporting emergentism. But that was not all he wrote on the topic! (and see Drossel’s comments in Chap. 4). On his 90th Birthday a conference was held in his honor entitled “PWA90: Emergent Frontiers of Condensed Matter”, and the proceedings were published in a book Pwa90: A lifetime of Emergence (Piers et al. 2015). The introduction states, As codified in his oft quoted statement ‘More is Different’, Phil has been the most forceful and persuasive proponent of the radical (in the 1970s), but now ubiquitous, viewpoint of emergent phenomena: truly fundamental concepts can and do emerge from investigations of nature at each level of complexity or energy scale.

Jeffrey Goldstein discusses this interestingly in his introduction to a reprinted version of ‘More is different’ (Anderson and Goldstein 2014), pointing out clearly that Anderson was opposed to ‘strident reductionists’, as does (Cat 1998). LM state “Anderson at no point argues that the new conceptual structure of the higher level of organization cannot be deduced from the lower-level constituents in principle”. Here I disagree. He states in the article (Anderson 1972, right hand column, page 1) At each level of complexity, entirely new properties appear . . . At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry.

This is quite different than claiming you can deduce these effective theories in a bottom up way from lower level theories.

15.2.5 Emergence and Life LM discuss this topic in their Section 5, without referring to what if anything EFTs might possibly add to the argument. Life in General The heading of this section in LM is “‘Purpose” in life and physics’. The rhetorical trick represented by the scare quotes is presumably intended to imply that the concept “Purpose” is suspect or meaningless. The obvious response is, Does any kind of purpose shape the actions of nuclear and particle physicists when they design and construct particle colliders, for example the LHC? For undeniable confirmation that the answer is Yes, see Weinberg on the history of the SSC proposal (Weinberg 2008). There is indeed purpose in the world that has major implications in terms of physical outcomes. Purposeful Design In commenting on some statements in my book (Ellis 2016) on the nature of life, LM conflate statements I made about life in general, and

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statements I made about intelligent life, resulting in a serious misrepresentation of what I claim. I made statements about an ineliminable teleological component to biology in general (page 373), which is correct (see below), and very much later (page 414) I refer to “Purposeful Design” in the very different context of brain function, referring to how the human brain can result in the construction of artefacts such as aircraft and teacups (Ellis 2005) (which is also true, see below). Having conflated the two, they then state We find such statements reminiscent of the arguments made by proponents of intelligent design (just replace the word Purposeful with Intelligent in the sentence above)

This is an example of the rhetorical trick I mentioned in Sect. 15.2.1, where an emotionally loaded catch phrase (“Intelligent Design”) is introduced in order to discredit my argument, after having misrepresented it. I am not, and never have been, a supporter of the Intelligent Design movement. Intelligent Life and Intelligent Design The key point is that intelligent life does indeed engage in intelligent design, and thereby creates complex systems such as aircraft, cities, digital computers, and teacups (Ellis 2005, 2016). This falls under the rubric of The Sciences of the Artificial as discussed by Nobel Prize winner Herbert Simon in his famous book of that name (Simon 2019). Computer science (Abelson et al. 1996; Abbott 2020) and the consequent causal power of algorithms (MacCormick 2011) is an example of the outcome of intelligent thought. Such purposeful design has nothing to do with the “Intelligent Design” (ID) movement as regards evolutionary theory. It is a straightforward outcome of the existence of a technological society resulting from our ability to reason in a symbolic way (Deacon 1997; Harari 2014). A nuclear physics example of intelligent design is the existence of the apparatus nuclear physicists construct in order to carry out their experiments, such as RHIC. That’s a classic case of strong emergence, No effective field theory determines either the existence or the detailed structure of that heavy-ion collider: the design is in principle not determined by physical interactions per se. The real link to physics is via the way the structure of proteins underlies brain functioning and so enables Deductive Causation (Section 6 of Ellis and Kopel 2019) by nuclear physicists to lead to their existence. Teleology and the Nature of Life It is clear that LM do not like the idea that biological organisms have purpose. That is contrary to the view of Nobel Prize winning biologist Leland Hartwell and colleagues as expressed in (Hartwell et al. 1999): Although living systems obey the laws of physics and chemistry, the notion of function or purpose differentiates biology from other natural sciences. Organisms exist to reproduce, whereas, outside religious belief, rocks and stars have no purpose. Selection for function has produced the living cell, with a unique set of properties that distinguish it from inanimate systems of interacting molecules. Cells exist far from thermal equilibrium by harvesting

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energy from their environment. They are composed of thousands of different types of molecule. They contain information for their survival and reproduction, in the form of their DNA. Their interactions with the environment depend in a byzantine fashion on this information, and the information and the machinery that interprets it are replicated by reproducing the cell.

Even proteins have functions (Petsko and Ringe 2009). This is all played out in the deep relation between structure and function in biology (Campbell and Reece 2008). Higher Level Variables This relates to the next point: LM state We also caution in using terminology that may be precise at one level, e.g. purpose, but ill-defined at another level as this ultimately adds confusion.

I strongly disagree. A central point as regards the nature of emergence is that words and variables that correctly describe causation at higher levels simply do not apply at lower levels. It is not a point of confusion, it’s a central aspect of emergence. They quote from Anderson (1972), “each level can require a whole new conceptual structure”. Just so; and that means new terminology. In the case of biology, unless that structure includes the concepts of purpose and function, it will miss the essence of what is going on, as pointed out by Hartwell et al. (1999). You also need to introduce the concepts “alive” and “dead”, which do not occur in biology at the levels lower than the cellular level, and do not occur at all in any physics level. Logical Branching Having made clear what they do not like, LM themselves do not give a characterisation of what life is. The view that I propose is that life can be characterised at all emergent levels by logical branching. That is, each level of biology operates according to a branching logic of the following form (Hoffmann 2012, 151–152) and (Ellis and Kopel 2019): a signal X is evaluated by a Truth Function T (X) in a context C, as follows GIVEN context C, IF T (X) THEN O1 ELSE O2.

(15.1)

where O1 and O2 are alternative dynamical paths. This is the way information is important (Nurse 2008; Davies 2019) and is the way cell signalling works (Berridge 2014) and so underlies metabolic networks and gene regulatory networks. This kind of logic is implemented by the conformational shapes of the relevant biomolecules and their interactions with each other, allowed by the underlying physics but not reducible to it because physical laws per se do not entail logical outcomes such as (15.1). But how does all this emerge from physics? Through symmetry breaking, as discussed above, together with time dependent constraints and the extraordinary dependence of molecular biology on the conformational shape of biomolecules (Ellis and Kopel 2019). Wonderful examples are given in Karplus (2014). The Barrier of Chemical Emergence The barrier to deriving any of this in a bottom up way from physics is to characterise emergence of biochemistry and molecular biology from physics, see e.g. (Karplus 2014; Chibbaro et al. 2014). Can

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EFT’s as characterised by LM do it? No, firstly because of symmetry breaking by biological molecules, excluded from their EFTs. The two orders of magnitude they mention do not get anywhere near molecular biology scales, nor can EFTs by their nature handle the kind of contextual logical branching (15.1) that emerges in biology (Hoffmann 2012; Ellis and Kopel 2019) because of the symmetry restriction EFT3 (Section 15.2.2). Evolutionary Origins This all came into being via Darwinian processes of natural selection (Mayr 2001): one of the best-established processes in biology, which is strongly emergent. Physics in general, and effective field theories in particular, do not begin to have the resources to deal with this theory, inter alia because the concepts of being alive or dead cannot be captured in strictly physics terms so ‘survival’ is not a concept physics can deal with. Whether an animal is alive of dead is a biological issue. And that is what underlies evolutionary theory. This is confirmed by this quote from LM: The detailed consequences of our theories are often extraordinarily hard to work out, or even in principle impossible to work out, so that we have to ‘cheat’ at various intermediate stages and look in the back of the book of Nature for hints about the answer. For instance, there is nothing in the quantum mechanics of the chemical bond which implies the genetic code in its detailed form, yet there is equally nothing in the operations of molecular biology which is incompatible with our quantum-mechanical understanding of the chemical bond, intermolecular forces, and so on.

Note the “even in principle impossible”, That is exactly right: it is a statement that the genetic code is strongly emergent, so it is a claim that strong emergence takes place. Evolutionary theory is a key example of downward causation because of the contextual dependence of outcomes, as discussed by Campbell (1974), Mayr (1988), and (Wagner 2014). Adaptive Landscapes LM state in this section However, it may very well be that the ‘purpose’ of some biological organism, seen from our limited point of view, is procreation and the continuation of its species, but at the same time is equivalent to the minimization of energy in some very complex phase space.

This is nothing other than the concept of a Fitness Landscape as proposed by Sewell Right (Wright 1932), and developed by many others (see for example (Kauffman and Levin 1987; McGhee 2006)). But this does nothing to further the reductionist project of LM. This is an Effective Theory in the sense explained in Castellani (2002), but has nothing to do with EFTs as described by LM, involving a power series expansions in terms of a physical parameter. A Fitness Landscape cannot be derived even in principle from the underlying physics by any deductive process that purely involves physics concepts. It can however be developed as a productive macro level effective theory if one introduces biological concepts and processes. What Is Life? As regards their comments about Schrödinger’s book What is Life? (Schrödinger 1944), I am not advocating any modification whatever to the laws of physics themselves: those are plausibly timeless, eternal, and unchanging. It is the outcomes of those laws that are strongly contextually dependent, through the

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existence of physiological structures and time dependent constraints (Noble 2012; Ellis 2016). It is through these effects that biology modifies outcomes of those laws at the physical level (Ellis and Kopel 2019). As described in Schweber (1993): Anderson believes in emergent laws. . . . But it is not enough to know the “fundamental” laws at a given level. It is the solutions to equations, not the equations themselves, that provide a mathematical description of the physical phenomena. “Emergence” refers to properties of the solutions - in particular, the properties that are not readily apparent from the equations

Interesting as this debate about life is, it is a debate about strongly emergent properties that have nothing to do with the EFTs discussed by LM.

15.2.6 Testability and Popper LM query whether the proposal of strong emergence is scientific: Using Popper’s scrutiny the concept of strong emergence is not ‘scientific’. We are not aware of any predictions its theories have made. To be very clear on this issue, we refer to a prediction by a quantifiable statement of a theory or model that is amenable to an experimental test.

Popper’s criterion has been the subject of substantial criticism (Shea 2021), nevertheless this is indeed a key issue that requires a response. I of course agree that scientific theories and models should be testable, indeed I have made myself unpopular with some segments of the physics community by making such remarks (see Ellis and Silk 2014). So how can this work in the case of strong emergence? The issue is this: Testability of strong emergence. Can one give examples where strong emergence takes place, so the outcomes are even in principle not determined by the underlying physics, yet the emergent theory makes specific predictions that can be experimentally verified?

The answer is yes. I will give a series of example where this is indeed the case. Condensed Matter Physics It was demonstrated in (Ellis 2020a) that strong emergence occurs in condensed matter systems where spontaneous symmetry breaking occurs. Have there been predictions in this area? Yes indeed (Anderson 1994; Piers et al. 2015). The strongly emergent feature of the existence of quasiparticles with fractional quantum numbers (Lancaster and Pexton 2015; Guay and Sartenaer 2018) was predicted by Robert Laughlin, and observed in several experiments (see Kvorning 2018). Topological insulators are strongly emergent because of their topological nature (Moore 2010) and provide many examples. Soft matter physics is another area where strong emergence occurs due to topological effects, with testable consequences (McLeish et al. 2019). Microbiology The molecular biology of the gene (Watson et al. 2013), the molecular biology of the cell (Alberts 2007), and the molecular biology of cell

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signalling networks (Berridge 2014) are extremely well tested extremely complex strongly emergent effective theories. Physiology At the macro biology level, animal physiology (Randall et al. 2002) and human physiology (Rhoades and Pflanzer 1989) are extremely well tested strongly emergent subjects, underlying veterinary practice and medicine. Neuroscience This is an extremely well researched and tested strongly emergent area of major complexity, see for example Hodgkin and Huxley (1952) and Kandel et al. (2013). Ecology This is another very well researched strongly emergent area with a strong tradition of experimentally testing model outcomes, see for example Odum and Barrett (1971). Complexity and Astrology At the conclusion of this section in their paper, LM state, referring to strong emergence and predictions: Furthermore, If there are any predictions [from strong emergence] it seems that the mere complexity of the systems in which it is intended to be applied to leaves very little room for direct falsifiability: there is always some conditional statements which can be concocted (after the fact) to ‘argue away’ negative findings. Under these circumstances strong emergence does not appear worthier than astrology.

This is a further example of the rhetorical trick I mentioned in Sect. 15.2.1, where an emotionally loaded word (“Astrology”) is introduced in order to discredit an argument. This statement will surprise all those engaged in all the subjects mentioned above. These academic fields are all strongly supported by a mass of experimental evidence. This statement represents a regrettable particle physics view of the rest of science.

15.2.7 Does Downward Causation Occur in Nuclear Physics? LM assume in their discussion that causation is only upward. So an interesting issue is, does downward causation occur in nuclear physics? Indeed it does. I will here give three examples where this is the case.3 Lifetime of Neutrons in a Carbon Atom Free neutrons decay into a proton, electron, and antineutrino via the weak force, with a lifetime in the range of 880– 884 s (Wietfeldt and Greene 2011). However when bound into carbon nuclei, they do not decay: they survive for billions of years (which inter alia is why life can exist). One either has to say, as in the Liquid Drop Model and the Independent-Particle Model, that individual neutrons exist in a carbon nucleus, but their lifetime has been

3 Apart

from the construction and operation of colliders and nuclear reactors.

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altered from 14 min to billions of years; or that the individual neutrons in a nucleus should no longer be regarded as existing as individual entities in their own right, as they have been merged into a collective entity, as for example in the Interacting Boson Model. In either case the context of being bound in the nucleus has had a dramatic effect on the neutrons themselves, by altering either their properties, or their very existence as individual entities. This is an important example of downward causation in nuclear physics. Primordial Nucleosynthesis An important nuclear physics process in the Hot Big Bang phase of the early universe is primordial nucleosynthesis (Cybert et al. 2016). The fraction of helium, deuterium, and lithium produced by these processes depends on the cosmological expansion rate at that time, which is determined by the Friedmann equation together with the densities of different matter components averaged at the cosmological scale. Consequently (Ellis 2016, 275), measurements of primordial element abundances place limits on the cosmological baryon density, and hence are a key feature for arguments for existence of dark matter in the universe (Peter and Uzan 2013). This is a definitive example of downward determination of outcomes of nuclear physics processes. Stellar Nucleosynthesis A similar case is stellar nucleosynthesis, briefly summarised in (Blundell and Blundell 2009, Chapter 35). A star exists because of the balance of gravitational attraction and thermal and radiative pressure, resulting in a radial dependence of density ρ(r), pressure p(r), and temperature T (r). Together with the fractional element abundances, this determines what nuclear reactions will take place at what radii in the star (Burbidge et al. 1957). It is in particular this context that enables the triple alpha process (Lähde et al. 2020) to occur. Together these effects result in the Hertzsprung-Russell Diagram relating stellar luminosities to surface temperatures. Similar examples are the determination of nuclear physics outcomes in nuclear reactors and nuclear bombs. In the real world, contexts determine outcomes; that is, downward causation takes place, and causal closure is an interlevel affair (Ellis 2020b).

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Ellis, G. F. R. (2020b). The causal closure of physics in real world contexts. Foundations of Physics, 50, 1057–1097. https://arxiv.org/abs/2006.00972 Ellis, G. F. R., & Drossel, B. (2018). Contextual wavefunction collapse: An integrated theory of quantum measurement. New Journal of Physics, 20, 113025. Ellis, G. F. R., & Drossel, B. (2019). How downwards causation occurs in digital computers. Foundations of Physics, 49, 1253-1277. https://arxiv.org/abs/1908.10186 Ellis, G. F. R., & Drossel, B. (2020). Emergence of time. Foundations of Physics, 50, 161–190. Ellis, G. F. R., & Kopel, J. (2019). The dynamical emergence of biology from physics. Frontiers in Physiology, 9, 1966. Ellis, G. F. R., & Silk, J. (2014). Scientific method: Defend the integrity of physics. Nature News, 516, 321. Ghirardi, G. (2007). Sneaking a look at God’s cards: Unraveling the mysteries of quantum mechanics. Princeton: Princeton University Press. Gillett, C. (2019). Emergence, downward causation and its alternatives: Critically surveying a foundational issue. The Routledge handbook of emergence (pp. 99–110). Milton Park: Routledge. Gu, M., Guay, A., & Sartenaer, O. (2018). Emergent quasiparticles. Or how to get a rich physics from a sober metaphysics. Individuation, Process and Scientific Practices (pp. 214–234). New York: Oxford University Press. Harari, Y. N. (2014). Sapiens: A brief history of humankind. New York: Random House. Hartmann, S. (2001). Effective field theories, reductionism and scientific explanation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 32, 267–304. Hartwell, L. H., Hopfield, J. J., Leibler, S., & Murray, A. W. (1999). From molecular to modular cell biology. Nature, 402, 6761:C47-C52. Hodgkin Andrew, L., & Andrew Huxley, A. F. (1952). A quantitative description of membrane current and its application. The Journal of Physiology, 117, 500–544. Hoffmann, P. (2012). Life’s ratchet: How molecular machines extract order from chaos. New York: Basic Books. Kandel, E., Schwartz, J. H., Jessell, T. M., Siegelbaum, S. A. & Hudspeth, A. J. (2013). Principles of neural science. New York: McGraw Hill) Karplus, M. (2014). Development of multiscale models for complex chemical systems. Angewandte Chemie International, 53, 9992–10005. Kauffman, S., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology, 128, 11–45. Kaxiras, E., & Joannopoulos, J. D. (2019). Quantum theory of materials. Cambridge: Cambridge University Press. Kvorning, T. K. (2018). Topological quantum matter: A field theoretical perspective. Berlin: Springer. Lähde, T. A., Meißner, U.-G., & Epelbaum, E. (2020). An update on fine-tunings in the triple-alpha process. The European Physical Journal, A 56, 56–89. Lancaster, T., & Pexton, M. (2015). Reduction and emergence in the fractional quantum Hall state. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 343–357. Leggett, A. J. (1992). On the nature of research in condensed-state physics. Foundations of Physics, 22, 221–233. Luu, T., & Meißner, U.-G. (2020). Misconceptions on effective field theories and spontaneous symmetry breaking: Response to ellis’ article. Foundations of Physics, 50, 1140–1151. MacCormick, J. (2011). Nine algorithms that changed the future. Princeton: Princeton University Press. Mayr, E. (1988). The limits of reductionism. Nature, 331, 475. Mayr, E. (2001). What evolution is. New York: Basic Books. McGhee, G. R. (2006). The geometry of evolution: adaptive landscapes and theoretical morphospaces. Cambridge: Cambridge University Press.

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McLeish, T., Pexton, M., & Lancaster, T. (2019). Emergence and topological order in classical and quantum systems. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 66, 155–169. Moore, J. E. (2010). The birth of topological insulators. Nature, 464, 194–198. Noble, D. (2012). A theory of biological relativity: No privileged level of causation. Interface Focus, 2, 55–64. Noble, R., & Noble, D. (2018). Harnessing stochasticity: How do organisms make choices? Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 106309. Nurse, P. (2008). Life, logic and information. Nature, 454, 424–426. Odum, E.P., & Barrett, G. W. (1971). Fundamentals of ecology. Philadelphia: Saunders. Penrose, R. (1990). The emperor’s new mind. New York: Oxford University Press. Peter, P., & Uzan, J.-P. (2013). Primordial cosmology. New York: Oxford University Press. Petsko, G. A., & Ringe, D. (2009). Protein structure and function. New York: Oxford University Press. Piers, C., Premi, C., & Gabi, K. (Eds.). (2015). Pwa90: A lifetime of emergence. Singapore: World Scientific. Randall, D., Burggren, W., & French, K. (2002). Eckert animal physiology: Mechanisms and adaptations. New York: W H Freeman. Rhoades, R., & Pflanzer, R. (1989). Human physiology. Fort Worth: Saunders College Publishing. Rivat, S., & Grinbaum, A. (2020). Philosophical foundations of effective field theories. The European Physical Journal, A, 56, 1–10. Schrödinger, E. (1944). What is life? The physical aspect of the living cell. Cambridge: Cambridge University Press. Schweber, S. S. (1993). Physics, community, and the crisis in physical theory. Physics Today, 46, 34–34. Sciama, D. W. (2012). The unity of the universe. North Chelmsford: Courier Corporation. Scott, A. (1999). Stairway to the mind: The controversial new science of consciousness. New York: Springer Science and Business Media. Shea, B. (2021). Karl popper: Philosophy of science. Internet Encyclopaedia of Philosophy. https:// www.iep.utm.edu/pop-sci/ Simon, H. A. (2019). The architecture of complexity. Sciences of the artificial. Cambridge: MIT Press. Singleton, J. (2001). Band theory and electronic properties of solids. New York: Oxford University Press. Snoke, D. (2020). Solid state physics: Essential concepts. Cambridge: Cambridge University Press. Wagner, A. (2014). Arrival of the fittest: Solving evolution’s greatest puzzle. New York: Penguin. Watson, J. D. & Levine, M. (2013). Rate and review. In Molecular biology of the gene. London: Pearson. Weinberg, S. (1994). Dreams of a final theory: The scientist’s search for the ultimate laws of nature. New York: Penguin Random House. Weinberg, S. (2008). From BCS to the LHC CERN courier. Wietfeldt, F. E., & Greene, G. L. (2011). Colloquium: The neutron lifetime. Reviews of Modern Physics, 83, 1173. Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proceedings of the Sixth International Congress on Genetics, 1(8), 355–366.

Chapter 16

Response to Part III: The View from the Life Sciences George F. R. Ellis

Abstract In this response, George Ellis comments on the publications of part III. He responds first to Denis Noble, before outlining his thoughts on Larissa Albantakis’, Francesco Massari’s, Maggie Beheler-Amass’ and Giulio Tononi’s piece.

16.1 The Principle of Biological Relativity: Origin and Current Status: Denis Noble Denis Noble has long been a source of inspiration and ideas to me. Because he is a physiologist, which is of necessity an integrative profession, he has a holistic view of biological functioning. Based on his deep knowledge of heart physiology, he strongly argues that downward causation takes place in biology. I agree so much with this chapter, that there is little that I need to say.

16.1.1 Higher Level Organising Principles: Attractors In Noble’s description of his route to understanding, he explains the key issue of biological oscillators. Instead of their being an oscillator component generating the heart rhythm it was interactions between model components that produces the rhythm. “That meant attributing the origin of the rhythm to a high-level property and that it would arise from the solution to the equations. In other words, it is an attractor.” This key example is nothing other than a case of the Higher Level Organising Principles discussed above in my response to Green and Batterman (Chap. 14,

G. F. R. Ellis () Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_16

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Section 2.6). The attractor does not emerge from lower level outcomes—it determines them. This is like the classical and quantum protectorates of Laughlin and Pines (2000), and is a form of downward causation. Noble asks how these downward arrows of causation are represented in the equations used in a multilevel model, and identifies them as being represented in the initial and boundary conditions at each level of organisation. Just so. But the existence of the attractors adds a new dimension to the dynamics: they represent solutions that are insensitive to initial conditions, just like feedback control loops do (Chap. 2 and Sect. 2.3 of Chap. 13). The contrast between the two cases is intriguing: feedback control does it via an explicit mechanism, dynamical attractors via a deep structure hidden in the equations (Arnold 1989). As Noble says, it is unexpected and a great example of downward causation because the lower level physics follows what this emergent structure entails. An explicit study in the case of the dynamics of the fission yeast cell-cycle regulatory network is given by Walker et al. (2016). More broadly, there are generic patterns that acts as higher level organising principles. Jacob stated in his Nobel lecture (Jacob 1966):1 The most striking observation that emerged from the study of phage production by lysogenic bacteria and of induction of β-galactosidase synthesis was the extraordinary degree of analogy between the two systems. Despite the obvious differences between the production of a virus and that of an enzyme, the evidence showed that in both cases protein synthesis is subject to a double genetic determinism: on the one hand, by structural genes, which specify the configuration of the peptide chains; on the other hand, by regulatory genes, which control the expression of these structural genes. In both cases, the properties of mutants showed that the effect of a regulatory gene consists in inhibiting the expression of the structural genes, by forming a cytoplasmic product which was called the repressor. In both cases, the induction of synthesis (whether of phage or of enzyme) seemed to result from a similar process: an inhibition of the inhibitor.

A basic key control mechanism such as this—a higher level organising principle— tends to be discovered a number of times. This is the phenomenon of convergence in biology (McGhee 2011). The same goes for feedback control systems (Bechtel in Boogerd et al. (2007)).

16.1.2 Systems Biology The emergence of cellular level functional properties in biology is the topic of Systems Biology, described by Boogerd et al. (2007) thus: Systems biology is concerned with the relationship between molecules and cells; it treats cells as organized, or organizing, molecular systems having both molecular and cellular properties. It is concerned with how life or the functional properties thereof that are not yet in the molecules, emerge from the particular organization of and interactions between its

1 Quoted

by R. C. Richardson and A. Stephan in Boogerd et al. (2007, 135).

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molecular processes .. It refers to function in ways that would not be permitted in physics. .. It shies away from reduction of the system under study to a collection of elementary particles.

Thus it is based in an explicitly emergentist philosophy. In the chapter of Richardson and Stephan in that book, the concept of emergence is based exactly on such a failure of system behavior to be calculated from the component properties: system behavior should be called (strongly) emergent only if system behavior cannot be inferred or predicted from the behavior of components in isolation (or smaller subsystems). This agrees with the definition of strong emergence by Chalmers (2006). However if one knows the behavior of components within the systemic context, then it is possible to give a mechanistic explanation of any system’s behavior. That does not however mean the behaviour is predictable. To make that point, note that digital computers are precisely a case where one has a mechanistic explanation of the system behaviour, but it is not predictable. Quite apart from the Halting Problem, if it was predictable, one would not need the computer! Why am I mentioning systems biology? Because it supports strongly the emergentist view of biology (Gibb et al. 2019). However (a) while it does not explicitly mention the equal existence of Effective Theories at each level, it certainly implies it. Thus on page 37, “reduction of molecular biology and biochemistry to the underlying physics and chemistry is rare, and not even an aim of these disciplines anymore; both disciplines are entirely successful on the basis of their own concepts and laws, immaterial whether these are reducible to physics and chemistry or not.” Second, (b) it does not mention downward causation from the cellular to the molecular level, much less to the physics level, even though it implies this. That it does indeed implicitly deal with downward causation is shown by the chapter by H. V. Westerhoff and D. B. Kell (page 34), where it is pointed out that the way in which an enzyme affects the behaviour of a network is fairly well described by the elasticity coefficients S for the metabolites with which it interacts. The equation for those coefficients shows that the role of the enzyme in the system is not only determined by that enzyme itself (through the Michaelis-Menten constant Km ) but also by its environment (the concentration [S] of the substrate) and by how it interacts with that environment (in terms of S/Km ). It is a shame that this literature is disjoint from the physiological literature represented by Fink and Noble (2008) and Noble (2008, 2016).

16.1.3 Constraints and Democracy of Levels I am delighted to have (inadvertently) led to Denis Noble arriving at his Principle of Biological Relativity, as he explains. However there is a key issue here. Biology after all emerges from physics. So how does his Figure 2 relate to the underlying physics?

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Fig. 16.1 Downwards causation to the physics level (extended Noble diagram)

There are two countervailing themes here. On the one hand, if biological causation is real at all those levels—the cellular level, the protein level, and so on— then the downward arrow must reach down to the underlying physics level (see Fig. 16.1). This must be the case because if there is for example a gene regulatory network determining biological outcomes, as happens not just during developmental processes (Carroll 2005) but also during ordinary biological functioning, for example in terms of memory processes (Kandel 2001), then causation (as understood by Pearl (2009)) must reach down from the effective theory EFL at that level L to the underlying physics levels. The biology decides what to do but the physics does the work. That has to be so in order for example that cell signaling networks (Berridge 2014) function as advertised; otherwise the emergent biological levels simply could not function (electrons and ions have to flow to enable biological function). But then you get caught in the reductionist’s nightmare: it seems that somehow the laws of physics are being violated by this process. The resolution, following on Juarrero (2002) and Green and Batterman (Chap. 2, Sect. 2.2), is to allow for the effect of time dependent constraints on the underlying physics. This occurs via processes such as messenger molecules opening and closing ligand gated ion channels, and voltages across cellular membranes opening and closing voltage gated ion channels (Hodgkin and Huxley 1952; Ellis and Kopel 2019; Noble 2020). Thus there is no violation of the physical laws: one is recognizing the causal effects of constraints (Juarrero 2002). At the macro level, they are physiological systems (Randall et al. 2002; Rhoades and Pflanzer 1989); at the micro level, the most important constraint is cell walls and their associated ion channels (Alberts et al. 2007; Berridge 2014).

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Constraints underlie mechanistic explanations (Salthe 1993; Wright and Bechtel 2007), where a specific structure carries out a specific function by channeling interactions: an escapement controls the rate of ticking of a watch, the heart pumps blood in the veins. They come into being either via engineering design, or via biological developmental process. In mathematical terms, they often turn the partial differential equations of the underlying physics (Maxwell’s equations, the Schrödinger equation, the diffusion equation) into ordinary differential equations and associated dynamical systems (Arnold 1989) that still need boundary conditions and initial conditions to determine outcomes, as in the case of the heart (Fink and Noble 2008). Thus I don’t see constraint as boundary conditions, but rather as structural features. In Aristotelian terms, they are Formal Causes (Chap. 1). The key point here, as emphasized in Ellis and Kopel (2019), is that constraints CL at level L can be time dependent, with the time dependence occurring via dependence of the constraints on variables aLC (t) determined at a higher level LC: CL (t) = CL (aLC (t)), {∂aLC /∂t = 0} ⇒ ∂CL /∂t = 0 .

(16.1)

I believe it would be useful to add an extra box in Noble’s Figure 3 to represent the effects of such interlevel time dependent constraints, for example shaped by cell signalling molecules (Berridge 2014) conveying information about higher level biological needs (Fink and Noble 2008). Thus one has control of gene expression by epigenetic factors, as stated by Nobel, and even by mental events (Kandel 1998, 2001). Given the downward link to physics from biology (Fig. 16.1), together with the usual upward link from physics to biology, Noble’s Principle of Biological Relativity (Noble 2012; Noble et al. 2019) extends to include the physics level as well. There is equal causal validity at all biological and physical levels (Ellis 2020b).

16.1.4 Causal Closure and Randomness A key issue in all of this is, what is the nature of causal closure? Noble and Noble (2019) assert that For many [emergent phenomena], causality in their development and maintenance is necessarily circular; the circularity occurs between levels of organization;

as is also stated by Hofmeyr (Boogerd et al. 2007, 217), Moreno (Boogerd et al. 2007, 243), Mossio and Moreno (2010) and Mossio (2013). Causal closure only make sense if it is regarded as an interlevel affair (Ellis 2020b). Because of the downward causation just discussed, the physics level isn’t causally closed without the presence of the biological signals that affect what happens at that level.

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Secondly, randomness occurs at various levels and confounds the idea that initial conditions always determine physical outcomes in a unique way. Apart from the effects of quantum uncertainty (Ghirardi 2007), which can get amplified to macro levels for example via its effect on DNA (Percival 1991), there is massive randomness at the molecular level: what Hoffmann dubs the “molecular storm” (Hoffmann 2012). This freeing up of outcomes from initial conditions opens the way allow to selective choice of outcomes so as to achieve higher level biological purposes (Hoffmann 2012; Noble and Noble 2019). This is one of the mechanisms allowing higher levels to act downwards via processes of adaptive selection. In Aristotelian terms, it is a Material Causation (Chap. 1). This is so important that I will give four quotes to support it. First, Noble (2017): Stochasticity is harnessed by organisms to generate functionality. Randomness does not, therefore, necessarily imply lack of function or ?blind chance? at higher levels. In this respect, biology must resemble physics in generating order from disorder. This fact is contrary to Sch¨rodinger’s idea of biology generating phenotypic order from molecular-level order, which inspired the central dogma of molecular biology. The order originates at higher levels, which constrain the components at lower levels. We now know that this includes the genome, which is controlled by patterns of transcription factors and various epigenetic and reorganization mechanisms. These processes can occur in response to environmental stress, so that the genome becomes a highly sensitive organ of the cell? (McClintock). Organisms have evolved to be able to cope with many variations at the molecular level.

Second, Noble and Noble (2018): Choice in the behavior of organisms involves novelty, which may be unpredictable. Yet in retrospect, we can usually provide a rationale for the choice. A deterministic view of life cannot explain this. The solution to this paradox is that organisms can harness stochasticity through which they can generate many possible solutions to environmental challenges. They must then employ a comparator to find the solution that fits the challenge. What therefore is unpredictable in prospect can become comprehensible in retrospect. Harnessing stochastic and/or chaotic processes is essential to the ability of organisms to have agency and to make choices

Third (Ilan 2020), which states Randomness characterizes many processes in nature, and therefore its importance cannot be overstated. . . . Through the chosen examples, we explore the seemingly paradoxical nature of life and demonstrate that randomness is preferred under specific conditions. Furthermore, under certain conditions, promoting or making use of variability-associated parameters may be necessary for improving the function of processes and systems. .. Randomness does not necessarily imply a lack of function. In fact, it is used by organisms to generate functionality

He gives the example of dividing cells. Randomness occurs when microtubules associate with mitotic kinetochores. However the outcome is reproducible with high fidelity because of the processes of chromosome segregation Finally Capp and Laforge (2020) make this kind of dynamic explicit: Single-cell analysis allows biologists to gain huge insight into cell differentiation and tissue structuration. Randomness of differentiation, both in vitro and in vivo, of pluripotent (multipotent) stem cells is now demonstrated to be mainly based on stochastic gene expression. The ontophylogenesis theory considers the generation of a differentiated state as a constrained random process: randomness is provided by the stochastic dynamics of

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biochemical reactions while the environmental constraints, including cell inner structures and cell-cell interactions, drive the system towards a stabilized state of equilibrium. In this conception, biological organization during development can be seen as the result of multiscale constraints produced by the dynamical organization of the biological system which retroacts on the stochastic dynamics at lower scales. This scheme makes it possible to really understand how the generation of reproducible structures at higher organization levels can be fully compatible with probabilistic behaviour at the lower levels. It is compatible with the second law of thermodynamics but allows to overtake the limitations of models based only on entropy exchanges which cannot cope with the description nor the dynamics of the mesoscopic and macroscopic organization of biological systems.

This makes explicit the downward action from higher to lower levels, the role of constraints, and how the randomness at lower levels undermines any concept of physical determinism governing biological outcomes (Ellis 2020a: Section 6.1). This is a key aspect of downward causation, enabling upper levels to be equally as causally effective as lower levels, and hence supporting Noble’s Principle of Biological Relativity. It is gratifying to read in his chapter what an impact it has had.

16.2 A Macro Agent and Its Actions: Albantakis, Massari, Beheler-Amass and Tononi This article deals with Integrated Information Theory (IIT), a sustained and very useful approach to emergence of complexity in modular hierarchical structures out of the underlying physics. Particularly important is its demonstration that strong emergence can take place because higher levels have greater causal powers than lower levels.

16.2.1 Nature of an Agent and a System The authors explain that an agent must be an open system that dynamically and informationally interacts with an environment. Indeed. This emphasizes openness (Peacock 1989) and the importance of information in the dynamics (Nurse 2008) (Davies 2019). The detailed structuring is complex, and I will not attempt to repeat it, rather just making some comments on the overall project. A System The notion of intrinsic information requires that there is a system in the first place, meaning one “whole” as opposed to multiple separate sets. Thus one needs boundaries to define the system. Boundaries Because it acts on their environment, it is important to be able to differentiate the system from the environment: “Agents require (causal) borders that separate them from the environment”. This is important, and corresponds to

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Friston’s use of the idea of a Markov Blanket (Friston 2010, 2012) characterising this separation, and interactions of a system with its environment. But this applies not just to the system as a whole, but to each module in the system. In informational terms, there must be a carefully specific interface of modules to their environment (Booch 2006). In microbiology that is via membranes and ion channels that control ingress and egress to a cell (Ellis and Kopel 2019), thus allowing controlled cell signalling processes (Berridge 2014).

16.2.2 Macro and Micro Networks IIT is very significant because it takes seriously, and explicitly models, dynamics of modular hierarchical structures, which are the key to emergence (Booch 2006; Ellis 2016). Now there is an issue here: in some cases, such as human physiology, one can characterise the structures in terms of constraints without representing them explicitly as networks, for example the skeletal system, the digestive system, and the hierarchical structure of the heart (Fink and Noble 2008; Rhoades and Pflanzer 1989). But in many cases, for example the central nervous system and interaction networks, a network representation is indeed appropriate. Then determining what are modules—subnetworks that should be characterised as such—is a complex issue (Ravasz et al. 2002; Papin et al. 2004; Wuchty et al. 2006). IIT offers a unique and plausible way to do it, based not in statistics but in causal organisation. That is a unique contribution. Given this basis, upscaling takes place by Black boxing, not coarse graining. This is a key feature of information based architectures (Ashby 2013) (Section 2.1 in Chapter 13), and is a key difference between physics and biology (Ellis and Kopel 2019) as well as playing a key role in engineering systems such as computers (Ellis and Drossel 2019). It enables irreducible higher level logical operations (Abbott 2020) to emerge from lower level ones (Tanenbaum 2006).

16.2.3 Cause-Effect Structure A set of causal principles, including notions such as causal specificity, composition, and irreducibility underlie the analysis. • Intrinsicality: Our goal is to evaluate the causal constraints specified by the set of elements S onto itself, above the background of external influences. Thus here we again get the emphasis on constraints that was a theme in Green and Batter man’s contribution (Chap. 2 and Chap. 13, Sect. 2.2). • Composition: IIT takes a compositional perspective on causation: Not only single elements, but also combinations of elements may specify their own constraints about other system subsets as long as they are irreducible

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• Information rather than testing for a counterfactual relation based on a single alternative, IIT considers all possible system states in its causal analysis, which can thus be expressed in probabilistic, informational terms. Excellent to see information being taken seriously here (compare Nurse 2008; Davies 2019). • Integration However, a subset only contributes to the intrinsic information of the system if this information is irreducible The definition of irreducible is key • Exclusion The cause-effect structure is constituted of irreducible mechanisms and the information they each specify. IIT offers a quantitative framework to characterize the causal structure of discrete dynamical systems. This contrast with the continuous dynamical systems characterised by Arnold (1989), whose attractors play a key role as emergent causal elements. All of this is of the nature of irreducible higher level variables. These relations cannot be characterised at lower levels (see Noble. Chap. 6, and Sect. 16.1.1).

16.2.4 Macro and Micro Integrated Information A system’s amount of integrated information  measures the causal constraints a system exerts onto itself and can peak at a macro level of description (Hoel et al. 2013, 2016). This characterizes emergence of higher level causal powers Comparing macro-micro structures: Irreducible higher order mechanisms The IIT formalism provides a complete account of a system’s causal structure, including irreducible higher-order mechanisms constituted of multiple system elements. This implies irreducible higher order variables.

16.2.5 Causal Chain for Actions The causal principles of IIT can also be employed to identify and quantify the actual causes of events (What caused what?), such as an agent’s actions: With respect to an agent’s action, the direct micro-level cause is rarely considered the cause with the greatest explanatory power (Woodward 1989). For example, while a motor neuron in the spinal cord may directly initiate a movement, we are typically more interested in identifying the cortical events or external stimuli that triggered the action. To that end, we can employ the actual causation analysis to trace the causal chain of micro occurrences back.

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16.2.6 Properties Associated with Autonomy and Agency The IIT formalism can also be applied across micro and macro spatio-temporal scales in order to identify those organizational levels at which the system exhibits strong causal constraints onto itself. . . . According to IIT principles, the particular spatio-temporal scale that specifies a maximum of integrated information defines the spatio-temporal scale at which the system specifies itself in causal terms.

This is a precise definition of the causal closure principle of Mossio (2013) and others (e.g. Noble et al. 2019) that I develop in Ellis (2020b), demonstrated by an example of a simulated agent, equipped with a small neural network, that forms a maximum of  at a macro scale. It is developed in depth in Hoel et al. (2016). There is however a challenge to be met. Walker et al. (2016) in a careful study of the informational architecture of the cell compared the calculated values of local and global information measures for the fission yeast cell cycle to the same measures as applied to two different classes of random networks, and found that IIT did not distinguish this biological network from random. Perhaps the network is not large enough to be characterised as being associated with autonomy. It would be good to have a response to this paper from Albantakis et al. (2021). Overall, this paper is a much appreciated confirmation of higher level causal power over lower levels, and hence a confirmation of downward causation.

References Abbott, R. (2008). Constructive emergence: Why is emergence still a mystery? academia.edu. Retrieved 07 July 2020. Albantakis, L., Massari, F., Beheler-Amass, M., Tononi, G. (2021). A macro agent and its actions. In J. Voosholz, M. Gabriel (Eds.), Top-down causation and emergence. Synthese library (Vol. 439, pp. 135–155). Cham: Springer. https://doi.org/10.1007/978-3-030-71899-2_7 Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., & Walter, P. (2007). Molecular biology of the cell. New York: Garland Science. Arnol’d, V. I. (1989). Mathematical methods of classical mechanics. New York: Springer. https:// www.springer.com/gp/book/9780387968902 Ashby, W. R. (2013). Design for a Brain: The origin of adaptive behaviour. Dordrecht: Springer. https://books.google.co.za/books?hl=en&lr=&id=Dc4hBQAAQBAJ&oi=fnd& pg=PR5&dq=Design+for+a+Brain+The+origin+of+adaptive+behavi&ots=-nP_sI85dm& sig=wyZSHHfNYV6FaBNSekBZwk-Ckxo#v=onepage&q=Design%20for%20a%20Brain %20The%20origin%20of%20adaptive%20behavi&f=false Berridge, M. (2014). Cell signalling biology. London: Portland Press. https://doi.org/10.1042/ csb0001001. http://www.cellsignallingbiology.co.uk/csb/ Booch, G. (2006). Object oriented analysis and design with application (2nd ed.). Reading: Addison Wesley. https://www.amazon.com/Object-Oriented-Analysis-Design-Applications3rd/dp/020189551X Boogerd, F. C., Bruggeman, F. J., Hofmeyr, J.-H. S., & Westerhoff, H. V. (2007) Systems biology philosophical foundations. Amsterdam: Elsevier.

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Capp, J.-P., & Laforge, B. (2020). A Darwinian and physical look at stem cell biology helps understanding the role of stochasticity in development. Frontiers in Cell and Developmental Biology. https://doi.org/10.3389/fcell.2020.00659 Carroll, S. B. (2005). Endless forms most beautiful. New York: WW Norton & Company. https:// en.wikipedia.org/wiki/Endless_Forms_Most_Beautiful_(book) Chalmers, D. J. (2006). Strong and weak emergence. In P. Davies & P. Clayton (Eds.), The reemergence of emergence: The emergentist hypothesis from science to religion. Oxford: Oxford University Press. https://ai-su13.artifice.cc/Chalmers-Emergence.pdf Davies, P. (2019). The demon in the machine: How hidden webs of information are solving the mystery of life. Chicago: University of Chicago Press. https://books.google.co.za/books? id=bYJbDwAAQBAJ&printsec=frontcover&dq=The+demon+in+the+machine&hl=en&sa= X&ved=0ahUKEwi-_YvSk6npAhVxRBUIHXvpB4UQ6AEIKDAA#v=onepage&q=The %20demon%20in%20the%20machine&f=false Ellis, G. (2016). How can physics underlie the mind? Top-down causation in the human context. Heidelberg: Springer. https://link.springer.com/book/10.1007/978-3-662-49809-5 Ellis, G. F. R. (2020a). Emergence in solid state physics and biology. Foundations of Physics. https://doi.org/10.1007/s10701-020-00367-z. http://arxiv.org/abs/2004.13591 Ellis, G. F. R. (2020b). The causal closure of physics in real world contexts. Foundations of Physics. https://doi.org/10.1007/s10701-020-00366-0. https://arxiv.org/abs/2006.00972 Ellis, G., & Drossel, B. (2019). How downwards causation occurs in digital computers. Foundations of Physics, 49, 1253–1277. https://link.springer.com/article/10.1007/s10701-019-003076. https://arxiv.org/pdf/1908.10186 Ellis, G., & Kopel, J. (2019). The dynamical emergence of biology from physics. Frontiers in Physiology, 9, 1966. https://www.frontiersin.org/articles/10.3389/fphys.2018.01966/full Fink, M., & Noble, D. (2008). Noble model. Scholarpedia, 3(2), 1803. http://www.scholarpedia. org/article/Noble_model Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11, 127–138. https://www.uab.edu/medicine/cinl/images/KFriston_FreeEnergy_ BrainTheory.pdf Friston, K. (2012). A free energy principle for biological systems. Entropy, 14, 2100–2121 https:// www.mdpi.com/1099-4300/14/11/2100/pdf Ghirardi, G. (2007). Sneaking a look at god’s cards: Unraveling the mysteries of quantum mechanics. Princeton: Princeton University Press. Gibb, S., Hendry, R., & Lancaster, T. (Eds.). (2019). The Routledge handbook of emergence. Abingdon: Routledge. https://www.routledge.com/The-Routledge-Handbook-of-Emergence/ Gibb-Hendry-Lancaster/p/book/9781138925083 Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application . . .. The Journal of Physiology, 117, 500–544. https://www.ncbi.nlm.nih.gov/pmc/ articles/PMC1392413 Hoel, E. P., Albantakis, L., & Tononi, G. (2013). Quantifying causal emergence shows that macro can beat micro. Proceedings of the National Academy of Sciences, 110, 19790–19795. https:// www.pnas.org/content/pnas/110/49/19790.full.pdf Hoel, E. P., Albantakis, L., Marshall, W., & Tononi, G. (2016). Can the macro beat the micro? Integrated information across spatiotemporal scales. Neuroscience of Consciousness, 2016(1), niw012. https://academic.oup.com/nc/article/2016/1/niw012/2757132 Hoffmann, P. (2012). Life’s Ratchet: How molecular machines extract order from chaos. New York: Basic Books. Ilan, Y. (2020). Order through disorder: The characteristic variability of systems. Frontiers in Cell and Developmental Biology, 8, 186. https://www.frontiersin.org/articles/10.3389/fcell.2020. 00186/full Jacob, F. (1966). Genetics of the bacterial cell. Science, 152, 1470–1478. Juarrero, A. (2002). Dynamics in action: Intentional behavior as a complex system. Cambridge: MIT Press. https://mitpress.mit.edu/books/dynamics-action

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Juel, B. E., Comolatti, R., Tononi, G., & Albantakis, L. (2019). When is an action caused from within? Quantifying the causal chain leading to actions in simulated agents. In The 2019 Conference on Artificial Life. https://www.researchgate.net/publication/334616646_When_ is_an_action_caused_from_within_Quantifying_the_causal_chain_leading_to_actions_in_ simulated_agents Kandel, E. R. (1998). A new intellectual framework for psychiatry. American Journal of Psychiatry, 155, 457–469. Kandel, E. R. (2001). The molecular biology of memory storage: A dialogue between genes and synapses. Science, 294, 1030–1038. http://teachline.ls.huji.ac.il/72336/sphira/ Kandelnobellecture.pdf Laughlin, R., & Pines, D. (2000). The theory of everything. Proceedings of the National Academy of Sciences of the United States of America, 97, 28–31. https://www.pnas.org/content/97/1/28 McGhee, G. R. (2011). Convergent evolution: Limited forms most beautiful. Cambridge: MIT Press. https://books.google.co.za/books?hl=en&lr=&id= QwDSr1qdqXUC&oi=fnd&pg=PR7&dq=George+McGhee&ots=Ejg7RAMnxm&sig= V5mocG9ZWB8Z9S3ms5DaiCN4YxQ#v=onepage&q=George%20McGhee&f=false Mossio, M. (2013). Closure, causal. In W. Dubitzky, O. Wolkenhauer, K.-H. Cho, & H. Yokota (Eds.), Encyclopedia of systems biology. Springer, New York (pp. 415–418). https://halshs. archives-ouvertes.fr/halshs-00792439/PDF/Closure_causal_2013.pdf Mossio, M., & Moreno, A. (2010). Organisational closure in biological organisms. History and Philosophy of the Life Sciences, 32, 269–288. Noble, D. (2008). The music of life: Biology beyond genes. Oxford: Oxford University Press. http:// www.musicoflife.website/ Noble, D. (2012). A theory of biological relativity: No privileged level of causation. Interface Focus, 2, 55–64. https://royalsocietypublishing.org/doi/full/10.1098/rsfs.2011.0067?url_ver= Z39.88-2003&rfr_id=ori:rid:crossref.org&rfr_dat=cr_pub%3dpubmed Noble, D. (2016). Dance to the tune of life: Biological relativity. Cambridge: Cambridge University Press. https://www.cambridge.org/core/books/dance-to-the-tune-of-life/ 721483A1B5BB01E837BC8A8435E52710 Noble, D. (2017). Evolution viewed from physics, physiology and medicine. Interface Focus, 7, 20160159. https://royalsocietypublishing.org/doi/pdf/10.1098/rsfs.2016.0159 Noble, D. (2020). The surprising heart revisited: An early history of the funny current with modern lessons. Progress in Biophysics and Molecular Biology. https://www.sciencedirect.com/science/article/pii/S0079610720300766?casa_token= nFC4c88rTbEAAAAA:744hBLCxVdnkJ32fbvqTenLwQJ-t80Mq1TrV72dITLTjHwPUX_Q8pFgg298WdZga6UI5NQMP9U Noble, R., & Noble, D. (2018). Harnessing stochasticity: How do organisms make choices? Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 106309. https://aip.scitation.org/doi/full/ 10.1063/1.5039668 Noble, R., & Noble, D. (2019). A-mergence of biological systems. In S. Gibb, R. Hendry, & T. Lancaster (Eds.), The Routledge handbook of emergence (pp. 387–399). Abingdon: Routledge. https://www.routledge.com/The-Routledge-Handbook-of-Emergence/GibbHendry-Lancaster/p/book/9781138925083 Noble, R., Tasaki, K., Noble, P., & Noble, D. (2019). Biological Relativity requires circular causality but not symmetry of causation: So, where, what and when are the boundaries? Frontiers in Physiology, 10, 827. https://www.researchgate.net/publication/334544377_ Biological_Relativity_Requires_Circular_Causality_but_Not_Symmetry_of_Causation_So_ Where_What_and_When_Are_the_Boundaries Nurse, P. (2008). Life, logic and information. Nature, 454, 424–426. http://brown.edu/ Departments/Engineering/Labs/Rose/papers/nurse_bioinfoflow.pdf Papin, J. A., Reed, J. L., & Palsson, B. O. (2004). Hierarchical thinking in network biology: The unbiased modularization of biochemical networks. Trends in Biochemical Sciences, 29, 641–647. http://www.academia.edu/download/49071369/j.tibs.2004.10. 00120160923-4646-tk788g.pdf

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Peacocke, A. R. (1989). An introduction to the physical chemistry of biological organization. Oxford: Oxford University Press. https://www.amazon.com/Introduction-ChemistryBiological-Organization-Publications/dp/0198555571 Pearl, J. (2009). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press. http://bayes.cs.ucla.edu/BOOK-2K/neuberg-review.pdf Percival, I. (1991). Schrödinger’s quantum cat. Nature, 351, 357. Randall, D., Burggren, W., & French,K. (2002). Eckert animal physiology: Mechanisms and adaptations, New York: W H Freeman. Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., & Barabási, A.-L. (2002). Hierarchical organization of modularity in metabolic networks. Science, 297, 1551–1555. https://science.sciencemag.org/content/sci/297/5586/1551.full.pdf?casa_ token=nLQLg9mzWUQAAAAA:8OwxxWpiM_kqJjRcCzwCS4r3a1iAnJT7j71hCTKeEpy7kwZefq1QZPQCr8nw5N7GoK3LztHToK0F87W Rhoades, R., & Pflanzer, R. (1989). Human physiology. Fort Worth: Saunders College Publishing. Salthe, S. N. (1993). Development and evolution: Complexity and change in biology. Cambridge: MIT Press. Tanenbaum, A. S. (2006). Structured computer organisation (5th ed.). Englewood Cliffs: Prentice Hall. Walker, S. I., Kim, H., & Davies, P. C. W. (2016). The informational architecture of the cell. Philosophical Transactions of the Royal Society, A374, 20150057. https://royalsocietypublishing. org/doi/pdf/10.1098/rsta.2015.0057 Woodward, J. (1989). The causal mechanical model of explanation. In P. Kitcher & W. Salmon (Eds.), Scientific explanation. Minnesota studies in the philosophy of science (Vol. 13, pp. 357–383). https://conservancy.umn.edu/bitstream/handle/11299/185689/13_11Woodward. pdf?sequence=1 Wright, C., & Bechtel, W. (2007). Mechanisms and psychological explanation. In Philosophy of psychology and cognitive science (pp. 31–79). Amsterdam: North-Holland. https://philpapers. org/archive/WRIMAP.pdf Wuchty, S., Ravasz, E., & Barabási, A.-L. (2006). The architecture of biological networks. In Complex systems science in biomedicine (pp. 165–181). Boston, MA: Springer. https://static. springer.com/sgw/documents/139921/application/pdf/4.Barabasi.pdf

Chapter 17

Response to Part IV: The Debate on Top-Down Causation and Emergence George F. R. Ellis

Abstract In this response, George Ellis comments on the publications of Part IV. He responds first to James Woodward, Richard Healey, Jan Voosholz, Simon Friederich and Sach Mukherjee, before outlining his thoughts on Max Kistler’s piece.

17.1 Downward Causation Defended: James Woodward I appreciate this positive and thoughtful article defending downward causation. It clarifies and gives a more philosophically rigorous elaboration of arguments that Denis Noble and I have made, which is very useful. It makes valuable contributions as regards the key issue of causal exclusion/overdetermination, and the related issues of multiple realisation/realisation independence/Conditional Causal Independence. As these are complete discussions, I will not pursue them further here. I consider in what follows, the relation to Aristotelian causation (Sect. 17.1.1), types of constraints (Sect. 17.1.2), effective laws and levels (Sect. 17.1.3), cyclic causation and causal closure (Sect. 17.1.4), and Higher Level Organising Principles (Sect. 17.1.5).

17.1.1 Causation, Intervention, and Aristotle The paper is based in Woodward’s deep thought on the topic of causation, codified in his counterfactual account of what a mechanism is Woodward (2002) and his book on causal explanation (Woodward 2005). He states,

G. F. R. Ellis () Mathematics Department, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. Voosholz, M. Gabriel (eds.), Top-Down Causation and Emergence, Synthese Library 439, https://doi.org/10.1007/978-3-030-71899-2_17

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The mark of a causal relationship is that causes are potential ‘handles’ for changing effects; causal relationships are those relationships that can be exploited ‘in principle’ for manipulation and control.

Indeed. A key point then is how downward causation, with causation determined in this way, relates to Aristotle’s four kinds of causation (Bodnar 2018). Physicists tend to regard only Efficient Causation as causation. I propose that • Each of Aristotle’s four kinds of causation is indeed causation in Woodward’s sense. • Efficient causation occurs at each emergent level L, and indeed defines what should be considered ontologically distinct emergent levels. • Downward causation can occur via each of Material, Formal, and Final causation. • A fifth kind should be added to Aristotle’s kinds, namely Abstract Causation. Efficient Causation At each emergent level L, an Effective Law EFL reliably relates initial data dL at that level to outcomes oL at that level, while obeying constraints CL on the variables at that level (Ellis 2020b). The ability to adjust initial data dL while respecting boundary conditions bL and constraints CL provides the causal ‘handle’ referred to by Woodward. Examples are the basic laws of physics (Newton’s Laws of motion, Maxwell’s laws of electromagnetism, etc (Feynman 1963)), higher level physics laws such as Ohm’s Law and the Laws of Thermodynamics (Feynman 1963), emergent network dynamics in molecular biology (Alon 2006), emergent dynamical systems (Arnold 1989), the emergent relations governing physiological systems such as the heart (Fink and Noble 2008), emergent neurophysiology (Kandel et al. 2013), and so on. Such Effective Laws occur at each emergent level, which in the case of biology is Noble’s Principle of Biological Relativity (Noble 2012) (discussed in Chap. 8). Indeed it is the existence of such effective laws that characterise a level L as being ontologically real (Ellis and Gabriel 2020). Material Causation This concerns the material out of which higher levels are constructed: different materials result in different emergent properties (making something out of copper or sand has a different result than making it out of carbon or stone). The key point here is that higher level conditions can • Create lower level elements Physics examples are phonons and Cooper pairs, which only exist because of specific crystal structures (Simon 2013; Snoke 2020; Ellis 2020a). A biology example is proteins, which only come into existence via the whole cellular machinery (Alberts et al. 2007) that enables protein synthesis on the basis of the DNA sequence of a gene (Hofmeyer 2018) • Alter their properties Physics examples are the way that a neutron has a half life of 11 min when free, but billions of years when bound in a nucleus (Feldman 2019). A biology example is the way that pluripotent cells are specialised to become specific cell types via the processes of developmental biology on the basis of positional information (Wolpert 2002; Carroll 2005; Gilbert 2006)

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• Selectively delete them Physics examples are quantum state vector preparation (Ellis 2012) and material purification processes in physical chemistry (Armarego 2017) removing unwanted material so as to leave a purified desired product. Selection is a central process in biology where variation and then selection according to higher order selection principles occurs in the adaptive immune system (Cooper and Alder 2006) and is the core of Darwinian evolution (Mayr 2001) and brain plasticity (Edelman 1987; Ginsburg and Jablonka 2019). In each of these cases, Woodward’s criteria applies: different higher level states result in different lower level elements underlying emergence. Thus they are all cases of material downward causation. Formal Causation This concerns causation that occurs via the way the material used is formed into emergent entities. It relates particularly to various kinds of constraints that shape outcomes: specifically, structural, containing, channeling, and gating constraints. It covers all of engineering, where large sums of money are devoted to functional shaping of materials, and in biology, for example in physiology (Randall et al. 2002; Rhoades and Pflanzer 1989), where they occur in the short term via developmental processes (Wolpert 2002; Gilbert 2006), and in the long term via Darwinian evolutionary processes (Mayr 2001) acting together in an intricate dance (Carroll 2005). A key example in biology is the structure of proteins (Petsko and Ringe 2009) which enables them to function as enzymes and as logic gates (Ellis and Kopel 2019) controlling the flow of ions in and out of cells thereby enabling action potential spike chains (Scott 1999) along axons. In each case the lower level effects are a direct result of the nature of the higher level structures, hence this also is causation in Woodward’s sense. Final Causation This is the ultimate reason something happens in the case of intelligent action, involving purpose, values, and meaning. It shapes all else that happens in the social world in a top-down way, for example the electrons flowing through gates in a digital computer are ultimately doing so in order to fulfill some purpose such as making someone richer, stealing an election, getting aid to people in need in order to improve their lives, and so on (Ellis and Drossel 2019). This again is clearly causation in Woodward’s sense It can be thought of as the topmost level of causation in the hierarchy of emergence and causation because it shapes all else that happens in a social context, for example if a country believes in the death penalty then the physical apparatus needed for an execution will exist; if their values preclude this, they will not exist. This is developed fully in Ellis and Noble (2021). Abstract Causation Finally there is a further kind of causation not noted by Aristotle: it is Abstract Causation, whereby abstract logic has a causal effect. It occurs via rational thought in the human mind, such as determining economically optimal outcomes of various alternative forms of action (Boulding 1941), rules that govern games such as the rules of chess,1 in engineering through design of artefacts that then get manufactured (Dieter and Schmidt 2009), and in digital computers via 1 Rules

of Chess, Wikipedia.

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algorithms that determine what sequence of operations will take place according to a strict branching logic (Knuth and Donald 1973). This is enabled in the case of digital computers via the branching operations enabled by transistors (Ellis and Drossel 2019). In the case of the human brain, it is enabled by neurons connected via synapses (Kandel et al. 2013), the underlying branching dynamics enabled by voltage gated ion channels (Ellis and Kopel 2019), and the specific structure of neural networks coding rational thoughts (Wu et al. 2020). A key point here is that although they are realised in physical terms, thoughts and algorithms per se are abstract entities that can be multiply realised in various physical forms (speech, text, in digital form for example). That is why this is abstract causation.

17.1.2 Types of Constraints Given that constraints indeed are a form of downward causation (Pattee 1973; Juarrero 2002; Blachowicz 2013), there are various kinds of constraints which act rather differently. 1. Structural or channeling constraints, e.g. a wheel or cylinder or bone (which are locally time independent) or a pipe or electric wire. They channel causation in a downward way (what current flows where, for example) but do so in a fixed way. 2. Contextual constraints e.g. temperature of a heat bath. This may be time dependent as for example nucleosynthesis in the early universe (Ellis 2016, 275). Altering this context gives different outcomes (Barnes and Lewis 2020). The diesel engine example is this kind. A channeling constraint becomes a signalling or controlling constraint if it can be altered, for example by changing a valve or switch. 3. Signalling or controlling constraints: Currents that operate relays or transistors control electron flows, and so are controlling constraints. The point is that they are variable in response to higher level conditions. Similarly shapes of ion channels are controlled by cell signalling messengers (Berridge 2014) or transmembrane voltages (Ellis and Kopel 2019); conduction channels in transistors are opened by electric currents determined by computer programs (Ellis and Drossel 2019). These are examples of gating constraints.

17.1.3 Example Emergent Effective Laws The examples are great. I particularly like the quenching of the sword. As regards energy cascades, Bishop (2008), Bishop (2012) discusses downward causation and

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convection. As regards the Hodgkin-Huxley equations, Scott (1999) has a useful discussion of strong emergence in this case, in particular emphasizing that none of the constants in those equations can be derived from fundamental physics—a hallmark of strong emergence. Mean Field Theories A nice example is the Galilean law of gravity on Earth, which governs engineering design and function to high precision, as well as biological structure and function, and daily life such as walking and climbing. The gravitational force on an object of mass m on the surface of the Earth is Fg = mg = mag ⇔ ag = g

(17.1)

where g is the acceleration due to gravity at the Earth’s surface, and the second equality on the left is Newton’s Law of Motion resulting in an acceleration ag . But this effective force derives from Newton’s Law of Gravity Fg = G

mMe GMe ⇔g= 2 Re2 RE

(17.2)

where G is Newton’s gravitational constant, and Me , Re are the Earth’s mass and radius respectively. Thus it is a contextual law: the value g is downwardly determined by the specific details of the Earth’s structure, namely its mass and radius (and varies slightly with altitude if one goes up a mountain). A different context (a planet of different mass or radius) results in a different value for g, so Woodward’s criterion for a cause is satisfied. Relating Different Levels There are different ways of obtaining the level L+1 effective laws from the level L effective laws (Ellis 2012). They usually depend on knowing emergent variables (Leggett 1992; Ellis 2020a). Coarse graining works in some cases (Penrose 2006) but does not for example cover the transition to emergence of branching logic in engineering (Ellis and Drossel 2019) or biology (Ellis and Kopel 2019). But then how does one relate different levels? Detailed modeling is needed, for example as to how transistors work (Simon 2013) or cell signalling takes place (Berridge 2014). In the case of neuronal modeling, Woodward says “Although there are more fine-grained models that describe the behavior of small individual ‘compartments’ of the neuron , these cannot be simply ‘aggregated up’ to produce a tractable model of the whole neuron.” Indeed. This is the issue of black boxing (Ashby 2013) rather than coarse graining. It is the way one must always proceed when logical operations are taking place, as in biology and in computers. Examples are given in Walker et al. (2016) and Ellis and Kopel (2019).

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17.1.4 Cycles and Causal Closure As discussed by Woodward, real causal relations are not instantaneous: they are diachronic rather than synchronic. That removes must of the alleged problems with supervenience, as discussed in Ellis (2019a). The issue of cycles is important. Woodward says, The presence of causal cycles is a real feature of many biological systems and for obvious reasons such cycles are an unavoidable part of feedback and control mechanisms that are ubiquitous in such systems and are necessary for restoring systems to an equilibrium from which they may have departed, avoiding runaway behavior etc. Cycles are also a common feature of many social and economic systems. We don’t want conditions on causation that have the consequence that such cycles are impossible

Indeed so. it is not a problem for downward causation, cyclic causation is an essential aspect of how downward causation together with upward causation enables causal closure to occur. Beginning with Mossio and Moreno’s account (Mossio and Moreno 2010; Mossio 2013), this is the key feature of causal closure I emphasize in (Ellis 2020b). Certainly it is non-linear. That is why it produces interesting irreducible results. They are a key feature of systems dynamics models (Alon 2006). There would be a problem if they acted instantaneously, but nothing works actually instantaneously—they work sequentially, just as computer model of such systems do. Specific examples are feedback control loops (Wiener 1948) and adaptive selection (Campbell 1974) where selection takes place at the individual or group level but chains down to the genotype level which then shape the phenotype level in a complex process interweaving developmental and evolutionary processes (Carroll 2005).

17.1.5 Autonomy and Higher Level Organising Principles An objection sometimes made is that on investigation, top-down causation (and for that matter, same level causation of emergent effects) does not turn out to be ‘really real’. Instead top-down causal claims just reflect shortcuts, approximations, idealizations and so on that are made for ‘pragmatic’ reasons, in order to get numbers out of scientific models, but with genuine causation always occurring at a lower-level. However in agreement with (Noble 2012), I have claimed that effective laws occurring at each level validate “real causation” (in the sense of Efficient Causation) occurring at each level according to its own logic, with the higher level effective laws coordinating lower level effects through the kinds of downward causation mentioned above. The physics enables what happens but does not determine what happens (Ellis 2005). Woodward says

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The account that I have provided respects what is sometimes called the causal closure of the physical—there is no invocation of causal facts that are not present in some form in the underlying physics.

Indeed. But that idea of physical causal closure is a fiction that only holds up of one ignores the contexts within which physics operates. The real issue that is referred to here is existence of a valid effective law at each physical level—quite a different thing. True causal closure is an interlevel affair involving high levels as well as physics levels precisely because of interlevel causal effects. This is discussed in depth in Ellis (2020b). It centres on the kind of views represented by Mossio and Moreno (2010), Mossio (2013), Noble (2020), and Noble and Noble (2020). Higher Level Organising Principles What then is higher level autonomy? Woodward says Autonomy has to do with the extent to which one can discover and formulate ‘good’ upper level causal relationships without reference to information about their underlying realizers and the laws and causal relations governing these realizers.

In other words, it is the issue of being able to determine the Effective Theories ETL that holds at each level L without having to know the effective theories at lower levels. And of course you don’t have to know particle physics in order to become a motor mechanic or a heart surgeon. This is the key feature of equal causal validity of all emergent levels (Noble 2012; Ellis 2020b). However the higher level laws do indeed emerge from the lower level laws. Is there a sense in which they are quite independent of that lower level base? I believe there is. I follow the idea of Laughlin and Pines (2000) that there exist Higher Level Organising Principles that shape dynamics at higher levels in engineering and biology, independent of the lower level dynamics.2 They are irreducible relationships valid at higher level not because they just happen to emerge from lower levels, but because they are natural irreducible principles for higher levels that will inevitably be discovered by an evolutionary process in biology or a creative developmental process in engineering. They are the ways that operating problems of complex systems situated in a possibly hostile environment can manage a safe and stable existence. These are discovered in both cases and shape appropriate effective laws at each level that promote survival and flourishing. Thus they do not arise out of lower level dynamics, rather they show contexts where lower level dynamics will fulfill these principles. They are attractors in adaptive landscapes (Kauffman and Levin 1987; Kauffman 1995; McGhee 2006). Some examples can make this clear. Containment and Channeling constraints These emerge at cellular level and at physiological system, with carefully controlled entry/exit to enable the right concentrations of ions and biomolecules to enable metabolic and informational

2 They

were actually talking about physics, see Ellis (2020a), but the same is true in biology and engineering.

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systems to function. The key issue is voltage gated and ligand gated ion channels (Petsko and Ringe 2009) that control ionic ingress and egress (Berridge 2014). Oscillatory Circuits There are many oscillators in physiological systems, for example in the heart, lungs, glycolytic oscillators, oscillators underlying smooth muscle contractions, network neuronal oscillators, and so on (Forger 2017). They form basis of attraction for dynamical systems. Feedback Control/Homeostasis One of the most fundamental principles in biology is feedback control/homeostasis (Hall 2016), enabling a system to attain a desired goal despite perturbations that may occur. It is one of Alon’s key network motifs (Alon 2006) occurring at various biological scales, governing body temperature, blood pressure, ionic concentrations, and so on. Adaptive Selection The principle of variation and then selection according to some higher level selection criterion (see Sect. 17.1.1) is fundamental to biology. It is core to evolutionary processes (Mayr 2001; Carroll 2005), to the adaptive immune system, to brain plasticity and learning processes (Edelman 1987), and to agency (Noble and Noble 2020; Noble 2020). Exploitation of Stochasticity Because of the ‘molecular storm’ (Hoffmann 2012), molecular machines do not fight stochasticity at the molecular level: they utilise it to achieve their goals. Adaptive selection plays a key role in biology, whereby stochasticity plays a key role in biological communication (Noble 2020) and in brain plasticity (Edelman 1987; Ginsburg and Jablonka 2019) and agency (Noble and Noble 2020) Logical Branching Biological systems collect various kinds of information and then use it to control logical branching in metabolic networks, gene regulatory networks, and neural networks via channeling constraints (Ellis and Kopel 2019). This is enabled by cell signalling processes (Berridge 2014) which enable the causal power of information (Nurse 2008; Davies 2019). Predictive Processing Incoming information is processed in a predictive manner that allows great savings in required computing power and rapid response to opportunities and threats (Clark 2013; Hohwy 2013; Clark 2016). It is the existence of these Higher Level Organising Principles that lead to evolutionary convergence (Conway Morris 2003; McGhee 2011). The challenge is to find a compelling complete set of such Higher Level Organising Principles for biology. Inter alia, it has very interesting implications for the search for interstellar life (SETI), as well as giving interesting hints for biomorphic engineering projects .

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17.2 A Pragmatist Perspective on Causation, Laws and Explanation: Richard Healey Healey offers an interesting take on the relation between laws, which he says derive their importance from their epistemic and methodological functions, causal concepts, whose primary role is in guiding action, and explanation, which leads to understanding. He emphasizes that some scientific explanations are causal, but others are not: many scientific explanations appeal to laws, but many do not. He illustrates by an intriguing set of examples: smoke detectors, measurements of the Hubble constant, and the Game of Life.

17.2.1 Causation and Explanation I very much applaud the argument relating to a smoke detector: a mechanistic explanation based in its structure gives a causal explanation. In Aristotelian terms, this is a formal cause (Sect. 17.1.1). One has an explanation in terms of mechanisms that are enabled by the underlying laws (Gillett 2007). In this case their operation is as it is because they were designed that way (Simon 2019). The Final Cause is to save life. Explanation After quoting views of explanation that include or exclude laws on the one hand and causation on the other, Healey explains his pragmatist position: As a pragmatist I see here a case in which explanation has multiple roles in science that may be played by different actors. If this is right, we should not seek a unified theory of scientific explanation, but an account of a variety of explanatory tasks and a corresponding variety of kinds of scientific explanation best suited to accomplish these.

The four kinds of Aristotelian causation give multiple kinds of explanation, as he desires. In particular an Effective Theory as characterised by Castellani (2002) occurs at each emergent level as an Efficient Law explaining the dynamics at that level. In effect this endorses the view in Luu and Meißner (2019) that all the tested laws of physics are Effective Theories, of Noble (2012) that all emergent biological levels are equally fundamental, and of Ellis (2020b) that generically each Effective Theory ETL at an emergent level L in physics, engineering, and biology is equally causally effective. He proposes the importance of unifying explanations which connecting otherwise separate items or branches of scientific knowledge, thereby both promoting economy of thought and strengthening the evidence supporting one or more hypotheses by adding links to newly relevant data. Indeed so. A key point here is that a number of the Higher Level Organising Principles discussed in Sect. 17.1.5 recur at different emergent levels, thereby arguably providing one kind of such unifying explanation. An example is homeostasis.

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17.2.2 Laws Laws apply across many contexts to determine how generic patterns apply in particular situations. From his pragmatic viewpoint, Healey regards laws as providing science with an epistemic infrastructure, not a metaphysical superstructure. By contrast, I regard them as providing a metaphysical structure because they determine what emergent levels exist (Ellis and Gabriel 2020) This leads to an important statement: Law statements [license] reliable inferences that connect not only singular statements but also other law statements and, through them, different theories and branches of science. To play this role a law statement need be neither universal nor even true. But endorsement of a law-statement commits one to its general reliability in an acknowledged domain of applicability (its scope).

The latter point is very important. It is common now in physics to ignore the fact that some theories, e.g. quantum theory, have limited scope (Ellis 2012). Healey gives nice examples of how laws are used to provide scientific explanations in various contexts, and to standardise fundamental constants.

17.2.3 Emergence and the Life World Healey uses Conway’s Game of Life as an example of emergence. Thus “A glider .. may be taken as an example of an emergent object, and its shape and location as examples of emergent properties of that object”. This is a case of abstract causation, and does not in my view throw any light on the nature of life or biological evolution, I have never found the Game of Life a useful example in considering biological emergence. There are far more interesting studies relating abstract causation to biology, such as Turing (1952) on the chemical basis of morphogenesis, Kim et al. (2014) on the fission yeast cell cycle regulatory network, and Walker et al. (2016) on the informational architecture of the cell. In each case abstract models provide convincing representations of real biological processes. In terms of investigating abstract causation per se, I find much more useful investigating issues such as how can symbolism and writing can usefully represent objects, actions, and meaning (Deacon 1997).

17.2.4 Downward Causation As Healey points out, before one can talk of downward causation one needs layering of reality into levels. After citing (Woodward 2015) against Kim’s arguments, he gives the game of life as an example, which as stated above I personally do not find exciting. However he then gives an excellent example of downward causation:

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depressing a key on a computer keyboard to produce a symbol on the screen. Tracing the steps by which that happens makes clear that downward causation is indeed taking place in the hierarchical structure of the computer (Tanenbaum 2006). This example by itself suffices to act as a proof by example that downward causation does indeed take place.

17.2.5 Program Explanation However as regards the Game of Life, the idea of computer programs enters. Healey says “Someone might claim that the real cause of a micro- or macro-property of the life-world is the program implementing that run” Certainly I would agree with that. One can experimentally show this is the case: run a different program and different outcomes occur (load a chess program and the computer will play chess instead, for instance). He rejects this because “[A]s a set of instructions, a program is an abstract object like a number or string of symbols, and abstract objects have no causal powers”. In my opinion, the conclusion is precisely the opposite: this shows that abstract objects such as algorithms (Knuth and Donald 1973) do indeed have causal powers (Sect. 17.1.1). They of course have to be realised in order that such causal powers are effective, but when a computer runs it is the algorithms that are contained in the programs that decide what happens and hence change outcomes in the real world. Computer programs and their associated data have genuine causal power (MacCormick 2011) through a computational process described by Abelson and Sussman as follows (Abelson et al. 1996, p. 1): Computational processes are abstract beings that inhabit computers. As they evolve, processes manipulate other abstract things called data. The evolution of a process is directed by a pattern of rules called a program. In effect, we conjure spirits of the computer with our spells. A computational process is indeed much like a sorcerer’s idea of a spirit. It cannot be seen or touched. It is not composed of matter at all. However it is very real. It can perform intellectual work. It can answer questions. It can affect the world by disbursing money at a bank or by controlling a robot arm in a factory.

His argument (“abstract objects have no causal powers”) is an a priori philosophical assumption which is shown to be wrong by his own example. When he says “Here, as elsewhere, there may be program explanations, but the program itself is not a causally relevant factor in the explanation: at most it directs attention to the existence of causally relevant factors, though perhaps without specifying what they are (at least at the micro-level) I think he is simply wrong. The program is certainly a causally relevant factor. How it relates to the microlevel that realise it is explained in detail in Ellis and Drossel (2019): the causally relevant factors at the micro level are electron flows in transistors. Which electron flows take place when is controlled by the sequential reading of code in the program at a high level. It’s a clear case of downward causation from the abstract (Abelson et al. 1996) to the electronic level via the hierarchical structure of digital computers (Tanenbaum 2006).

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17.2.6 The Mind Healey accepts that downward causation takes place in the brain, but similarly to the previous case, queries if thoughts and plans have causal powers. Firstly in effect he queries the interlevel causal loop which makes this possible, whereas in agreement with Mossio and Moreno (2010); Mossio (2013) I regard such interlevel relations as essential to causal closure (Ellis 2020b). The neurons enable the thoughts to occur, and the specific thoughts being entertained activate specific re-entrant resonant neural connections that realise these thoughts. Secondly he states “One can certainly appeal to plans, models and theories in an explanation of the existence and features of a physical object like an Airbus (Ellis’s example). But the explanation will not be causal: these abstracta do not cause it to exist, though physical representations of them clearly do play a causal role in the construction of the relevant physical object.” Again I believe he is wrong. The logic of abstract mathematical and physical argumentation, based for example in Bernoulli’s equation for fluid flow and the mathematics of feedback control systems, decides which thoughts will occur when designing the Airbus (what the shape of the wing will be, what kinds of electronics will be used, and so on). Deductive causation (Ellis and Kopel 2019) is without doubt causally effective, because (assisted by computer models) it results in an aircraft that flies. The underlying physics (electron and ion flows in axons) is entrained to fulfill these higher level purposes by time dependent constraints (see above, in Chapter 8). Do the plans and theories play a causal role? Of course they do—at the psychological level. They are represented via electron flows in neural networks at a lower level. Each of these levels is equally causally effective (Noble 2012). What decides what thoughts are encoded in those electron flows? The logic that they represent. If one does not believe this then one believes in some kind of magic whereby the plane meets its design specifications without these specifications having any influence on the process of design and manufacture. This power of abstract relations to shape physical outcomes via the neural network structure of the brain is explained in a remarkable book: Plato’s Camera by Paul Churchland (Churchland 2013). Hence despite Healey’s criticisms, I stand by the description of the causal power of the brain explicated in Ellis (2016). Healey ends by stating “For a naturalist, there are two senses in which physics underlies not only the mind but every phenomenon studied by science. The first sense is just that if there were no physical things there would be no minds: naturalism precludes disembodied spirits. This raises the issue of why physical things exist. Inter alia, life only exists because of the downward causation associated with natural selection (Campbell 1974). Second he states Physics claims the entire natural world as its domain of applicability, unlike other sciences which focus on phenomena that manifest themselves only in special circumstances— chemistry only where in space-time there are atoms and molecules, biology only where there is life, neurophysiology only where there organisms with brains or at least central nervous systems, psychology only where there are agents with mental states. But each science retains a certain autonomy for its laws and explanations (whether or not these are

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causal): different specialized concepts prove useful in understanding and intervening in the physical world in different domains. Phenomena (weakly) emerge that are best described and understood using these specialized concepts.

This is a nice explanation of why in a sense physics is indeed a more foundational subject than the others. Here he is correctly stating the existence of Effective Theories ETL at each level L with its own concepts and variables. But he slips in with no justification whatever the statement that this is all weak emergence. Furthermore physics is not one unified subject. It is a conglomerate of theories each with their own domain of applicability, and in fact not solidly tied together. Perhaps he has in mind the alleged Theory of Everything (TOE), which may or my not exist; if it does, we do not know what it is. In fact all tested physics theories are effective theories, not fundamental in the sense of a TOE (Luu and Meißner 2019). Yes the Standard Model of Particle physics does apply to everything. But it is not a TOE, it is an effective theory, and for example solid state physics is strongly emergent (Ellis 2020a)—as is the Second Law of Thermodynamics, because of the Arrow of Time issue (Ellis and Drossel 2020). All real world applications of physics also involve theories (solid state physics, acoustics, quantum optics, plasma physics, astrophysics, etc) which manifest themselves only in specific circumstances. And when applied in such cases, it is not really the fundamental theory that is used (see Leggett (1992), and Drossel in this volume). Rather a pragmatic adaptation of the principles of the fundamental theory are used, which can be reasonably justified after the fact. They provide the relevant effective theory that can be used in practice at each level.

17.3 Top-Down Causation Without Levels: Jan Voosholz This paper makes an interesting contribution by criticizing the levels view of nature that underlies my work, but nevertheless offers an alternative which provides a foundation that validates the work.

17.3.1 The Level-Picture of Nature My view on the Modular Hierarchical Structure (MHS) of emergent entities in biology and engineering contexts (Ellis 2020a) is based in profound arguments that this is the only way that true complexity can emerge in functional terms (Pattee 1973; Ahl and Allen 1999). The importance of modularity was argued convincingly by Herbert Simon in the case of artificial systems in general (Simon 2019) and developed in depth by Grady Booch in the case of computer software (Booch 2006), setting forth in Chap. 2 (pp. 41–65) principles that apply to all complex systems: abstraction, encapsulation,

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modularity, hierarchy. The hierarchical aspect of computers, leading to a tower of virtual machines, is developed in detail in Tanenbaum (2006). The hierarchy in the case of biology is taken for granted in Noble (2012), and in standard textbooks such as (Campbell and Reece 2008, pp. 4–5) and (Randall et al. 2002, p. 6). In the case of the brain it is presented by Scott (1999) and Churchland and Sejnowski (2016). These two principles work together, as explained in Booch (2006), § 1.2: Not only are complex systems hierarchic, but the levels of this hierarchy represent different levels of abstraction, each built upon the other, and each understandable by itself. At each level of abstraction we find devices that collaborate to provide services to higher levels.

He gives the examples of the structures of plants and animals, the structure of matter, and the structure of social institutions However Voosholz asks, “Why should there be distinct levels in this ontologically robust way? Why not speak of a gradient of complexity (or rather multiple gradients of complexity) in any direction where natural systems form wholes and parts without clear borders?”

17.3.2 The Main Points It is certainly legitimate to make this query. The answer is contextually dependent. • In physics there are certain well defined levels: nuclei, atoms, molecules, crystals for example, each with their own physical scale and descriptive concepts, and correspondingly physics is split into theories that deal with different levels: particle physics, nuclear physics, atomic physics, solid state physics, astrophysics, etc. • In biology it may be less clear but again there are certain well defined levels: biomolecules, cellular components, cells, physiological systems, organisms, populations, species (Campbell and Reece 2008). • In the case of digital computers, levels are very well defined because they have been designed to make this so (Tanenbaum 2006). There is a hierarchy of virtual machines, each with their own language and variable structure. The levels are related to each other via compilers or interpreters. • In general networks, the modular hierarchy may not be so clearly defined. This is discussed in Ravasz et al. (2002), Papin et al. (2004), and Wuchty et al. (2006). • However one can certainly often split them into finer levels, depending on the issue of interest, for example in the case of astronomical entities one may or may not be interested in the distribution of sizes of planets as opposed to thinking of planets as a category as a whole. In the case of digital computer structure, one can for example give a more detailed level analysis of the levels from electrons to crystals (Ellis and Drossel 2019) than is given in Ellis (2016). Effective Laws and Levels The key issue is, If we propose a specific level L exists ontologically, is there a valid Effective Theory ETL applicable at that level, where ‘valid’ means it makes testable predictions that have been confirmed? Here

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following Ellis (2020a) one can characterise an Effective Theory ETL (aL ) valid at some level L as follows: An Effective Theory ETL (aL ) at an emergent level L is a reliable relation between initial conditions described by effective variables vL ∈ L and outcomes oL ∈ L: ETL (aL ) : vL ∈ L → ETL (aL )[vL ] = oL ∈ L

(17.3)

in a reliable way, where aL are parameters of the relation, and ETL (aL ) may be an exact or statistical law. The parameters aL may be vectorial or tensorial.

Now one can invert this: I propose that An ontologically meaningful level exists if and only if there is such an effective theory ETL (aL ). Determining that relation is in effect epistemology, but its existence indicates the underlying ontology (Ellis and Gabriel 2020).

A key point is that ETL (aL ) operates on the variables vL associated with that level. In many cases (particle spin, molecular structure, and so on) they will be uniquely associated with that level. In some cases (mass, momentum, energy, and so on) the concept will transcend levels but the variable appropriate to a specific level L will be associated with an averaging scale SL (Batchelor 2000). In the latter case, different levels can be related by Coarse Graining (Penrose 2006); otherwise, this is not possible (Ellis 2012).

17.3.3 The Eight Points on Levels, and Responses Voosholz lists my assumptions about levels as follows (L1 to L8), and then queries L6 and hence L1. From that queries about the rest follow. Here I summarise his view of my proposals (Items L1..L8), his proposed revisions of those proposals (Items A1..A8), and my responses (Items E1..E8). 1. L1 Levels are structures in nature and real in the sense of existing independently of our (or any) knowledge of them. A1 Levels are layers in the constitutional hierarchy of fully or partly concrete (meaning existing in spacetime) objects or systems and real in the sense of existing independently of our (or any) knowledge of them. There is an infinite number of parallel and intersecting hierarchies for all such entities and therefore infinitely many levels (from now on designated as CH-levels, for “constitutional hierarchy”). E1 The first part is fine. The second part is problematic firstly because infinity is a mathematical rather than physical concept: our models of reality may use the concept, but it does not occur anywhere in nature (Ellis et al. 2018). I pick up the response to infinity in E6 below. But the key issue is as noted above: most of the variables at higher levels are simply different from those at lower levels. There is no continuous transition between them.

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2. L2 Any fully or partly concrete (meaning: existing in spacetime) object or system is situated on a certain level in nature and behaves according to a set of principles and laws effective on this level, which can possibly be discovered by science. A2 Any fully or partly concrete entity can appear in a context with its own local ontology and behaves according to a set of principles and laws effective in that context, which can potentially be discovered by science. E2 Indeed. This is the statement that an effective theory ETL (a) holds at each emergent level L (see (17.3)). 3. L3 Levels are ordered by the degree of complexity of the objects and systems that are found on them. It is unclear whether there is either a top or a bottom level (or which ones they would be). A3 CH-Levels are ordered by the part-whole relationships of the hierarchy to which they belong. It is unclear if there is either a top or a bottom CH-level (or also which ones that would be) in any hierarchy. All fully or partly concrete entities in and across contexts are ordered by their degree of complexity, their properties and their relations with one another, which are all subjects of the local ontology of a context or of an intersectional ontology of an intersection of many contexts. E3 I ordered levels not by complexity but by scale (on the physics side and the biology side up to the level of organisms) and at higher biology levels, according to part-whole relationships of control. This only approximately corresponds to complexity. If one for example characterizes such complexity by the number of variables involved and the number of interactions between them, the cellular and molecular levels (Alberts et al. 2007; Watson et al. 2013; Berridge 2014) are at least as complex as the emergent physiological levels (Randall et al. 2002; Rhoades and Pflanzer 1989). 4. L4 To describe different levels (and the associated objects, systems, structures, laws and principles), we need to deploy different scientific languages and different variables suited to any one level. This results in the disunity of sciences, where for every level we have one (or more) science studying it. A4 To describe different local or intersectional ontologies (and the associated entities they contain—the types of objects, systems, structures, properties, relations, laws and principles) we need to deploy different scientific languages, scales and variables suited to any one local or intersectional ontology. This results in a disunity of sciences where for every local or intersectional ontology we have one (or more) science studying it. It is important to note that, depending on the local ontology, scales and variables can be structures in SV-levels (for “scale and variable”, they do not have to be structured in this way), which are epistemic and should not be confused with CH-levels. E4 This corresponds to the idea that there is a different Effective Theory ETL at each level L, indeed that is what characterizes levels. As stated above, if this is done carefully, epistemic and ontological levels agree. 5. L5 For any system S on level n we can identify parts of it either on level n or n−1 . For any object O, located on level n, considered as a whole, there are proper parts of it either on level n or n−1 .

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A5 For any system S in context n we can identify parts of it either in context n or an intersection i of different contexts, constituting the next lower level in the constitutional hierarchy of S. For any concrete object O, located in context n, considered as a whole, there are proper parts of it either in context n or contextintersection i. E5 Fine. 6. L6 Levels are distinct entities with clear boundaries, which are marked by emergent objects and systems with corresponding properties, structures, principles, laws, and variables, which can neither be found at, nor explained by, nor fully accounted for by the next lower or higher level. A6 CH-Levels are marked by emergent objects and systems with corresponding properties, structures, principles, laws, and assigned variables which can neither be found at, nor explained by, nor fully accounted for by the next lower or higher CH-levels. E6 Indeed. But what about the infinities mentioned in A1? The resolution lies in my careful definition (17.3) above (generalising that in Ellis (2020a)) and Ellis (2020b)). The point is that the definition ETL (aL ) incorporates the parameter set aL . What characterizes the level L is the functional form of ETL (aL ), and there is not a meaningfully infinity set of possible functional forms. The values of the parameters play a key role in outcomes, for example allowing bifurcations to occur in dynamical systems (Arnold 1989); but that is still within the dynamics of the effective theory that defines the level L. In summary, there can be an infinity but its not in the levels, its in the parameters that define dynamical outcomes at specific levels.3 The key point An effective theory ETL (aL ) is characterised by its functional form, which depends on the continuous parameter aL . It is not a one-parameter set of theories, it is a theory dependent on a parameter. It is such theories that determine which levels L exist.

7. L7 For any level n (apart from a theoretically existing bottom level) there exists exactly one lower level n−1 , which constitutes the complete set of basic parts for all systems and objects on n. In this sense the lowest physical levels are the basis for everything else in nature. A7 For any CH-level l (apart from a theoretically existing bottom-level) in any hierarchy Hs of a physical system S there exists a finite number of neighbouring lower CH-levels l −1a ; l −1b ; . . . , which constitute the complete set of basic parts for all (sub)systems and objects on l. In this sense, the lowest physical CH-levels

3 The

parameters can be continuous variables, hence in effect hiding an infinity in that continuity, and this perhaps is what underlies Voosholz’s concern. But this infinity is physically meaningless (Ellis et al. 2018; Del Santo and Gisin 2019); in the real world only a finite number of decimal places count. There can in principle be an infinity of parameters, for example f (x) = an x −n , but again firstly it is this functional form that defines the level, not the number of parameters or their values; and secondly in any case only a finite number of them matter in physical terms.

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in any constitutional hierarchy of concrete objects or systems are the basis for everything else in nature. E7 Actually there is no known and tested bottom-most level. Rather all levels, including physics levels, are effective levels (Luu and Meißner 2019; Ellis 2020b). 8. L8 For any level n (apart from a theoretically existing top-level) there exists one higher level n+1 , which might be branched. This means it is possible that different higher levels of complexity are constituted by the same lower levels. This is the case for levels 4 and 5, where 4—the level described by atomic physics—forms the basis for level 5, on which the branch of life departs from the branch of inanimate nature, as represented in the sciences of chemistry and physical chemistry. 1 ; S 2 ; . . . of A8 It is possible that many different lower CH-level states Sl1 l1 system S constitute S with exactly the same properties in its context ns . E8 I think this is just the key issue of multiple realisability, with which I certainly agree.

17.3.4 Arguments for and Against the Level-Picture Voosholz gives arguments for and against the levels picture. Arguments for the Level Picture 1. The argument from genuine complexity, principles and laws As stated above, I rest my case on the existence of different effective theories and variables at each level, with a key set of levels being those shown in Ellis (2016) for example. “It does not prove that these particular constitutional hierarchies can all be integrated into the general branching hierarchy Ellis shows us in table 1 or 2, where all systems fall into one of ten levels. Indeed. I stand by those particular levels as being physically meaningful. But they can certainly be divided into finer levels or split into different branches that have physical meaning and are epistemologically useful in particular studies. If for example one is a cell biologist, one splits the cell level into sublevels; if one is a solid state physicist, one will use different ones. 2. The argument from the disunity of scientific language This is essentially the same as the previous because each effective law has its own variables and vocabulary that identify it as such. As explained above, I do not see how one can have an infinity of meaningful variables and associated laws. 3. The local ontologies argument This is the position I support on the basis of the idea of effective laws at each level as formalized above and on Ellis (2020a) and Ellis (2020b). These ideas have been developed since I wrote my book (Ellis 2016) and so take the argument further than the text Voosholz is responding to. Arguments Against the Levels Picture In continuing the argument, two items are raised.

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1. Infinite hierarchies Here we have, with interesting examples, “Even for a small local ontology with a limited set of entities, one has to deal with vast number of levels”. Agreed. We deal with a smaller number for convenience, and it works— the coarser graining is real, just as the finer one is. But there is a world of difference between ‘a vast number of levels’ and an infinity of levels (Ellis et al. 2018). They are simply quite distinct categories. The first is physical, the second is not. 2. Against distinctness The criticism is that the same lower level structure can occur in many different higher level contexts, playing different roles in those different contexts: Yet some entities seem to appear simultaneously in different ontologies: Electrons show up in explanations in material science, particle physics, and physiology (in explanations of neural activity for instance); N2 H + -molecules are referenced by astronomy and chemistry alike; the Google search algorithm appears in sociology and computer science . . . [It] is a proper object of study for sociology and computer science alike, as is fear for physiology, psychology and political science, or water in chemistry, geology and solar system science. All of these appear as proper entities in different ontologies, i.e. target systems in different sciences, not only as parts or subsystems.

This is an interesting issue, and interesting examples. Yes indeed these variables can play those multiple roles in different contexts, and one can validly study those different roles without engaging with all the other roles they can play. Does this argue against a levels explanation with say 100 levels? No it does not. Rather there is an upward chain: each of these variables plays a role at higher levels because if vL plays a role at level L, it underlies (in a contextual way) what happens at level L+1 and so on, chaining all the way up. The fact that it is playing such a role may get hidden, but it is still doing so. Multiple realisability means that the specific details at the lower level do not matter, its equivalence classes that are the causal element (Sect. 2.4 in Chap. 13).

17.3.5 Top-Down Causation Without Levels Overall, this is a thoughtful and stimulating paper. With small modifications to what I have written, the overall idea of downward causation and related strong emergence are still solid, as Voshoolz argues. Our main disagreement is about infinities, which I deal with above.

17.4 Causation as a High-Level Affair: Simon Friederich and Sach Mukherjee This is an excellent article that fits in well with my world view. They argue that “higher level causation is a legitimate and useful notion whereas causation

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at a more fundamental physical micro-level may be either derivative or hypersensitive with respect to changes in background conditions.” Perfect! This is a classic statement of both strong emergence and downward causation.

17.4.1 Cause-Effect Relations The strength of the article is that it is rooted in everyday reality, rather than perpetuating the myth of physics in isolation that underlies typical causal exclusion arguments. In effect, the theme of the paper is, Real world causation: On taking the interventionist account of causation seriously (Woodward 2005), the causal exclusion argument gets inverted.

They give the example of smoking and lung cancer, a well established effective law at the physiological level (Pearl and Mackenzie 2018): Inasmuch as we can characterize the conditions in which “Smoking causes lung cancer obtains”, we do so in higher-level language. Here,“higher level” means relative to the fundamental micro-physical level: note that even the most detailed current explanation of a phenomenon such as the carcinogenicity of cigarette smoke (in the language of molecular biology, biochemistry or biophysics) would be very high level relative to quantum field theory (say). Hence, the very idea of robust causal relations between truly micro-physical variables P1 and P2 are in a sense parasitic on our understanding of a robust higher level causal relation.

The point here is that there is a mass of evidence that that is indeed a causal law at the physiological level. Actually it crosses several levels: causal closure in this case is a multilevel affair (Ellis 2020b) that must extended from the organism (whole individual) level, which is the lowest where one can characterise the concept “He/she is smoking a cigarette”, down to the cellular level and the underlying molecular level, where gene regulation takes place. There is no way it can be characterised at any of the lower levels per se. But it then must reach down to the underlying proton/electron level, for that is where the dynamics of gene regulation is enabled in physics terms. And that link occurs via time dependent constraints due to changes in molecular conformations (Ellis and Kopel 2019)

17.4.2 Intervention and Causation in Complex High-Level Systems This leads to the interventionism-based reply to the causal exclusion argument, defending the compatibility between higher-level causation and non-reductive physicalism, as set out by Shapiro and Sober (2012) and Woodward (2015). Basically one assumes that one can intervene at the higher level, a process which is known to be possible and can only be described in higher level terms. There is an effective

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theory ETLM at the higher level LM characterised by the variables appropriate to that theory (in the case at hand, the concept of smoking a cigarette). If it supervenes on a lower level LM then whether or not we know what that lower level theory is and what the appropriate variables at that level are, the higher level must set the context for the dynamics of those lower level variables so that this outcome arises at the higher level. This applies equally to the molecular biology level where gene regulation occurs and the quantum electrodynamic level where interactions between electrons and protons occurs. The causal relations on the different levels can coexist without any problems, because this is manifestly what happens in practice. Downward causation takes place (and yes it is causation) from the cigarette smoking level (“cigarette” cannot be identified as a relevant variable at any lower level) to each of these lower levels. The multiple realisability of higher level relations at lower levels means there are billions of ways the higher level causal relation can be raised at lower levels (Chap. 13, Sect. 2.4, and see Eq. (2) there). Upward emergence, downward realisation, and horizontal causation all take place (Ellis 2016) in a synchronised way. Actually downward realisation is a causal relation too (stop smoking, and gene regulation changes).

17.4.3 Sensitive and Insensitive Causation This is an interesting aspect of their argument. The distinction between sensitive and insensitive causation appeals to the background condition with respect to which causal relations obtain. A causal relation is sensitive if even rather small changes in background conditions disrupt it. Otherwise it is insensitive.

This is an important aspect of downward causation. It relates to the issue of all aspects that underlie everyday life that can be taken for granted precisely because they do not change, or if they do, it is unimportant. However there is never any guarantee that the environment will not change so as to cause drastic effects. This can happen in two ways. Firstly, chaotic dynamic systems (Arnold 1989) associated with strange attractors can make physical outcomes unpredictable in practice, as is the case with weather (Lorenz 1969). However there is of course a problem with the fabled butterfly wing flapping in Brazil that alters weather here: there is more than one butterfly in Brazil. By and large their effects will tend to cancel out (as in the Feynman path integral derivation of classical outcomes). But for example the Solar System is a chaotic dynamical system (Todoroviˆc et al. 2020) because it is an N-body gravitational system Secondly, Black Swan events (Taleb 2010) can occur, and destroy our carefully planned futures, as in the case of the Coronavirus pandemic (Ellis 2020b).

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17.4.4 Hypersensitive Causation in Fundamental Physics Given that understanding, the heading of Sect. 4 (“Causation in fundamental physics tends to be (hyper-) sensitive”) at first looks rather implausible, until it becomes clear it is referring to the very real context of the experiments that underlie our understanding of particle physics and general relativity. Then it makes perfect sense. They give two important examples. First, detection of the Higgs particle at the Large Hadron Collider (LHC), where the background conditions potentially affecting the detection events must be so carefully controlled that the trajectories of the decay products are accurately predictable, and other potential causes of the detection events can be excluded. Second, gravitational wave detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) where one has enormously expensive vibration isolation to stabilize distances between two mirrors so as to allow detection of a change in distance between LIGO’s mirrors on the order of 10−19 m when a gravitational wave passes. Top-end physics experiments are very sensitive detectors of downward causation.

17.4.5 Higher Level Causation The conclusion states it just right: The causal exclusion argument has it backwards. Causation, far from being confined to the physical micro-level comes into its own in particular in the higher-level sciences. .. the [lower level] variables P1 and P2 are usually not independently characterizable in practice and in that sense could even be regarded as in a way hypothetical.

This is based on an interventionist view of causation, and the fact of multiple realisability of lower level states. One cannot in general determine what specific lower level state will be realised, but only an equivalence class of billions of them. This is all one can achieve in normal circumstances. There is however an interesting question one can ask: Are there any cases where one can in fact act downwards on specific microlevel states? The answer is yes: optical trapping and optical tweezers (Ashkin 1970) is about this. Single photon and ion control is possible (Hinds and Blatt 2012). And that requires just as much sensitivity—isolation from noise and heat—as the cases mentioned by the authors. But this is highly exceptional, only occurring in extraordinarily carefully controlled laboratory contexts. In terms of causal closure, the real world situation is the opposite than usually stated. The authors make this case very strongly, and conclude that High-energy particle physics experiments can be seen as giant background conditioncontrolling machines that allow one to extract precious bits of information about the properties of the colliding and decaying particles as well as of the decay products. There are, we conclude, specific circumstances in which applying causal reasoning in fundamental

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physics is not only possible but in fact highly useful. . Outside of those circumstances, causation remains a distinctly high-level affair.

Indeed so. Causal reasoning is back (Pearl and Mackenzie 2018), and this paper shows why that is important in terms of the issues of emergence and downward causation.

17.5 Models of Downward Causation: Max Kistler Kistler argues for downward causation in the context of the idea that the mind influences the physical world, which is often claimed to be incompatible with physicalism. He does so on the basis of frameworks of phase space and of structural equations. He shows that the Exclusion principle is false in models constructed within both frameworks, and explains why downward causal influence is not only conceivable and compatible with the ‘Closure’ principle but in fact occurs in practice.

17.5.1 Causal Closure and Physicalism He explains that physicalism is the doctrine according to which (a) Everything is either physical or exclusively composed of physical parts, (b) All properties of all objects supervene on the physical properties of those objects. The key question arises whether mental events can influence physical events. He gives good examples of such causation. First, thoughts about the relation of the mind to the body indirectly causing words representing those thoughts to appear on the screen of a computer. Second, behavioral therapy of patients suffering from OCD results in decreased rates of glucose metabolism in the head of the right caudate nucleus of their brains. Given these examples which strongly suggest that such causation does indeed occur, the aim is to evaluate the argument in Kim (1998) against downward causation, which would preclude this.

17.5.2 Downward Causation in the Framework of Phase Space First, Kistler looks at the framework of dynamical systems theory as a way of thinking about causal influences, through looking at trajectories of physical systems in state space. But he explains that we want more:

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We want to know, not only what was the trajectory .. but also what made her raise her arm at t1 , or, in other words, what fact .. was causally responsible for the fact that she raised her arm at t1 . . . The decision of a person to raise her arm causes her arm to rise. This is downward causation in the hierarchical sense, because the cause is psychological and the effect physiological

One might suggest this relates to Aristotle’s different types of causation (Falcon 2006), as developed by Russell Akoff (see Chaps. 1 and 8), as well as to van Gulick’s question: “Who’s in charge here? And who’s doing all the work??’ (Van Gulick 1995). Kistler nicely formalizes this in terms of regions of phase spaces, which I believe corresponds to the idea of an equivalence class of lower level states that correspond to a higher level state (discussed in Sect. 2.3 in Chap. 13). The projective state corresponds to the basin of attraction (Arnold 1989). The conclusion is that “there can be situations where both a physical (or physiological) and a psychological causal explanation is available for some physiological fact, and where the psychological (downward) causal explanation is the more relevant one” (which agrees with the conclusion of the previous chapter). That is very satisfactory, and corresponds to Ackoff’s view of how complex systems work (Ackoff 1999). Causation has multiple dimensions that are all valid at the same time. Each serves a different explanatory role. Each corresponds to a different Effective Theory EFL at a different level L (Ellis 2020a) (see Eq.(17.3) above). However one should also note that the physicalism postulate “(a) Everything is either physical or exclusively composed of physical parts” has in effect been denied, because of the acceptance of the psychological explanation. Thoughts and plans are not physical.

17.5.3 Downward Causation in the Context of Structural Equations This section discusses the method of representing the search for causes by models using structural equations (Pearl 2009). From my viewpoint, it is the way that one looks for the Effective Theories EFL at each level L (see (17.3) as just discussed). Kistler nicely lays out the formal structure underlying this, depending on the distinction between Endogenous variables (with their values determined by other variables within the model), and Exogenous variables with values determined independently of other variables of the system (this parallels Friston’s characterisation of a Markov Blanket between internal and external variables (Friston 2010, 2012). He then shows how this dynamic must therefore represent a downward influence from a psychological predicate to a physiological one, for example at the neuron level. In essence, this is because of the multiple realisability of the higher level state by lower level states (discussed further in Sect. 2.3 of Chap. 13). In the present argument, the interesting move is the separation of structural equations into those representing the non-causal dependence relation between a psychological property

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and the underlying neurological properties, and the causal dependence between the decision and bodily movement. One attains explanations at multiple levels. In his model, not only is there a downward causal influence from the decision, but it is more relevant to mention this downward causal influence in a causal explanation of the resultant motion of the arm than to mention the parallel same level neural cause because the downward causal influence is specific whereas the same-level influence is not.

17.5.4 Rejection of Causal Closure at the Physics Level Kistler develops an argument for rejection of physical causal closure, and proposes a better view based in the view that while there is indeed a physical cause at time t, only the mental cause is specific (or proportional). Thus this is why it is in general more appropriate to mention the mental cause in a causal explanation of an event of raising ones arms to a specific level at a specific speed. While this is indeed correct, I think it is useful to put this argument in a larger context: namely that causal closure in real world situations is in fact an interlevel affair involving many higher levels than the physical, as is discussed in depth in Ellis (2020b). One can to be sure determine an effective theory ETL at any level, including the underlying physical level, but one cannot do that by involving only causation at that level. On the contrary, it involves the mental level at which the experimenter thinks of and analyses the experiment, and the social level that produces the equipment needed to carry it out. Causal closure only occurs when one takes all these higher levels into account. The same is true in terms of their outcomes in real world contexts, such as gene regulatory processes occurring in neurons while a person is thinking (Kandel 1998, 2001) (enabled by the underlying physics via time dependent constraints in the Hamiltonian (Ellis and Kopel 2019)). Hence the Kim account of causal closure purely at the physics level is a myth in either engineering or biological contexts. In any case, at which physics level is he claiming such alleged causal closure occurs? The quantum physics level involving the Schrödinger equation, in the case of the molecular quantum mechanics underlying life (Atkins and Friedman 2011)? But that supervenes on the level of Quantum Field Theory and the Standard Model of Particle (SMPP) physics (Oerter 2005). This is taken as the effective base level by many physicists. But that is also only an effective level, it is not the base level (Luu and Meißner 2019). The alleged causal closure of physics at either level falls apart for this reason too: each supervenes on an unknown Theory of Everything (Weinberg 1994), so if Kim is right, neither of them is causally complete. His theory is not based on any known bottom level physics theory. What actually makes sense is that each emergent level L is equally causally effective (Noble (2012), Ellis (2020b) and Chap. 8).

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17.5.5 Top-Down Determination Relations? Kistler consider Gillett’s synchronic top-down determination of properties of parts of composed objects by properties of those whole objects (Gillett 2017, 2019) and decides that his version of downward causation does not need such “machretic” relations. However, from my viewpoint, machresis is a crucial process of determination of properties of lower level entities in biology. I agree it does not occur in all cases of downward causation, but there are many cases in biology where it does indeed occur and is important. The classic case is developmental biology (Wolpert 2002; Carroll 2005; Gilbert 2006; Gilbert and Epel 2009) where pluripotent cells get adapted to the task they need to fulfill according to their position in the developing embryo. This is clearly a downward process mediated by positional indicators (morphogens) that determines what kinds of cells they become, for example via HOX genes. Note however that it is not a synchronic process: it takes place over developmental time. Furthermore, Kistler himself gives an example in footnote 4, where he says “In (Kistler 2017) I give an example from physics: Heating (i.e. a modification of a macroscopic property) of piece of Nickel modifies the properties of microscopic parts of that piece of Nickel." That is a great example. It does indeed occur (Ellis and Gabriel 2020) and is important in some contexts. It can be regarded as Material Causation (Chap. 1).

17.5.6 Emergence and Reductionism in Society Finally, there are significant resources not mentioned in the mainstream literature on reductionism and emergence (e.g. (Gibb et al. 2019)) that are relevant to Kistler’s article. First, there are studies on downward causation and emergence in the case of society and the individual (Berger 1963; Berger and Luckmann 1991),4 (Donald 2001) and between the individuals and institutions in society (Elder-Vass 2010, 2012). Secondly, there is the associated social neuroscience underlying these relations in terms of how social interactions shape and are shaped by neural structure (Cacioppo et al. 2002). Thirdly, there is a very large literature from management studies that is dealing with the hard edge of this relationship: how these interlevel relationships work out in terms of making organisations function. Here I will just mention two that make the interlevel relationships explicit. First there is Stafford Beer, who in his book Brain of the Firm (Beer 1972) explicitly explores the modular hierarchical structures of

4 The

latter is one of the most cited papers in sociology. It has over 62,000 citations.

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organisations, and the interplay between upward and downward causation in them. He emphasizes the informational and control issues that come into play, particularly Ross Ashby’s Law of Requisite Variety, and the importance of decentralising control as much as possible. Then there is Russell Ackoff who explicitly explores issues of reductionism and emergence in the case of organisations in a deeply thought out way (Ackoff 1999). He discusses the relation between analysis, reductionism, determinism, and mechanism on pages 8–12. On page 16 he explains the essential properties of a system: “The essential properties of a system as a whole derive from the interactions of its parts, not their actions taken separately. Therefore, when a system is taken apart, it loses its essential properties. Because of this—and this is the critical point—a system is a whole that cannot be understood by analysis” [that is, by understanding its parts.] “Synthesis, or putting things together, is the key to systems thinking.”

He continues to explain that systems thinking always involves teleology (pages 22– 24): systems thinkers focus on teleological (purposeful and goal-seeking) systems. This covers biology (Hartwell et al. 1999) and digital computers (Tanenbaum 2006) in particular, but also organisations. A key feature in all this is the system’s interaction with its environment. Finally, the really hard edge of this is the huge literature on control systems in engineering, and its underlying mathematical theory (Ogata and Yang 2002). Practitioners in chemical, electrical, and aeronautical engineering take downwards causation for granted—it is the core of their work—and will just laugh at anyone who denies its causal efficacy. Their daily work provides experimental confirmation par excellence. All of this depends of course on the brains underlying society, and the relation of the mind to the underlying neural structures that are discussed by Kistler and others, for example (Murphy and Brown 2007). The function and existence of society is possible only because of the resulting interlevel causal closure.

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