Reality And Its Structure: Essays In Fundamentality 0198755635, 9780198755630

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Reality and its Structure

OUP CORRECTED PROOF – FINAL, 6/4/2018, SPi

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Reality and its Structure Essays in Fundamentality

edited by

Ricki Bliss and Graham Priest

1

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Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © the several contributors 2018 The moral rights of the authors have been asserted First Edition published in 2018 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2017959735 ISBN 978–0–19–875563–0 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

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Contents List of Contributors 0. The Geography of Fundamentality: An Overview Ricki Bliss and Graham Priest

vii 1

Part I. The Hierarchy Thesis 1. Grounding Orthodoxy and the Layered Conception Gabriel Oak Rabin

37

2. Symmetric Dependence Elizabeth Barnes

50

3. Grounding and Reflexivity Ricki Bliss

70

4. Cosmic Loops Daniel Nolan

91

5. Metaphysical Interdependence, Epistemic Coherentism, and Holistic Explanation Naomi Thompson

107

6. Buddhist Dependence Graham Priest

126

7. Bicollective Ground: Towards a (Hyper)Graphic Account Jon Erling Litland

140

Part II. The Fundamentality Thesis 8. Indefinitely Descending Ground Einar Duenger Bohn

167

9. Inheritance Arguments for Fundamentality Kelly Trogdon

182

10. From Nature to Grounding Mark Jago

199

11. Grounding in Mathematical Structuralism John Wigglesworth

217

12. Fundamentality and Ontological Minimality Tuomas E. Tahko

237

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vi contents 13. The Structure of Physical Reality: Beyond Foundationalism Matteo Morganti

254

Part III. The Contingency and Consistency Theses 14. On Shaky Ground? Exploring the Contingent Fundamentality Thesis Nathan Wildman

275

15. Heidegger’s Grund: (Para-)Foundationalism Filippo Casati

291

Index of Names General Index

313 316

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List of Contributors Elizabeth Barnes University of Virginia Ricki Bliss Lehigh University Filippo Casati Kyoto University Einar Duenger Bohn University of Agder Mark Jago University of Nottingham Jon Erling Litland University of Texas at Austin Matteo Morganti University of Rome Tre Daniel Nolan University of Notre Dame Graham Priest The Graduate Center of the City University of New York, and the University of Melbourne Gabriel Oak Rabin New York University Abu Dhabi Tuomas E. Tahko University of Helsinki Naomi Thompson University of Southampton and University of Gothenburg Kelly Trogdon Virginia Tech John Wigglesworth University of Vienna Nathan Wildman University of Glasgow and Tilburg University

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0 The Geography of Fundamentality An Overview Ricki Bliss and Graham Priest

Reality is a rather large place. It contains protons, flamingos, economies, headaches, sentences, smiles, asteroids, crimes, and numbers, amongst very many other things. Much of the content of our reality appears to depend on other of its content. Economies, for example, appear to depend upon people and the way they behave, amongst other things. Some of the content of our reality also appears to be, in some significant sense, more important than other of its content. Whilst none of us would wish to deny the very important role that economies play in our lives, most of us would agree that without matter arranged certain ways in space, for example, there could be no economies in the first place. The reality that we happen to occupy is, in some important sense, a physical one. Accordingly, matter is afforded a special place in our story about it. Indeed, not only is matter accorded a special place in our ontology, but some from amongst its elements are also thought to be particularly important. Chairs and flamingos and people are made from parts, and those parts from further parts and so on—with most folks being of the view that at some point these dependence chains must terminate in absolutely basic, or simple, parts which themselves have no further parts. It is these basic parts, so the story goes, that give rise to everything else. The content of reality to which these parts give rise is arranged relatively neatly into layers: facts about economies and crimes reside at a higher level than facts about biological systems, which reside at a higher level than facts about chemical systems and so on. Or perhaps we might prefer to say that economic systems are further up the Great Chain of Being than ecosystems, which are further up the chain than carbon compounds.1 This picture, or something very much like it, looms large over contemporary analytic metaphysics: a picture according to which reality is hierarchically arranged with chains of entities ordered by relations of ground and/or ontological dependence terminating in something fundamental. 1

The Great Chain is normally taken as running downwards, with the ground at the top; we upend it here.

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 the geography of fundamentality: an overview The historical literature is also littered with what appear to be variations on this kind of view. Consider both Plato and Aristotle, for example. The former believed that everything was grounded in the Forms, with all of the Forms being ultimately grounded in the Form of the Good. The latter distinguished between primary and secondary substances, with a priority ordering amongst them—along, arguably, with making appeal to prime matter, without which there would be nothing whatsoever. Just as very many of the Medievals (Aquinas, for example) and Early Moderns (Descartes, Spinoza, Leibniz) thought that everything depended on God, the need to establish a fundamental ground breaks out in certain of the Continental thinkers, such as Heidegger, in the form of The Problem of Being: there must be something (fundamental), Being, if we are to account for the fact that anything has being at all. Turning also to non-Western traditions, we see that the idea that reality is structured by metaphysical dependence relations, where there is something fundamental, is by no means an unfamiliar one.2 Various of the Indian, Chinese, and Japanese traditions rely heavily on notions of metaphysical dependence and fundamentality. In fact, whole schools were formed based on disagreements over the fundamental structure of reality. According to the Indian Abhidharmika tradition, for example, there must be dharmas—simples—as there are aggregates which are built from them. And according to Kyoto School thinker Nishida, the ultimate ground of everything is consciousness, which is also absolute nothingness. The idea that reality is structured, and that there must be something fundamental, is by no means the monopoly of contemporary Western analytic thought. The kind of view, or cluster of views, that appear to dominate the contemporary analytic debate can be thought of broadly as, or as species of, metaphysical foundationalism. As will become clearer in due course, there are, in fact, a variety of ways in which one can be a metaphysical foundationalist; with different species of foundationalism involving different core commitments. Although this list is by no means exhaustive, we assume the following to be amongst the core commitments of metaphysical foundationalism as commonly endorsed in the contemporary literature. 1. The hierarchy thesis: Reality is hierarchically structured by metaphysical dependence relations that are anti-symmetric, transitive, and anti-reflexive. 2. The fundamentality thesis: There is some thing(s) which is fundamental. 3. The contingency thesis: Whatever is fundamental is merely contingently existent. 4. The consistency thesis: The dependence structure has consistent structural properties. Strictly speaking, in order to be considered a species of foundationalism, a view needs only commit to the the fundamentality thesis: 2., then, is both necessary and

2

See Bliss and Priest 2017.

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ricki bliss and graham priest  sufficient for a view to count as a kind of foundationalism. For proponents of what we can think of as the standard view, however, all four theses are necessary, with no one of them being sufficient.3 Is this the only view of the fundamental, or basic, structure of reality that is available to us, though? Of course it isn’t. To be sure, deviations from the standard view exist in the literature.4 But the full spread of possible views has, so far as we can tell, been both grossly underestimated and grossly underexplored. It is important and interesting to note that in foundational epistemology—where the structuring relations are strikingly similar to those invoked in talk of foundational metaphysics—one can be an epistemic foundationalist (of various sorts), an epistemic infinitist, or an epistemic coherentist. Is a similar spread of possible views available to us in foundational metaphysics? We are inclined to think that it is, as do Morganti and Thompson (this volume). Just as an epistemic infinitist thinks that chains of beliefs ordered by an anti-symmetric, anti-reflexive, transitive relation orders beliefs without termination, a metaphysical infinitist thinks that chains of entities ordered by an antisymmetric, anti-reflexive, transitive relation orders entities without termination. So too for coherentism. Just as an epistemic coherentist thinks that beliefs are organized into a highly integrated web, with justification emerging from it, the metaphysical coherentist thinks that entities are organized into a highly integrated web with something like being or reality emerging from it. As one might expect, there will also be various possible shades between. The papers contained within this volume can be thought of as contributing to a broader discussion of the reasons for which we are supposed to believe aspects of the standard view, the reasons we might have for embracing one or other of the alternatives, and what those alternatives might be like. Not all of the papers in this volume endorse types of anti-foundationalism, but each of them speaks to, and challenges, in some way or other, one or other of the core commitments of metaphysical foundationalism as noted above. In some cases, our authors even support one or other of the assumptions, with the aim of their contribution being to highlight weaknesses in the arguments commonly offered in their defence. The papers in this volume are arranged, then, according to the core assumption that they primarily address.

3 The idea that the world is ontologically ‘flat’, with everything being fundamental—a rejection of 1— has been described by Bennett 2011 as ‘crazy pants’, for example. Just as many philosophers baulk at the suggestion that the fundamentalia are necessary beings. 4 It is worth noting that it does not follow from the appearance of a smattering of papers challenging the standard view that the standard view is not still just that, the standard view. A handful of dissenting papers does not a heterodoxy make. Although some authors have challenged aspects of the foundationalist picture, the dominant paradigm that drives many contemporary analytic research programmes is one according to which reality has a layered structure and a fundamental level. Even though a small number of philosophers have challenged aspects of the standard view, to the best of our knowledge, these challenges have not resulted in research programmes of their own, nor have they impacted upon the way much research is conducted.

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 the geography of fundamentality: an overview In what remains of this introduction, we take up the mantle of introducing and engaging with some of the most important issues that we believe need to be dealt with if foundationalism is to be a view that we actually have good reasons to endorse; and if the alternatives are to be considered not just logically, but also metaphysically, possible.

1 The Lie of the Land Many philosophers accept a view according to which the world has an overarching causal structure. Thunderstorms cause trees to fall down, and water is caused to boil by the application of heat. This volume takes as one of its starting assumptions that the world (also) has an overarching metaphysical structure. Of course, causal structure is a kind of metaphysical structure; however, what philosophers tend to mean nowadays when they speak of metaphysical structure is that this structure is induced by relations of ground and/or ontological dependence.5 We refer to these as metaphysical dependence relations, and they are the relations around which the ideas presented in the following essays are centred. There is a lot that has been, and continues to be, written on metaphysical dependence relations. And there is an enormous amount of disagreement over even the most basic of concepts in operation in the relevant literature.6 Is grounding to be understood on the operator view or the sentential connective view? Is grounding just explanation? How are grounding and ontological dependence related? Is grounding unitary? These are amongst some of the many issues that those working on issues pertaining to the structure of reality are concerned with. This volume is not primarily concerned with most of those disagreements, however. We leave it to our contributors to assume what they will regarding how they define their terms and the conceptual connections that they take to be in operation; and we leave it to our readers to find appropriate reading material if what they are interested in are those debates. For the sake of clarity in this introduction, however, we think it wise to say something about how we shall be understanding things. It is not uncommon to see a distinction drawn in the literature between relations of ground and ontological dependence. Relations of ground, say many, obtain between facts, where relations of ontological dependence obtain between entities of any and all categories.7 So, where one would say that the fact that the weather is miserable today is grounded in the fact that it is pouring, one would say that the shadow ontologically depends on the object that casts it. And where one would say that the fact that the sky is blue or we are in Australia, is grounded in the fact that the sky 5 See Schaffer 2016 for a discussion of the relationship between grounding and causation, and a view according to which grounding is a kind of causing. 6 See Bliss 2014 for an overview of some of the major sources of disagreement. 7 See Schaffer 2009 for the development of a view according to which grounding obtains between entities of any and all categories and cross-categorically.

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ricki bliss and graham priest  is blue, one would also say that the fact that the sky is blue ontologically depends on its constituents—the sky and blueness. Again, when we talk about relations of metaphysical dependence, we mean this term to act as a covering term for both grounding and ontological dependence. Where, in this introduction, we think it necessary to discriminate between the two, we say as much. We also don’t think much as regards the reasons to endorse one fundamental view of reality over another is going to turn on whether grounding obtains between facts alone, for example. What bears consideration when settling the kinds of matters that this volume is concerned with will be the same, we believe, whether it turns out that ontological dependence just is a kind of grounding or not. It is a plank of the grounding literature that grounding is somehow involved with metaphysical explanation. It is an open question, however, whether the relations are merely associated with metaphysical explanation or whether they are identical with it. Thompson (this volume) offers us some compelling reasons to think that grounding is better thought of as being an explanatory relation. She argues that were grounding relations to be relations that underwrite our explanations, we would still need to account for how the relations and the explanations they back are related to one another. If the way they are related to one another is via grounding, then we are really in trouble, says Thompson, because the notion of a metaphysical explanation is typically invoked to shed light on how we are supposed to understand grounding in the first place. Trogdon (this volume), on the other hand, thinks it natural to assume that grounding relations back metaphysical explanations. So far as we can tell, not much turns on resolving this particular issue for what we have to say here in this introduction. It is enough for us to point out that we assume that grounding is most certainly involved with metaphysical explanation, however that turns out to be, and move on. It has been suggested that the connection between ontological dependence and explanation is weaker than the connection between ground and explanation. Tahko and Lowe suggest, for example, that the existence of hydrogen and oxygen—upon which water depends—do not, alone, explain the existence of water.8 Whilst we agree that the mere existence of hydrogen and oxygen does not fully explain the existence of water, we struggle to understand how the existence of the two could fail to be appealed to in an explanation of the other. Perhaps Tahko and Lowe are correct that the connection is weaker, but we here feel confident proceeding on the assumption that ontological dependence is sufficiently strongly tied to metaphysical explanation nonetheless. Let us turn now to the notion of fundamentality itself. We assume that the categories of fundamental and derivative are exclusive and exhaustive. Some entity is either fundamental or derivative but never both.9 The category of derivative things is just

8

See Tahko 2015.

9

See Barnes 2012 for arguments against the exclusivity assumption.

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 the geography of fundamentality: an overview the category of metaphysically dependent things; which is just to say it is the category of grounded and ontologically dependent entities. It is true by definition that a derivative entity is dependent and, thus, that it has a metaphysical explanation. The fundamentalia, on the other hand, by definition, depend upon nothing else (except perhaps themselves) and are, thus, without metaphysical explanation (except perhaps in terms of themselves). This is not to say, however, that being independently existent is a sufficient condition for being fundamental (on some accounts, it’s not even necessary). There may well be a plethora of independent entities that, nonetheless, do not serve as candidate fundamentalia.10 Although there are alternative ways of understanding fundamentality, such as discussed by Takho and Barnes (this volume), Fine, and Sider, we are happy to proceed on the independence understanding.11 It is open, and indeed the case on many accounts, that the fundamental facts be fundamental qua grounding structure and yet dependent qua ontological dependence structure. This is because for any account according to which a fact is dependent upon its constituents, a fundamental fact will be ungrounded and yet, nonetheless, dependent. The term ‘fundamentalia’ can then be taken to refer to either fundamental facts or fundamental things depending upon which ordering one wishes to foreground. We recognize that there are also subtly different ways in which the notion of being fundamental can be formally cashed out. One distinction that we think it particularly important to mention is that between the relation being well-founded and it having a lower bound.12 To say that dependence relations are well-founded is to say that (i) chains ordered by the relation downwardly terminate in a fundamentalium, and (ii) that there is a finite number of steps between any member of a chain and the fundamentalium that it terminates in. Although it’s not uncommon to hear philosophers speak in the language of well-foundedness, what they often mean is that any chain of entities ordered by that relation has a lower bound. Importantly, where a relation is bounded from below, there need not be a finite number of steps between any member of that set and the fundamentalium that grounds it. To better understand this, consider the relationship between God and the contents of reality; although there may be an infinite number of steps between, say, the number 7 and God, the number 7, along with everything else, depends on him nonetheless. In order to remain neutral on an understanding of fundamentality as well-foundedness and fundamentality as lower boundedness, we choose to capture this aspect of foundationalism formally in terms of the notion of extendability (E) and its negation; more of which anon.

10 Facts about numbers, for example, may be independent, without that entailing that they are therewith fundamental. 11 Fine 2001 and Sider 2011. See Raven 2016 for another alternate account of fundamentality. 12 See Dixon 2016, and Rabin and Rabern 2016, for formal treatments and discussions of different possible ways of understanding fundamentality.

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ricki bliss and graham priest 

2 Taxonomy The hierarchy thesis says that the dependence relation is anti-symmetric, transitive, and anti-reflexive. The fundamentality thesis says that there must be something fundamental. Although it is common to assume that the relevant dependence relations have some combination of the aforementioned properties, a variety of different combinations are at least logically possible. To see this, let us first introduce some notation.13  We write ‘x depends on y’ as x → y.14 (We may write x → x as x .) Next, four structural properties: Anti-reflexivity, AR. • ∀x¬ x → x [Nothing depends on itself.] • So ¬AR: ∃x x → x [Something depends on itself.] Anti-symmetry, AS. • ∀x∀y(x → y ⊃ ¬ y → x) [No things depend on each other.] • So ¬AS: ∃x∃y(x → y ∧ y → x) [Some things depend on each other.] Transitivity, T. • ∀x∀y∀z((x → y ∧ y → z) ⊃ x → z) [Everything depends on anything a dependent depends on.] • So ¬T: ∃x∃y∃z(x → y ∧ y → z ∧ ¬x → z) [Something does not depend on what some dependent depends on.] Extendability, E. • ∀x∃y(y = x ∧ x → y) [Everything depends on something else.] • So ¬E: ∃x∀y(x → y ⊃ y = x) [Something does not depend on anything else.] We can now give a taxonomy, which is as follows. After the enumeration column, the next four columns list the 16 possibilities of our four conditions.

1 2 3 4

13

AR Y Y Y Y

AS Y Y Y Y

T Y Y N N

E Y N Y N

Comments Infinite partial order Partial order Loops Loops

Special Cases I A, F, G I F, G

The contents of this section are reproduced from Bliss and Priest 2017. One may distinguish between full dependence and partial dependence. (See e.g. Dixon 2016, sec. 1.) Just to be clear: the notion of dependence we are concerned with here is partial dependence. 14

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 the geography of fundamentality: an overview 5 6 7 8 9 10 11 12 13 14 15 16

Y Y Y Y N N N N N N N N

N N N N Y Y Y Y N N N N

Y Y N N Y Y N N Y Y N N

Y N Y N Y N Y N Y N Y N

× × Loops of length >0 Loops of length >0 × × × × Preorder Preorder Loops of any length Loops of any length

I F, G

C, I C, F, F  , G I F, F  , G

Consider, next, the Comments column. Here’s what it means. • There is nothing in categories 5, 6, since if there are x, y, such that x  y, then   by T, x  y , contradicting AR. (¬AS and T imply ¬AR.) • There is nothing in categories 9–12, since if for some x, x → x, then for some x and y, x  y, contradicting AS. (¬AR implies ¬AS.) • All the other categories are possible, as simple examples (left to the reader) will demonstrate. • In cases 13–16, since ¬AR implies ¬AS, the second column (AS) is redundant. • In categories 1 and 2, → is a (strict) partial order; and in category 1, the objects involved must be infinite because of E. • In categories 13 and 14 → is a (strict) preorder, so loops are possible. (A loop is a collection of elements, x1 , x2 , . . . , xn−1 , xn , for some n  1, such that x1 → x2 → . . . → xn−1 → xn → x1 .) • In cases 3, 4, 7, 8, 15, 16, transitivity fails, and there can also be loops. In cases 7, 8,  there are no loops of length zero, x , since AR holds. Turning to the final column, this records some important special cases. • The discrete case is when nothing relates to anything. Call this atomism, A. In this case, we have AR, AS, T, ¬E. So we are in case 2 (though this is not the only thing in case 2). • If → is an equivalence relation (reflexive, symmetric, transitive), we have ¬AR, ¬AS, T, so we are in cases 13 or 14 (though this is not the only thing in these two cases). In case 13, there must be more than one thing in each equivalence class, because of E. A limit case of this is when all things relate to each other: ∀x∀y x → y. Call this coherentism, C. • Call x a foundational element (FEx) if there is no y on which x depends, except perhaps itself: ∀y(x → y ⊃ x = y). Foundationalism, F, is the view that everything grounds out in foundational elements. One way to cash out the idea is as

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ricki bliss and graham priest  follows.15 Let X0 = {x : FEx}, and for any natural number, n ∈ ω: x ∈ Xn+1  iff x ∈ Xn or ∀y(x → y ⊃ y ∈ Xn ). X = Xn . F is the view that everything n∈ω

is in X, ∀x x ∈ X.16 Intuitively, this means that everything is a foundational element, or depends on just the foundational elements, or depends on just those and the foundational elements, and so on. E entails that there are no foundational elements. Hence, this is incompatible with F. So, given F, we must be in an even numbered case—except those that are already ruled out by other considerations. (All are possible. Merely consider x → y → z. z is foundational; add in arrows as required to deliver the other conditions.) • A special case of foundationalism is when the foundational objects, and only those, depend on themselves: ∀x(FEx ≡ x → x). Call this view F  . Since AR must fail in this case, we must be in cases 14 or 16 of the taxonomy. • Another special case of foundationalism is when there is a unique foundational object on which everything else depends: ∃x(FEx ∧ ∀y(y = x ⊃ y → x) [Something is a foundational element, and everything else depends on it.] The x in question does not depend on anything, except perhaps itself, and it must be unique, or it would depend on something else. Call this case G (since the x could be a God which depends on nothing, or only itself). This is a special case of F, and could be in any of the cases in which F holds. ∗ • Write x → y to mean that y is in the transitive closure of → from x. That is, one can get from x to y by going down a finite sequence of arrows. An element, x, is ultimately ungrounded, UGx, if, going down a sequence of arrows, one never ∗ comes to a foundational element: ∀y(x → y ⊃ ¬FEy). Infinitism, I, is the view that every element is ultimately ungrounded: ∀x UGx.17 We note that Infinitism allows for the possibility of loops, that is, repetitions in the regress. Thus, we have the following possibility: x → y → z → x → y → z →. . . . However, if → is transitive and anti-symmetric (T and AS), such loops are ruled out. Infinitism entails Extendability, E. So if I holds we must be in an odd numbered category of our taxonomy (which is not ruled out by other considerations). All such are possible, as simple examples demonstrate. (Merely consider x0 → x1 → x2 → x3 →..., where these are all distinct. Add in other arrows as required.) Note that if there are at least two elements, then C is a special case of I.

15 We note that, how, exactly, to cash out the idea of foundationalism is contentious. For some discussion of the matter, see Dixon 2016. We suspect that the notion may be vague, to a certain extent, and so susceptible to different precisifications. The definition we give here is strong, simple, and very natural. 16 One may, if one wishes, iterate the construction into the transfinite, collecting up at limit ordinals in the obvious way. 17 We note that Infinitism, also, is certainly susceptible to various precisifications. For example, one might require that only some element is ungrounded. Again, the definition we give here is strong, simple, and natural.

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 the geography of fundamentality: an overview • A final special case. Let x  y iff x → y ∨ y → x. Then x and y are connected along the dependence relation, xCy, iff for some n  1: x  y ∨ ∃z1 z2 . . . zn (x  z1 ∧ z1  z2 ∧ . . . ∧ zn  y) [Everything relates to everything else along some sequence of dependence relations.] → itself is connected iff ∀x∀y xCy. In all of the ten possible cases, → may be connected or not connected. G is a special case of connectedness; C is an extreme case of connectedness; and A is an extreme case of disconnectedness. Let us finish this section with an informal summary. The taxonomy is built on four conditions. (i) Anti-reflexivity, AR: nothing depends on itself. (ii) Anti-symmetry, AS: no things depend on each other. (iii) Transitivity, T: everything depends on whatever a dependent depends on. (iv) Extendability, E: everything depends on something else. This gives us 16 (= 24 ) possibilities. Six of these are ruled out by logical considerations, leaving ten live possibilities. Within these, some special cases may be noted. Atomism, A: nothing depends on anything. Foundationalism, F: everything is a fundamental element or depends, ultimately, on such. F  : Foundationalism, where the fundamental elements and only those depend on themselves. G: Foundationalism where the fundamental element is unique. Infinitism, I: there are no fundamental elements. Coherentism, C: everything depends on everything else.

3 On the Metaphysical Possibility of the Alternatives So far, we have seen that alternatives to metaphysical foundationalism in general, and the standard view in particular, are logically possible: lines 1–4, 7, 8, and 13–16. One might wonder, however, if they are metaphysically possible. In this section, we will argue that they are. But before turning to a discussion of the viability of the alternatives to the standard view, let us first address one particular issue that we will face time and again. It is quite common to hear friends of the standard view defend their commitments to various aspects of the view by appeal to their intuitions. These philosophers will claim to have intuitions that there is something fundamental, that nothing can ground itself, and so on. Moreover, these philosophers appear to take their intuitions to serve as something like arguments in defence of the view: these philosophers will not only claim to have said intuitions, but also that nothing more needs to be said on the matter. We simply do not share these intuitions. In fact, neither of us has any intuitions whatsoever regarding a subject matter as abstract and recherché as the fundamental structure of reality. But, more importantly, we also firmly believe that intuitions are no replacement for actual arguments. That intuitions have been allowed to play the role they have in the dependence/fundamentality debates thus far is, in our view, why alternative views have been so poorly explored, and why actual arguments in defence of the view have been allowed to be so bad.

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ricki bliss and graham priest  In what follows, although appeal to intuition is often made in defence of one commitment or another, we will not respond to them further. Our response in each case is as stated here. Let us continue our investigation, then, by turning to a consideration of actual arguments, beginning with the hierarchy thesis.

3.1 The Hierarchy Thesis According to the proponent of the standard view, reality is hierarchically arranged. That reality is like this, we are told, is intuitive and somehow obvious.18 It has been suggested that to challenge the idea that reality has such a shape, by questioning whether dependence relations are transitive, irreflexive, and anti-symmetric, is preposterous for the reason that metaphysical dependence relations are introduced into the philosophical vernacular exactly to capture this aspect of reality. A reason often cited in favour of abandoning talk of supervenience—a symmetric and reflexive relation—in favour of, say, grounding talk, is that we need a relation that can capture reality’s hierarchical structure. We agree that if metaphysical dependence relations are introduced exactly to allow us to capture the idea that reality has a hierarchical structure, then it makes little sense to call into question the properties that are securing that structure. But the important question, we think, is why we ought to believe reality has such a structure in the first place. And it is when we focus on this question that reasons so often offered to commit to the hierarchy thesis look less compelling. Let us now consider them.

.. anti-reflexivity In defence of the claim that dependence relations are necessarily anti-reflexive, philosophers have tended to argue that it would be absurd to assume that something can ground itself, or that, given the tight connection between grounding and explanation, as it is a principle of explanation that nothing explains itself, it ought to also be a feature of dependence relations.19 Let us first consider why one might think it absurd to assume that metaphysical dependence relations can be reflexive. As dependence talk is about reality, it is reasonable to wonder if self-dependence is absurd because there is some way that the world would have to be, such that things can depend on themselves, which is unacceptable. But what might this be? A first worry about self-dependence is that anything that depends upon itself would have to bootstrap itself into being. But why think this is a problem? In the case of causation, the problem is apparent: something that is self-caused would have to exist prior to itself in time in order to bring itself into existence. But metaphysical dependence relations are typically thought of as being synchronic, so what goes

18 19

See Raven 2013 for a well-articulated defence of the hierarchy thesis. See Jenkins 2011for a somewhat different discussion of dependence and irreflexivity.

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 the geography of fundamentality: an overview for causation here does not (necessarily) go for metaphysical dependence.20 As metaphysical dependence relations are thought of as inducing a priority ordering, perhaps the problem, then, is that where the relations are reflexive, the very idea of a priority ordering goes out the window. This may well be the case, but of course this is no reason to think that dependence relations cannot be reflexive, for it is just to assert that the relation must be anti-reflexive in the first place. Exactly what is required in order to have a priority ordering is that the ordering relation is anti-symmetric and anti-reflexive. Anyone with even a passing familiarity with the historical literature would be aware that there is, in fact, precedent for a view according to which there is at least one thing that is self-dependent, namely, Leibniz’s account of God. According to Leibniz, God exists, indeed, exists necessarily. He does so because existence is part of his essence; but to say this means, inter alia, that God necessarily exists. So God necessarily exists because he necessarily exits. One might wonder, then, if a good reason to reject the possibility of reflexive instances of ground is that anything that is self-grounded would be a necessary being. Now, of course this is only going to be a problem if the wrong things, or kinds of things, turn out to be self-grounded; take, for example, the fundamentalia. A potential serious worry, then, is that if the fundamentalia are necessary beings, and they ground the being of everything else, then there is only one way the world can be, which is exactly how the world actually is.21 Are we compelled, though, to accept this story—the story according to which self-grounded entities are necessary beings? Bliss (this volume) suggests that we are not. But if this is the case, we seem no closer to understanding (i) what reflexive dependence amounts to and (ii) why it is unacceptable. Failing all else, one might simply worry that the idea that anything can depend upon itself is absurd just because it is plain weird. Maybe it is weird (the judgement of which would seem to require knowing what self-dependence actually amounts in), but we struggle to see how selfdependence is any weirder than the commonly held belief that there are some entities that pop into being from nowhere and for no reason at all—which is exactly what the fundamentalia are like by most people’s lights. Metaphysically speaking, it is not so clear what is so bad about something’s being self-dependent. More compelling, we think, are explanatory reasons for thinking that reflexive instances of dependence are unacceptable. It is a plank in much of the literature on explanation that reflexive explanations are trivial, uninformative, and explanatorily useless. A reflexive explanation, so the thought goes, is as good as no explanation at all. We are inclined to think, though, that whilst there may be something to this, matters here are thornier and more subtle than they appear.22 For a start, not all

20

There are reasons to believe that there are cases of non-synchronic grounding, just as there are cases of synchronic causation. Obviously the intricacies of these issues cannot be covered here. 21 See Dasgupta 2016 for a discussion of this view according to which it would not be a problem. 22 See Keefe 2002 for a most illuminating discussion of issues relevant to this debate.

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ricki bliss and graham priest  circular explanations are trivial—we have already seen this in the case of God and his explanatory relationship to himself—nor are they necessarily uninformative or useless. After all, coming to understand that something has no further explanation is coming to understand something more about that thing. In the worst case, what we may be dealing with is a problem with explanatory superfluity: something’s explaining itself is as good as it having no explanation whatsoever, so why bother permitting selfdependence in the first place. As things stand, the reasons to disavow self-dependence appear to be fairly thin on the ground. Metaphysically speaking, it’s not clear how a world would have to be such that things depend on themselves, leaving us with explanatory considerations. But if this is the conclusion it is hardly welcome. Suddenly the problems with reflexivity appear to be epistemic rather than metaphysical which would seem to fly in the face of how the friends of foundationalism understand the overarching structure of reality.

.. anti-symmetry Let us now turn our attention to anti-symmetry. Advocates of the standard view rely on (some combination of) arguments from intuition, arguments from the data, and arguments from structural similarities with explanation. Appeal is also made to what we might call arguments from relative fundamentality. The argument from relative fundamentality is just a variation on the kind of argument in terms of structure that we mentioned in the introduction to this section. We consider these first. According to the argument from relative fundamentality ‘dependence is intimately connected to (and perhaps even explains or is one and the same things as) relevant notions of fundamentality, priority, grounding, etc. Dependence is the kind of relation that explains the connection between the fundamental and the derivative (the dependent) to the fundamental (the independent). Any relation that plays this role must be asymmetric’ (Barnes, this volume). The idea that reality is ordered into a hierarchical structure is a very old one that can be traced back to the Ancient Greeks. Indeed, right the way through the history of the Western tradition, many philosophers have been engaged in some way or other with filling in the details of this picture.23 That some folks claim to have intuitions regarding the structure of reality is hardly surprising given the pervasiveness of this view (and imagery) in the history of Western thought.24 As Barnes points out, if moving us from the fundamental to the derivative is the role that dependence is supposed to play, then it seems right to suppose that dependence must be anti-symmetric. Indeed, as already mentioned, it just follows from the idea 23 See Lovejoy 1934 for an informative and charming discussion of the notion of the Great Chain of Being and its centrality to the development of Western metaphysics. 24 The idea that reality is hierarchically structured has not only been the purview of the metaphysician, but was also commonplace in the sciences, art, and theology up until the end of the nineteenth century. This view went out of vogue with the momentous changes to our understanding of the world precipitated by scientific developments.

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 the geography of fundamentality: an overview that reality is hierarchically structured that the structuring relation is anti-symmetric. But exactly what the argument from relative fundamentality does not provide us with is a reason to suppose that the relation is anti-symmetric—it simply assumes it. One way to respond to the relative fundamentality argument, then, is to challenge the idea that we have reasons to suppose that reality is hierarchically structured in the first place. To put the point more finely, we can challenge the idea that reality exhibits a robust hierarchical structure by arguing that metaphysical dependence relations are either symmetric (which might generate a species of metaphysical coherentism) or that they are non-symmetric (a weaker claim that may yet allow for a hierarchy to emerge nonetheless). Whilst we agree that the world appears to present us with cases of anti-symmetric dependence, that dependence relations are necessarily anti-symmetric is not obvious to us at all. As Barnes and Thompson (this volume) argue, some of our most beloved metaphysical theories appear to posit symmetric instances of dependence; or at least make more sense if they do. Consider, for example, Armstrong’s account of states of affairs. Armstrong’s picture is one according to which atomic states of affairs are ontological rock-bottom with their constituents as abstractions from those states of affairs. The problem with this picture is that the states of affairs really seem to depend on their constituents, with those constituents explaining the nature and existence of those states of affairs. Barnes suggests that if Armstrong were to allow symmetric instances of dependence, then he could have his cake, as it were, and eat it too: atomic states of affairs depending on their constituents, but the constituents depending on their state of affairs. Theoretical cases aside, consider also the relationship between the north and south poles of a magnet: without the north pole, the south pole would not exist and without the south pole, the north pole would not exist. The list, it would seem, goes on. We appear to have compelling reasons to temper our commitment to anti-symmetry and endorse the more modest suggestion that the relation(s) is non-symmetric. What about the much stronger claim that dependence is, in fact, symmetric? Can the case be made for such a strong view? Well, it can because it has been. As Priest (this volume) discusses, the Chinese Huayan Buddhist tradition endorses a species of full-blown coherentism with everything depending symmetrically upon everything else.25 It has been suggested that as metaphysical dependence is intimately involved with explanation, we can infer from the structural properties attributed to (good) explanations on some models that metaphysical dependence relations also share such properties. As explanations are anti-symmetric, so the objection goes, so too are dependence relations. But as both Barnes and Thompson (this volume) point out, there are alternative (very good) explanatory models on which explanations are not 25 See also Priest 2014, esp. chapters 11–13, for a contemporary presentation of a coherentist picture inspired, in part, by Huayan.

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ricki bliss and graham priest  necessarily anti-symmetric. Indeed, according to Barnes and Thompson, explanation as understood wholistically, may well do a better job of capturing certain aspects of our everyday and theoretical explanatory praxis. That metaphysical dependence relations are introduced to capture reality as hierarchically structured does not provide us with a reason to think reality has that structure in the first place. Although ‘the data’ suggests that some instances of dependence relations are anti-symmetric, this is also no reason to suppose that the relation is in general. Indeed, the cherry-picking of instances of dependence relations that appear to be anti-symmetric to use as our paradigmatic cases of dependence ought not blind us to the presence of other instantiations of the relation that are plausibly thought to be symmetric. All told, there seems to be good reasons to suppose that metaphysical dependence relations are at least non-symmetric.

.. transitivity There is something natural-seeming about the idea that metaphysical dependence relations are transitive. Where a person depends on their vital organs, it also seems true that they depend upon the cells that compose those vital organs. However, a number of authors, including Nolan (this volume), have pointed out that at the very least, we could well allow that some instances of dependence relations fail to be transitive, and hold a view according to which metaphysical dependence is nontransitive. Why question the transitivity assumption? Well, one good reason is that reality appears to present with actual cases of failures of transitivity. Schaffer asks us to consider the following propositions: (1) the fact that o has a dent, d, grounds the fact that o has shape S, (2) the fact that o has shape S grounds the fact that o is more or less spherical, and (3) therefore, the fact that o has a dent grounds the fact that o is more or less spherical. If grounding were transitive, then we would expect this argument to go through but, Schaffer argues, it does not because o ‘is more-or-less spherical despite the dent, not because of it’.26 As far as Schaffer is concerned, the fact that o has a dent does not ground the fact that o is more or less spherical, in which case grounding is not necessarily transitive.27 Or consider other problematic cases: singleton Obama is dependent upon its member Obama, and Obama is dependent upon his parts, and yet we might well not want to say that the existence of Obama’s heart (partially) explains the existence of singleton Obama. One way to respond to these sorts of cases is to point out that dependence is not univocal. What one might think is going on in these cases is the chaining together of instances of dependence relations that don’t, in fact, properly belong together. One might try and argue, for example, that the way in which a singleton depends upon 26

Schaffer 2012, p. 127. This is not the only purported failure of transitivity that Schaffer presents us with. See also Raven 2013 for a defence of the thought that grounding is transitive. 27

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 the geography of fundamentality: an overview its member is different to the way in which the member depends upon its parts.28 Were one to pursue such an approach, however, one must remain mindful of the costs such an approach might incur: do we really want or need a proliferation of species of dependence relations, for example?29 Another approach might be to distinguish between relations of mediate and immediate dependence, where the former is transitive and the latter is not. Indeed, in the literature, philosophers have suggested that we should take seriously a distinction between immediate and mediate dependence.30 Purported failures of transitivity can then be understood as involving the transitive closure of an intransitive relation. So what appears to be a failure of transitivity, in fact, involves a case of mistaken identity. There are advantages to admitting a distinction between a transitive and a nontransitive species of the relation. On the one hand, it allows us to avoid a proliferation of relation-types in response to the purported problem: where part/whole relations are a species of dependence relation, truthmaking another and so on. And, on the other hand, it allows for certain possibilities. Nolan (this volume) suggests, for example, that some species of dependence, or instances of the relation, may fail to be transitive allowing the possibility of giant cosmological loops. And more generally, where there is a species of the relation that is intransitive, loops of various sizes could be admitted without being forced to sacrifice anti-symmetry and anti-reflexivity. All told, there are reasons to doubt that metaphysical dependence relations are necessarily transitive. Not only do we appear to be in possession of counterexamples to the transitivity thesis, but we have reasons to suppose that admitting an intransitive species of the relation to our repertoire would be to our advantage. Of course there is so much more to be considered regarding the widespread commitment to the hierarchy thesis, and the possible alternatives to it. Rabin (this volume) believes that unorthodox accounts of grounding allow us to better capture the layered conception of reality. Looking to other traditions, as Priest (this volume) does, we can see that a number of accounts from the Asian Buddhist traditions, for example, reject the idea that reality is hierarchically structured. Anyone seriously interested in non-standard conceptions of the structure of reality would do well to look beyond the Western canon. And Litland (this volume) argues that, what he calls a bi-collective account of ground, may have interesting applications for certain types of coherentist structures.

28 Consider what happens when we say that Harry banks on Sally and Sally banks on Tuesday. No one would claim that, therefore, Harry banks on Tuesday. Nor would anyone claim that the relation banking on, as demonstrated by this example, is not, therefore, transitive. What we would be inclined to say is that the expression ‘banks on’ picks out different relations in the two cases. 29 See Wilson 2014 for a defence of the claim that all we need are the many different kinds of smallg grounding relations with which we are familiar—supervenience, parthood, etc.—rather than one big-G grounding relation. 30 See, for example, Fine 1994, 1995, and 2013 for discussions of such possibilities as regards both ontological dependence and grounding.

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ricki bliss and graham priest 

3.2 The Fundamentality Thesis One might well have the impression that nary a paper is produced in analytic metaphysics these days that does not make reference to the notion of fundamentality.31 Somewhat surprising, then, is the dearth of good arguments available in the literature in defence of the fundamentality thesis. Broadly construed, there appears to be at least three types of argument on offer. The first of these, as might be expected, are arguments from intuition; the second of these are arguments from vicious infinite regress; and the third, arguments from theoretical virtue. In keeping with our promise above, we desist from discussing arguments from intuition and turn immediately to regress arguments.

.. regress arguments What explains the fact that we exist? A good place to start will surely involve appeal to facts about the existence of our parents and the genetic material they have bequeathed to us, our vitals organs, and so on. Of course, we are causally dependent upon on our parents, but we are also metaphysically dependent upon them: it’s not simply that our parents cause us to exist, but they also ground our existence as well. Although the story of the existence of any one of us is metaphysically complex, most of us would feel confident in assuming that we have some rough idea of how to tell it. Suppose, now, that we also wish to explain the existence of our parents and our vital organs. Again, a complex matter, but surely one that will involve appeal to their parents—our grandparents—and the cellular structure of the organs and so on. At each stage, it would appear as though we have explained something about the entities for which we are seeking an explanation, and that this process could go on successfully without termination. But exactly what the fundamentality thesis tells us is that it doesn’t (or can’t) go on forever, and a justification for this position is going to have to tell us why this is the case.32 One obvious seeming thought is that where we have limitless descending dependence chains, although we have explained something (probably even a lot), we haven’t yet explained everything that we need an explanation for.33 Or another thought might be that where we have limitless descending dependence chains, although we have explained something, we haven’t yet arrived at an explanation that is complete, or at least completely satisfactory. And, of course, there is a way of understanding these two explanatory concerns that is intimately related, for an explanation will surely be

31 One needs not only be reading from the dependence/fundamentality literature to notice this. Appeal to fundamentality is made in the literature ranging from topics as diverse as the philosophy of mind to aesthetics and ethics, to offer but a few examples. 32 See Bliss (forthcoming), from which much of the following discussion in this section is borrowed, for a more sustained elaboration of these thoughts. 33 See Bliss 2013.

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 the geography of fundamentality: an overview unsatisfactory exactly when we have failed to explain everything that we need an explanation for. Both of these kinds of concerns are echoed by various authors in the literature. Schaffer, for example, claims that where there is nothing fundamental ‘being is infinitely deferred and never achieved’.34 Dasgupta suggests that it is at least plausible to think that we might justify our commitment to fundamentality as ‘the desire for this special kind of explanation . . . in which one looks at the surrounding mountains and oceans and thinks “good grief, how come it all turned out like this?”’35 Where the ‘special kind of explanation’ he refers to is exactly the kind of explanation we don’t have when we point out that mountains depend upon arrangements of matter in space, and so on. Although concluding that the best reason we have for supposing that there is something fundamental is that it would be better to have a unified explanation of everything that needs explaining, Cameron also states that ‘for if there is an infinitely descending chain of ontological dependence, then while everything that needs a metaphysical explanation (a grounding for its existence) has one, there is no explanation for everything that needs explaining. That is, it is true for every dependent x that the existence of x is explained by the existence of some prior object (or set of prior objects), but there is no collection of objects that explains the existence of every dependent x.’36 And finally, concerned with satisfaction, Fine suggests that ‘ . . . given a truth that stands in need of explanation, one naturally supposes that it should have a “completely satisfactory” explanation, one that does not involve cycles and terminates in truths that do not stand in need of explanation’.37 An unfortunate consequence of the alleged obviousness of the fundamentality thesis is that remarks such as these are seldom presented in the form of arguments in the literature. It is not uncommon, nor unreasonable, to suppose that comments such as these can be reconstructed in the form of arguments from vicious infinite regress. One might suppose, for example, that where there is nothing fundamental, a regress is generated, and it is vicious because it leaves us without an explanation for something that we think needs explaining, or that we are left without an explanation that is completely satisfactory. We think, however, that there is a simpler way of reconstructing arguments in defence of fundamentality of this stripe that does not make direct appeal to arguments from vicious infinite regress.38 Reconstructing the arguments after such a fashion has the added advantage of allowing us to bring to the fore an assumption crucial to the foundationalist view that appears to have gone largely unnoticed in the literature. One way of reconstructing the kinds of claims mentioned above as arguments requires two assumptions. The first of these is an assumption that stipulates an

34

35 36 Schaffer 2010, p. 62. Dasgupta 2016, p. 4. Cameron 2008, p. 12. Fine 2010, p. 105. 38 This approach also fits with our view—which we have argued for independently—that the infinite regress is, in most cases, never the disease but, rather, a symptom. See Bliss 2013 and Priest 2014, 1.4. 37

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ricki bliss and graham priest  explanatory target. Such a stipulation might make appeal to something that needs to be explained; or it might make appeal to a type of explanation. In light of the discussion above, our explanatory targets might include (i) why anything has being whatsoever, (ii) why things turned out this way rather than any other, or (iii) that we need completely satisfactory explanations of everything that we think needs explaining. But note that having stipulated what our explanatory target is, or could be, we do not yet have an argument in defence of fundamentality. For it is not enough that we know that there is something that needs explaining, or some particular kind of explanation that we are after, but we also need an assumption that tells us that no dependent entity is up to the task to hand. Arguments in defence of fundamentality rely, crucially, on a second assumption which tells us that no dependent entity can do the kind of explanatory work that we are after. For the sake of economy let us reconstruct two possible arguments in defence of fundamentality; arguments that are congruous with suggestions made in the literature.39 Assuming that the world divides exclusively and exhaustively into the fundamental and the derivative: Argument I 1. There is an explanation for why anything has being whatsoever. 2. No dependent entity can explain why anything has being whatsoever. 3. Therefore, there must be something fundamental. Argument II 1. There is a complete metaphysical explanation for things that have metaphysical explanations. 2. No dependent entity can generate a complete explanation for things that have metaphysical explanations. 3. Therefore, there must be something fundamental. What are we to make of these arguments? In particular, are these good arguments in defence of the fundamentality thesis? Let us begin by considering the first assumption of our first argument. It seems obvious that what is at issue on this kind of reconstruction is a variation on an old theme: the cosmological argument. Understood in this way, the foundationalist is concerned to answer some version or other of a cosmological question. Indeed, many historically important figures have been engaged with such explanatory projects, including, as Casati (this volume) points out, Heidegger. Foundationalism, so understood, is of course not motivated by a concern to establish an ultimate cause of reality, but, rather, by a concern to establish an ultimate ontological ground. 39 We are of the view that many of the philosophers who worry about the grounds of being, or explaining the existence of everything, and so on, are, in fact, circulating roughly in the same waters. These philosophers are concerned with age-old questions such as why are there any beings whatsoever.

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 the geography of fundamentality: an overview Before assessing the merits of these arguments, it is interesting to note that their very appearance would appear to be in tension with what is a common view amongst contemporary analytic thinkers. Inspired by Hume, it is not uncommon for philosophers to suppose that having explained the existence of this thing here, and the existence of that thing there, everything that needs a (causal) explanation has one. This is just to say that, following Hume, many folks are of the view that there is nothing left over that needs to be explained and therewith, no blazing cosmological questions that demand an answer. Indeed, some philosophers have even gone so far as to claim that cosmological questions are ill-formed and non-sensicle.40 It is an item of curiosity why it is, then, that in the causal case, cosmological arguments (and the kinds of questions they are offered in response to) are passé and, yet, in the metaphysical case they are not. This is not to say that there is not a principled reason for the difference, but that it would be nice to know what it is. Sociological observations aside, there is what we believe to be a considerable concern with the use of cosmological questions to motivate metaphysical foundationalism: they appear to rely on an application of the principle of sufficient reason (PSR). Although there may be a suitably constrained version of the principle in the vicinity, the employment of the full-blown principle—according to which every thing has an explanation for its existence—to motivate foundationalism would be a disaster for the view: exactly what the foundationalist believes is that not everything has an explanation. Metaphysical foundationalism, so motivated, runs the risk of pulling the rug out from beneath itself. Let us now turn to the second argument and consider the thought that there is a complete metaphysical explanation for things that have metaphysical explanations. We do not wish to be distracted by how we have formulated the assumption here. Whether we formulate the target as all or only some things that have metaphysical explanations have complete explanations, what we are concerned with is why we should think anything that has a metaphysical explanation has a complete one in the first place. So what can we say about this assumption? One might suppose, as Fine does, that it is a plausible demand on explanations that they be completely satisfactory. Alternatively, one might be of the view that, independently of any general explanatory considerations, it is a plausible demand on metaphysical explanations in particular that they be completely satisfactory. But there appears to be a lot to be concerned about with the first assumption in our second argument as well. First and foremost, there is a way of understanding the assumption that looks as though it simply begs the question. We assume that no argument in defence of fundamentality can contain an assumption from which it follows that there is something fundamental. But the demand that some (or all) of our metaphysical explanations be complete just seems to be the demand that those

40

See Maitzen 2012 and 2013.

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ricki bliss and graham priest  explanatory chains terminate, which, of course, is just to say that there must be something fundamental. A good reason to think that our metaphysical explanations ought to be complete is that there is something wrong with explanations (in general) that are incomplete. But explanations are not typically rendered defective by dint of being incomplete. If someone wants to know why their window is broken, a story that makes appeal to the storm the previous night would be adequate. It is simply not the case that an explanation for a broken window is rendered defective in virtue of its failing to make appeal to the origins of the universe. Of course, what goes for causal explanations needs not go for metaphysical explanations, and the foundationalist may well be better off making recourse to the idea that there is something special about metaphysical explanations in particular which means they must be complete. We think it is worth pointing out at this juncture that there is something of an odd tension between the demand, on the one hand, for completely satisfactory explanations that can only be achieved by terminating our dependence chains and, on the other hand, the notion of a full ground. Let us suppose that singleton Socrates— {Socrates}—is fully grounded in Socrates. The way we are often encouraged to understand what full grounding amounts to is that, in this case, the existence of {Socrates} is fully explained by the existence of Socrates. If, however, where the nonterminating dependence chain of which these two are members leaves us with an incomplete or a not completely satisfactory explanation of {Socrates}, this would indicate that Socrates doesn’t completely explain {Socrates} in the first place. If, on the other hand, Socrates does completely explain the existence of {Socrates}, then there must, in fact, be something else at issue such that our explanations are not satisfactory unless there is something fundamental. Returning to broader explanatory considerations, one thought might be that whilst causal explanations may be incomplete, metaphysical explanations cannot be, for it is the purview of metaphysical explanations to afford us a complete explanation of reality. We can’t help but think that something a bit slippery has gone on here, though. First, where there is something fundamental, exactly what we don’t have is a complete explanation of reality, for we have the fundamentalia that are unexplained. Second, this proposal looks a lot like a cloaked version of the question-begging insistence that there is something fundamental mentioned above. Let us turn now to a consideration of the second assumptions in our arguments. As pointed out above, to note that there is something that has not yet been explained, is not yet to have an argument in defence of fundamentality. What is further required is an assumption that stipulates that no dependent entity is up to the task to hand. Without such an assumption, we have no need to move beyond the collection of dependent entities and, thus, no need to posit the existence of something fundamental. If our foundationalism, however, is to be well motivated, we need to know why this is the case. We need an answer to the question, why can’t any dependent entity explain where, say, being comes from?

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 the geography of fundamentality: an overview We think there are at least five prima facie plausible reasons to suppose that no dependent entity is able to be invoked to explain that for which it is being invoked. We list these as follows: (a) the reflexivity objection; (b) the never-ending questions objection; (c) the same questions objection; (d) the predicate-satisfaction objection; (e) the same kind objection. We discuss each in their turn. Some versions of cosmological arguments to the existence of God arrive at their conclusion by pointing out that no contingent thing can explain why there are any contingent things at all on pain of violating an anti-reflexivity assumption. They claim that as any contingent thing would be amongst the collection of things to be explained, were something contingent to explain why there are any contingent things at all, then the collection would be self-explanatory. Or put slightly more formally, let [A] be the state of affairs described by A. Suppose that there only two states of affairs, [A] and [B], and that [A] causally explains [[A] and [B]], then [A] causally explains [A] (and [B]). One might think that an analogous worry is what motivates the metaphysical foundationalist. The worry in this case would be that where [A] grounds [[A] and [B]], [A] grounds [A] (and [B]). We think there are at least two reasons to reject this concern as a reason for accepting the second assumption of the proposed foundationalist argument. The first of these pertains to understanding the explanatory target as a conjunctive fact. Cashing out the foundationalist concern over the ground of being in terms of a giant conjunctive fact doesn’t seem to really respect the concern that is driving the view in the first place. Moreover, the logic of ground, as it is commonly understood, is such that conjunctions are grounded in their conjuncts—exactly what explains the super conjunction are its conjuncts. Our second reason for rejecting this way of understanding the foundationalist concern also relates to the logic of ground. Although [[A] and [B]] necessitates [A] and [B] it does not metaphysically explain them. Quite on the contrary, as we have seen. The reflexivity objection, we would like to suggest, provides us with no good reason to suppose that no dependent entity can explain why anything has being whatsoever. Perhaps the reason we ought to endorse the second assumption, then, is that were our chains not to terminate we would be forced to ask a never-ending series of questions: dependent entities, by their very nature, have explanations, and for every new dependent entity that we invoke, we can ask of it ‘why does this thing exist?’ (or something of the like) ad infinitum. It’s not hard to see how some of the concerns extant in the literature can be understood in these terms. Exactly what a neverending series of questions would seem to leave us without is a completely satisfactory explanation, for example. Once again, we find this line of reasoning—the never-ending questions’ objection— wanting. Why? In short because it appears to us to beg the question. When do we cease to ask questions? When we arrive at the existence of something that does not demand that we ask of it certain (relevant) questions. And when do we arrive at the existence of such a thing? When we arrive at something fundamental, of course. To insist that

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ricki bliss and graham priest  our explanatory chains terminate is just to insist that there is something fundamental. Or put another way, to insist that our explanations be completely satisfactory is just to insist that there is something fundamental. What would not be a question-begging motivation for endorsing the never-ending questions’ objection would be if we had an independent reason for endorsing it: a reason over and above the mere stipulation that explanatory chains need to terminate. An independent reason to endorse the never-ending questions objection might just be that where we are forced to keep asking questions this must be because we haven’t answered the question we are seeking an answer to in the first place. This is one way we might interpret Schaffer’s concerns over the grounds of being, for example. Where of each new thing we are compelled to ask ‘and what explains the being of this thing?’ one might suppose we have not really answered the question that we were seeking an answer to in the first place. Be that as it may, this reason to endorse the second assumption of the argument is peculiar. Our reason for thinking so is that it seems to trade on a confusion. Where we are forced to ask a never-ending series of questions, the problem may not be that the chain does not terminate, but that one may be going about answering the question in the wrong way. Put differently, the never-ending questions are not themselves the disease, but, instead, a symptom of a deeper problem. Interesting as this may be, this is not a good reason to suppose that no dependent entity can explain where being comes from. Why? Let us grant that the series of neverending questions and answers is generated because we are going about answering the questions in the wrong way. But if this is the case, what good will terminating the chain do? How does terminating the chain at some, likely arbitrary, point solve our problem if the problem is generated by a mismatch between question and answer in the first place? It is hard to see how it could. Moreover, what reason could we have for supposing that our answers are incorrect? If this reason for endorsing the second crucial assumption is to play the justificatory role that we need it to, it cannot be because we are lumbered with a never-ending series of questions and answers because no dependent entity can explain why anything has being whatsoever. Exactly what we appear to be left without is a motivation for the assumption. Let us turn, then, to the same questions objection. Suppose one of us were to ask you why there are any flamingos whatsoever. Suppose that you responded that there are flamingos because there are an enormous number of them living in the Rann of Kutch. Dissatisfied with your response, we might press you and say, ‘Ok, fine. So why are there those flamingos?’ Were you to respond by pointing out that those particular flamingos exist because their parents existed, we would be forced to suggest that you seem to be missing the point. Whilst it is surely true that the particular flamingos presently inhabiting the Rann of Kutch exist because their parents existed, no number of flamingos can help us explain why there are any flamingos whatsoever. By parity of reasoning, no dependent entity—entity with being—can help us explain why there are any beings whatsoever. What is going wrong in both of these cases is that we are

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 the geography of fundamentality: an overview invoking the very thing for which we are seeking an explanation in our explanans.41 The problem is not that we have an infinitude of explanations, but rather that things go badly out of the gate. We are forced to keep asking the same question because we simply never receive an answer to it. Whilst we find this line of reasoning compelling, what it seems to supply us with—as with one interpretation of the never ending questions’ objection—is more a restatement of the principle for which we are seeking a justification and less a justification itself. The same questions objection seems to presuppose the idea that no dependent entity can explain where being comes from rather than justify it. But perhaps there is some principle lurking in the background here according to which where F is any predicate that applies to dependent entities only, you can’t explain why there are any F things at all by invoking only those things that are F, even if your explanations go on forever.42 Let us call this principle the predicate satisfaction principle. According to the predicate satisfaction objection, no dependent entity can be invoked to explain why anything has being whatsoever because this would violate the predicate satisfaction principle. Although plausible seeming, we don’t think this is the right reason to endorse our second assumption. The reason for this is that we do seem to allow explanations where the G things explain the F things, but all the Gs happen to be Fs as well: all that is required to explain why there are any F things at all is the G things that happen to be the F things as well.43 Consider explanations of pain in terms of C-fibre firings. Anything that satisfies the predicate ‘being in pain’ will also satisfy the predicate ‘has C-fibre firings’, according to an appropriate version of physicalism, for example. As much as we can explain why there are any pains at all, some theories do so in terms of C-fibre firings, even though what satisfies the former predicate will also satisfy the latter. Or how about the predicate ‘is the auditory threshold for the normal human ear’? Let this predicate be denoted by F. The instantiation of this predicate is explained by the G things—‘sounds falling within a range of 16 to 32 hertz’—where everything that is a G is also an F. Other, non-scientific, examples also come to mind. Let F be ‘is money’ and G be ‘is used as money’, for example. At first blush, the predicate satisfaction principle appears intuitive and plausible, but it seems to be a principle stronger than one that we ought to accept. We frequently explain why there are any F things by making appeal to things that are, in fact, F things. So let us set this principle aside. Finally we come to what we call the same kind objection. According to this objection, no member of a kind can explain why that kind exists at all. A reason to endorse our second assumption would be that no dependent thing can explain, say,

41

See Bliss 2013 and Passmore 1970. See Maitzen 2013, p. 263 for the formulation of the principle from which the one here was borrowed. 43 See Keefe 2002 for a discussion of ways in which explanations that fit this structure can be unproblematic, and Maitzen 2013, p. 264 for an elaboration of the same point. 42

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ricki bliss and graham priest  why anything has being whatsoever because dependent things form a kind and no member of a kind can explain why that kind exists at all. Again, at least one of us finds this argument compelling (which is not to say it is well motivated!). And allusion to the idea that no member of a kind can explain why that kind exists at all can be found at various places in the literature.44 The argument also appears to be in keeping with at least one of the aforementioned motivations for foundationalism. Let us return to the idea that metaphysical explanations must be complete because it is the job of a metaphysical theory to give us a complete story of reality. In previous remarks, we suggested that there is at least one problem with this understanding of foundationalism cum metaphysical theory of everything: it leaves something out, namely, the fundamentalia. What appears to be implicit in this line of reasoning, however, is the idea that what we need an explanation for is all the dependent entities. It at least accords with foundationalism understood in this way that the world carves into two fundamental kinds—the derivative and the fundamental—and that whatever is of the same kind as the derivative cannot explain why there are any derivative things in the first place. Understanding what motivates foundationalism in these terms, and as ultimately being motivated by the same kind of objection, whilst plausible, brings with it its own problems. There are going to be difficult issues associated with the thought that ‘dependent entity’ and ‘fundamental entity’ are kind-terms. Where ‘dog’ seems like a good example of a kind term, it is less clear that ‘dependent entity’ is. Secondly, foundationalism, so motivated, seems to land us in the awkward position whereby the fundamentalia are invoked to explain the being of the dependent entities, but the being of the dependent entities also explains the fundamentalia!

.. arguments from theoretical virtue To the best of our knowledge, only one philosopher, Cameron, has explicitly endorsed an argument from theoretical virtue in defence of the fundamentality thesis.45 Cameron argues that a theory of reality on which we have a unified explanation of everything that needs an explanation is more virtuous than one on which we have no such unity. And metaphysical foundationalism, unlike its rivals, is just such a theory, according to Cameron. In addition to the argument from theoretical virtue that is available in the literature, one can imagine other possible arguments in the same spirit in defence of the fundamentality thesis. One might argue, for example, that metaphysical foundationalism has the virtue of being parsimonious where its rival, metaphysical infinitism, does not. Just as one might argue that foundationalism is simpler or more elegant than coherentism.

44

See Lowe 2003, p. 91.

45

Cameron 2008.

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 the geography of fundamentality: an overview Arguments from theoretical virtue are not designed to determine whether a theory is impossible. Rather, their role is to help us adjudicate between theories that we already believe to be possible. No argument from theoretical virtue, then, can lead us to conclude that any one from amongst our theories is to be stricken from our list of possibilities. But of course, what these arguments can do is help us make choices as to which of our theories are better than the others. That said, arguments from theoretical virtue are tricky, it seems, at least twice over. On the one hand, how we are to understand the virtues is a matter of contention. And, on the other hand, how the virtues interact with one another can make it hard to determine, in some cases, when a theory is, in fact, better than another. Consider the thought that foundationalism is more parsimonious than infinitism. Are we to understand this as a claim regarding quantitative or qualitative parsimony? If it’s the former, it is not entirely clear why we should believe this to be the case. Moreover, it is not clear why we should believe that any foundationalist could, in fact, run such an argument. Even though the infinitist denies that there is a fundamental level, and is, therewith, committed to infinitely descending chains, foundationalism says nothing about the number of entities that reside at the fundamental level; or any other for that matter. It is not at all obvious, then, that infinitism is more ontologically splashy than foundationalism after all, if what we are concerned with is the number of things. Things may look differently, however, if what we are counting are the levels themselves. Foundationalism does seem to do better as it does not commit us to ever deeper layers or levels. But again, things here aren’t as straightforward as they might appear. Were the world to be open at the top—with infinitely ascending layers, then whether or not there is something fundamental makes little difference to the parsimony of either view.46 Of course, it is not unreasonable to suppose that the world is closed at the top, but how both infinitism and foundationalism fare in terms of quantitative parsimony will be both complex and intimately involved with additional commitments. More often that not, what philosophers claim to be concerned with is qualitative rather than quantitative parsimony. But here, again, matters do not appear to be straightforward. Which view is more parsimonious than the other will depend upon which kinds we think are there to be counted. On one way of carving up the space, metaphysical infinitism is, in fact, more parsimonious than foundationalism; where foundationalism has two fundamental kinds (the derivative and the fundamental) infinitism only has one (the derivative). Suppose one were to argue, instead, that qualitative parsimony pertains to kinds and not categories, and that terms such as ‘fundamental thing’ are category terms. What we ought to count, so this argument goes, is all the cats, protons, and wave functions (rather than derivative and fundamental things), and that where there is nothing fundamental there is surely an obnoxious

46

See Bohn 2009 and Schaffer 2010 for contrasting discussions of this possibility.

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ricki bliss and graham priest  number of kinds instantiated in the world. But even here, if we want to push such an argument through, we require some additional assumptions. We would need to assume, for example, that for the foundationalist there is only a finite number of kinds of things that reside at the fundamental level. Alternatively, it might be the case, as has been suggested by Tahko (this volume) that below a certain level for the infinitist there are repetitions. It is possible, then, that in spite of not committing to a fundamental level, the infinitist is still not committed to there being an infinite number of kinds in the world. Matters are more complex still when we consider virtues such as simplicity or explanatory power. One might suppose that a reality with a hierarchical structure and a fundamental level is simpler than one on which, say, everything depends on everything else. But why this is the case is not altogether clear. It certainly seems simpler, but that could just be because it is the picture in terms of which most of us are accustomed to thinking. Arguably, a picture of reality on which everything is at the same level is simpler than one that contains multiple levels. Just as it is not clear which one of our theories wins the prize regarding explanatory power. On the one hand, foundationalism looks to do well as the presence of a fundamental level allows us to explain the existence of everything else. On the other hand, anti-foundationalisms look to do better as there is nothing that is posited that does not have an explanation. The balance could tip here, however, if it turns out that where there is nothing fundamental there is something that is unexplained. As we have seen in the discussion above, what anti-foundationalisms might leave us without an explanation for is, say, why anything has being at all. But of course, this is its whole own additional commitment that, as we have seen, brings with it its own potential strife. Much work remains to be done on the virtues of metaphysical foundationalism and its alternatives. What we think the outcome of such work will be is that it is far from clear that metaphysical foundationalism is obviously the most virtuous of the theories available to us. Of course there is much more to be said regarding the fundamentality thesis and the kinds of arguments offered in defence of it. Bohn (this volume) argues that we do not have good reasons to support the fundamentality thesis. Moreover, he argues in addition to this that we even have good reasons to think that it is false once we consider arguments involving gunk, junk, and hunk, and what he calls the metaphysical principle of sufficient reason. Trogdon (this volume) suggests that we can better understand Schaffer’s concern over the grounds of being in terms of the notion of reality inheritance and that the argument so understood doesn’t work. This is not to say, thinks Trogdon, that we, therewith, have no argument(s) in defence of the fundamentality thesis, but that we need to understand fundamentality (as motivated by the inheritance principle) as a kind of causal foundationalism or concrete foundationalism. Jago (this volume), on the other hand, proposes an account of a thing’s nature or essence that can allow us to provide grounding conditions for that

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 the geography of fundamentality: an overview thing. Essences, so understood, vindicate the hierarchy thesis as endorsed by the proponent of the standard view, but allow that the relation may be non-well-founded. It is somewhat surprising that the literature on metaphysical dependence and different kinds of structuralisms are not brought more often into dialogue with one another. Wigglesworth (this volume) argues that there are species of mathematical structuralism that can plausibly be understood (i) to involve metaphysical dependence relations and (ii) to challenge almost all of the structural features typically attributed to those relations. In particular, he argues, there are species of structuralism that involve both infinitely descending grounding chains and something fundamental. Tahko (this volume) argues that standard accounts of fundamentality are generally framed in terms of a kind of atomism. He argues that the fundamentality thesis, so understood, has problems accounting for the picture of reality that emerges from certain kinds of structuralisms. In place of this he proposes an account in terms of ontological minimality which, interestingly, can accommodate both species of fundamentality and infinitism. Morganti (this volume) undertakes a more general investigation of alternative conceptions of physical reality. In particular, he defends the idea that physics may well be able to be interpreted as supporting both infinitist and coherentist structures, supporting a kind of pluralism about metaphysical structure.

3.3 The Contingency and Consistency Theses We come now to a consideration of the contingency and consistency theses. We discuss each in their turn. As Wildman (this volume) correctly points out, how fundamentality intersects with modality is a spectacularly underexplored topic in the current grounding literature. It is safe to assume, however, that the standard view is one on which the fundamentalia are contingently existent. Of course, it is not necessary for a foundationalist to believe that the fundamentalia are merely contingently existent. Indeed, paradigmatic accounts of fundamentality have it that the fundamentalia are necessary beings: consider God or Plato’s forms, for example. The problem for such views, however, is how we are to preserve contingency in the world, for where the fundamentalia are necessary beings, and beings that necessitate the existence of everything else, there is only one way that the world can be, namely exactly how it actually is.47 Not everyone agrees that this problem is as serious as it sounds. Dasgupta, for example, has argued that a sufficiently constrained picture of reality on which the fundamentalia are necessary existents (facts about essences in his case) is plausible and appealing in certain ways.48 In his contribution to this volume, Wildman argues that there is a further issue related to the contingency thesis that has, thus far, not been treated in the literature. Whatever the modal status of the fundamentalia, is being fundamental itself a 47 See Skiles 2014 for a defence of the thought that grounding does not involve necessitation and Trogdon 2013 for a defence of the thought that it does. 48 Dasgupta 2016.

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ricki bliss and graham priest  necessary or merely contingent property of the fundamentalia? Whilst a number of combinations of views are possible—where the fundamentalia are, say, necessary beings and necessarily fundamental—Wildman argues that several prominent accounts appear to assume that the property of being fundamental is a merely contingent property of the fundamentalia. Wildman aims to explore how one might go about thinking about the intersection between modality and fundamentality, and argues that the contingency of fundamentality is not as problematic as one might suppose. Let us turn to the consistency thesis. Although one of us has developed and defended vigorously both logics and metaphysical accounts according to which contradictions are tolerable or even actual,49 there is no denying that the idea that contradictions are insufferable is a stalwart in the Western tradition. As noted above, some philosophers have been willing to question the first three of the foundationalists’ core commitments, but to the best of our knowledge, no one, to date, has challenged the thought that whatever properties grounding structures have, they have them consistently. As we have seen, in the case of the first three of the foundationalist’s commitments, philosophers have either offered, or it is at least possible to see, what the reasons might be for defending or rejecting any of these commitments. In the case of the consistency thesis, were a philosopher to defend their commitment, they would likely make appeal to the host of arguments commonly levelled against inconsistencies already available in the literature. We have no desire to rehearse or discuss the relevant arguments here.50 In the final paper in this collection, Casati develops an account of the ‘second Heidegger’ according to which we can understand him as espousing a kind of parafoundationalism; where the grounding structure both is and is not anti-symmetric, anti-reflexive, and extendable. One way of making sense of the later Heidegger, argues Casati, is to bite the bullet, accept that he endorses contradictions, and with it, a view according to which the grounding structure has inconsistent properties. Let us return momentarily to the taxonomy presented in §2. Recall that there were a number of lines—combinations of formal properties—that we dismissed as impossible. We said, for example, that the dependence structure cannot be symmetric, transitive, and anti-reflexive. Our taxonomy, along with every paper with one exception in this volume, has assumed the consistency thesis. In our taxonomy, we rule out multiple views as impossible on the assumptions that for each of our four formal properties a grounding structure either does or does not have (but not both) that property. Our taxonomy assumes consistent axioms and rules out as impossible any combination of views that, in spite of this, yields an inconsistency. But the kind of view presented by Casati does not appear in our taxonomy for the reason that, unlike us, the axiomatic system he proposes is itself inconsistent—a view so radical that it does not appear on our taxonomy in order to be ruled out in the first place. Rather

49

See e.g. Priest 1987, 2006.

50

Discussion can be found in Priest 2006.

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 the geography of fundamentality: an overview than return to the same old arguments in defence of consistency, and the arguments against them, we prefer to say a few words about why one might go to the trouble of challenging the consistency thesis to begin with. The history of philosophy (East and West) is a history littered with accounts that are plausibly construed as harbouring contradictions. This is not to suggest that the history of philosophy is a history of dialethism, for, indeed, many of The Greats found themselves deeply troubled by the appearance of contradictions in their systems. What it is to suggest is that many interesting and important philosophical accounts have invariably involved contradictions, and that one way of dealing with these contradictions is just to accept them. Of course, contradictions can crop up all over the place, but what we are particularly interested in are accounts of the structure of reality—accounts that are plausibly construed as being couched in the language of metaphysical dependence relations—that involve contradictions. Consider the picture of reality espoused by twentieth-century Japanese thinker Nishida.51 What emerges from his writings in influential texts such as his Basho is the idea that to be an object just is to be enplaced—what it is for an object to be a cat is to lie in the place ‘being a cat’. In the same way, a cat lies in the place ‘being a mammal’, and a mammal lies in the place of ‘being an animal’, and so on and so forth. This cannot go on forever, thinks Nishida, and there is the ultimate place—the place of all places—which for Nishida is absolute nothingness (which also happens to be pure consciousness). Importantly, if the place of all places is to do the work required of it, it must not, itself, lie in a place; which is just to say it cannot be an object. However, this is where the trouble begins. Indeed, as we have stated above, we know that, according to Nishida, absolute nothingness does not lie in any place. But it turns out that what this means is that absolute nothingness lies in at least one place, which is the place of not lying in a place! So it turns out that for Nishida, the ultimate ground both is and isn’t an object, which means it both is and isn’t fundamental. Faced with this seeming contradiction at the bottom of his world, one might suppose that Nishida was confused and that his system ultimately failed. There is textual evidence to support the thought, though, that pure consciousness as a dialethia was, in fact, exactly how Nishida intended it to be. Supposing that the enplacement relation is a metaphysical dependence relation, we appear to have an historical example of an inconsistent grounding theory.52 It is not simply that inconsistent grounding theories might be a useful tool for engaging with certain historical figures. They may well have other interesting applications. Let us suppose that the membership and parthood relations are kinds of metaphysical dependence relations. If this is the case, then it would seem that inconsistent set theory, inconsistent mathematics, and inconsistent mereologies all 51 52

See Maraldo 2015. Nishida’s view is closely related to the view of nothingness discussed in Priest 2014, ch. 13.

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ricki bliss and graham priest  entail, or at least have need of, inconsistent grounding theories. Of course, this will not convince anyone who is not on board with these particular research programmes in the first place, but the connections between the two, given a small number of very plausible assumptions, are wide-ranging and interesting.

4 Taking the Alternatives Seriously The taxonomy we presented in §2 makes certain matters clearer. We can now see, for example, that there are, in fact, many more logically possible views about the structure of reality than commonly supposed. But the taxonomy, and our classifications of certain views, have their limitations. As is clear, our taxonomy rules out as impossible very many combinations of properties of the dependence relations. Were we to employ certain types of non-classical logics, however, these views might become worthy of further consideration. We have also seen that our taxonomy fails to include the type of para-grounding account Casati (this volume) believes to be attributable to Heidegger. Moreover, the way in which we have distinguished between foundationalism, infinitism, and coherentism is overly simplistic. Had we tried to accommodate all the possible ways in which species of these views could be, the taxonomy would have become unwieldy and enormous. Much will turn on matters of definition, but it certainly seems that mixed worlds might be possible. One can imagine a world in which some dependence chains terminate in fundamentalia, where others do not; what we call such a view will depend upon how foundationalism and infinitism are defined. Understanding coherentism as a view according to which everything depends upon everything else is particularly strong. It is possible to understand coherentism as a kind of view, where various species of it may be possible. One might think that views that allow ontological loops of any kind ought to be considered weaker species of coherentism. If this is the case, it is worth pointing out that the mere presence of loops does not entail a denial of the fundamentality thesis, as defined. One can imagine a world in which there is something fundamental—even a world in which every grounding chain terminates in the fundamental—but some grounding chains contain loops. What we call such a view will depend upon how foundationalism and coherentism are defined. Indeed, we can even imagine a world in which some grounding chains are infinitely descending, some chains terminate in something fundamental, and some chains contain loops of various sizes. Our taxonomy, unfortunately, does not cater for such nuances. The metaphor of the Great Chain of Being has wielded very significant influence— both overt and covert—on the history of Western philosophy. It is about time to think outside that particular box. We believe that the contents of this volume provide ample evidence for this claim. Reality may well not have the metaphysical structure of a wellfounded chain, but a much more complex and fascinating one.

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 the geography of fundamentality: an overview

References Aikin, S.F. (2005), ‘Who is Afraid of Epistemology’s Regress Problem’, Philosophical Studies, vol. 126, pp. 191–217. Armstrong, D.M. (1997), A World of States of Affairs, Cambridge University Press. Audi, P. (2013), ‘A Clarification and Defence of the Notion of Grounding’, in Metaphysical Grounding: Understanding the Structure of Reality, Fabrice Correia and Benjamin Schnieder (eds), Cambridge University Press. Barnes, E. (2012), ‘Emergence and Fundamentality’, Mind, vol. 121, pp. 873–901. Bennett, K. (2011), ‘By our Bootstraps’, Philosophical Papers, vol. 25, pp. 27–41. Bliss, R.L. (2013), ‘Viciousness and the Structure of Reality’, Philosophical Studies, vol. 166, pp. 399–418. Bliss, R. (2014), ‘Viciousness and Circles of Ground’, Metaphilosophy, vol. 45, pp. 245–56. Bliss, R. (forthcoming), ‘What Work the Fundamental?’, Erkenntnis. Bliss, R. and Priest, G. (2017), ‘Metaphysical Dependence and Reality: East and West’, in Buddhist Philosophy: A Comparative Survey, Steven Emmanuel (ed.). Basil Blackwell. Bliss, R.L. and Trogdon, K. (2014), ‘Metaphysical Grounding’, in E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/grounding/. Bohn, E.D. (2009), ‘Must There Be a Top Level?’, The Philosophical Quarterly, vol. 59, no. 235, pp. 193–201. Cameron, R. (2008), ‘Turtles All the Way Down’, Philosophical Quarterly, vol. 58, pp. 1–14. Corkum, P. (2013), ‘Substance and Independence in Aristotle’, in Varieties of Dependence: Ontological Dependence, Supervenience, and Response-Dependence, Benjamin Schnieder, Alex Steinberg, and Miguel Hoeltje (eds), Basic Philosophical Concepts Series, Philosophia Verlag, pp. 36–67. Corkum, P. (2016), ‘Ontological Dependence and Grounding in Aristotle’, Oxford Handbooks Online in Philosophy, Oxford University Press. Dasgupta, S. (2016), ‘Metaphysical Rationalism’, Noûs, vol. 50, no. 2, pp. 379–418. Dixon, T.S. (2016), ‘What is the Well-Foundedness of Grounding?’, Mind, vol. 125, pp. 439–68. Fine, K. (1994), ‘Essence and Modality’, Philosophical Perspectives, vol. 8, pp. 1–16. Fine, K. (1995), ‘Ontological Dependence’, Proceedings of the Aristotelian Society, vol. 95, pp. 269–90. Fine, K. (2001), ‘The Question of Realism’, Philosopher’s Imprint, vol. 1, pp. 1–30. Fine, K. (2010), ‘Some Puzzles of Ground’, Notre Dame Journal of Formal Logic, vol. 51, pp. 97–118. Fine, K. (2013), ‘Guide to Ground’, in Metaphysical Grounding: Understanding the Structure of Reality, Fabrice Correia and Benjamin Schnieder (eds), Cambridge University Press. Jenkins, C.S. (2011), ‘Is Metaphysical Dependence Irreflexive?’, The Monist, vol. 94, no. 2, pp. 267–76. Keefe, R. (2002), ‘When Does Circularity Matter?’, Proceedings of the Aristotelian Society, New Series, vol. 102, pp. 275–92. Lovejoy, A. (1934), The Great Chain of Being, Harvard University Press. Lowe, E.J. (2003), ‘Individuation’, in The Oxford Handbook of Metaphysics, Michael J. Loux and Dean W. Zimmerman (eds), pp. 75–99. Lowe, E.J. (2009), More Kinds of Being: A Further Study of Individuation, Identity and the Logic of Sortal Terms, Wiley-Blackwell.

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ricki bliss and graham priest  Lowe, E.J. (2013), ‘Asymmetrical Dependence in Individuation’, in Metaphysical Grounding: Understanding the Structure of Reality, Fabrice Correia and Benjamin Schnieder (eds), Cambridge University Press. Maitzen, S. (2012), ‘Stop Asking Why there’s Anything’, Erkenntnis, vol. 77, pp. 51–63. Maitzen, S. (2013), ‘Questioning the Question’, in The Puzzle of Existence: Why is there Something Rather than Nothing?, Tyron Goldschmidt (ed.), Routledge. Maraldo, J.C. (2015), ‘Nishida Kitar¯o’, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), http://plato.stanford.edu/entries/nishida-kitaro/. Passmore, J. (1970), Philosophical Reasoning, Duckworth. Priest, G. (1987), In Contradiction, Martinus Nijhoff. Second edition, Oxford University Press (2006). Priest, G. (2006), ‘Doubt Truth to be a Liar’, Oxford University Press. Priest, G. (2014), One, Oxford University Press. Rabin, G.O. and Rabern, B. (2016), ‘Well Founding Grounding Grounding’, Journal of Philosophical Logic, vol. 45, no. 4, pp. 349–79. Raven, M. (2013), ‘Is Ground a Strict Partial Order?’, American Philosophical Quarterly, vol. 50, pp. 191–9. Raven, M. (2018), ‘Fundamentality Without Foundations’, Philosophy and Phenomenological Research, vol. 93, no. 3, pp. 607–26. Schaffer, J. (2009), ‘On What Grounds What’, in Metametaphysics: New Essays on the Foundations of Ontology, David Manley, David J. Chalmers, and Ryan Wasserman (eds), Oxford University Press, pp. 347–83. Schaffer, J. (2010), ‘Monism: The Priority of the Whole’, Philosophical Review, vol. 119, pp. 31–76. Schaffer, J. (2012), ‘Grounding, Transitivity and Contrastivity’, in Metaphysical Grounding: Understanding the Structure of Reality, Fabrice Correia and Benjamin Schnieder (eds), Cambridge University Press, pp. 122–38. Schaffer, J. (2016), ‘Grounding in the Image of Causation’, Philosophical Studies, vol. 173, pp. 49–100. Sider, T. (2011), Writing the Book of the World, Oxford University Press. Skiles, A. (2014), ‘Against Grounding Necessitarianism’, Erkenntnis, vol. 80, pp. 717–51. Thomasson, A. (2007), Ordinary Objects, Oxford University Press. Trogdon, K. (2013), ‘Grounding: Necessary or Contingent?’, Pacific Philosophical Quarterly, vol. 94, pp. 465–85. Tahko, T.E. and Lowe, E.J. (2015), ‘Ontological Dependence’, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), http://plato.stanford.edu/entries/dependence-ontological/. Wilson, J. (2014), ‘No Work for a Theory of Ground’, Inquiry, vol. 57, pp. 535–79.

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PA R T I

The Hierarchy Thesis

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1 Grounding Orthodoxy and the Layered Conception Gabriel Oak Rabin

1 Introduction Our world contains a shocking variety of stuff, from the very large (planets, quasars, galaxies) to the very small (quarks, leptons, bosons), with lots in between (koalas, canyons, coins). Here’s a common thought: All this stuff can be organized into a hierarchy of levels. The galaxies and quasars are “on top”, the canyons and koalas lie in the middle, below them come molecular compounds, and at the very bottom are the tiny particles and other phenomena (nuclear forces, electromagnetism) discussed in fundamental physics. The idea of “levels” in the special sciences reflects this hierarchical conception of the world. In the layering of special sciences, physics occupies the bottom, with chemistry, then biology, then psychology, then economics, lying on top. What makes one phenomenon “higher” than another? One answer is that a relation of dependence creates the hierarchical structure. Psychology depends on biology, which depends on chemistry, which depends on physics. Of course, it’s not the sciences themselves that depend on each other (psychology predates chemistry), but rather the phenomena the sciences study. Which psychological states I have depends on which biological states I have, but not vice versa. Which biological states I have depends on which chemical states I have, but not vice versa. Et cetera. Let’s use the phrase ‘the layered conception of reality’ (‘the layered conception’ for short) as a label for the general idea that reality is layered in a hierarchy structured by relations of dependence. We can add a claim about fundamentality to the layered conception: the lower tiers of the layering are more fundamental than the higher tiers. I will make this further assumption in what follows. Much philosophical ink has been recently spilled inquiring into the nature of ground. Ground is alleged to be a/the relation of metaphysical dependence, explanation, and/or priority. It is that relation the physicalist alleges to hold between the mental and the physical, that the utilitarian claims holds between moral facts and the facts about pleasure and pain, and that many claim to hold between the fact that P and the fact that P or Q. In each case, the ground makes the grounded obtain.

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 grounding orthodoxy and the layered conception The grounded metaphysically depends on is metaphysically explained by, and/or is ontologically posterior to, the ground. Ground should be distinguished from causal dependence. Ground often (and perhaps always) holds synchronically, between two relata at the same time. For example, the physicalist claims that my current pain is grounded in my current brain state. In contrast, causal dependence relates items across time. The dualist can admit that my past brain state caused my current pain, while denying that pain is grounded in the brain.1 Once we have a notion of ground on board, it seems natural to slot that notion into the layered conception. After all, relations of dependence generate the layering, and ground is metaphysical dependence. Voila! Let’s plug in everything we’ve learned in all the literature on ground to generate the layered picture of the world. Theorists of ground have had exactly this idea (deRosset [2013]). In fact, much of the appeal of the notion of ground, and its recent rise to prominency in metaphysics, comes from the intuitive appeal of the layered conception. Using ground to generate a hierarchy of dependence, and thereby vindicate the layered conception, is a nice thought, but it faces serious obstacles. Only a relation with certain formal features is capable of delivering the layered conception of the world. For example, a layered hierarchy generated by a relation that loops will contain X above Y, above Z, but X will appear again down below Z! Loops aren’t amenable to creating the type of structure characteristic of the layered conception. Thankfully, the orthodox views on ground hold that ground has several features that ensure that ground will be able to provide the structure characteristic of the layered conception. Let’s label the conjunction of the following four theses ‘the orthodoxy’. (All of these claims should be interpreted as preceded by universal quantifiers ∀X, ∀Y, ∀Z.): (TS) Transitivity: If X grounds Y and Y grounds Z, then X grounds Z. (AS) Antisymmetry: If X grounds Y, then Y does not ground X. (IR) Irreflexivity: X does not ground X. (FD) Foundationalism: Everything is ultimately grounded in a bottom layer with no further ground.2 A relation that is transitive and antisymmetric cannot contain loops. This takes care of the worry that ground might generate loops, and thereby be unable to vindicate the layered conception. Or does it? The problem here is that every component of the orthodoxy has been challenged. Schaffer [2012] denies transitivity. Barnes [2018] denies antisymmetry. Jenkins [2011] questions irreflexivity. Bliss [2014] even argues that ground might generate loops! 1 I leave open the possibility that causation might, in the end, turn out to be a form of ground. Or vice versa. But prima facie, they look different, despite sharing some similarities. 2 This constraint sometimes goes under the banner that ground must be “well-founded” (Schaffer [2010]: 37). This is an unfortunate choice of terminology: a relation of ground that is not well-founded in the set-theoretic sense can still have a foundation. For clarification of these issues and of what “well-founded” amounts to when it comes to ground, cf. Rabin & Rabern [2015].

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gabriel oak rabin  For the most part, theorists have either ignored the alleged counterexamples and continued to insist on the orthodoxy, or fought against the counterexamples outright (e.g. Litland [2013]). A major reason for maintaining the orthodoxy in the face of alleged counterexamples is the worry that without the formal features the orthodoxy provides, ground will prove unable to vindicate the layered conception. In the rest of this paper, my goal will be to alleviate this worry. I will argue that, even without any of the formal features listed above—transitivity, asymmetry, irreflexivity, or foundationalism—ground can still provide the dependence structure the layered conception requires. In fact, I will argue that relaxing the assumptions in the orthodoxy actually makes ground better able to generate the structure characteristic of the layered conception. Here’s a roadmap for the remainder of the paper. In the next section (2: “Ground as the Generator as Layers”), we put some flesh on the bones of the idea of the layered conception and how ground interacts with it. Each of Sections 3–6 explores how ground fares in its ability to vindicate the layered conception under the relaxation of some element of the orthodoxy. We consider abandoning foundationalism, antisymmetry, irreflexivity, and transitivity (in that order). The conclusory Section 7 steps back to consider the resulting overall picture.

2 Ground as the Generator of Layers The layered conception is admittedly vague. In this section, we examine ways to put flesh on the bones of the bare idea and how we might utilize ground to elucidate the structure the layered conception mandates. The layered conception, at first pass, looks something like this: economics

psychology

biology

chemistry

physics

As I mentioned before, the claim is not that the sciences themselves, considered as fields of inquiry, depend on each other. Economists can and should go about their business without asking chemists for instructions. Instead, the phenomena studied by one field of inquiry depend on, and are determined by, phenomena studied by another

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 grounding orthodoxy and the layered conception field of inquiry. But that is not quite right. Biology depends on chemistry, but the camouflage in Arabian cuttlefish (a biological process) has absolutely nothing to do with the oxidization of steel beams (a chemical process) in a shipyard in New Orleans. Most particular concrete biological happenings have nothing to do with, and certainly don’t depend on, most particular concrete chemical happenings. The same is true at the level of types. It’s likely that the biological phenomenon of cuttlefish camouflage has nothing to with the chemical process of oxidization. (The marine biologists could prove me wrong here, but I feel like I’m on safe ground.) However, the camouflage patterns of a particular cuttlefish do depend on some chemical facts about that particular cuttlefish. And the camouflage of a different cuttlefish depends on chemical facts about that cuttlefish. Furthermore, the two instances of cuttlefish camouflage might depend on the very same type (not token) of chemical property—call it ‘C’. If the pattern is widespread, then we might claim a dependence of cuttlefish camouflage on chemical property C. This yields a lesson. We infer dependencies between types of properties from patterns in dependencies of particular tokens of those properties. We now come to ground. Ground is typically understood as a dependence relation between particular facts, states of affairs, particulars, or properties. The mass of this table is grounded in the mass of these four legs and this tabletop. Ground gives us the particular instances of dependency. From these particular token-dependencies we can infer the type-dependencies characteristic of the layered conception. Sometimes, the type-dependencies are specific, such as when the firing of neurons is grounded in an electrical imbalance between positively charged potassium ions and negatively charged sodium. But these cases are rare. More often, the dependency is not specific, and a higher-level type, such as cuttlefish camouflage, does not depend on only one lower-level type, such as potassium/sodium interaction. In each particular case of cuttlefish camouflage, there is some chemical processes underlying it. But it needn’t be the same type of chemical process in each case. These points are familiar from research on multiple realizability. Most phenomena are realizable, or groundable, in a wide variety of underlying lower-level phenomena. The various lower-level phenomena that all give rise to a single type of higher-level phenomenon might have little in common, other than the fact that they ground, or give rise to, the same type of higher-level happenings. Of course, these lower-level happenings, despite their dissimilarities, remain, for example, chemical. So at the very least, we can say that cuttlefish camouflage, even if it does not depend on any particular chemical type, depends on “chemistry”, or “the chemical level”. Call a complete story of the world’s grounding relations between particular facts a grounding graph (so called because it can be represented by a graph in the mathematical sense: a set of nodes with directed relations between them). The grounding graph gives us both more and less than we want from the layered conception. It gives us more because it gives us thousands of cuttlefish camouflage dependences—one for each cuttlefish. That’s more than we need. But the grounding graph also gives us less.

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gabriel oak rabin  psychology

geology

chemistry

Figure 1.1. Option (i): geology and psychology on the same level, equally fundamental. psychology

geology

chemistry

Figure 1.2. Option (ii): geology and psychology incommensurable, neither more, nor less, nor equally fundamental.

The layered conception says that biology is above chemistry. This entails that cuttlefish x’s biological camouflage is above cuttlefish y’s chemical properties. But grounding relations don’t deliver this verdict. There are no grounding relations between the two. In mathematical terms, the layering conception seems to demand a total order, in which every pair of items is related by either the “higher than”, “lower than”, or “at the same level as” relation. In contrast, ground is a (very) partial order. A randomly chosen pair of items is unlikely to be related by ground at all. There’s no easy recipe for generating a total order from a partial order. However, there are reasons to be optimistic that the ordering characteristic of the layered conception can be gleaned from the grounding graph. First, as discussed above, we can look for patterns in the particular grounding claims. There are many such patterns. Sometimes the patterns are specific (neural firing depends on potassium–sodium ion imbalance). Other times they are not (each instance of cuttlefish camouflage depends on some chemical property). But the patterns are there. If they weren’t, the layered conception wouldn’t be so appealing in the first place. Second, we may not want the layered conception to deliver a total ordering. Both geology and psychology are above chemistry. Neither lies above the other. Two options remain: (i) they are at the same level or (ii) they are incommensurable. If the layered conception demands a total ordering, then (i) is the only option. A total ordering does not permit cases in which two items are incommensurable. However, I think that option (ii) is preferable, and that we should give up the idea that the layered conception requires a total ordering. Here’s why. It remains open to discover some other range of phenomena, below psychology, but which contains no grounding relations to geology. Computation provides a potential example. If all psychological phenomena are ultimately grounded in computational phenomena (a not implausible hypothesis), then psychology will lie above computation. Suppose

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 grounding orthodoxy and the layered conception we choose option (i), placing geology on the same level with psychology. Ground tells us to place computation below psychology, which we’ve placed on the same level as geology. We’re now forced to put computation below geology. This seems wrong. The relation between computational phenomena and geological phenomena is exactly the same as the relation between psychological phenomena and geological phenomena: nil. Whatever the reasons in favor of placing psychology and geology on the same level were, exactly the same reasons apply to placing computation and geology on the same level. It would be arbitrary to place geology and psychology on the same level with computation below, rather than, say, geology and computation on the same level, with psychology above. The desire to place neither geology nor psychology above the other can be satisfied without placing them at the same level in the layered conception. Instead, we should give up the idea that the layered conception mandates a total ordering. Once we do so, ground, with its very partial order, looks better as a guide to reality’s layers (as conceived by the layered conception). Admittedly, the layered conception demands an ordering that is closer to total than the ordering provided by ground. But patterns among ground’s partial ordering can bridge the gap between ground’s very partial order and the layered conception’s less partial order.

3 Foundationalism and the Layered Conception Foundationalism is the easiest bit of the orthodoxy for the fan of the layered conception to reject. Simply put, the layered conception does not require a foundation. The Greek philosopher Xenophanes was an early proponent of the layered conception (Patzia [n.d.], Lesher [1992]). Arguably, he also believed foundationalism to be false, and that the world consisted of alternating layers of earth and water.3 Of course, one could build foundationalism into the layered conception, forming the-layered-conception-with-a-bottom. In so doing, one would make the layered conception developed via ground incompatible with rejection of foundationalism about ground. But one certainly need not insist on a bottom layer. The basic idea of a reality structured by relations of dependence does not require a foundation.

4 Anti-Symmetry and the Layered Conception The basic idea of using ground to generate the layered conception comes from the following principle: (The Simple Principle) If x grounds y, then x is at a lower level / more fundamental than y. 3

Xenophanes believed in an infinite temporal descent of watery and earthy stages (Hippolytus of Rome [2015] attributes this view to Xenophanes in his Refutation of All Heresies: 1.14). Whether this entails anti-foundationalism of ground will turn on whether temporal, or causal, dependence can be parlayed into metaphysical dependence.

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gabriel oak rabin  The simple principle gets us from claims about grounding relations between particulars (facts, objects, or properties) to claims about where those particulars fit into reality’s layers. To generate the full layered conception, we still need to discern patterns concerning where certain types of things occur in reality’s layers. But, via the simple principle, ground gives us a good start. The simple principle does not work so well, however, if ground fails to be antisymmetric. According to the simple principle, if x grounds y, then x is lower than y. If y grounds x (violating anti-symmetry), then y is lower than x. And that doesn’t make sense, at least in so far as I understand the layered conception. Biology can’t be both above and below chemistry. There are decent prima facie considerations in favor of rejecting the anti-symmetry of ground. Barnes [2018] argues that we should accept symmetric dependence in a wide variety of cases, from immanent universals to states of affairs to mathematical ontology. In one example, she argues that it is essential to the evacuation at Dunkirk that it is part of World War II. And it is essential to World War II that it contain the evacuation at Dunkirk. If this is correct, it is plausible to maintain that each of World War II and the evacuation at Dunkirk depend on the other. Voila: symmetric ground! This is neither the time nor the place to have the fight over whether ground is or is not anti-symmetric. Barnes presents some plausible cases. At the least, proponents of the theory-combinations Barnes discusses might want to take advantage of a non anti-symmetric (i.e. sometimes symmetric) notion of ground. For their sake, it’s worth exploring how rejecting the orthodoxy regarding the anti-symmetry of ground interacts with the layered conception. I believe that, ultimately, rejection of anti-symmetry for ground does not impugn ground’s ability to vindicate the layered conception. In fact, cases of symmetric ground might help us better understand how reality is layered. I argue for these claims in the remainder of this section. The simple principle, above, is one way to infer layering from relations of ground. But once we recognize the possibility of symmetric ground, we can opt for the following slightly less simple principle. (The Slightly Less Simple Principle) If x grounds y, and y does not ground x, then x is more fundamental/at a lower level than y.

The Slightly Less Simple Principle is a clear improvement over the Simple Principle. If ground is anti-symmetric, then the ‘y does not ground x’ clause in the Less Simple Principle is vacuous, and the Less Simple Principle reduces to the Simple Principle. But if symmetric ground does occur, the Slightly Less Simple Principle avoids the problematic result above, where x is both above and below y in reality’s layering. In cases of symmetric ground, what should we say about the layering relations of the items that ground each other? We should not place either above the other. This leaves two options, which we’ve already seen: (i) they are at the same level or (ii) they are incommensurable. I believe that (i) is the better option here. x and y are related

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 grounding orthodoxy and the layered conception by ground. It seems odd to say that they bear no relation to each other in reality’s layering. The layering is still a layering based on dependence. And x and y depend on each other. I propose we place x and y on the same level. Considerations involving the transitivity of ground further support placing x and y on the same level. The transitivity of ground will guarantee that, in cases of symmetric ground, the symmetric grounders will be at the pseudo-same level. For any x and y, x and y are at the pseudo-same level in reality’s layering if and only if for any z, if z is above x, then z is above y, and if z is below x, then z is below y. In simple terms, two items at the pseudo-same level are both above, and below, all the same stuff. This does not quite guarantee sameness of level. x and y might still be incommensurable. It is worth noting that this case is slightly different than the geology–biology case discussed earlier, in which I argued for incommensurability of level. In that case, computation lay below biology, but remained incommensurable with geology. This would not be possible if geology and biology were incommensurable but at the pseudo-same level. Their pseudo-sameness would guarantee that if biology were higher than computation, geology would be too. I admit that my arguments leave some space for claiming that symmetric grounders are incommensurable in level. But given that (a) they are related by dependence and (b) they are at the pseudo-same level, I believe we should say that they lie at the same level in reality’s layering.

5 Irreflexivity and the Layered Conception Grounding orthodoxy holds that ground is irreflexive: nothing grounds itself. Jenkins [2011] has challenged the orthodoxy, claiming that it’s better to leave open the possibility that something could ground itself. For example, an identity theorist in philosophy of mind might simultaneously claim that (a) consciousness is identical to electrical flow in the brain’s dorsal stream and (b) mental phenomena, including consciousness, are grounded in brain phenomena, such as electrical flow in the dorsal stream. If the orthodoxy is correct, this position is incoherent: ground is irreflexive. Consciousness can’t be grounded in electrical flow in the dorsal stream, to which it is identical. Understandably, Jenkins argues that our conception of ground should not rule out by fiat the combination of metaphysical views espoused by the envisioned identity theorist. We want ground to provide a useful philosophical tool for conceptualizing various debates in metaphysics. In so far as an irreflexive conception of ground makes unintelligible a plausible and popular view in the philosophy mind, it fails to accomplish this goal. The best solution, argues Jenkins, is to give up the irreflexivity of ground. The result is not that ground is reflexive (i.e. everything grounds itself), but that sometimes, things do ground themselves. There are ways to resist this line of thought. But acceptance, in certain cases, of reflexive ground, seems desirable, particularly so in light of specific philosophical

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gabriel oak rabin  views, like the identity theory in philosophy of mind. How much does giving up the irreflexivity of ground affect ground’s ability to vindicate the layered conception? The answer is, “Not much.” In combination with the simple principle, cases of irreflexive ground cause problems. Continuing with the identity claim as our example, the two will entail that conscious experience is above itself (and below itself) in the layered conception. That’s weird. Like with symmetric ground, a shift from the simple principle to the slightly less simple principle saves the day. The slightly less simple principle avoids the result that conscious experience is above (and below) itself in reality’s layering. The choice between an irreflexive conception of ground and a reflexive conception might be partly terminological. In the semantics of Fine [2012], weak ground, in which everything grounds itself, is taken as the primitive notion. Fine does this partly for reasons of simplicity. But we might think that formal simplicity provides some reason for taking the reflexive conception of ground to be more fundamental, even if talk of an entity’s grounding itself rubs against thought of ground as a form of metaphysical explanation and/or determination. One important difference between giving up irreflexive ground and giving up antisymmetric ground is worth noting. If ground is reflexive, that is, if everything grounds itself, there is no serious challenge to the layered conception. We need simply shift from the unreflective simple principle to the slightly less simple principle. Such a move will avoid the unsavory implications of cases of reflexive ground (e.g. that conscious experience is both above and below itself), but still allow ground to play its intended role in generating the remainder of reality’s layering. On the other hand, if ground is symmetric, that is, if every time x grounds y, y grounds x, the goal of using ground to generate reality’s layering falls into serious jeopardy. There’s no simple fix for symmetric ground. (Thankfully, to my knowledge no one has suggested that ground is symmetric.) The basic thought behind using ground to generate the layered conception is that if x grounds y, x is lower than y in the layered conception. In the first instance, ground relates tokens, or particular facts. The layered conception relates types (as well as tokens of those types). Some theorizing is required to get from the tokens to the types. Adoption of a reflexive conception of ground, in which everything grounds itself, requires only minimal modification of the basic idea. A shift from the basic idea, expressed in the simple principle, to a more nuanced version of the same idea via the slightly less simple principle, does the trick and rescues a reflexive conception of ground’s ability to generate reality’s layering. In contrast, symmetric ground, in which every time x grounds y, y also grounds x, completely voids the basic idea. Ground will never give us the result that x is above (or below) y in reality’s layering. In Section 4, I argued that in cases of symmetric ground we should maintain that the symmetric groundees should be placed at the same level in reality’s layering. If this is correct, then ground will provide some, but not much,

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 grounding orthodoxy and the layered conception guide to reality’s layers. Ground will be sufficient for sameness of level. But some other relation will be required to do the heavy lifting in the generation of reality’s vertical hierarchy. In sum, I claim that neither acceptance of particular cases of reflexive ground nor acceptance of a fully reflexive conception of ground seriously challenges the ability of ground to vindicate the layered conception. Particular individual cases of symmetric ground can be easily handled. But a full-blown symmetric conception of ground will void ground’s ability to provide reality’s layering.

6 Intransitivity and the Layered Conception Lastly, we come to the transitivity of ground, which says that if x grounds y, and y grounds z, then x grounds z. Schaffer [2012] has challenged this principle. One of his arguments revolves around a dented sphere. Schaffer claims that while it’s plausible that (a) the fact that the dented sphere has a dent grounds that fact that it has determinate shape S and (b) the fact that the dented sphere has determinate shape S grounds the fact that it is more-or-less spherical, it is implausible that (c) the fact that the dented sphere has a dent grounds the fact that it is more-or-less spherical. After all, writes Schaffer, “the thing is more-or-less spherical despite the minor dent, not because of it” (127). There are ways to resist the argument, but I do not wish to weigh in on the issue here. Schaffer’s example is prima facie plausible, and he provides other alleged counterexamples to transitivity. At the least, some will want to deny the transitivity of ground. For their sake, it’s worth exploring how such a denial will affect ground’s interaction with the layered conception. The layered conception’s hierarchical structure is transitive. If biological phenomena lie above chemical phenomena, and psychological phenomena lie above the biological, then psychological phenomena lie above chemical phenomena. We need some transitivity in the layered conception. Consider a graphical representation of the world’s grounding relations, in which nodes represent the relata of grounding relations and arrows between nodes represent relations of ground. (Arrows point from the ground to the grounded.) From the graph, we can observe the beginnings of reality’s layering. The fact that my brain contains proton p lies below the fact that my brain contains potassium molecule m, which lies below the fact that my brain contains neuron n. This layering of particular facts proceeds from the physical to the chemical to the biological. The generation of this layering does not require an arrow, or a relation of ground, between proton p and neuron n or their associated facts. A failure of transitivity, say, between the proton and the neuron, will not interfere with the generation of this layering. From a formal standpoint, this should be no surprise. For any non-transitive relation R one can always take the transitive closure of R to generate a transitive

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gabriel oak rabin 

neuron n

molecule m

proton p

electron e

relation R* that will contain R as a subset, in the sense that if Rab, then R*ab. Even if ground is not transitive, we can take ground’s transitive closure to generate ground*. But we need not resort to such formal tricks. The layered conception involves a layering of fundamentality. The chemical is more fundamental than the biological. “More fundamental than” is transitive, as are “higher than” and “lower than” in reality’s layering. Ground and fundamentality are linked by the simple and/or slightly less principle we’ve discussed. Grounding relations have implications for relations of relative fundamentality and for reality’s layering. But ground can fail to be transitive, and even be anti-transitive, yet still have these implications for the transitive relations for “more/less fundamental than” and “lower/higher in reality’s layering than.” Assuming this transitivity, a double application of the simple (and/or slightly less simple) principle yields the result that if x grounds y, and y grounds z, then x is more fundamental than z, and x is lower than z in reality’s layering. This is so even if x does not ground z. One final worry goes as follows. If ground is not transitive, but the hierarchical structure of the layered conception is, what is the layered conception a hierarchy of? The preceding discussion should alleviate the worry. The layered conception’s hierarchical structure captures relations of relative fundamentality, which have an intimate relation to ground, despite the fact that they remain transitive even when ground is not. We can get the transitive structure constitutive of the layered conception even if ground fails to be transitive. The transitivity can come in later, with the relations (“more/less fundamental than,” “lower/higher than”) that properly constitute reality’s layering, and to which ground is a guide.

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 grounding orthodoxy and the layered conception

7 Conclusion The key to making unorthodox views about the formal properties of ground compatible with the layered conception is to recognize that there is a gap between what grounds what and the layered conception. One can’t just “read off ” reality’s layering from the facts about ground. The move from what grounds what to reality’s layering is substantive. I believe we should be optimistic about gleaning from the facts about ground a useful and informative structure that roughly matches our pre-theoretic conception of how the features of reality are layered. First, principles linking ground and layering, or fundamentality, such as the simple and/or slightly less simple principle, give us a healthy start in generating a layering from ground. But the task of evaluating the patterns in the grounding relations between particulars, and gleaning from those patterns a layering of the various properties, and types of properties (geological, biological), remains. Second, we may have to abandon some of our pre-theoretic ideas about reality’s layering. I argued that we should abandon the claim that reality’s layering generates a total order. Geology and biology are incommensurable; neither lies above or below the other. The layering’s order is closer to total than ground’s order. But both are partial. The gap between ground and layering both helps and harms. It harms because it makes the task of discerning reality’s layering more difficult. Even after we possess a complete story of what grounds what, we must still do philosophical work to determine what is more fundamental than what. It helps because it permits the layering to be well-behaved even when ground is not. For example, symmetric cases of ground don’t force us to claim that the symmetric groundees each lie above (or below) the other in reality’s layering. The grounding orthodoxy ensures that ground behaves nicely. It will be a good little transitive, anti-symmetric, irreflexive, foundationalist relation. This obedient behavior ensures the absence of problematic grounding structures, such as loops, that create problems when we move from ground to reality’s layering. But the heretics are out there. Not all theorists of ground believe in the orthodoxy. I’ve covered a variety of reasons to doubt various parts of that orthodoxy. These theorists will probably be willing to give up some nice behavior in order to have a theoretical tool that can do the metaphysical work they want done. For this reason alone, it’s worth exploring how reality’s layering might go if we accept an unorthodox view about ground and want to maintain an intimate link between ground and the layered conception. There are good reasons for the orthodoxy. The principles seem prima facie correct. It’s convenient to have a formally well-behaved relation. But there are good reasons to doubt the orthodoxy. Cases like Jenkins’ reflexive dependence of pains on brains, or Barnes’ symmetric dependence of World War II and the evacuation at Dunkirk, should force us to seriously reconsider. There is something to the idea of mutual dependence in those cases. This dependence should at least be taken into consideration when we move to generate reality’s layering. A non-orthodox conception of

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gabriel oak rabin  ground will better reflect whatever it was about dependence that Barnes and Jenkins latched on to, and which we want reflected in the reality’s layering. Even staunchly orthodox views, when they move from the grounding graph to reality’s layering, might decide to reflect that symmetric relation in reality’s layering, even if they do not choose to call it ‘ground.’ In this way a non-orthodox conception of ground better reflects reality’s relations of dependence, and enables the generation of a more, rather than less, accurate, picture of reality’s layering. In the end, we might reject the arguments of Barnes, Bliss, Jenkins, and Schaffer, and maintain that the orthodoxy about ground is correct. But knowing that the layered conception is perfectly compatible with the heretical views that challenge the orthodoxy should grease the wheels for rejecting that orthodoxy (a move with which I have considerable sympathy). A non-orthodox view of ground can not only have a nice layering of reality, but the non-orthodox view is, in various ways, better suited to that layering. The grounding heretics can have their (layered) cake and eat it too.4

References Barnes, Elizabeth. Symmetric Dependence. 2018. In Bliss, Ricki and Priest, Graham (eds), Reality and its Structure: Essays in Fundamentality. Oxford: Oxford University Press. Bliss, Ricki. 2014. Viciousnesss and Circles of Ground. Metaphilosophy, 45, 245–56. deRosset, Louis. 2013. Grounding Explanations. Philosophers’ Imprint, 13(7), 1–26. Fine, Kit. 2012. A Guide to Ground. Pages 37–80 in Correia, Fabrice and Schnieder, Benjamin (eds), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press. Hippolytus of Rome. 2015. Refutation of All Heresies. CreateSpace Independent Publishing Platform. Jenkins, Carrie. 2011. Is Metaphysical Dependence Irreflexive? The Monist, 94, 267–76. Lesher, J.H. 1992. Xenophanes of Colophon: Fragments: A Text and Translation with Commentary. University of Toronto Press. Litland, Jon. 2013. On Some Counterexamples to the Transitivity of Grounding. Philosophical Essays, 14, 19–32. Patzia, Michael. Xenophanes. The Internet Encyclopedia of Philosophy, http://www.iep.utm. edu/xenoph/. Rabin, Gabriel and Rabern, Brian. 2016. Well Founding Grounding Grounding. Journal of Philosophical Logic, 45(4), 349–79. Schaffer, Jonathan. 2010. Monism: The Priority of the Whole. The Philosophical Review, 119(1), 31. Schaffer, Jonathan. 2012. Grounding, Transitivity, and Contrastivity. Pages 122–38 in Correia, Fabrice and Schnieder, Benjamin (eds), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge: Cambridge University Press.

4 Thanks are due to two anonymous referees for extremely helpful comments and suggestions, and to Ricki Bliss and Graham Priest for inviting me to think about these topics and contribute to this volume.

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2 Symmetric Dependence Elizabeth Barnes

Metaphysical orthodoxy maintains that the relation of ontological dependence is irreflexive, asymmetric, and transitive. The goal of this paper is to challenge that orthodoxy by arguing that ontological dependence should be understood as nonsymmetric, rather than asymmetric. If we give up the asymmetry of dependence, interesting things follow for what we can say about metaphysical explanation— particularly for the prospects of explanatory holism.

1 Background: Ontological Dependence The term ‘dependence’ is employed in different ways across different sub-literatures. So I first need to be clear about what I mean by ‘dependence’, and what specific literature I’m focusing on. To begin with, I’m concerned with ontological dependence. There are no doubt other forms of dependence—causal, conceptual, logical, and so on—but such relations aren’t my target here. What is ontological dependence? That’s a vexed question. Moreover, it’s not a question I’m going to attempt to answer in full here—not the least because many contemporary metaphysicians take it to be primitive. Rather, I’m going to highlight some key features of the relation, which will hopefully be enough for my purposes.

1.1 Paradigm cases Talk of ontological dependence is typically introduced via paradigm cases or examples. The whole ontologically depends on its parts. The mental ontologically depends on the physical. Secondary qualities ontologically depend on primary qualities. Esthetic ontology depends on non—esthetic ontology. And so on. One thing to note about these paradigm cases is that—fitting with the orthodoxy— dependence holds asymmetrically in each of them. The whole depends on the parts, but the parts don’t depend on the whole.1 The mental depends on the physical, but the 1

Or, at least, there is a dependence relation between part and whole. Most people think wholes depend on parts, but not everyone does—see especially Schaffer (2010b).

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elizabeth barnes  physical doesn’t depend on the mental. And so on. From this, it is sometimes reasoned that we have justification for thinking that the relation of dependence is asymmetric. For example, Kathrin Koslicki remarks, after introducing a list of paradigm cases of dependence, that if in fact ‘[these cases] do constitute examples of pairs of entities related by an ontological dependence relation of some sort, the dependence relation in question may plausibly be taken to be asymmetric.’2 Yet it’s a mistake to reason as follows: ‘Paradigm cases of F are , therefore all cases of F are .’ All the paradigm cases of redness are determinately red. But you can’t conclude from that that all cases of redness are determinately red.

1.2 Hyperintensionality So what do these paradigm cases of dependence—the mental on the physical, a whole on its parts, and so on—have in common with one another? What is the relation of dependence? It’s been, in recent times, very common to try to appeal to modal concepts to answer this question—to try to give some sort of modal definition or analysis of dependence. The usual thought is that the salient modal notion is ‘can’t exist without’. The xs depend on the ys just in case the xs can’t exist without the ys, or duplicates of the xs can’t exist without duplicates of the ys, and so on. Yet these modal analyses look too coarse, for a variety of reasons.3 To begin with, there is the problem of necessary co-existents. Kit Fine (1995) gives, as an example, the famous case of Socrates and {Socrates}, which exist in all the same worlds and yet while {Socrates} depends on Socrates, the dependence does not hold in the other direction. A further problem is created by necessary existents. Suppose, for example, that there are, necessarily, numbers. It shouldn’t follow from this that everything is dependent on numbers, simply because nothing can exist without numbers. Likewise, the theist believes in a necessary existent (God). Yet, while some theists might be interested in defending the claim that everything depends on God, it doesn’t look like this dependence claim should simply follow from the idea that God exists necessarily. These concerns have led many contemporary metaphysicians to argue that we need a hyperintensional account of dependence. Nothing modal is going to be fine-grained enough to do the work we want dependence to do, for example, to allow us to say that sets are dependent on their members but not vice versa, or that numbers exist necessarily but nothing non-numerical depends on them, and so on.

2

Koslicki (2013), p. 32. The counterexamples I give are phrased as counterexamples to the modal analysis of dependence as ‘can’t exist without’. But given some plausible assumptions, they’re also counterexamples to the modal analysis in terms of duplicates. So, for example, if there’s a necessary existent, x, that has all of its intrinsic properties essentially (which is plausible in the case of numbers, and perhaps also for the theistic God), then not only can nothing exist without x existing, but nothing can exist without a duplicate of x exists. Likewise, if we assume that the intrinsic nature of sets supervenes on the intrinsic natures of their members, you can’t have a duplicate of Socrates without a duplicate of {Socrates}. 3

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 symmetric dependence Opting for hyperintensionality—and thereby divorcing dependence from modal notions like ‘can’t exist without’—opens up some interesting options for dependence claims in the presence of contingency. For example, it’s common to say that the whole depends on the parts. And yet unless we adopt a strong form of mereological essentialism, we don’t want to say that the whole can’t exist without its parts—we want to allow that the whole could have been composed of different parts. What does this do to our dependence claim? Those attracted to modal definitions need to do some fancy footwork here—they need to argue, for example, that there’s a difference between de re and de dicto dependence (or between rigid and generic dependence, or the like). The whole depends on having some parts or other, but not on the parts it in fact has. But why should we think that the whole is necessarily a complex object, even if it is actually so? Perhaps that there are possible worlds in which this thing which is in fact a complex object is instead an extended simple, for example. And so we can introduce a further complication—talk of duplicates. Yes, the whole could exist without having any parts at all. But a duplicate of the whole can’t exist without having some parts or other. And so we continue, the modal definitions getting more and more intricate. But once dependence is divorced from the modal notion of ‘can’t exist without’, it’s not clear that any such complication is needed—or, indeed, that we need a distinction between de re and de dicto dependence at all. Once we give up on modal analyses of dependence, we might consider the option that necessary connections aren’t even necessary, let alone sufficient, for dependence. We could then say simply that the whole depends on its parts—on the parts it in fact has in the actual world. Yes, there’s a possible world in which the whole has different parts. Yes, there’s a possible world in which the whole has no proper parts at all. But none of that precludes us from saying that, in the actual world, the whole depends on the parts it actually has. Not all accounts of dependence will want to embrace this option, certainly—more on this in §4.3—but its availability is an interesting upshot of separating dependence and modality. Saying that dependence is hyperintensional doesn’t preclude trying to give a definition or analysis of dependence—it just precludes giving that analysis in modal terms. Kit Fine (1995), for example, characterizes dependence via essence—x depends on y just in case part of what it is to be x involves y—y is a constituent of some essential property of x. In a similar vein, Benjamin Schnieder (2006) defines dependence via metaphysical explanation—x depends on y just in case there exists some F such that x exists because y is F. In recent work, Karen Bennett (2017) defines dependence via her notion of a building relation. Something is independent just in case it is unbuilt, otherwise it is dependent. Others take dependence as primitive. Schaffer (2010b), for example, argues that we can say many informative things about dependence, but that we shouldn’t attempt to define or analyze it. Rosen (2010) likewise eschews attempts at defining dependence in favor of giving examples of it and then showing what work it can do.

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elizabeth barnes  In what follows, I’ll remain neutral on this issue. I don’t have any particular definition of dependence in mind, nor am I assuming dependence cannot be defined. My arguments should be applicable no matter which of these competing accounts of dependence you favor.4 But it is important for my purposes—as will be clear—that dependence is understood hyperintensionally.

1.3 Unification Finally, there is the question of whether there are lots of different varieties of ontological dependence, or whether there is just a single relation of ontological dependence. There’s been somewhat of a cottage industry devoted to identifying different types of ontological dependence—distinguishing between, say, rigid existential necessary dependence and generic existential necessary dependence and identity dependence.5 Discussions of these varying types of dependence, and how we can define and distinguish them, has generated a complex literature with lots of epicycles. But, perhaps as a backlash to this increasing complexity, it’s become prevalent in recent discussions in metaphysics to assume that there is a single, unified relation of ontological dependence. This is the strategy employed in, inter alia, Cameron (2008a), Rosen (2010), Schaffer (2010a), and Schnieder (2006). In what follows, I’ll proceed along similar lines and speak of ontological dependence simpliciter. But I’ll argue in §4.3 that nothing much hangs on this choice.

2 The Orthodoxy Orthodoxy about dependence includes the claim that dependence is asymmetric. But a striking feature of this orthodoxy is that little in the way of argument is given to support it.6 The asymmetry of dependence is very often simply assumed without further comment,7 and is perhaps something we’re meant to find intuitive or obvious. Perhaps the most prevalent argument for the asymmetry of dependence has less to do with dependence itself, and more to do with other relations or concepts that dependence is often assumed to be connected to: in virtue of, grounding, priority, fundamentality, and so on. Dependence is often mentioned in the same breath with

4 An exception here is Bennett (2017)’s definition of dependence. Bennett defines the independent as the ‘unbuilt’ (in her terminology). But in cases I’ll give below, there are things which are plausibly ‘unbuilt’ in Bennett’s sense, but which I’m arguing are dependent. So if you accept Bennett’s definition of independence, you won’t find these cases persuasive. But I’m hoping that the cases will give you reason to reconsider Bennett’s definition of dependence. 5 See especially Lowe (2009) for an overview. 6 See especially Bliss (2012) for a very helpful overview of the relative paucity of argument for many of the key assumptions in discussions of dependence and cognate notions. E.J. Lowe (1994) gives a brief suggestion at an argument for asymmetry (p. 39), saying that our objection to symmetric cases of dependence is analogous to our objection to circular arguments. I’m not exactly sure what to make of this argument, other than to say that there’s a difference between circular arguments and holistic explanations. 7 As in, inter alia, Bennett (2017), Cameron (2008a), Schaffer (2010a), and Rosen (2010).

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 symmetric dependence these other (equally fashionable) notions. More significantly, even, as perhaps the least esoteric of this cluster, dependence is often used as something which can help explain or get traction on the somewhat more slippery notions of priority, grounding, and in virtue of.8 So, for example, Karen Bennett (2017) remarks: ‘I do not think there is any question that independence is a–the–central aspect of our notion of fundamentality.’ Similarly, Schaffer (2010b) takes a rejection of limitless or circular dependence to be a consequence of the claim that some things are fundamental and that ‘all being must originate in basic being’ (p. 37). And Koslicki (2013) proposes (although acknowledging it to be controversial) the ability to illuminate disputes about fundamentality where there is not a dispute about what exists as a criteria of success for accounts of ontological dependence. Relations of priority and relative fundamentality are, insofar as I have any grip on them, plausibly asymmetric. And that is because they need to be asymmetric in order to do the work we want them to do. These are relations that are introduced in an attempt to take us from the derivative (the constructed, the grounded, the nonfundamental) down toward the bedrock (the ultimate grounds, the fundamental, the basic). It’s not a constraint of such relations that they ultimately bottom out.9 But it does seem to be a constraint that they’re headed in a single direction. Their asymmetry is built into the work we want them to do—it’s part of what they are for.10 The case is somewhat less clear for in virtue of and grounding.11 But certainly, if you want to treat these as relations that take you from something you should treat with less ontological seriousness (or even, something that is ‘less real’; see Fine (2001) or McDaniel (2013)) to something that you should treat with more ontological seriousness, then you need them to be asymmetric. The basic point, then, is this: relations which purport to take us from the derivate to the fundamental are plausibly viewed as asymmetric. So here is an argument that dependence must be asymmetric. Dependence is intimately connected to (and perhaps even explains or is one and the same thing as) relevant notions of fundamentality, priority, grounding, and so on. Dependence is the kind of relation that explains the connection between the fundamental and

8 So, for example, Schaffer (2010a), (2010b) and Cameron (2008a) both explain priority partly in terms of dependence (and Schaffer especially often uses dependence-talk and priority-talk interchangeably); Rosen (2010) explains ‘in virtue of ’ in terms of dependence; Bennett (2017) explains relative fundamentality in terms of dependence; and Wilson (2014) identifies the relation of grounding as the target of ‘the idioms of dependence’. 9 See Cameron (2008a) for discussion. 10 This is evidenced by the way we use them. We say ‘prior to’ and ‘more fundamental than’. I genuinely cannot make sense of what it would mean to say ‘x is prior to y and y is prior to x’ or ‘x is more fundamental than y and y is more fundamental than x’, nor do I know what locutions we might replace these with that would render such claims coherent. So, at least as they are commonly used, I simply cannot make sense of symmetrical cases of priority or relative fundamentality. 11 Wilson (2014) makes a case for the non-symmetry of grounding, for example.

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elizabeth barnes  the derivative—it takes us from the derivative (the dependent) to the fundamental (the independent). Any relation that plays this role must be asymmetric. And so dependence must be asymmetric. I think it’s correct that if dependence is to play this role, then dependence must be asymmetric. But what I’m going to argue is that it’s far too quick to simply assume that this is the kind of role dependence ought to play. And a big part of the reason it is far too quick is that there’s good reason to think that dependence isn’t asymmetric. The idea that dependence and fundamentality come apart is one that we might find plausible regardless of whether we think dependence is asymmetric, and it’s an idea that can be put to useful work. For example, in previous work I argue that dependence and fundamentality come apart in both directions—that there can be fundamental dependent entities and derivative independent entities.12 Distinguishing the two notions lets us make sense of a range of interesting (and independently motivated) positions in metaphysics, including Agustin Rayo’s (2013) trivialism about mathematical ontology (according to which numbers are plausibly construed as independent but not fundamental13 ) and ontological emergence, which can be plausibly understood as the idea that there are fundamental dependent entities.14 In what follows, I’ll give a further reason for thinking that dependence and fundamentality come apart: dependence should be understood as a non-symmetric relation.

3 The Case for Non-Symmetry To make the case that dependence should be understood as non-symmetric, rather than asymmetric, I’m going to make the case that dependence can sometimes hold symmetrically. And to make the case that dependence can sometimes hold symmetrically, I’m going to proceed by a series of examples. Of course, any of the particular cases I offer can be resisted. But when viewed as a whole, the range of cases is striking. Examples of apparently symmetrical dependence are not hard to come by—they can be found across a wide range of metaphysical theories, and in wide variety. The upshot of this, I’ll argue, is that we can’t maintain that dependence is asymmetric without ruling out wide swathes of the metaphysical landscape. And that quite simply isn’t the job of a notion of dependence—which is, after all, meant to be neutral across various ontologies—especially in the absence of independent argument that dependence must be asymmetric. In discussions of ontological dependence, there are at least two (potentially distinct) ways of characterizing dependence: via essence and via explanation. The Finean 12

See Barnes (2012). See especially chapter 3. 14 Indeed, it’s for precisely this reason, i.e. that emergence is the idea that there are fundamental things which are also dependent things, that Bennett (2017) argues that emergence is deeply mysterious, and possibly nonsensical. But absent further argument that dependence and fundamentality must go together, such skepticism is unmotivated. 13

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 symmetric dependence account of dependence says that x depends on y just in case what it is to be x involves y (y is a constituent of some essential property of x). Whereas an explanatory approach (like the one endorsed by Schnieder) says that x depends on y just in case x exists, or is the way it is, because y is F. I’m not endorsing either of these characterizations of dependence. But in what follows, I take these two criteria—the essentialist claim and the explanatory claim—as indicators of dependence, and I provide cases that motivate symmetrical dependence for each.15

3.1 Immanent universals and essentialism The first case I’ll offer is inspired by neo-Aristotelian metaphysics. Here are two claims that are broadly Aristotelian in spirit: universals are immanent and membership in natural kinds is had essentially. If universals are immanent, then universals require the existence of their instantiations. An uninstatiated universal is impossible, perhaps even incoherent. Universals don’t exist in some Platonic heaven and then get stapled on to their instances (or not, if they’re uninstantiated). Rather, universals are intimately bound to their instances, and, more generally, to being instantiated.16 If kinds are had essentially, then for any x that’s a member of kind K, part of what it is to be x is to be a member of K. Both these claims are quite naturally understood as dependence claims. Immanent universals depend on their instances. Part of what it is to be a universal, on this picture, is to have instances. And individuals depend on their kinds—part of what it is to be those particular individuals is to instantiate those kinds. If being F is essential to x, then anything that fails to instantiate F isn’t x. Part of what it is to be x is to be F. And so, plausibly, we can say that x depends on being F. But the combination of these two doctrines straightforwardly yields symmetrical cases of dependence. Suppose that being an electron is a universal, the instantiations of which make up a natural kind (the electrons). If universals are immanent, then the universal of being an electron depends on its instances. But, likewise, if natural kinds are essential then its instances depend on the universal—all the things that are electrons wouldn’t be the very things they are without the universal of being an electron. And so, on this sort of neo-Aristotelian picture, we get cases where dependence holds symmetrically. For those universals which correspond to natural kinds—and, in general, to essential properties—the universal depends on instances, and the instances depend on the universal.

15 I am being explicitly neutral about whether modal connections such as ‘can’t exist without’ are a necessary condition for dependence, but I am taking it that Fine’s essentialist criterion for dependence is at least an indicator of dependence (though perhaps not necessary for dependence). In what follows, I’ll assume that Schnieder’s explanatory criterion—which I’m assuming doesn’t appear to have the same modal consequences as Fine’s essentialist criterion (e.g. a complex object, x, could exist or be the way it is because it’s parts, the ys, are arranged in a certain way F, even if there are possible worlds where that very thing x is mereologically simple)—is also an indicator of dependence. 16 See especially Armstrong (1978b) for an overview and defense of immanent universals.

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elizabeth barnes 

3.2 Armstrongian states of affairs Consider the states of affairs metaphysic popularized by David Armstrong. There’s a deep puzzle in Armstrong’s metaphysics regarding the relationship between states of affairs and their constituents (particulars and universals). Consider the state of affairs of Jane being human.17 That state of affairs binds together two constituents: the particular individual Jane and the universal of being human. But the puzzling question for Armstrong is what the relationship is between states of affairs and their constituents. Do states of affairs depend on their constituents? Or do constituents depend on states of affairs? The trouble is that embracing either horn of this dilemma is problematic for Armstrong. If we say that states of affairs depend on their (independent) constituents, we get a picture in which the explanatory bedrock is particulars and universals. But if what’s ultimately independent are the constituents of states of affairs—rather than the states of affairs themselves—then Armstrong’s metaphysics loses its Tractarian ambitions. Armstrong wants an ontology of facts—a ‘world of states of affairs’— in which facts are fundamentally explanatory. For Armstrong, what explains the existence of the particular Jane and the universal being human ought to be the existence of the state of affairs—the worldly fact—of Jane’s being human. The reason there are particulars and properties, on a Tractarian metaphysics, is because there are things having properties—that is, because there are states of affairs. This picture is undermined, however, if Armstrong takes particulars and universals as independent and understands states of affairs as asymmetrically dependent on—and thus asymmetrically explained by—particulars and universals. But Armstrong encounters a different problem if he takes states of affairs to be independent, and constituents to be dependent on states of affairs. If this horn of the dilemma is embraced, then the metaphysic becomes explanatorily impoverished. For example, we want to be able to say that the states of affairs of Jane’s being human and Tom’s being human have something in common. But if the ultimate explanatory bedrock is just the states of affairs, and not their constituents, then it’s hard to see how we could explain this commonality. We want to be able to say that the constituents of a state of affairs explain why that state of affairs is the way it is. Jane’s being human is the state of affairs it is because of the constituents Jane and being human, and it is more similar to Tom’s being human than to Rex’s being a dog because of the constituents involved in each state of affairs. The most stable position for Armstrong, I contend, is that states of affairs are a case of symmetrical dependence. States of affairs depend on—and are thus explained by—their constituents. But likewise individual constituents depend on—and thus are

17 Armstrong wouldn’t allow that things like Jane and being human are constituents of fundamental ontology. So replace Jane and humanness with more scientifically respectable terms, if you’re worried about that.

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 symmetric dependence explained by—states of affairs. That is, the most stable position for Armstrong is a type of explanatory holism (discussed in more detail in §5.1). But if we separate dependence from fundamentality, this doesn’t preclude Armstrong from saying that both states of affairs and their constituents are fundamental. They are fundamental, but they each depend on the other. This allows Armstrong to respond to the resemblance problem, and it allows him to have his world of facts. The cost of this picture is, of course, a cost to parsimony—we end up with a fundamental ontology of both states of affairs and their constituents. But the claim here is that this is the most stable way of making sense of the fact-based ontology that Armstrong wants to defend.

3.3 Tropes and the problem of ‘bare mass’ According to trope metaphysics, properties are individual ‘particular thisnesses’.18 A traditional property metaphysics says that if the rose and the carnation are both red, then they both have the same property—they both instantiate redness. But the trope theorist says that properties are particulars. The rose’s redness and the carnation’s redness are two different (non-repeatable) things. What the rose and the carnation have in common is that the rose’s redness and the carnation’s redness are similar (perhaps exactly similar). Trope theory is commonly combined with bundle theory—the view that objects are nothing more than collections of properties.19 According to trope bundle theory, objects just are collections of particular thisnesses (there is not an underlying substance which instantiates or is the bearer of properties). The combination of tropes and bundle theory gives rise to an explanatory puzzle sometimes called the problem of ‘bare mass’ or ‘free mass’.20 If properties are particulars, and objects are nothing more than collections of properties, could you have an object that was nothing but an individual mass trope? Nothing about trope bundle theory rules this out, and yet it seems incoherent. So much the worse for trope bundle theory. But allowing that dependence can hold symmetrically gives the trope bundle theorist an easy line of response to this objection. The problem for the bundle theorist is that she cannot appeal to an underlying object on which properties depend— objects just are collections of properties. But if dependence can hold symmetrically, what she can say instead is that there are tropes which mutually depend upon each other.21 You cannot have a mass trope without a size trope and a shape trope, for example. And so on, mutatis mutandis, for shape tropes and size tropes. The picture here is one of ‘dependence clusters’—mass depends on shape and size, size depends on mass and shape, and so on. Part of what it is to have mass is to have shape and 18 The contemporary discussion of tropes goes back to at least Williams (1953). See Maurin (2013) for an excellent overview and discussion. 19 See Paul (2013) for a good introduction and overview. 20 See, inter alia, Armstrong (1997) and Schaffer (2003) for discussion. 21 This sort of interdependence between tropes is posited as a solution to the free mass problem in both Denkel (1996, 1997) and Simons (1994).

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elizabeth barnes  to have size, for example. And part of what it is to have shape is to have mass and to have size. And so on. These properties are all interdependent. And so the resulting ontology that trope bundle theory can offer includes clusters of interdependence— properties are particular ‘thisnesses’, but that doesn’t mean that ‘particular thisnesses’ are independent. Trope bundle theory needn’t encounter the problem of bare mass if dependence can hold symmetrically between tropes.

3.4 Mathematical ontology Thinking that there are numbers might also give you good reason to accept symmetrical cases of dependence. This is particularly evident if your mathematical ontology is that of non-eliminativist structuralism. That is, you think there are numbers, and you think that what numbers are are nodes or positions in a mathematical structure.22 Non-eliminativist structuralists often say that each node of the structure depends on all the others nodes—and perhaps even on the structure itself as well. And, as Linnebo (2008) persuasively argues, it’s easy to see why such dependence claims are needed. What it is to be a particular node in the structure is bound up in the other nodes being what they are. Consider the number six.23 The non-eliminativist structuralist is a realist about mathematical ontology. She thinks that the number six exists. Moreover, she thinks that what the number six is is a particular node in a complex mathematical structure. But that particular node is the number six in virtue of the relations it stands in to the other nodes in the structure. Likewise, the fact that the particular node is the number six is explained by the relations it stands in to the other nodes in the structure. And so for the non-eliminativist structuralist, the number six is dependent on the other numbers (which are, mutatis mutandis, themselves dependent on the other numbers). The non-eliminativist structuralist is (plausibly) committed to symmetrical cases of dependence in order to explain her ontology.24 While the case for symmetrical dependence is most vivid for the structuralist, other versions of realism about mathematical ontology might have similar explanatory need for such inter-dependencies. On a Finean conception of dependence, for example, x depends on y if what it is to be x involves y—that is, if y is a constituent of some essential property of x. On such an understanding of dependence, numbers are plausibly interdependent—that is, they depend on each other. The mere fact of their necessary co-existence doesn’t entail interdependence, but the explanatory 22

See especially Shapiro (1997) for explication and discussion of this view. Linnebo argues that the structural realist shouldn’t think this about all mathematical ontology—it is implausible for sets, for example—but maintains that it’s a central part of the structuralist picture in many cases. My use of natural numbers here is no doubt not the most compelling instance of symmetry— Linnebo (2008) provides much more sophisticated examples in his paper. 24 It’s worth noting that structuralisms in general—whether mathematical or not—are likely to give rise to symmetric dependencies, simply because of the holistic style of explanation they favor. Structural realism about the ontology of physics might similarly be interpreted as involving claims of symmetric dependence between individuals and structures, for example. See e.g. French (2014). 23

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 symmetric dependence connections will. What it is to be the number six is bound up in what it is to be the number five and the number seven, and so on. The number six would not be the thing it is were it not the successor of five, but it also would not be the thing it is were seven not its successor, so the number six is dependent on the numbers five and seven; but seven would not be the thing it is were it not the successor of six, and so seven is dependent on six; and so on.

3.5 Events Many people who endorse an inflationary metaphysics of events are attracted to both the idea that at least some events contain/are constituted by smaller events and to the idea that at least some events have some of the smaller events they contain/are constituted by essentially.25 The event WWII contains many smaller events—some insignificant (such as a particular lighting of a cigar by Winston Churchill) some much more significant (such as the evacuation of Dunkirk). And while WWII might have been the same event without that particular lighting of Churchill’s cigar,26 it’s plausible that WWII just wouldn’t have been the same event without the evacuation at Dunkirk. Without the evacuation at Dunkirk, it literally would have been a different war—the evacuation is an essential part of the war. But, similarly, we might think that being a part of WWII is essential to the evacuation of Dunkirk. Sure, you could have a duplicate of that event that doesn’t take place in the wider context of WWII. But that duplicate isn’t the evacuation at Dunkirk—part of what it is to be the evacuation at Dunkirk is to be a part of WWII. It’s part of the character of the event that it had the goals it had, that it was part of a wider mission, that it took place within the particular geopolitical context that it did, and so on. But if the events-ontologist accepts both these claims, she accepts a symmetric case of dependence. The event of the evacuation depends on the event of WWII. A qualitatively similar event that isn’t a part of WWII isn’t the same event. But likewise the event of WWII depends on the event of the evacuation. An event that doesn’t contain the evacuation at Dunkirk isn’t WWII. The two events—WWII and Dunkirk—each depend on each other to be what they are.

3.6 Summing up I have presented a range of cases—across a variety of topics and debates in metaphysics—which might motivate the claim that dependence can hold symmetrically. None of these cases are, by themselves, knock-down reasons to reject

25

See Hornsby (1997), chapter 3, for an excellent articulation of the former claim. Hornsby also seems in many places to endorse the latter, although this is less explicit. 26 Although see Lombard (1986) for an argument that we should embrace a radical form of essentialism about events.

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elizabeth barnes  asymmetric dependence. But their dialectical force when taken together is, I’ll argue, greater than the sum of their parts. Orthodoxy assumes that dependence is asymmetric. But, as already noted, there’s very little in the way of argument to support this tenet of orthodoxy. It is, more often than not, assumed rather than argued for. And it’s against this backdrop that I give this range of cases in which dependence is better understood as non-symmetric, rather than asymmetric. These cases are, taken collectively, quite striking. Cases where dependence holds symmetrically were not hard to find—there are plenty of them, including some very popular and well-known theories in metaphysics (and if the goal of this paper had simply been to list potential examples then the list could have continued for some pages). Nor is it a single niche area or type of view that’s giving rise to such cases—rather, the examples come from across a wide range of theories in metaphysics, and from a variety of different traditions. This makes a default, undefended assumption of asymmetry in dependence look odd—to say the least. Suppose we take on board the default assumption that dependence is asymmetric. If I’m right that the above cases should plausibly read as ones in which dependence holds symmetrically, then to take this assumption on board is to rule out these cases. That is, to assume that dependence is asymmetric is to rule out vast swaths of interesting, historically grounded metaphysics—or at least to force on them unpalatable interpretations. That—I contend—isn’t dialectically appropriate. Absent some compelling argument that dependence must be understood as asymmetric, it isn’t the role of a notion of dependence to simply rule out (or even severely constrain) diverse and promising metaphysics. That’s not what a notion of dependence is for—if we can rule out all such views simply by pointing out that they run afoul of the asymmetry criteria of metaphysical dependence (which, again, there isn’t much argument for) then dependence is doing too much work.

4 Objections 4.1 These cases are all impossible I’ve presented the above examples as more or less argument by cases. But a clear objection is simply this. Most metaphysicians don’t think the views described in the cases above are true. Most metaphysicians think that whatever ultimate metaphysical theory is true is necessarily true. Therefore most metaphysicians will think that the views I’ve described are necessarily false. Why think you can convince people that dependence can sometimes hold symmetrically by giving a bunch of impossible cases? In reply, let me clarify an important point. I’m not arguing that there are in fact cases of symmetrical dependence. Here’s what I’m arguing, in a nutshell: • People assume that dependence is asymmetric. They shouldn’t. • People assume that asymmetry is built into the concept of dependence. It isn’t.

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 symmetric dependence • Insofar as we want a relation of dependence that is neutral across varying ontologies (as it’s often assumed to be in the literature on dependence), dependence needs to be non-symmetric, not asymmetric. • Insofar as we’re warranted in talking about a relation of dependence, a nonsymmetric relation seems to fit our purposes better than an asymmetric relation. • We shouldn’t rule out ontologies just because they allow for symmetric cases of dependence. All of that is compatible with it being the case that dependence only ever in fact holds asymmetrically. Suppose Jonathan Schaffer (2010b) is right, and monism is the true theory of fundamental metaphysics. If monism is true, then everything asymmetrically depends on the world. Does that mean that Schaffer should think dependence is in fact asymmetric? Well, it depends on what role dependence is playing in the dialectic. If dependence is something that’s supposed to be neutral across different ontologies—something that we can use to explain common structures between ontologies, or some kind of generic explanatory principle—then the fact that it only ever occurs asymmetrically doesn’t mean the relation itself is asymmetric. Schaffer seems to use dependence in this specific-ontology-neutral sense. (As do Bennett, Koslicki, Fine, Rosen, etc.) Indeed, Schaffer (2010b) starts out with general reflections about dependence (not tied to any particular ontology) that include the claim that dependence is asymmetric, and then uses these reflections about dependence as part of his motivation for monism. It would be an odd sort of bootstrapping, to say the least, to then point to the asymmetry of dependence in monism as an argument for the general claim that dependence is asymmetric. Dependence might, prior to commitment to a particular ontology, turn out to be non-symmetric, and so we shouldn’t simply assume that it’s asymmetric, and shouldn’t use the assumption that it’s asymmetric to rule out particular ontologies.

4.2 These cases aren’t symmetric dependence, they’re joint dependence Another way of objecting to what I’ve said above is that in the cases I describe, the reason it looks like you get two things which depend on each other is that they each depend on the same further thing. These are cases of joint dependence, not symmetric dependence. But this move doesn’t look like it’s available for all the cases given above. If we combine Aristotelian universals with essentialism, it doesn’t look like there’s anything further we can point to that both universals and their instances depend on. (Aristotle himself may have thought that everything ultimately depends on the Aristotelian god, but I doubt this move will be particularly popular.) Likewise, for trope bundle theory, it doesn’t seem plausible that there’s any one supertrope on which all the other tropes in the bundle depend. So as an across-the-board response, appeal to joint dependence doesn’t work.

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elizabeth barnes  In other cases, there might be candidates for joint dependence. Maybe what we ought to say about structuralist realism in mathematics is that all the nodes depend on the structure itself, but that the structure doesn’t depend on the nodes. But this option looks ad hoc and forced. Why would the structure be independent of the nodes? How could it be? The ontology we’re forced into if we want something we can say is a source of joint dependence begins to look mysterious and bizarre. Why go in for such an ontology, rather than just allowing that this is a case where dependence holds symmetrically? The answer had better not be an assertion that dependence just has to be asymmetric.

4.3 These cases only arise because you failed to distinguish different kinds of dependence As outlined in §1, I’m following the tradition in the literature that treats dependence as a single, unified relation. But it could be objected that it’s precisely the refusal to distinguish between different varieties of dependence that’s leading to apparent cases of symmetric dependence. After all, it’s prima facie cases of symmetry like the dependence of universals on their instances and instances on universals that, for example, motivates Jonathan Lowe (1994) to distinguish between generic existential necessary dependence and rigid existential necessary dependence, and between existential and identity dependence.27 And similar worries have motivated the distinction between de re and de dicto dependence. So we don’t, if we’re careful, really have a case where we’ve got a single relation that’s holding symmetrically—we’ve just got two (or more) different forms of dependence. The key thing to say about this objection, once again, is that it doesn’t look like a response that can be leveled at all the cases I give above. Even if we allow for different forms of dependence, whatever sense in which a trope bundle’s shape trope depends on its size trope is the same sense in which its size trope depends on its shape trope. And likewise for individual nodes in a mathematical structure, and for Dunkirk and WWII. So even if we granted that there are different kinds of dependence—a view which, as discussed in §1.2, has its problems—that wouldn’t eliminate all apparent cases of symmetrical dependence. But let’s consider the case of de re and de dicto dependence. Someone might object that de re and de dicto dependence are very different things—in the case given in §3.1, for example, the particulars depend on that very universal, but the universal merely depends on having some particulars or other that instantiate it. This, it might be protested, is not the same relation of dependence in both cases. And so the case is not, in fact, a case of symmetric dependence.

27 Interestingly, though, some of Lowe’s arguments for accepting multiple kinds of dependence seem to rest on the assumption that there cannot be symmetrical cases of (strong) ontological dependence. The above discussion can be taken as a reason to apply modus tollens where Lowe applies modus ponens.

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 symmetric dependence As discussed in §1.2, divorcing dependence from modality might give us reason to push back against this thought. The motivation for a deep distinction between de re and de dicto dependence seems like an after-effect of modal accounts of dependence. The universal could exist without any of the things that in fact instantiate it—it just has to be instantiated by something, not by the particular things that in fact instantiate it. Whereas the particular things that instantiate it couldn’t exist without the universal. But if ‘couldn’t exist without’ doesn’t give us a grip on dependence, why think this is relevant to the question of whether the universal depends on the things that in fact instantiate it, just as the things that in fact instantiate it depend on the universal?28 Not all accounts of dependence can accept this. Someone attracted to Fine (1995)’s essentialist account of dependence, for example, will want to maintain something like the de re/de dicto distinction for this case—part of what it is to be the particulars is that they instantiate that very universal, but it’s not part of what it is to be that universal that it is instantiated by those particulars (part of what it is to be that universal is simply that it’s instantiated by some particular or other). For these accounts of dependence, there are two points to make. The first is again simply that the cases given in §3.3, §3.4, and §3.5 (and perhaps §3.2 as well) look to be cases of symmetrical de re dependence.29 The second is that even if you think that, in a case like §3.1, it’s not the same relation of dependence going in both directions, the resulting picture—where both particulars and universals are dependent, even if they are dependent in different ways—yields an interesting explanatory structure that further undercuts that idea that fundamentality and independence always go together. A more complicated case is that of the distinction between full and partial dependence. For those inclined to think this distinction is important, the cases given above might seem like they only give support to the idea that partial dependence can sometimes hold symmetrically. The Aristotelian universal is partially dependent on each of its instances, but not wholly dependent on any of them. The mass trope is partially dependent on the size trope and the shape trope, but not wholly dependent on either. And so on. Perhaps full dependence is asymmetric, regardless of whether partial dependence might be non-symmetric. And perhaps full dependence is the more important, bedrock notion.

28 This point is particularly salient if we separate dependence from relations like priority—which, once the prospect of the non-symmetry of dependence is raised, I think we should. It’s plausible to think that certain kinds of necessitation claims go along with priority. If the xs are prior to y, then necessarily if you have the xs you have y. That’s one way of interpreting the idea that, if the xs are prior to the y, then in some sense having the xs gets you y ‘for free’. 29 And it’s also possible to motivate symmetric cases of de dicto dependence. In some of the medieval discussion of ‘substantial form’, the relationship between matter and form seems to suggest such dependence. The account of substantial form given by Suarez, for example, seems to suggest a reading in which matter depends on having some form or other (but not on having any particular form), and likewise form depends on being realized in some matter or other (but not on any particular matter). See Pasnau (2011), pp. 561–3.

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elizabeth barnes  But I’m skeptical that there’s an important difference between full and partial dependence—or at least I’m skeptical that if there is an important difference, the cases I’ve given only address the latter. Full dependence seems simply like the limit case of partial dependence, rather than something different in kind. Consider again the case of Aristotelian universals. Universals depend on their instances, but they don’t wholly depend on any particular instance—they partially depend on each instance, and collectively depend on all their instances. But if universals depend on their instances, it looks like it’s possible for a universal to depend on a single instance. Suppose that all natural kinds correspond to universals, and suppose further that the elements of the periodic table each represent natural kinds. Many of the elements of the periodic table are plentiful and naturally occurring, but some can only be made in specialized laboratory conditions, and have only ever been made a few times. An element like Einsteinium, for example, has only had a few instances. Now consider the possible world in which Einsteinium is only made once. That’s a world in which Einsteinium only has one instance. In that world, the universal Einsteinium wholly depends on the single instance, and the single instance wholly depends on the universal Einsteinium.

5 Morals of the Story 5.1 Holistic explanation If dependence is non-symmteric, why does it matter? Another objection to symmetric cases of dependence that will doubtless crop up is that symmetric cases of dependence license unacceptable circular explanations. Dependence—whatever else it may be— is inextricably linked to metaphysical explanation. If x depends on y, then x is at least in some sense explained by y. But suppose that we have a case of symmetric dependence—x depends on y and y depends on x. In that case, the explanation suggested is that x explains y and y explains x. Surely that’s unacceptable circularity. However, I think that allowing such forms of explanation is a feature, not a bug, of understanding dependence as non-symmetric. What non-symmetric dependence allows is a certain kind of explanatory holism. The existence of the state of affairs explains the existence of its constituents. The existence of the constituents explains the existence of states of affairs. The existence of the mass trope explains the existence of the shape and size tropes. The existence of the shape and size tropes explains the existence of the mass trope. And so on. The most common models of explanation in metaphysics are analogous to foundationalism in epistemology. Chains of explanation ultimately ground out in primitive, unexplained explainers. But that needn’t be the only way that explanation in metaphysics can work. We could have alternative pictures that are more like coherentism: the overall explanatory structure can be holistic, and there are no unexplained explainers. Certainly, the availability of this kind of explanation is one reason why people have in fact objected to non-symmetric dependence. E.J. Lowe (1994) and (2009), for

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 symmetric dependence example, remarks that our objection to symmetric cases of dependence is analogous to our objection to circular arguments. But it’s hard to know what to make of this claim. Circular arguments are valid. The reason that they’re bad arguments is an epistemic reason—they don’t provide any new information, or any further warrant, for thinking that the conclusion is true. And so they don’t play the justificatory role we want arguments to play. But metaphysical explanation is explicitly non-epistemic. When we say that x explains y and y explains x, we’re not saying that the way we come to have knowledge of x is via y, and the way we come to have knowledge of y is via x, or something along those lines. So it’s not clear what the analogous objection to circular arguments would be in the case of metaphysical explanation.30 Another way of motivating a circularity objection can be found in Fraser MacBride (2006). MacBride objects to the symmetry of dependence in mathematical structuralism (or at least explores the following objection without fully endorsing it). In order for a relation to obtain between two objects, MacBride argues, those objects need to be: independently constituted as numerically diverse. Speaking figuratively, they must be numerically diverse ‘before’ the relation can obtain; if they are not constituted independently of the obtaining of …[the] relation then there are simply no items available for the relation to obtain between. (p. 67)

But symmetric cases of dependence seem to be cheating in this regard—it’s the very obtaining of the relation that allows for the existence of the objects (because they depend on each other). On MacBride’s picture—at least as I understand it— objects are like pins in a bulletin board and relations are like bits of string that you can hang between pins. You’ve got to have the pins there before you can hang the string. It can’t be the hanging of the string that somehow magically gives you the pins. But on this very flat-footed reading, MacBride’s objection carries just as much weight against dependence-as-grounding or dependence-as-priority as it does against symmetric cases of dependence (like the mathematical structuralist). On such understandings of dependence, if x depends on y, then x isn’t ‘independently constituted as numerically diverse’ in a way that’s explanatorily prior to the obtaining of the dependence relation. It’s precisely because x depends on y—that is, precisely because the relation of dependence obtains between x and y—that x exists. Symmetric cases of dependence aren’t asking us to countenance anything radically different. They’re just positing a case in which both relata—rather than one relatum—require the obtaining of the dependence relation for their existence.

30 Lowe (2009) further asserts that metaphysical explanation is asymmetric, and therefore dependence— because it tracks or is intimately bound up with metaphysical explanation—must likewise be asymmetric. But he gives no argument for the claim that metaphysical explanation must be asymmetric. Schaffer (2010b) appears to endorse this claim of Lowe’s, but likewise does not say why. Schnieder (2006) makes a similar claim, but again does not argue for the asymmetry of explanation.

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elizabeth barnes  But a MacBride-esque worry that cuts directly against symmetric cases of dependence would be this: we need to have the existence of at least some of the relata of a relation independently of the obtaining of that relation. We need, as MacBride puts it, a relatum ‘before’ (figuratively speaking) we can have a relation. In symmetric cases of dependence, though, the very existence of the relata requires the obtaining of the relation—the relata depend on each other. But put this way, the objection just sounds like a denial of (rather than an argument against) the sort of explanatory holism that non-symmetric dependence allows. It’s important not to be misled here by the temporal metaphor. The objection is not whether we need objects temporally before the obtaining of relations between those objects. Rather, the point—at least as I understand it—is that we need at least some objects to be explanatorily prior to the obtaining of any dependence relations. Or, to put it more simply, we need some objects to be independent. That’s not an argument against holism—that’s just a denial of holism. Holistic explanations have a long and rich history in philosophy. They are, it’s safe to say, out of fashion in much of contemporary metaphysics.31 But it isn’t clear that they should be, especially considering the interesting work that holistic explanation can do, and the interesting explanatory models it provides. And more importantly, holistic explanations don’t look like the kind of thing that we should dismiss without argument, simply by asserting that dependence is asymmetric. A nonsymmetric dependence relation allows for holistic as well as foundationalist models of metaphysical explanation, and that’s one major reason why non-symmetry, rather than asymmetry, should be the default assumption for dependence.

5.2 Dependence and grounding relations The other main moral of the story is this: if dependence can be non-symmetric, then dependence needs to be separated from talk of grounding, priority, in virtue of, and so on. These relations are relations that aim to take us from the derivative to the fundamental. They take us from things we treat with less ontological seriousness, or ‘get for free’, down to the ultimate ontological bedrock. But if dependence is nonsymmetric, it can’t play this role, and it can’t be jumbled together with these other relations. Suppose that the symmetric dependence interpretation of Armstrong really is the best interpretation. If that’s the case, then for Armstrong nothing is independent. His basic ontology is states of affairs and their constituents. But both are dependent (each depend on the other). That doesn’t mean that Armstrong should think nothing is 31 Although if you look a little outside of ’mainstream’ metaphysics—especially to feminist metaphysics—you will find plenty of champions of holistic explanation. See especially Haslanger (1995). Some of the most salient examples can be found in feminist discussions of social construction and social kinds. See, for example, Haslanger (2016) and Witt (2011). Much of the discussion of holism in feminist philosophy is more directed toward epistemology, but often has striking consequences for metaphysical holism—see especially Haraway (1991) and Harding (1993).

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 symmetric dependence fundamental. It just means that dependence isn’t a good guide in all cases to getting at fundamentality. Dependence is something distinct from theoretical gizmos—like grounding, priority, and in virtue of—tailored specifically to take us from the less fundamental to the more fundamental. Dependence can do a lot of interesting work in our theories, but it can’t do that. Nor can dependence be used to explain priority, grounding or the like. Whatever sense (if any) we can make of those other relations and whatever work they can do (if any) in our theories, they need to be clearly separated from dependence.32

References Armstrong, David M. (1978a). Nominalism and Realism, volume 1 of Universals and Scientific Realism. Cambridge: Cambridge University Press. Armstrong, David M. (1978b). A Theory of Universals, volume 2 of Universals and Scientific Realism. Cambridge: Cambridge University Press. Armstrong, David M. (1997). A World of States of Affairs. Cambridge: Cambridge University Press. Barnes, Elizabeth (2012). ‘Emergence and Fundamentality’. Mind 121(484), pp. 873–901. Bennett, Karen (2017). Making Things Up. Oxford: Oxford University Press. Bliss, Ricki (2012). ‘Viciousness and the Structure of Reality’. Philosophical Studies (online first): http://link.springer.com/article/10.1007%2Fs11098-012-0043-0. Cameron, Ross (2008a). ‘Turtles all the Way Down: Regress, Priority and Fundamentality’. The Philosophical Quarterly 58(230), pp. 1–14. Cameron, Ross (2008b). ‘Truthmakers and Necessary Connections’. Synthese 161(1), pp. 27–45. Denkel, Arda (1996). Object and Property. Cambridge: Cambridge University Press. Denkel, Arda (1997). ‘On the Compresence of Tropes’. Philosophy and Phenomenological Research 57, pp. 599–606. Hornsby, Jennifer (1997). Simple Mindedness: In Defense of Naive Naturalism in Philosophy of Mind. Cambridge, MA: Harvard University Press. Fine, Kit (1995). ‘Ontological Dependence’. Proceedings of the Aristotelian Society 95, pp. 269–90. Fine, Kit (2001). ‘The Question of Realism’. Philosophers’ Imprint 1(2), pp. 1–30. French, Steven (2014). The Structure of the World: Metaphysics and Representation. Oxford: Oxford University Press. Haraway, Donna (1991). ‘Situated Knowledges’. In Donna Haraway, Simians, Cyborgs, and Women: The Reinvention of Nature. New York: Routledge. Harding, Sandra (1993). ‘Rethinking Standpoint Epistemology: “What is Strong Objectivity?”’ In Linda Alcoff and Elizabeth Potter (eds), Feminist Epistemologies. New York: Routledge, pp. 49–82.

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Many thanks for helpful feedback and discussion to Ross Cameron, Sally Haslanger, Kris McDaniel, Trenton Merricks, Daniel Nolan, Jason Turner, Robbie Williams, two anonymous referees, and audiences at the Pacific APA, Birmingham University, Harvard University, Leeds University, and the University of Virginia.

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elizabeth barnes  Haslanger, Sally (1995). ‘Ontology and Social Construction’. Philosophical Topics 23, pp. 95–125. Haslanger, Sally (2016). ‘What is a (Social) Structural Explanation?’ Philosophical Studies 173(1), pp. 113–30. Koslicki, Kathrin (2013). ‘Ontological Dependence: An Opinionated Survey’. In B. Schnieder, M. Hoeltje, and A. Steinberg (eds), Varieties of Dependence: Ontological Dependence, Grounding, Supervenience, Response-Dependence (Basic Philosophical Concepts). Munich: Philosophia Verlag, pp. 31–64. Linnebo, Øystein (2008). ‘Structuralism and the Notion of Dependence’. Philosophical Quarterly 58, pp. 59–79. Lombard, Lawrence (1986). Events: A Metaphysical Study. London: Routledge. Lowe, E.J. (1994). ‘Ontological Dependency’. Philosophical Papers 23(1), pp. 31–48. Lowe, E.J. (2009). ‘Ontological Dependence’. The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), ed. Edward N. Zalta: http://plato.stanford.edu/archives/spr2010/entries/ dependence-ontological/. MacBride, Fraser (2006). ‘What Constitutes the Numerical Diversity of Mathematical Objects?’ Analysis 66(1), pp. 63–9. McDaniel, Kristopher (2013). ‘Degrees of Being’. Philosophers’ Imprint 13(19), pp. 1–18. Maudlin, Tim (2007). The Metaphysics Within Physics. Oxford: Oxford University Press. Maurin, Anna-Sofia (2013). ‘Tropes’. The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), ed. Edward N. Zalta: http://plato.stanford.edu/archives/fall2013/entries/tropes/. Pasnau, Robert (2011). Metaphysical Themes 1274–1671. Oxford: Oxford University Press. Paul, L.A. (2013). ‘Mereological Bundle Theory’. In Hans Burkhardt , Johanna Seibt, and Guido Imaguire (eds), The Handbook of Mereology. Munich: Philosophia Verlag. Rayo, Agustin (2013). The Construction of Logical Space. Oxford: Oxford University Press. Rosen, Gideon (2010). ‘Metaphysical Dependence: Grounding and Reduction’. In Bob Hale and Aviv Hoffmann (eds), Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press. Schaffer, Jonathan (2003). ‘The Problem of Free Mass: Must Properties Cluster?’ Philosophy and Phenomenological Research 66(1), pp. 125–38. Schaffer, Jonathan (2010a). ‘The Internal Relatedness of All Things’. Mind 119(474), pp. 341–76. Schaffer, Jonathan (2010b). ‘Monism: The Priority of the Whole’. Philosophical Review 119(1), pp. 31–76. Schnieder, Benjamin (2006). ‘A Certain Kind of Trinity: Dependence, Substance, Explanation’. Philosophical Studies 129, pp. 393–419. Shapiro, S. (1997). Philosophy of Mathematics: Structure and Ontology. Oxford: Oxford University Press. Simons, Peter (1994). ‘Particulars in Particular Clothing: Three Trope Theories of Substance’. Philosophy and Phenomenological Research 54, pp. 553–75. Williams, D.C. (1953). ‘On the Elements of Being I’. The Review of Metaphysics 7(1): pp. 3–18. Wilson, Jessica (2010). ‘What is Hume’s Dictum and Why Believe It?’ Philosophy and Phenomenological Research 80, pp. 595–637. Wilson, Jessica (2014). ‘No Work for a Theory of Grounding’, Inquiry 57, pp. 535–79. Witt, Charlotte (2011). The Metaphysics of Gender. Oxford: Oxford University Press.

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3 Grounding and Reflexivity Ricki Bliss

Philosophers interested in the notion of ground are commonly of the view that the grounding, or metaphysical dependence, relation is necessarily asymmetric, irreflexive and transitive: they deny that anything can be self-grounded or self-dependent. What the reasons are for this commitment, however, are less than clear. One might suppose that this attitude is born from a commitment to the unacceptability of circularity more generally. The coherence theory of truth, for example, was eschewed by many for reasons of circularity. Just as the appearance of a seemingly vicious circle in the foundations of naive set-theory leads philosophers either to abandon the reality of sets, or to set about the formidable task of refining its axioms. The kinds of circles with which this paper is concerned are not those generated when we try, directly or indirectly, to explain grounding in terms of itself. Nor are the kinds of circles with which we are interested those generated where we have circular arguments, or become tangled in circular reasoning. The reason for this is that metaphysical explanations are not arguments, and the issue is, presumably, not one of trying to convince anyone of anything. Nor is the matter to hand to be confused with what it is to suggest that some fact is self-evident. Suppose that I happen upon a crime scene where the victim is laid out with a dagger in his chest. Although we might suggest that it’s self-evident how the man met his end, we do not infer from this that the poor fellow drove a knife into his own chest; or that what explains the man’s death is the fact that the man is dead. Self-evident facts may bear no explanatory relationships to themselves whatsoever. And self-grounded facts may not be selfevident by anybody’s lights. The kinds of cases this paper addresses are cases in which we say that some fact is either fully or partially grounded in itself. Which is just to say that the kinds of cases we are interested in are cases in which some fact bears the right kind of real, or perhaps merely explanatory, connection to itself. But what does this even mean? And why, as we are so often told, is it absurd or unacceptable? If real relations of ground are a feature of objective reality, we might suppose that there are metaphysically laden reasons for denying that there can be reflexive instances of dependence: perhaps the consequences for the reality that the relation structures

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ricki bliss  would be unseemly—on some, as yet undefined, sense of unseemly. Or perhaps the way facts would have to be, such that they can be self-grounded, is metaphysically incoherent or impossible. Alternatively, one might be of the view that even though there are real relations of ground that structure reality, instances of self-dependence are completely innocuous. It has been suggested, for example, that the identity relation is a relation that things bear harmlessly to themselves. One might wish to suggest, then, that grounding—or some sub-species of it—behaves in just this way as well. Why, exactly, instances of self-dependence would then be considered to be a problem is a little bit difficult to see. Perhaps it is simply that there is no real need to posit them in the first place for they add little to nothing of value to our theory. Bearing in mind that ground is associated with explanation, however, we may, instead, discover that there are powerful explanatory reasons for supposing there can be no circles of ground. Indeed, for anyone who refrains from positing the existence of real relations of ground, explanatory concerns may well be the most likely locus of justifications for the commitment to the no-circularity assumption. Suppose that reflexive instances of ground give rise to explanations of the form ‘x because x’; these explanations might be unacceptable simply because they are trivial, uninformative, and explanatorily useless.1 Or, alternatively, the connection between reflexivity and non-well-foundedness might itself ensure the place for a particular kind of explanatory failure on our catalogue of reasons to eschew the possibility of circles of ground: where the step between non-well-foundedness and explanatory failure would be mediated by an argument from vicious infinite regress. This paper aims to focus the reasons for which we might find reflexive instances of dependence unacceptable: a task that necessitates an investigation into what it even means for a fact to ground itself. In §1, I introduce the notion of ground along with the kinds of circles of ground I will be considering. In §2, I present several different reasons to motivate the need to think about circles of ground more seriously. In §3, I discuss possible metaphysically substantive reasons to deny that anything can be self-dependent. Both historically and contemporarily, philosophers have expressed worries over the ontological priority ordering, bootstrapping, and the connection between self-dependence and the necessary and the divine. In §4, I turn to a consideration of explanatory reasons to avoid circles of ground. I discuss connections between circularity, non-well-foundedness, and viciousness, along with the thought that circles of ground are unacceptable for the more (deceptively) humdrum reason that they give rise to trivial and uninformative explanations. I conclude that the most salient reasons we have for supposing grounding is irreflexive are explanatory rather than metaphysical, and that reasons to reject or accept instances of reflexivity need to be assessed with a greater eye to other of our commitments.

1

See Keefe 2002 for a discussion of the problems with circular accounts.

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 grounding and reflexivity

1 Grounding and Circularity Broadly, we can distinguish two different approaches to the notion of ground. The first approach, amongst whose proponents are philosophers such as Kit Fine and Fabrice Correia, hold what we can call the sentential connective view.2 According to this view locutions such as ‘because’ (on certain appropriate uses), ‘makes it the case that’ (on certain appropriate uses) and ‘in virtue of ’ (on certain appropriate uses), connect sentences. Importantly, although it can be convenient to talk in terms of facts, we need not take the view as committing us to the existence of facts. Take the sentence ‘the table exists because its legs exist’. We could well recast this sentence in the language of facts, but we need not. And even if we did, we need not take the sentence to commit us to their (the facts’) existence. The second approach, as endorsed by philosophers such as Trogdon and Schaffer does involve a commitment to a realm of facts.3 This approach, which we can refer to as the relational view, holds that real relations of ground obtain between facts. In understanding grounding in this way, we are committing both to the existence of facts, and to the existence of relations of ground that hold between them. Here I understand the relational view to align with what I will refer to as the property transfer view: relations of ground transmit a property.4 There are a variety of kinds of properties that the grounding relation might transmit: modal properties are amongst them. It is at least prima facie plausible to suppose that some fact will inherit its modal status from the facts upon which it depends. The property-transfer view, as I understand it, though, involves a commitment to the idea that there is some property that is the property that the grounding relation transmits. Candidates for the kind of property at issue are the properties of existence (or being), reality, and truth.5 Grounding is involved with metaphysical explanation. We say that where the fact that it is raining grounds the fact that it is raining or it is not raining, it also, in a distinctively metaphysical sense, explains it. Similarly, we might think that where the physical facts ground the mental facts, or the natural facts ground the moral facts, they also explain them. One reason advocates of the relational view cite in defense of their commitment to real relations is that there are good reasons to suppose that successful explanations are always backed by real relations.6 For advocates of this approach it is because grounding

2

Fine 2012 and Correia 2010. Schaffer 2009 and Trogdon 2013a. Schaffer believes that the relata of grounding relations can be drawn from all ontological categories, and is committed to the existence of whatever it is that we take real relations of ground to obtain between. 4 Not all proponents of the relational view explicitly endorse the property transfer view. One could advance the relational view without holding the property transfer view; although it seems natural to suppose that there is some property or other at issue where relations are instantiated. See also Trogdon (Chapter 9, this volume) for a further elaboration of this view. 5 Bliss 2013, pp. 406–8, mentions this way of understanding the grounding relation. Morganti 2014 also discusses grounding in these terms. 6 Kim 1994. 3

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ricki bliss  is involved with explanation that we ought to assume it to be a real relation.7 Advocates of the sentential connective view, on the other hand, tend to think that grounding just is metaphysical explanation. To say that some fact grounds another just is to say that it metaphysically explains it. All parties agree, however, that grounding is intimately involved with a distinctively metaphysical kind of explanation. We can distinguish between cases of full ground and cases of partial ground. The fact that I am happy partially grounds the fact that I am happy and rich, whereas the fact that I am happy fully grounds the fact that I am happy or rich. The fact that I am happy, and the fact that I am rich, together fully ground the fact that I am happy and rich. We come now to the matter of circles of ground. Circles of ground can be achieved in a number of different ways. Suppose we were to introduce a further distinction between mediate and immediate ground. Intuitively, whilst the fact that I exist is immediately grounded in facts about the existence of my vital organs, it is only mediately grounded in facts about the existence of fundamental properties, for example. It is to this relation of mediate ground that philosophers commonly refer when they talk of grounding. This relation, as we already know, is transitive. The relation of immediate ground, however, is not. With these two conceptions of ground in mind, we can imagine a situation in which grounding loops are formed by chaining together instances of the immediate relation, where these chains double back on themselves. As the relation is not transitive, these chains do not collapse into themselves, avoiding reflexivity. Alternatively, circles of ground can be formed where the relevant notion of ground is symmetric. Consider the relationship between the north and south poles of a magnet.8 The fact that the north pole exists is grounded in the fact that the south pole exists, and the fact that the south pole exists is grounded in the fact that the north pole exists. The two poles are symmetrically dependent upon one another.9 Where the relation is transitive, such cases will also yield instances of reflexive dependence. Where the relation is not transitive, they will not. It is with the possibility of reflexive instances of ground that I shall be concerned in this paper. Although there is much that can be said on circles of ground more generally, I restrict myself here to a discussion of circles yielded by reflexive instances of the relation.

2 Why Circles of Ground Matter One might wonder why we should bother thinking about circles of ground at all. Perhaps more pertinently, one might worry that the line of inquiry pursued in this 7

See Thompson (Chapter 5, this volume) for a reason to doubt that grounding involves real relations. Priest, 2014, p. 178. 9 Note, this dependence is not merely nominal. The poles of a magnet are, by their natures, symmetrically dependent upon one another. Note also that the fact that the poles are symmetrically dependent may well be grounded in further facts about the existence and/or nature of magnetic fields. 8

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 grounding and reflexivity paper is simply illegitimate. After all, isn’t it just true by definition that grounding is asymmetric, transitive, and irreflexive?10 Let’s consider briefly the notion of well-foundedness. Grounding is commonly described as a relation that is asymmetric, transitive, irreflexive, and well-founded. But although we can stipulate that the relation is well-founded, we are still under obligation to offer not only an elaboration of what we think that amounts to—an underexplored topic in the literature—but also the reasons for which we believe that to be the case.11 And we can see from exploring some of the contemporary literature that philosophers have, indeed, felt the need to conduct just this kind of investigation.12 To the best of my understanding, then, no one infers from the claim that grounding is, by definition, well-founded, that it is illegitimate to ask whether or not, or why, we should believe it to be the case, that reality comports with our definition. As should also be the case, I venture to suggest, with the property of irreflexivity. We can stipulate that grounding is irreflexive and yet still wonder whether or not reality is like this. And, arguably, where philosophers are emphatic that a relation cannot have a certain property, we have all the more reason to suppose that there is a principled reason for the view; and all the more reason to want to know what that is. Matters here might seem to become complicated by the fact that some philosophers, at least, are willing to grant the existence of a second, reflexive notion of ground. Fine, for example, distinguishes between strict and weak ground, where the latter is not only possibly, but necessarily, reflexive.13 For proponents of the distinction, it will not be the case, then, that there is anything particularly bad about circles of ground, but rather, that where there are such circles we must realize that we are dealing with a distinctive flavour of the relation.14 But this distinction, for those who grant that it is there to be drawn, is itself informative, for it appears to reveal assumptions both about the relation that can be reflexive and about the one that we are told cannot be. We can wonder, for example, if the weak relation is something like a degenerate cousin of the strict—irreflexive— relation. If this is the case, what reasons have we to suppose that the strict relation is the central notion of ground? Surely whatever these reasons are, they are informed by the reasons we have to suppose that the strict relation cannot be reflexive. Does every fact weakly ground itself? If so, are we to infer from this that the kind of grounding relation that a fact bears to itself is somehow harmless? Assuming the relational view, is self-grounding harmless because the relation fails to deliver some property to the relevant fact? Or is it harmless because the relation does deliver a property to the fact,

10

I have met with this response on a surprising number of occasions. See both Dixon 2016 and Rabin and Rabern 2016 for excellent discussions of what we might mean when we talk about the well-roundedness of grounding. 12 See Bliss 2013, Morganti 2009 and 2014, Tahko 2014. 13 Fine 2012, pp. 51–3. 14 I have borrowed this expression from Fine 2012. 11

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ricki bliss  but does so unproblematically? Are we then to distinguish between a metaphysically substantive relation of strict ground—say, a property delivering relation—and a soft, or inert—non-property delivering—relation of weak ground? If so, is this because there is something wrong with circles of ground after all? Drawing distinctions between different flavors of the relation only piques, rather than satisfies, the curiosity. In what follows, however, when attempting to ascertain what is so bad about circles of ground, I mean to ask this of whatever relation we are told is not, or cannot be, reflexive. Coming to understand why some particular relation of ground is necessarily irreflexive will surely help us to understand grounding, the reality that it orders, and why it is, if indeed it is, that some flavors of ground can be reflexive. Before turning to an exploration of self-grounded facts, though, I first consider some further reasons that might motivate us to think more carefully about circles of ground. The first of these is that reality appears to be populated with example instances of them.15 Fine provides us with a number of cases.16 Take the fact that everything exists—[everything exists]. This fact, itself an existent, helps ground [everything exists]. [everything exists] partially grounds [everything exists]. Or consider the proposition . This proposition is, itself, either true or false. If it is true it helps ground its own truth, so too if it is false. Similarly with the sentence ‘every sentence is true or false’. Fine considers these cases to present us with a kind of puzzle exactly because it seems undeniable that these are instances of partial self-grounding, and yet, this situation is, according to fine, ‘an absurdity, given that nothing can hold in virtue of, or partly in virtue of, itself ’.17 Jenkins, on the other hand, suggests that mind/brain identity theories may present us with a host of instances of circles of ground.18 According to some versions of mind/brain identity theories, token mental states are identical to token brain states. Someone’s being in pain state x just is them being in brain state y. These theories may also assume there to be an explanatory connection between facts about tokens of the one and facts about tokens of the other. Understanding these theories in terms of a notion of ground, we appear to have cases in which pain states are both explained by, and identical to, brain states, thus giving us instances of self-dependence. Paseau points out that it is conceptually possible that at least some things are selfdependent.19 For this reason, he is critical of the tendency to build irreflexivity (and asymmetry) into our definitions of dependence and ultimate ontological basis. Moreover, he cites the existence of non-well-founded sets—self-membered sets—as

15 16

See Raven 2013, for a treatment of some purported cases of reflexivity. 17 18 Fine 2010. Fine 2010, p. 98. Jenkins 2011. 19 Paseau 2010, p. 171. Although Paseau talks in the idiom of ontological dependence, it is acceptable to assume this point to also hold true in the case of grounding. This is because Paseau’s paper is a response to Ross Cameron on fundamentality. In that paper Cameron also talks in the idiom of ontological dependence, but he now considers the discussion to be one that subsumes the notions of ontological dependence and ground. Cameron’s original paper was written during a time in which it was not commonplace in the literature to distinguish between relations of ontological dependence and relations of ground.

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 grounding and reflexivity examples of actual cases of self-dependence. And Graham Priest not only suggests that it is possible that everything is partially self-grounded, but he argues that everything is actually partially self-grounded.20 Changing tack now, a further compelling reason to take self-dependence seriously is that a theory of reality on which some things are self-dependent may be, all things considered, better than one on which they are not. Consider metaphysical foundationalism: there is a derivative metaphysical superstructure that is grounded in a fundamental ontological ground. This is far and away the most commonly held view amongst metaphysicians who embrace a notion of ground. Whether that which is fundamental is singular—as in some kind of monism—or plural—as in pluralism—the fundamentalia/um grounds/gives rise to/explains everything else. But why suppose there is something fundamental? Why not be metaphysical infinitists, for example? Ross Cameron argues that although we have no good reason to suppose that metaphysical foundationalism is necessarily true, we do have good reason to suppose that it is contingently true of the actual world.21 All things considered, claims Cameron, a theory that affords a unified explanation of the phenomenon under consideration is more virtuous than one that does not. Metaphysical foundationalism, claims Cameron, is just such a theory: positing the existence of fundamentalia allows us a unified explanation of the contents of reality. Putting aside questions of what it means for a theory to be unified, amongst other issues, what this line of argumentation brings to our attention is the role considerations of theoretical virtue can play in our theorizing about the fundamental structure of reality. We might then wonder whether a theory that leaves a large number of things out (i.e. the fundamentalia) is ceteris paribus better than one that does not.22 Is a theory that posits unexplained fundamentalia obviously more virtuous than a theory that posits nothing fundamental, but in which everything is explained? Maybe it is. At least maybe it is if denying the existence of something fundamental ushers in infinitely long grounding chains. But maybe it isn’t. Perhaps a theory that posits the existence of quasi-fundamental phenomena—fundamental in the sense of being metaphysically ‘rock bottom’—but then allows that they are self-explanatory, or selfdependent does better. This way, everything has an explanation—nothing is left out— but we are not forced to violate considerations of quantitative parsimony, for example. I’m not suggesting that this view is correct, but just that it is not prima facie incorrect. And whether or not the theory is apt to have its virtues considered would seem to turn, at least partly, on whether or not anything can be self-dependent. 20 Priest 2014, p. 179. Although he describes everything as interpenetrating with itself, given other of Priest’s assumptions, this claim is tantamount to stating that everything is (partially) grounded in itself. 21 Cameron 2008. 22 Foundationalism does not purport to explain the fundamentalia and one might worry that it is unfair to criticize a theory for failing to explain that which it never attempted to explain in the first place. Nonetheless, we can still weigh theories against one another and evaluate them on their virtues.

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ricki bliss  A final reason to think we ought to think more carefully about the possibility of circles of ground comes from noting the parallels between issues in foundational epistemology and issues in foundational metaphysics.23 In foundational epistemology, one can be an epistemic foundationalist—the dominant view—an epistemic coherentist, or an epistemic infinitist. All three views, although varying in degree of popularity, are established, developed views. It is a striking feature of foundational metaphysics that metaphysical foundationalism is the only view that is well-developed. Some philosophers have defended the possibility of metaphysical infinitism, but metaphysical coherentism—species of which would admit circles of ground—remains wholly unexplored.24 Owing to the similarities between the relation of ground as it orders reality—on some views at least—and the relation of justification as it orders our beliefs, we may have good reason to think that where epistemic coherentism gets going, metaphysical coherentism might just get going as well.

3 The Problems Jenkins suggests that the term ‘dependence’ is quasi-irreflexive.25 What she means by this is that ‘ . . . it always sounds bad to say “x metaphysically depends on x” or “x grounds itself ”’.26 One reason that reflexive statements of ground might sound bad is if they are just plain false. Suppose I claim that I exist because I exist. I would seem to have uttered a falsehood. I exist because, amongst other things, a certain sperm met with a certain ovum, for example. But exactly whether or not it is necessarily false— indeed false at all—to utter statements of this form is exactly what is under issue. We cannot assume that such statements are necessarily false as a premise in an argument to the conclusion that reflexive grounding claims are necessarily false. Moreover, we cannot infer from a single case—or class of cases—that no one may be suggesting are instances of self-dependence in the first place, that nothing can be self-dependent at all. This would be like contemplating the number seven, believing it not to have any causes and inferring from this that nothing whatsoever is ever caused. Let’s assume that the truth of statements of ground place demands on reality— this is just what I mean when I claim that grounding talk is metaphysically laden. Broadly construed, this just means that for any statement of ground to be true, the world must be thus and such a way. On some views, as we have seen, this will also involve an additional commitment to a binary relation of ground and the facts that it holds between.27 Reflexive statements of ground will come out as false where the entity under consideration does not happen to ground itself; and necessarily false if it is unacceptable, or impossible, that anything ground itself. 23 See Bliss 2012, and Morganti 2014 and (this volume), for discussions that draw out some of these similarities. 24 See Morganti 2009 and Schaffer 2003 for two different discussions of the possibility of infinitism. 25 26 Jenkins 2011, p. 1. Jenkins 2011, p. 2. 27 For the suggestion that relation needs not be binary, see Jenkins 2011 and Schaffer 2012.

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 grounding and reflexivity So why might it be unacceptable or impossible that anything ground itself? One reason could be that if something’s being self-grounded commits us to a further metaphysically substantive thesis regarding the nature of the self-grounding fact, or the reality that it structures; and whatever this thesis commits us to is impossible or unacceptable. What I have in mind here, in the case of the facts themselves, is that where some fact grounds itself, how that fact is such that it is the kind of fact that can ground itself is (i) non-trivial, and (ii) problematic. The metaphysically laden view could then be either what we might think of as substantive or shallow. On the shallow view, the truth of ‘x because x’ demands nothing more of the world other than x grounding itself. We might think of something’s being self-identical in just this same way: it is metaphysically laden—it is about the world— but shallow—there is no further interesting story to be told about why things are such that they are self-identical. This is just how things are. Owing to the relationship between grounding and explanation, perhaps there will be additional explanatory reasons for denying that grounding can be reflexive. Such reasons may turn out to be the main locus of problems for the shallow approach to self-dependence. In particular, we might worry that where a grounding tree contains a loop, that tree will be non-well-founded, issuing in a vicious infinite regress. This generates an explanatory concern for the simple reason that where a grounding tree is non-well-founded, we fail to explain anything within that tree at all. Alternatively, we might wonder if the appearance of tight grounding loops is unacceptable just because the explanations that they issue in are trivial, uninformative, and explanatorily useless. On this last approach, we require nothing metaphysically untoward in order to have good, albeit epistemic, reasons to think grounding is irreflexive. At this stage, I would like to address a worry that some of these suggestions might raise. I can imagine an interlocutor objecting that the metaphysical explanations associated with grounding are objective and thus devoid of any epistemic or cognitive dimensions. According to this objection, it would be a mistake to entertain anything that looks like an epistemic reason to reject reflexivity. I think this objection is wrong-headed. First, how, exactly, we are to understand the notion of a metaphysical explanation is far from clear. In the grounding literature to date, there is a tendency to point to the connection between grounding and metaphysical explanation without elaborating upon how we are to understand the relevant notion of explanation. Of course, one can stipulate that metaphysical explanations are purely objective, but without good reasons to think this is the case, such a stipulation does not help us very much. Importantly, though, the idea that the objective nature of an explanation entails that it is altogether devoid of any epistemic dimension is a mistake: a mistake that likely turns on conflating objectivity with mind-independence.28 To claim that an explanation is objective is not to claim that 28 Consider money. Money is not a feature of mind-independent reality, and yet there are plenty of objective facts about it: it is important to our lives, the source of much evil, and so on. Mind-independence and objectivity are not one and the same thing.

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ricki bliss  it is mind-independent. The suggestion that our cognitive lives play a role in our explanatory praxis does not necessarily threaten the objectivity of explanations.29 In order for objectivity to be threatened, we would need to have our cognitive lives playing very particular kinds of roles in our accounts of explanation, and not just any old role whatsoever. Second, in light of our epistemic innocence regarding the reasons for which we are to reject the possibility of reflexive instances of ground, it is incumbent upon us to explore the field of options before us. If it turns out that the best reasons we have to reject reflexivity are epistemic rather than metaphysical, and we are wedded to the idea that there is no place for our cognitive lives in our theory of metaphysical explanation, then we need to revise our commitment to irreflexivity. Alternatively, if it turns out that the best reasons we have to reject reflexivity are epistemic, we may need to revise our understanding of metaphysical explanation. Grounding, we are so often told, is about reality. In fact, grounding is assumed by many to be the relation that structures reality. Even on the sentential connective view, we are still urged to understand the (relevant) sentences, and the connectives that join them, as expressing truths about reality. If this is correct then we might expect that reality itself provides us with reasons to suppose there is something wrong with circles of ground.

3.1 Metaphysical worries At various places in the literature, both historical and contemporary, philosophers have gestured at what purport to be metaphysically laden reasons for supposing that nothing can be self-dependent. In the second of his Five Ways, Aquinas states the following: The second way is from the nature of efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible.30

The notion of efficient causation in operation here is to be understood in terms of the medieval notion of causation per se. Causes per se exist contemporaneously with their effects and sustain them. In this respect at least, this notion of efficient causation is similar to our notion of ground. Aquinas is suggesting that it is impossible that anything is the efficient cause of itself, for it would then be prior to itself. But why is this? Were the notion of causation at issue here one on which causes temporally preceded their effects, this objection might make sense, for it seems correct that nothing can exist prior to itself in time. But the dependence relation we are concerned with is not like this: grounds, and that which they ground, exist contemporaneously.

29 30

See Trogdon 2013b, p. 473 for a similar observation. Aquinas 1964, Part 1, Question 2, Section 3.

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 grounding and reflexivity So the worry cannot be that things would have to exist before they exist in order to cause themselves to be. The notion of priority also plays a role in contemporary discussions of the structure of reality. Putting aside Aquinas exegesis, the contemporary worry is best understood against the backdrop of a commitment to the idea of reality as hierarchically structured, or composed of levels. Regimenting the worry in the language of facts, it might be that any fact that is self-grounded would exist prior to itself within this structure: it would reside at two different levels of the structure at the one time. If levels are individuated by their occupants, however, two levels that contain all of the same occupants would be indistinguishable. The real problem, then, seems to be that reflexive instances of ground conflict with the very idea of a priority ordering itself.31 Where grounding is reflexive, there is no ontological hierarchy and with it, no priority. But as a reason to suppose that grounding cannot be reflexive, this objection will not do. We cannot argue that grounding cannot be reflexive because it conflicts with the notion of priority, where that priority is achieved by way of a relation that is asymmetric, transitive, and irreflexive. That is as good as saying that grounding cannot be reflexive because it cannot be reflexive. Of course, one could argue this, were one to be in possession of independent reasons to believe this to be the case. And what some such independent reasons are is exactly what the present exploration is hoping to uncover. A related worry, or perhaps just another way of presenting the same worry, is in the language of relative fundamentality.32 One might worry that exactly what an irreflexive notion of ground is introduced to capture is the idea that some things are more or less fundamental than others: where grounding is reflexive—or nonreflexive—this notion is no longer captured by our notion of ground. One might think that just as nothing can be larger than itself, nothing can be more fundamental than itself. It seems right that this is true—nothing can, presumably, be more fundamental than itself. But such a line of reasoning goes no way towards justifying why we are supposed to think anything is more or less fundamental than anything else in the first place. Stipulating that some things are more or less fundamental relative to other things does not provide us with reasons to suppose that reality exhibits such a structure in the first place. As exactly what we are after is a reason to suppose that grounding is necessarily irreflexive, the appeal to relative fundamentality goes no way towards helping us uncover such a reason. There is an issue here that I would like to pause and address. Some philosophers claim that the very reason that we need a notion of ground is that we need a relation that captures the hierarchical structure of reality (a notion that captures relative

31

Paseau 2010 objects to Cameron’s (2008) use of the term ‘ontological priority’ as the converse of ‘ontological dependence’ for he claims that it ‘…encourages the assumption, ex vi termini, that both relations are irreflexive’ (footnote 5, p. 171). The notion of priority carries with it that of irreflexivity. 32 Thank you to an anonymous referee for pointing out the need to address this issue.

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ricki bliss  fundamentality). These philosophers will claim that we already have relations at our disposal that are symmetric and reflexive, such as supervenience and identity. What work is grounding to do at all, if not to capture this hierarchical structure, thinks the philosopher of this ilk. The relationship between grounding and supervenience is complicated, and I make no attempt to discuss this here.33 The most oft-cited advantage that ground has over supervenience is that it allows us to capture the asymmetry of dependence: where supervenience picks out modal companionship, ground allows us to say what depends on what. But the advantage a notion of ground has over that of, say, supervenience, isn’t simply that it captures asymmetric dependencies. Ground is just, I take it, a richer notion. When wielding a notion of ground, we are not just suggesting that two facts are yoked to one another across possible worlds, we are pointing to the fact that two facts are related in a particularly rich and important way. Grounds metaphysically explain that which they ground, in a way that the supervenience base does not explain what supervenes upon it.34 The point is just that ground plus reflexivity does not necessarily yield supervenience. Of course, it remains to be seen whether anything can explain itself in any kind of interesting way, but ground remains an, in principle, richer notion than that of supervenience nonetheless. Admitting that some things can ground themselves is not necessarily just to reintroduce supervenience in ground’s clothing. Returning to the central discussion, the question I am interested in addressing is why is it that some instances of ground, in all its richness, cannot be reflexive? One very good reason to think that grounding is necessarily irreflexive is that reflexive instances of ground are unacceptable or impossible. But absent such independent reasons, the kinds of objections we have seen so far are useless. Fortunately, an example of an independent reason to think that no fact can ground itself has been alluded to in recent discussions: nothing can be self-grounded because anything that exists in this way would have to bootstrap itself into being.35 This objection sounds like it is in keeping with the spirit of the worry conveyed by Aquinas, but it is also as enigmatic. Again, the relevant relation is non-temporal, so selfdependent things would not need to exist before themselves in time in order to bring themselves into existence. Indeed, grounding doesn’t seem to be involved with bringings of things into being or existence at all. Perhaps what the bootstrapping objection is getting at is that it is just plain weird to think that something could be its own ground. I confess that I find this concern a little bit difficult to appreciate. A pervasive view amongst metaphysicians is that there is a fundamental level populated by brute, independent fundamentalia: they are ungrounded and without explanation.36 But suppose, now, for argument’s sake, that 33

See Leuenberger 2014 for a recent and interesting discussion on grounding and supervenience. See McLaughlin and Bennett 2014. 35 I am not aware of anyone who has stated this in print. I have, however, heard this concern expressed on a number of separate occassions. 36 Cameron 2008, Schaffer 2009. 34

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 grounding and reflexivity our fundamentalia turn out to be self-dependent. It is far from clear how something bootstrapping itself into being (whatever that turns out to mean) is any weirder, or any more or less explanatory, than something that gets flung into existence from nowhere and for no reason whatsoever. In the particular case of the contrast with brute facts or existents, it is not clear why one view is more acceptable, or less weird, than the other. And this is all the more so the case where we understand our fundamental facts to be contingent. Whilst necessary facts, one might think, do not stand in need of explanation, contingent facts seem to be exactly the kinds of facts that do need explanations! Weirdness to which we have become accustomed—as in the case of brute, contingent facts—is still weirdness after all. And if it’s weirdness that we wish to avoid, then the proponent of brute, contingent facts also has some work to do. One way that we might try and make something of the bootstrapping worry is in light of the property-transfer view: where a fact grounds itself, the relation transfers some property from that fact to itself, and this is unacceptable. But, again, why? The success of this objection would seem to turn on the idea that properties—even if only of a certain kind—have to originate from somewhere else. But why is this? The contrast with brute, contingent facts here is, again, pertinent—why is the idea that something lends a property to itself any more bizarre than the idea that something plucks a property out of thin air? After all, we seem perfectly willing to countenance that there are some things that don’t borrow certain, important, properties from anything else—the fundamentalia—so why can’t some facts garner certain properties from themselves?37 At the very least, we would seem to have a problem of superfluity. If something already possesses a property, such that it is available to lend it to itself, we can wonder why we need to go to the trouble of invoking that thing and its property possession to explain where that property came from in the first place. If some fact already possesses a particular property, there is no need to invoke the grounding relation it bears to itself to explain where that property comes from. But is there anything more serious or troubling going on than a potential explanatory breakdown? Perhaps the real problem for this view is if there is some way that facts need to be such that they are the kinds of facts that can ground themselves, and however this is is unacceptable. That is to say, a good reason to deny the possibility of reflexive instances of ground is if it commits us to a further, metaphysically substantive, yet unacceptable, thesis regarding the natures of the entities that are involved. There is historical precedence for the positing of self-explanatory facts. According to Leibniz, if God exists, He exists because He exists. God’s existence, or the fact that God exists, is self-explanatory. But far from being trivial, God’s existence is selfexplanatory because it is in His essence to exist. There is, then, a further, metaphysically substantive, story to be told regarding God’s self-explanatory existence. And importantly, this is not the end of the story. It follows from God’s essential existence 37 In claiming that the fundamentalia are ungrounded, no one wishes to deny that they have being, for example.

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ricki bliss  that He is also a necessary being, as essential properties are necessary properties; and that self-explanatory facts about God’s existence are necessary facts. There is a route from some fact’s being self-explanatory to its being necessary and it is via the necessary existence of its constituents: the kinds of facts that could be self-explanatory facts, then, would be existence facts. Moreover, once we are in the business of presenting explanations for how some fact is such that it can ground itself, we might think that the explanatory demand that got us this far also obliges us to present an explanation for why it is that God is the kind of being that can exist essentially.38 After all, I have lots of my properties essentially—such as being human—but I am excluded from having the property of existence in this way. Leibniz proposed that the appropriate explanation here is in terms of God’s divinity: God has the property of existence essentially because He is perfect.39 Putting the pieces together, we might wonder if the problem with self-grounded facts is that they would be (i) necessary facts, where (ii) the subjects of those facts are essential existents, which are (iii) in possession of divine properties. Of course, the idea of a necessary fact is not particularly controversial. What would be controversial, however, is a picture of reality on which the fundamental facts are necessary. The reason for this is that where the fundamentalia are necessary, and everything else follows from them by necessity—assuming necessitarianism about grounding—then the only world that exists is the actual world. All contingency drops out of the picture and we are left with full-blown necessitarianism.40 First (iii) and the connection between self-groundedness and the divine. It was wielding a Principle of Sufficient Reason (PSR) that Leibniz was driven to invoking God’s divinity as an explanation for why it is that God exists essentially. Without such a principle, however, we are not compelled to make the additional step from essential existence to the possession of divine properties. The proponent of the notion of ground is not normally wont to make appeal to a Principle of Sufficient Reason, and without it, I see no reason to suppose that one would be forced to account for why it is that some things exist in a certain way, namely, essentially, whilst others do not. For anyone who did make use of a PSR, however, things may look a little bit different. Nonetheless, even where some explanation or other of why it is that some thing exists essentially is warranted, are we really forced to frame such an explanation in terms of divine attributes? Perhaps there are other kinds of explanations available to us that allow us to explain why it is that some things exist essentially and others not?

38 As Schopenhauer 1974 wittily remarks on the Principle of Sufficient Reason, ‘the causal law therefore is not so accommodating as to let itself be used like a hired cab, which we dismiss when we have reached our destination. . . . ’ 39 Dasgupta 2016 also notes the potential to draw this connection between necessary facts and the divine, but he dismisses it in the context of his broader project. The reason for this, so far as I understand it, is that there are examples of necessary beings, such as numbers, that we have no reason to suppose are divine (see esp. p. 26). 40 See Dasgupta 2016 for a riveting discussion of how things would be at such a world.

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 grounding and reflexivity Let us turn, now, to (i) and the purported connection between self-groundedness and the necessary. A move that could be made at this stage would be to question the very idea that any individual can have the property of existence essentially. If existence is not a property (of individuals), as has been suggested by the likes of Kant and Frege, then no individual can have it essentially. If this is the case, however things need to be, such that facts about their existence are self-grounded, it cannot be because the subjects of our existence facts have existence as an essential property. But for anyone who does accept that existence is a property, surely this is not an option. Another possibility would be to take issue with the notion of an essence: nothing can exist essentially because nothing has an essence whatsoever. Again, however facts need to be such that they are self-grounded, it cannot be because the subjects of those facts exist essentially. More promising, I believe, would be to question the connection between selfdependence and essential existence altogether (ii). Recall that the reason we were discussing the connection between self-grounded facts and essential existence was because we were exploring an extant account of how the world needs to be such that some facts ground themselves. But does citing God’s essential existence really yield a situation in which the fact that God exists explains itself? Does it not yield a situation in which the fact that God exists is explained by the fact that God has it in His essence to exist? We appear to have two separate facts here and not, actually, a case of one grounding itself. Absent the connection between self-dependence and essential existence, have we any other reason to suppose that self-grounded facts force us to commit to a metaphysically substantive thesis that is otherwise undesirable? In particular, is there any other route from self-dependence to necessity that is not mediated by a thesis regarding the essential existence of the subjects of our self-grounded facts? It is not clear to me that there is. Even if we wished to argue that necessary facts are self-explanatory, there is no obvious entailment from a fact’s being self-grounded to its being necessary. Moreover, if David Lewis is right, there may even be examples of self-explanatory facts that are contingent. Loops formed where a time-traveler visits himself with instructions on how to build a time-machine involve a series of contingent, self-explanatory facts.41

3.2 Explanatory worries Far more salient, in my view, are the explanatory reasons for finding the prospect of circles of ground troubling. I will canvas two clusters of explanatory worries, along with arguing that the issues are both more complex and less disturbing than they may initially appear. The first set of worries involve infinite regresses, and the second explanatory failure. Grounding chains, or trees, that contain loops may well be non-well-founded. A reason to reject the possibility of circles of ground, then, is that they would commit 41

Lewis 1976.

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ricki bliss  us to the possible existence of (downwardly) non-terminating grounding structures.42 Whether or not this is a compelling reason to reject the possibility of reflexive instances of ground will turn upon how powerful the reasons are for supposing that grounding chains must (downwardly) terminate. Chief amongst the arguments often offered in defense of fundamentality are arguments from vicious infinite regress.43 Philosophers will claim that where our grounding chains do not (downwardly) terminate we are off on an infinite regress and the regress is vicious. But infinite grounding regresses are not, however, necessarily vicious; sometimes they are benign.44 If this is correct, then the pertinent questions to ask in the current context are, in fact, two: do reflexive instances of ground generate infinite regresses, and if they do, are those regresses vicious or benign? Reflexive instances of ground generate loops of the form [A] grounds [A]. These loops could be expressed by sentences of the form ‘A because A’. Whether or not a regress is generated at all, I venture to suggest, will depend upon what we think is required a regress to make. Consider first that such a tight loop contains only one relatum, [A] and a single instance of a relation, G. How are we supposed to generate an infinite regress from this? Of course, where [A] grounds itself, [A] follows from itself, but it does not follow from this that there are, say, an infinite number of instances of [A], and an infinite number of instances of the grounding relation that obtain between [A] and itself.45 From what materials, exactly, are we supposed to construct our regress? From a single relatum and a single instance of the grounding relation we can, however, draw an infinite number of explanatory inferences should we choose to; each at a later moment in time. In such a case, we could generate an infinite sequence of sentences ‘A because A. A because A. A because A . . . . ’ Why one would wish to continue on in this way, however, is somewhat difficult to imagine. But that one could continue on in this way seems to be reason to suppose that an infinite regress of sorts can be generated. Suppose, though, that we are willing to grant that an infinite explanatory regress can be generated, we are then compelled to establish whether it would be vicious or benign. Consider the fact that X—[X]. Suppose also that this fact is a dependent fact. As dependent facts have grounds [X] must also have a ground. Suppose that what grounds [X] is [Y]. In citing [Y], we have, in some sense of explains, explained [X]. Where [Y] is itself a dependent fact, we might worry that although [Y] explains [X], it cannot completely explain [X]. This is because [Y] also stands in need of explanation. Supposing that our grounding chain is infinitely descending, at each stage of the 42

Dasgupta 2016, p. 6 also notes this possibility. The role regress arguments play in defenses of fundamentality are, in my view, often underestimated. I suspect this might be because of their cryptic and commonly terse nature. For examples of regress arguments in defense of fundamentality, see Fine 2010 and Schaffer 2012, for example. For a discussion of how to understand regress arguments in the context of the notion of ground, see Bliss 2013. 44 45 Bliss 2013. Bliss 2014, §3 and Gratton 2010, esp. ch. 4. 43

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 grounding and reflexivity regress, although we have said something of the facts at the level above, we may not have explained everything for which we think we need an explanation.46 Although there is no hope of adequately covering the thicket of issues associated with arguments from vicious infinite regress here, enough can be said, I hope, to satisfy the reader. Arguments from vicious infinite regress require the inclusion of an assumption that stipulates an explanatory target; which is exactly what we fail to reach where a regress is generated. And the very same regress can be considered vicious or benign depending on the explanatory target we have in mind.47 Where that for which we are seeking an explanation is some dependent fact or other, that fact is, presumably, explained by the facts upon which it depends. Regresses generated after this fashion are benign. Regresses are not benign, however, where what we wish to explain is something that no member of the regress, or the entire regress taken together, can explain. Good candidates for such explanatory targets are: why there are any dependent entities whatsoever; why everything turned out this way rather than that way;48 or the expectation that dependent entities have complete metaphysical explanations. There is not the space to address all of the relevant issues here, but it is enough to recognize that in order to establish whether a regress is vicious or benign, we need to be clear on what our explanatory target is in the first place. In cases in which some fact purportedly explains itself, though, it might appear that, in citing that fact as its own explanation, we have explained nothing about that fact whatsoever. Let’s, for argument’s sake, assume as much. Importantly, we need not be embarked upon an infinite number of moves through our very tight loop to make such an observation. The explanatory failure that may be noted at infinity is an explanatory failure that presents itself having moved through the loop but once. The infinite explanatory regress that could be generated is, therewith, superfluous, for the problem presents itself at the very first stage: explaining some fact in terms of itself is as good as offering no explanation of that fact at all. What does this mean, though, for cases in which the entire structure has a self-grounded fact at the tip of one of its branches? Can something that has no explanation serve as the terminus point of such a structure? The standard view is that it certainly can. Exactly what the metaphysical foundationalist thinks is that there is a fundamental level of ungrounded facts that explain everything else. Once again, at the very least, it is not clear that self-grounded facts are any worse off than ungrounded, fundamental facts.

46 If grounds do not explain (or ground) that which they ground, I have no idea why anybody bothers talking about grounding in the first place. To deny that grounds do any work at all seems preposterous (for anyone who cares to employ a notion of ground, that is. There may be good reasons to wish to deny grounding talk altogether. My target with this comment is the person who (i) embraces a notion of ground, but (ii) tries to claim that grounds don’t do any work). 47 See Aikin 2005 and Bliss 2013 for discussions of the regress problem in these terms. See also Passmore 1970. 48 See Dasgupta 2016 for an account of fundamentality in these terms.

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ricki bliss  This brings us to the second, and final, cluster of explanatory worries that I will consider. The most conspicuous form that a reflexive explanation can take is ‘A because A’. This explanation of A in terms of itself would seem to be trivial, uninformative, and explanatorily useless. We might suppose that it is for the reason of explanatory failure that philosophers express an aversion to the possibility of circles of ground. At first blush, these explanatory worries seem convincing. It does, indeed, seem to be the case that ‘A because A’ is trivial, uninformative, and explanatorily useless. Trivial explanations are bad, we might think, because they are uninformative and explanatorily useless. But are explanations of this form necessarily trivial? Earlier in the discussion, we saw that although on some accounts it is true to say of God ‘He exists because He exists’ it is not the case that God’s existence is trivial. Although I argued that the way God is, such that we can say of Him that He is self-explanatory, seems problematic, that is not to say that there may not be some other way that self-dependent things are, such that they are self-explanatory. Far from being trivial, what the appearance of a reflexive metaphysical explanation may alerts us to is that something is such that it is able to explain itself. Alternatively, what the appearance of a reflexive metaphysical explanation could alert us to is simply that we have reached an explanatory dead end. Reflexive metaphysical explanations let us know that we have arrived at a breakdown in our explanatory progress. One reason for this breakdown might be that we have arrived at some fact that simply does not stand in need of further explanation. Good candidates for such facts may be facts about essences.49 I would feel confused if someone asked me to explain why it is in my essence to be a human. And this is not because I think there is some further story to be told, but happen not to know what it is. Rather, it is because there isn’t anything else to say. Arguably, all necessities might involve us in explanatory dead ends of this kind. Or perhaps a reflexive explanation could just be taken to indicate that we have arrived at something that may well have an explanation but we don’t, given our current state of knowledge, happen to know what it is. There are a variety of different reasons for which our explanatory progress can be halted. Perhaps we do not achieve the kind of explanation we are looking for, but this does not mean that we have not explained anything whatsoever. In this sense, then, reflexive instances of ground could be metaphysically laden—they are about the world—but shallow—there is no special way that self-grounded facts have to be in order to ground themselves. There is a further issue, or set of issues, that complicate these matters though. Assume the sentence ‘S is in pain state x because S is in brain state y’. This sentence, in fact, involves two sentences joined together with the sentential connective ‘because’. It suggests an explanation of a token pain state in terms of a token brain state. 49 These kinds of facts are facts that Dasgupta 2016 describes as autonomous—they stand in no need of further explanation.

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 grounding and reflexivity We can represent this explanation more simply as ‘A because B’. Sentences express propositions, but it would be a mistake, however, to suppose that the foregoing sentential version of our explanation can necessarily be rendered into its propositional form as explains . According to identity-based reductionism, token pain states and token brain states are (contingently) identical. As names denote referents, ‘pain state x’ and ‘brain state y’ share a referent. On a broadly Russellian view of propositions, propositions are built up out of worldly entities. The propositions is built up from Sally and Louis and the loving relation. Sally and Louis enter into the proposition directly. As the expressions ‘brain state x’ and ‘pain state y’ are co-referring terms the two sentences in our explanatory statement above express one and the same proposition. This means that the explanans and explanandum of our explanation are identical. On a Russellian view of propositions, token identity theories that are also explanatory will yield technically circular explanations.50 On a Fregean view of structured propositions they will not. According to broadly Fregean views, we can distinguish between senses and referents, where structured propositions are composed of senses. Two terms that share a referent may diverge in their senses. What this means in the case of identity theories that involve reductive explanations is that, as the terms ‘pain state x’ and ‘brain state y’ differ in their senses, they express different propositions. On a Fregean view of structured propositions, our explanations in these cases are not even technically circular. Identity theories are controversial, and it is a matter of debate whether they can afford us any kind of explanation whatsoever. The problem generalizes beyond mind/brain identity theories, however. Many scientific explanations are also thought to involve identities: Water = H2O and genes = DNA molecules, and yet we use the latter to explain the former all the time. Whether or not we even have reflexive explanations in these cases will depend, in part, on how we fine grain what we assume to be our explanatory relata.51 Whether or not we are dealing with genuine cases of explanatory circularity, and the reasons for which they may be trivial, will be sensitive to very many of our theoretical commitments.52 50 In her discussion of how we might avoid reflexive metaphysical explanations in cases where we say that pain states are grounded in brain states, Jenkins 2011 suggests that we go hyperintensional. How successful this route is, however, will depend upon what we understand the relata of explanations to be and what, where our relata are propositions, the metaphysics of those propositions are. Suggesting that we ‘go hyperintensional’ is not yet sufficient to deal with the problems of circularity. 51 For the proponent of the view that real relations of ground obtain between facts, establishing where we have genuine instances of reflexivity will involve clarifying both the relationship between propositions and facts, and the particular metaphysic of facts or propositions employed. 52 Ruben also notes that certain facts, on certain accounts, will yield problems with reflexivity. Recognizing this trouble he states, ‘…explanation is not just a relation between facts as constituted by worldly particulars and their properties, apart from how they are conceptualized. If P=Q, the fact that x is P and the fact that x is Q introduce the same feature. What matters in explanation isn’t only property introduction, but the way in which we conceptualize the property, viz. whether the property P is introduced as property P or as property Q’ (Ruben 1990, p. 176).

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ricki bliss 

4 Concluding Remarks Philosophers are generally adamant that grounding is necessarily irreflexive. What the reasons are for this commitment, however, are not often clear. One might suppose that there are a host of metaphysical reasons for supposing that grounding cannot be reflexive. I have explored variations on what I understand to be the most salient metaphysical reasons to reject the possibility of tight grounding loops and found them wanting. I have also explored some explanatory reasons to suppose that grounding is necessarily irreflexive. Although these reasons are more compelling, this result has the upshot that our cognitive lives play a far greater role in what counts as a good or a bad metaphysical explanation than friends of the notion of ground would commonly like to acknowledge. Reflexive explanations are bad because, in some cases, they are trivial and uninformative. That said, we need to be tremendously careful because the charge of triviality will be sensitive to other of our theoretical commitments; and our explanatory demands will play an important role in fixing what counts as an adequate metaphysical explanation.

References Aikin, S.F. (2005), ‘Who is Afraid of Epistemology’s Regress Problem’, Philosophical Studies, vol. 126, no. 2, pp. 191–217. Aquinas, T. (1964), ‘The First Three Ways’, Summa Theologica, Blackfriars, pp. 13–15. Bliss, R.L. (2012), ‘Against Metaphysical Foundationalism’ (unpublished PhD dissertation, University of Melbourne). Bliss, R.L. (2013), ‘Viciousness and the Structure of Reality’, Philosophical Studies, vol. 166, no. 2, pp. 399–418. Bliss, R.L. (2014), ‘Viciousness and Circles of Ground’, Metaphilosophy, vol. 45, no. 2, pp. 245–56. Cameron, R. (2008), ‘Turtles All the Way Down’, Philosophical Quarterly, vol. 58, no. 230, pp. 1–14. Correia, F. (2010), ‘Grounding and Truth-Functions’, Logique et Analyse, vol. 53, no. 211, pp. 1–29. Dasgupta, S. (2016), ‘Metaphysical Rationalism’, Noûs, vol. 48, pp. 1–40. Dixon, T. Scott (2016), ‘What is the Well-Foundedness of Grounding?’, Mind. Fine, K. (2010), ‘Some Puzzles of Ground’, Notre Dame Journal of Formal Logic, vol. 51, no. 1, pp. 97–118. Fine, K. (2012), ‘Guide to Ground’, in Fabrice Correia and Benjamin Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality, Cambridge University Press, pp. 37–80. Gratton, C. (2010), Infinite Regress Arguments, Springer. Jenkins, C.S. (2011), ‘Is Metaphysical Dependence Irreflexive?’, The Monist, vol. 94, no. 2, pp. 267–76. Keefe, R. (2002), ‘When Does Circularity Matter?’, Proceedings of the Aristotelian Society, New Series, vol. 102, pp. 275–92.

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 grounding and reflexivity Kim, J. (1994), ‘Explanatory Knowledge and Metaphysical Dependence’, Philosophical Issues, vol. 5, pp. 51–69. Leuenberger, S. (2014), ‘From Grounding to Supervenience’, Erkenntnis, vol. 79, pp. 227–40. Lewis, D. (1976), ‘The Paradoxes of Time Travel’, American Philosophical Quarterly, vol. 13, no. 2, pp. 145–52. McLaughlin, B. and Bennett, K. (2014), ‘Supervenience’, The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta: https://plato.stanford.edu/entries/supervenience/. Morganti, M. (2009), ‘Ontological Priority, Fundamentality and Monism’, Dialectica, vol. 63, no. 3, pp. 271–88. Morganti, M. (2014), ‘Dependence, Justification and Explanation: Must Reality be WellFounded?’, Erkenntnis, vol. 60, no. 3, pp. 1–18. Paseau, A. (2010), ‘Defining Ultimate Ontological Basis and the Fundamental Layer’, The Philosophical Quarterly, vol. 60, no. 328, pp. 169–75. Passmore, J. (1970), Philosophical Reasoning, Duckworth. Priest, G. (2014), One: Being an Investigation into the Unity of Reality and of its Parts, Including the Singular Object which is Nothingness, Oxford University Press. Rabin, G.O. and Rabern, B. (2016), ‘Well Founding Grounding Grounding’, Journal of Philosophical Logic, vol. 45, no. 4, pp. 349–79. Raven, M. (2013), ‘Is Ground a Strict Partial Order?’, The American Philosophical Quarterly, vol. 50, pp. 191–9. Ruben, D. (1990), Explaining Explanation, Routledge. Schaffer, J. (2003), ‘Is there a Fundamental Level?’, Noûs, vol. 37, no. 3, pp. 498–517. Schaffer, J. (2009), ‘On What Grounds What’, in David Manley, David J. Chalmers, and Ryan Wasserman (eds), Metametaphysics: New Essays on the Foundations of Ontology, Oxford University Press, pp. 347–83. Schaffer, J. (2012), ‘Grounding, Transitivity and Contrastivity’, in Fabrice Correia and Benjamin Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality, Cambridge University Press, pp. 122–38. Schopenhauer, A. (1974), The Four-fold Root of the Principle of Sufficient Reason, trans. E.F.J. Payne, Hackett. Tahko, T. (2014), ‘Boring Infinite Descent’, Metaphilosophy, vol. 45, no. 2, pp. 257–69. Trogdon, K. (2013a), ‘An Introduction to Grounding’, in Varieties of Dependence: Ontological Dependence, Grounding, Supervenience, Response-Dependence, Basic Philosophical Concepts, Philosophia Verlag. Trogdon, K. (2013b), ‘Grounding: Necessary or Contingent’, Pacific Philosophical Quarterly, vol. 94, no. 4, pp. 465–84.

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4 Cosmic Loops Daniel Nolan

1 Introduction Those of us interested in thinking about outré possibilities will be familiar with scenarios where there are large temporal and causal loops—for example, scenarios where time goes in a loop, so that, for example, a big crunch is immediately followed by a big bang. (I intend here a “one time around” loop, as opposed to the kind of eternal recurrence where there are infinitely many bang-to-crunch stretches, laid end to end.) In these scenarios, there are temporal loops and causal loops, but only ones that go all the way around the history of the universe. One example of these, of more than just metaphysical interest, is the closed temporal loop universe described by Gödel 1949, which appears to show that such temporal loops are allowed by Einstein’s general theory of relativity. Scenarios that are less familiar are ones where there are cosmic grounding loops: where the whole structure of grounding ensures that if you follow the chain around from any point, after enough steps you can arrive back where you started. In this paper I want to distinguish several interesting ways of thinking about such grounding loops, argue for the coherence of such models of grounding, consider whether they are metaphysically possible, and discuss how we might embed grounding structures which are locally irreflexive, anti-symmetric, and transitive in worlds with such cosmic loops. Any loop of grounding, of course, enables one in principle to trace it around and get back to the start. What is distinctive about cosmic loops is that they would require going around “the whole way”, in a way that is analogous to the way that a cosmic temporal loop would require going through every other time to arrive back at the original time. The nice thing about times is that, when they are well behaved, they come with a complete ordering, but this is not true in general for objects that stand in grounding relationships. So it is a bit harder to say what “going around the whole way” would amount to for a grounding loop. It would be convenient if everything came with a grounding “level”, as is supposed by some simple versions of the “layer cake” model of the special sciences: chemistry on top of physics, biology on top of chemistry, psychology on top of biology, and so on. Then we could insist that a cosmic loop of

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 cosmic loops ground pass through all of the levels before coming back to the original one. Other patterns in the world come with convenient layers that are less all-encompassing: the relation of part-to-whole can be used to order my fingernail as part of my finger, my finger as part of my hand, my hand as part of me. On its own, it will not serve as a convenient way of ordering everything, since there are distinct hierarchies of parts: my table leg is not part of my leg, nor vice versa. We would have a cosmic loop of part-to-whole if we started with one world (call it world 1) which had many atoms at one end of the part–whole hierarchy, and at the other end of the part–whole hierarchy a Universe that contained everything as parts, and considered another world, world 2, with the same pattern of part-to-whole except that the thing which was the Universe of world 1 was part of all the things which were atoms of world 1. In world 2, you could follow the chain of “part of ” relations starting at the object which is world 1’s Universe, right around to that very object again. World 2 would plausibly contain a cosmic grounding loop too, given the common assumption that wholes are grounded in their parts. (Perhaps world 2 would only be an impossible world, rather than a possible one: more on this question in Section 3 below.) While I have hopefully said enough to get the idea of cosmic loops across, I have not yet provided a general definition. Rather than bogging down in a specification that avoids various tricky corner cases, I will present some exemplars which we may use as paradigms: especially since the issues that arise for my exemplars don’t really depend on whether we have pinned down a unique concept of cosmic loops. One thing I do want to leave open, at least as far as the definition of “cosmic loop” goes, is that cosmic loops of ground might co-exist with shorter loops of ground. Again, time provides a useful analogy: even if the entire universe is a great temporal loop, say with a big bang at the “start” also serving as a big crunch at the “end”, there may also be shorter loops created by time-travel machines or unusual spatio-temporal wormholes. Likewise, even if there are cosmic loops of ground that go “all the way around”, there may also be short loops (e.g. the fact that there are some facts may ground itself1 ). I also want to allow that a loop can be cosmic without bringing everything in a universe into its scope: a layer-cake universe might have several cosmic loops that contain a member from each layer, but do not share any members. When we are considering cosmic loop scenarios, which loops will be grounding loops will depend on what kinds of relationships go along with relationships of grounding in those scenarios. I suppose that we could brutally stipulate grounding connections between different entities or facts, but it will be more natural, and more familiar, to think of grounding as going along with other relationships, such as the part–whole relation or the determinate–determinable relation. (Though there are of 1 See Fine 2010, though of course Fine himself is not tempted to allow that this fact grounds itself. It is instructive to see how difficult it is to avoid allowing it to be a ground of itself, if we make some other standard assumptions about grounding.

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daniel nolan  course debates to be had about which direction grounding goes even in these cases: part-to-whole, or whole-to-part, or sometimes one and sometimes the other, for example.) Rival theories of grounding differ on whether grounding claims are most perspicuously to be expressed using a sentential or propositional connective, or a relational predicate. That is, if we wish to express a particular grounding connection to do with being scarlet and being red, whether G(Apple A is scarlet, Apple A is red), or G(A’s scarletness, A’s redness) best gets to the heart of the matter, assuming determinates ground determinables. I will talk as if grounding is a relation between objects in this paper, but this for convenience rather than to take a stand on this question. I will also not be making much of the distinction, often drawn, between full and partial ground: some cases I will discuss below are best seen as loops of full grounding and others only of partial grounding, but little relevant will hang on which are which. Finally, I will restrict my discussion to talk of singular grounding, instead of also talking about cases where some things collectively ground another (or some things are collectively grounded by a thing, or when some things collectively ground some others): this is not to take a stand on whether there is any irreducibly plural grounding, but again only because that distinction is not important for current purposes. Warning: well-brought up readers of this paper are likely to have been taught that no sense can be made of talk of loops of grounding, cosmic or otherwise, so may find the cases to be discussed below repugnant to their grounding sensibilities. I would encourage those readers to do their best to get their heads around the cases, perhaps in the spirit of intellectual exploration of foreign conceptual landscapes. I will turn to discussing whether any of these examples are possible, coherent, or even conceivable in Section 3.

2 Examples of Cosmic Loops One of my favourite thought-experimental curiosities is a universe described by Rudy Rucker in his Infinity and the Mind (Rucker 1982, pp. 33–4).

2.1 The Rucker Loop What appears to be our entire universe is just a sub-atomic particle in a larger universe, which is but a sub-atomic particle in a yet larger “universe”, and so on ad infinitum. This is also true in the other direction: what seem to us now to be our smallest subatomic particles have the internal structure of an entire “universe”, the sub-atomic particles of which are entire “universes” themselves, and so on ad infinitum. What is distinctive about Rucker’s thought is that this world also loops: go up through enough stages and you will arrive back at one of our sub-atomic particles, or go down through enough stages and you will reach our entire universe.

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 cosmic loops Rucker focuses on aspects of this imagined world like it having no absolute scale from smallest to largest (nothing is once-and-for-all the smallest or the largest, for example), and the prospect that it could nevertheless contain finitely many objects, despite, for example, everything being divisible without end. But the Rucker Loop suggests an interesting pattern of grounding, as well. It is often thought that a whole is grounded in its parts: and when there is a loop like this, that suggests that there is a loop in grounding. Even if we reversed this grounding connection, so that the parts of our cosmos are all grounded in the cosmos, we would get a loop of grounding—our cosmos grounded in the one “above”, grounded in the one “above” that . . . grounded in our cosmos. Furthermore, we can suppose the loop (or the many loops) are allencompassing—that no cosmos lacks a step in the loop, and that we have to go through a cosmos of each other level before arriving back at the cosmos we began with. Let us focus on one of the loops in this world, that begins and ends with our familiar cosmos. This loop is cosmic in the sense I have in mind for this paper. Another cosmic loop of the part-to-whole relationship that has been discussed in the literature is one suggested by a story of Borges (Borges 2000, originally published 1949). In Borges’s story, he describes an object, “the Aleph”, which, on one reading, has everything in the universe as a proper part, even though it itself is a small globe found in a cellar in Buenos Aires. (On another reading, the Aleph merely provides a viewpoint on everything. Borges notes this reading within the story, suggesting that the true object that contains everything else in the universe may be a pillar in Cairo. I suppose it could be contested whether the part-to-whole loop goes all the way around mereological levels in this case, but Borges seems to describe at least a near-cosmic-sized loop.) Sanford 1993 and Parsons unpublished both discuss Borges’s Aleph, on the interpretation where the Aleph does contain everything as a part (and so looking into the Aleph, one even sees the Aleph itself within its basement, containing within itself the whole universe . . .). They both find it worthwhile to try to make coherent sense of it as a possibility. Parsons further seems to suggest that if the Aleph is genuinely possible then the part–whole relationship is not anti-symmetric and transitive. I am not sure of Parsons’s reasoning here, but perhaps he is using “antisymmetric” in a way that a relation is anti-symmetric only if necessarily the relation does not relate an object to a distinct object and also vice versa. Once the option of cosmic loops is noticed, it is easy to come up with other examples. Here are two examples that may be of use as thought experiments, or as pieces of speculative theology for those who are so inclined.

2.2 The last shall be first In this scenario, there is a god—let me label Her TLSBF (for “the last shall be first”). TLSBF is both immanent and transcendent in the following way. (Leave aside any quibbles for now about whether this characterization is strictly “immanence” or “transcendence” in the senses used in, e.g. Christian theology.) TLSBF is within in the smallest places: let Her be a proper part of each space–time point, or if you prefer let

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daniel nolan  physical space–time be gunky with no atomic physical parts, with Her being a proper part of every region. We could also directly specify that She is located within every point (or every gunky region), or perhaps her being parts of those points and regions will be enough, on some conceptions of location, to already guarantee this. Thus She is immanent in her world. (We may add that She is also part of every physical object too, if you wish.) TLSBF is at the “bottom”. But She is also at the “top”. There is a region which has all other regions as sub-regions (the “universal region”), and TLBSF is located at that region. There is an entity which has everything in the universe as parts (as is standard in most theories of parts and wholes), and that universal entity is identical to TLSBF Herself. Let us explicitly include all the space–time regions among her parts. Finally, let us stipulate that in this scenario, entities are grounded in their proper parts: so TLSBF is grounded in her parts, and there is a chain of grounds that lead from TLSBF to Herself. Let us restrict our attention to concrete objects, and leave aside questions about the grounding of abstract objects (if any) in our scenario. The TLSBF scenario is incompatible with classical extensional mereology, which does not allow an object to be a proper part of itself (or indeed to stand in the ancestral of “proper part” to itself—since classical extensional mereology insists that “proper part” is transitive, in ruling out one it rules out the other). Indeed, even much weaker mereologies may rule out this scenario unless we can find some other part of space–time points to be co-parts of those points with TLSBF.

2.3 The One and the cosmos: emanating and constituting Another class of cosmic loop scenarios come into view if we pay attention to the option of saying that there are several kinds of grounding (whether this is because grounding is a genus which admits of various species, or because grounding, though unified, holds in different kinds of cases). Consider a world which is in one respect rather neo-Platonist. The One is the ultimate source of emanation, and this relationship passes through Soul, Wisdom, and other such luminaries, down through Forms, through the Intelligences that are to be found throughout the world, and finally to brute material entities, furthest from the One. Emanation goes with grounding, so that, for example, Wisdom is immediately grounded in the One, the Soul is immediately grounded in Wisdom . . . and the small material parts of intelligences are grounded in the intelligences they emanate from. (I don’t suppose that this specific emanation structure matches that posited by any particular neo-Platonist, but you should be able to tinker with the emanation structure somewhat without affecting the point of the example.) On the other hand, the smallest material parts make up the objects they belong to; those larger material objects constitute the Intelligences, the natures or activities of the Intelligences constitute the Forms, the Forms compose the Soul, which constitutes

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 cosmic loops Wisdom, which is the constitution of the One itself. Wholes are grounded in their parts, and the constituted by what constitutes it (at least in the scenario being described), so in this respect, grounding runs from the lowest to the highest. This is not the same kind of loop as in the previous two cases. In the other two cases, the cosmic loop followed a circle: while we could pick our universe as the place to start and end in the Rucker Loop, it occupied no particularly privileged place, and while TLSBF served both as a proper part of space–time points and as the Universe, we could follow the entire loop around by going from part to whole at each step. In this case, however, we have two grounding arrows facing in opposite directions: partto-whole and constitution going in one direction, and emanating coming from the other. To follow grounding around to get a loop requires going all the way up and then all the way down again. A variant of this case can be imagined that would have a hybrid kind of loop. In this variant, the meanest of the material particles, furthest along the path of emanation from the One, each directly constitute the One and so directly and fully ground it. (Perhaps they do this by being simple, and therefore they are the ones that give rise to the One. Perhaps our hypothetical neo-Platonist constructing the account of this scenario has been meditating on the second half of Plato’s Parmenides.) This loop connects most saliently at the One, which directly grounds Wisdom through emanation, and is directly grounded by each of the ones through constitution. While grounding goes in a circle in this variant, none of the relations that go along with grounding do: emanation and part–whole are one-way only, as is the “direct constitution” link from the material simples to the One. Imaginative readers will probably be able to think of other interesting scenarios containing cosmic loops, but the three examples above should be enough to illustrate the idea and give some idea of the range of cosmic loop scenarios. The three cases presented are all cases taking entities to be grounded by other entities: those interested in expressing grounding using a sentential connective in the manner of Fine 2001 should be able to construct further scenarios where there are cosmic loops of such grounding without involving any cosmic loops of grounding between entities, but I have stretched our theoretical imaginations enough for one paper, so I will refrain from exploring any options of that sort here.

3 Cosmic Loops and Principles of Ground Cosmic loops, on the face of it, conflict with some standard constraints on a theory of ground put forward in the literature. Ground is normally defined so that it is transitive, asymmetric, and irreflexive, which would rule out loops: any loop would result, by transitivity, in something grounding itself. Furthermore, the correct principles of ground, whatever they are, are often thought to be necessary. (At least metaphysically necessary, though sometimes these principles are discussed as if they are partially

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daniel nolan  definitional of ground, so may be intended to be analyticities as well.) Can cosmic loops be dismissed as impossibilities? I would be tempted to argue that such loops are possible in some generous sense, since descriptions of them are coherent.2 But even if they are not possible at all (in any worldly or alethic sense, as opposed to being, e.g. doxastic possibilities), I do not think this would justify an immediate dismissal of any discussion of cosmic loops. One main reason for this is that we are interested in deciding what to think about which principles of ground are correct, so even if alternatives to the true theory of ground are all metaphysical impossibilities, working out which theory of ground is correct may well require us to judge between alternatives to select the best one. In metaphysical inquiry, as elsewhere, dogmatic rejection of alternative theories as even being fit for discussion would be a terrible methodology, since it is often only by appreciating what alternative theoretical options there are to one’s preferred views that we can work out whether our current opinions are better than alternatives, and so whether they are worthy of our continued belief. Those uncongenial to these cosmic loop scenarios might doubt that they are even coherent. Anti-symmetry and transitivity are often put forward as if they are axiomatic of grounding, so some may suspect that it is a conceptual truth (or perhaps an analytic truth) that there are no loops of ground.3 Perhaps there is some concept of a grounding-like relation that, by conceptual stipulation, is anti-symmetric and transitive. But I doubt that such a concept is a very useful tool for investigating the world. One of the central aims of a theory of grounding, I would have thought, would be to discover what sorts of fundamental (and less-than-fundamental) metaphysical relationships obtain between entities (and/or what connections, more broadly speaking, hold between facts). If the important relationships in our world display the sort of loop structure suggested, a theory of ground should reflect that: it would be far less fruitful to declare that we have discovered there is no grounding, but there is merely grounding*, a relation that is found where we thought grounding might be, with all of the features of grounding except (e.g.) transitivity. Substantial metaphysical progress is not to be made by analytic stipulation, so we should select our conceptual tools with an eye to what can be used to illuminate our target of inquiry, rather than to try to bake in some of our favoured conclusions about that target in advance. Those who insist that according to their concept of grounding we can rule out cosmic loops of ground as incoherent are invited to deploy a concept better suited for substantive inquiry.

2 They are possible in at least some of the ways I distinguish as candidates to be “metaphysical possibility” in Nolan 2011, though perhaps not in all. 3 A similar concern can be raised about whether it is a conceptual falsehood that the part–whole relation allows of loops: van Inwagen 1993, in response to Sanford’s Aleph example (see p. 94, this chapter), takes the line that the Aleph case involves a conceptual falsehood. I am tempted by a similar response in the case of part–whole as I am in the case of grounding: I would argue against the conceptual truth of, e.g. asymmetry and transitivity of the part–whole relation, just as I argue against elevating principles of grounding to conceptual truths in the main text.

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 cosmic loops Some readers may find cases of cosmic loops so bizarre or outrageous that they may doubt that cosmic loops are even conceivable. (I intend to use “conceivable” in its ordinary sense, or something like its ordinary sense, and not in any of the stipulative senses introduced by philosophers such as Chalmers 2002.) As against this, it is hard to know what to offer in response beyond the plain fact that I and others do conceive of such scenarios—Rucker seems to have conceived of one of the scenarios above, I came up with two of the scenarios above myself, and I hopefully described them in enough detail to get across what is going on in them, at least to those not antecedently committed to finding such scenarios unintelligible. Perhaps some familiarity with neo-Platonist emanation will help for scenario 3. No doubt there will be those who suspect neo-Platonist emanation is unintelligible on its own: those people face an interesting psycho-historical challenge in explaining how hundreds of people over hundreds of years seemed to communicate and debate about emanation, without any of them conceiving of it. Why would there be resistance to the claims that these scenarios are intelligible or imaginable or conceivable? One source of such resistance will be from people who think that conceivability is a good guide to possibility (Yablo 1993), and who also judge the scenarios I described to be impossible. Once one thinks that one’s grasp of possibility is usually mediated by conceiving, it will be easy to pass from the thought that something seems impossible to the thought that it must be inconceivable. While being able to conceive of something often goes along with its possibility, trying to insist on too tight a connection either leaves one at the mercy of counterexamples to be found everywhere from philosophical theorizing to Escher to the far reaches of speculative fiction, or encourages a dangerous attitude that the thing to do with an alternative one takes to be impossible is to try to convince oneself that one does not understand it. That would be an unhelpfully dogmatic move in many areas of science—imagine if opponents of the general theory of relativity had all reacted that way—and it seems no less dogmatic in philosophy.4 Another source of resistance will be less motivated by theory: I expect some people will find it difficult to understand the scenarios described, and not (necessarily) due to any defect in my presentation. One the face of it, one might have thought that people would take their own inability to conceive something as very weak evidence that it is inconceivable, especially when there are others who apparently conceive of the scenario under discussion. In some areas, this does seem to be people’s response: those who find they cannot conceive of relativistic space–time, for example, are often willing to defer to experts who claim to conceive of it, and so count relativistic space–time as conceivable. But it is a curious fact that philosophers who have trouble conceiving of a

4

A third option would be to allow that many more things are possible than one might have thought, just because we can form some conception of them: see Mortensen 1989. But why engage in a large revision of our views of what is possible rather than a minor revision of a theory of the connection between conceivability and possibility?

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daniel nolan  scenario proposed by other philosophers are often keen to pronounce such scenarios inconceivable. (This often happens to me in conversation with philosophers when I claim to conceive things others claim they cannot, at least.) To those inclined to take these cases to be inconceivable for this reason, let me remind them that familiarity with unusual scenarios can be mind-expanding, and to play with cosmic loop scenarios for a while before being confident that the scenarios are inconceivable, and not merely ruled out by principles that they endorse.

4 Recovering “Local” Irreflexivity, Symmetry, and Transitivity in Cosmic Loops A scenario can be a cosmic loop scenario even if grounding is closed under transitivity in it: these are cases where everything in a circle of ground grounds everything in that circle, including itself. But there is a more natural way to understand many of these circles of ground as being intransitive: while A grounds B which grounds C which grounds D which grounds E which . . . grounds A, these are not scenarios where A grounds itself or is somehow a causa sui. Or at the very least, this seems plausible for many of the entities in these loops: maybe TFSBL or the One are most naturally thought of as self-grounders, but entities in the “middle” of each loop, a given human hand, for example, are not naturally thought of as self-grounders. Even aside from this natural thought, it will be interesting to explore what the options are here for recovering local irreflexivity, asymmetry, and transitivity in cosmic loop scenarios. That is, to what extent can we “save the appearances” and allow that even if, on some cosmic scale, there is a loop of grounding, we need not change our attitudes to the grounding relationships that hold, for example, between the cells and other components of my hand and my hand itself, or between the distribution of rain, clouds, and lightning, on the one hand, and a thunderstorm, on the other? Can things as we ordinarily take them to be be embedded in a cosmos containing one or more cosmic loops at scales we are unfamiliar with? (Compare: in a universe with a unique big crunch that is immediately before its unique big bang, the direction of time might still be locally one-way, with no small loops letting people live through 2014 before 2013.) What would “local” mean in this context? One stab at characterizing it would be to say that grounding is locally irreflexive, asymmetric, and transitive iff when we restrict the domain of entities quantified over to some domain D, then for all x in D, x does not ground x, for all x and y in D, if x grounds y then y does not ground x, and for all x, y, and z in D, if x grounds y and y grounds z, then x grounds z. Then we should insist on some restrictions on the appropriate D so that it is appropriately “local”. We would be aiming to capture the idea that with a certain “distance”, grounding behaves as if it is irreflexive, asymmetric, and transitive, and cases where there are loops of ground only show up when we look at “long distances”. The challenge then is to specify the relevant

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 cosmic loops domains D that are “local” to each other, or alternatively to specify a “distance” so that any entities within that distance of a given object O count as belonging to the same domain D as O. One way to pursue the former strategy would be to find some independent way of specifying domains and which objects share a common domain. Perhaps each of Rucker’s “universes” could be its own domain, for example. One way to pursue the latter strategy would be to say that a domain D is local if there are no more than n steps of immediate grounding between any two members of D, for some suitably low n. This would require that we rely on a notion of “immediate ground”, and find a way to apply it to the grounding chains we are concerned with. Sometimes it is easy to see what immediate ground would be: intuitively, the singleton of Socrates is immediately grounded in Socrates, but the singleton of the singleton of Socrates is plausibly immediately grounded only in the singleton of Socrates, and its grounding in Socrates is only mediate. In other cases, though, it is harder to draw the distinction. Am I immediately grounded in my cells, or only immediately grounded in objects such as my brain and liver, and only mediately (partially) grounded in my liver cells? Or am I immediately grounded in all my parts, down to the quarks and leptons? If we were to apply notions of immediate and mediate grounding in one’s parts in the Rucker world, for example, we would at least want it to turn out that I was not immediately grounded in any of the galaxies that are parts of one of my electrons: though we may have to add stipulations to the original thought experiment if we wanted to guarantee this. While an account of locality that appeals to immediate ground might capture a sufficient condition for a domain D to be of objects “local” to each other, it is probably too restrictive, in several ways. One is that there may well be cases where there is grounding, but no immediate grounding. This could be because some forms of grounding do not lend themselves to an immediate/mediate distinction, and it could also be because there may well be cases where a kind of grounding is in general amenable to that distinction, but unusual cases defy categorization. Consider this sort of structure: suppose that we have an infinite sequence where, for each finite stage, each stage after the first is immediately grounded in the stage below. Suppose now that this sequence has a first “infinite” member: if we were ordering the stages by ordinals, we would assign that stage the ordinal ω. That stage may be plausibly grounded in the stages that came before, but not plausibly immediately grounded in any of them: there is no stage “immediately before” it in the series. One might even think the ordinals themselves are like this. It is more usual to think that ordinals are immediately grounded in all the ordinals that precede them (if “member of ” corresponds to immediate grounding, and we accept the von Neumann definition of ordinals), but orthodoxy here is not compulsory. Another challenge the particular account of “locality” offered here faces, even apart from any concerns about its relying on a notion of immediate ground, is that it does not yet rule out gerrymandered “neighbourhoods”. A selection of a handful of things that do not stand in any chains of grounding to each other will count as

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daniel nolan  a “neighbourhood”: one of my electrons, the singleton of Socrates, and Abraham Lincoln’s last thought are an example of a three-membered domain that we may want to rule out as one of the relevant domains D that we are defining locality over. On the other hand, we do not want to insist that every member of D either grounds, or is grounded by, every other: if we want these domains to include ones we typically think about, we might want to include me, and all of my quarks and leptons, as well as intermediate parts, in a single D, without insisting that each of my electrons either grounds, or is grounded by, each of the others. I will resist the temptation to go down the rabbit hole of developing and critiquing different criteria we might have for selecting a domain D, and ensuring that each domain shares a “locality” in an intuitive sense. Instead, I will turn to a different challenge. To ensure that grounding can be “locally” irreflexive and asymmetric, transitivity must fail somewhere in the cosmic loop—otherwise everything in the loop will ground itself, for example, since we will be able to go from a thing back to itself by steps of grounding. (A failure of irreflexivity is automatically also a failure of asymmetry). The challenge then is to say how grounding could fail to be transitive around the whole loop while being locally transitive, especially if we desire that it is locally transitive everywhere: otherwise enough applications of local transitivity might take us around the whole loop, provided the “locations” overlap. There are a few ways to try to satisfy the demand for local transitivity in the face of this need for a counterexample to transitivity somewhere in the loop. The most conservative way would be to abandon the demand for local transitivity everywhere: perhaps there are no counterexamples to transitivity in parts of the cosmos we are familiar with, but the counterexamples occur somewhere else. A version of this strategy that would work with case 3 would be to insist that grounding per se is not transitive, but only the species of grounding are (in case 3, emanation and constitution). In the second variant of case 3, for example, the obvious point where the counterexample to transitivity of grounding would occur is from the ones to the One and then to Wisdom, since the ones constitute the One but Wisdom only stands in the emanation relation from the One. Suppose we wanted to get closer to the idea that grounding was always locally transitive. We could tinker with our account of what entities are “local” to which, so counterexamples to transitivity only occur when entities do not share a locality (e.g. if there were clear borders between cosmoi in the Rucker loop, perhaps two entities would need to share a cosmos to be local to each other). Or we could wheel out more high-powered philosophical resources. One traditional area where philosophers have struggled with the conflicting desires to have a local inheritance principle that fails over longer distances is in dealing with the paradoxes of vagueness: in the sorites paradox, for example, we would like to hold onto the idea that subtracting one grain of sand from a heap always leaves a heap, but also to the idea that subtraction of enough grains of sand turns a heap to a non-heap. Likewise, if we want local transitivity without full-strength transitivity, we would like the ground of a ground to always

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 cosmic loops be a ground, but there to be some number of iterations of the immediate grounding relation that takes us from a ground to a non-ground, with it being vague where the series breaks down. Perhaps resources developed to help with the sorites could be employed to help with the marriage of local transitivity to a failure of full-strength transitivity? The literature on ways to resist the sorites paradox is vast, and so I will not try to list all the available options here. Options include taking the transitivity principle to have no false instances, but some instances that fail to be true (as with supervaluationist approaches, for example); or to think that some instances of the transitivity principle are almost fully true, and perhaps all steps involving immediate grounding are true enough to assert, though the slow leakage of truth from antecedent to consequent in each instance allows us to have a series of steps of x1 immediately grounding x2 , x2 immediately grounding x3 , and so on, without it being at all true that x1 grounds x1000 (as in fuzzy-logical treatments of vagueness). Both of these approaches compromise the (full) truth of the general transitivity principle, while salvaging the absence of some kinds of counterexamples—there will be no particular “break” in the chain to be identified. Other, slightly more exotic, options, would be to retain the full truth of the transitivity principle but weaken our logical resources so that we cannot validly apply it multiple times: just as we cannot validly reach the conclusion that a single grain of sand is a heap, we will not be able to validly reach the conclusion that x1 grounds x1000 , even if x1 grounds x2 , and x2 grounds x3 , and grounding is transitive. Ways of doing something similar in the case of the sorites include the contraction-free approach explored by Slaney 1988 and Restall 1994 ch. 8, and the intransitivityof-validity approach explored by Cobreros et al. 2015, among others. Yet another option would be to adopt an approach that rendered at least the material version of transitivity true while making it unsuitable for use in inferring the consequent from the antecedent, by analogy with the subvaluational approach to vagueness explored in Hyde 1997. I am inclined to think that any commitment to transitivity of grounding would not be strong enough to motivate these sort of logical modifications to preserve local transitivity of grounding: but those already keen on these resources, perhaps to preserve tolerance principles in vague cases, may find it appealing to treat apparent failure of transitivity in cosmic loop cases with similar resources. Armed with an understanding of how to ensure local transitivity and asymmetry without global transitivity in cases of loops of grounding (whichever understanding we might adopt), we can apply the same resources to other relations of interest, including those that appear to underpin grounding relationships. One thing that makes Rucker loops so mind-bending, for example, is that they challenge our assumptions about the part–whole relationship: that I, for example, could be a proper-part of a proper-part of a proper-part of . . . myself. That would be impossible were the properpart relation both asymmetric and transitive. However, one thing that makes the case less mind-bending than short loops of the proper–parthood relation (e.g. just

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daniel nolan  stipulating that A is a proper part of B and B is a proper part of A) is that in a Rucker world with local transitivity and asymmetry the relation of proper-part to whole would behave just as it actually does in cases we are familiar with: I am part of the Milky Way galaxy, but the Milky Way galaxy is not part of me. This is not the only way to conceive of a Rucker loop, of course: another way would be to conceive of the Milky Way as being one of my parts, but just much further down a natural chain of part-to-whole than one might have thought. But at least the option of retaining local transitivity and asymmetry gives us one way to think of the Rucker loop scenario as being one in which our ordinary particular judgements about what is part of what do not need to be revised. Similar devices could also be deployed if we wished to claim there was local neartransitivity, near-asymmetry and near-irreflexivity of ground and of other notions. After all, a number of authors have wanted to motivate exceptions to each of these principles independently of anything to do with very long chains of ground. See, for example, Jenkins 2011 on reflexivity, Barnes 2018, on symmetry, Schaffer 2012 on transitivity, and Bliss 2011 on all three, as well as many of the other papers in this volume. One, perhaps inelegant, way to modify local transitivity to local neartransitivity, for example, would be to say that except for such-and-such cases grounding is locally transitive within a domain D. A more elegant way to specify local neartransitivity would be to have a positive story about when, for entities among a given D, it is the case that when x grounds y and y grounds z, x also grounds z. Even more elegant would be such a principle that applies to all “local” domains D at once, rather than separately specified principles about each D individually. Suppose we do secure local transitivity (or something close to it) without requiring transitivity tout court. What advantages could that offer a theory that postulated a cosmic loop? One advantage is that grounding relationships would be more selective. A grounding loop which is transitive requires everything in the loop to ground everything else in that loop, which might sometimes seem counterintuitive: even if both the Milky Way and an electron in it are part of the one Rucker loop, intuitively the electron partly grounds the Milky Way and not the other way around. Perhaps we should think that cosmic loops where grounding is transitive, and so everything in a loop grounds everything else in that loop, are also conceivable and maybe possible: but it is natural to think that not all grounding loops are like this, and perhaps not the ones that most naturally come to mind when presented with cases like those given in Section 2. Another advantage follows if we antecedently thought that instances of grounding we are familiar with appear to never relate entities to themselves, relate in an asymmetric “direction”, and at least appear transitive. While there are many papers in this volume that will argue that even grounding we are familiar with need not always be like this, we retain the option of leaving our theory of the grounding relationships between familiar entities as being traditional, while accepting (or leaving open the possibility) that there are cosmic grounding loops outside our familiar domain. The

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 cosmic loops options for preserving local transitivity will also be valuable, apart from any doctrines about grounding, when dealing with other metaphysical relationships we are tempted to think are asymmetric and transitive, such as the relation of part-to-whole. The Rucker loop, for example promises to shed light on the conceivable, and perhaps possible, options for mereology as well as for grounding. Those suggesting philosophical innovations, or even scepticism about received wisdom, are often under pressure to “save the phenomena”: to explain why it seemed that the old orthodoxy was right, or why we can often rely on generalizations or inferences supported by the old orthodoxy. For example, the nihilist about tables and chairs owes us a story of our apparent success in home decoration and lunch preparation, or the dialetheist logician owes us a story about why classical mathematics seems to have been such a success in the twentieth century while apparently relying on classical logic. One way to “save the phenomena” is to corral exceptions to previous orthodoxies to cases that are relatively unusual: classical physics can be used to build bridges or aim cannons, because, for example, moving objects do not get appreciably more massive as they speed up until they are close to the speed of light. Recovering “local” transitivity, asymmetry, and irreflexivity for grounding is one way to show how the exceptions to those principles do not show up in the cases we were most familiar with. Grounding loops will appear exotic to many, but if a theory postulating a grounding loop only offends our intuitions in cases far removed from those with which we are familiar, then we may not wish to trust our intuitions very far about those cases. The comparison with theorizing about causation may be instructive: while we are, in my view, properly reluctant to abandon the view that rock throwings sometimes cause window breakings or that stock market crashes cause unemployment, we are much less certain about our ordinary causal generalizations and intuitions when considering cases like quantum mechanical phenomena or the Big Bang. And rightly so: exotic phenomena might behave exotically. To work out whether there are cosmic loops of ground, or of part–whole, or other such relations, we would do well not to just trust our off-the-cuff generalizations but to carefully investigate cases outside familiar ones.

5 Conclusion Cosmic loops are of intrinsic interest: thinking about them can satisfy the same urges to grapple with the unfamiliar which are satisfied by various sorts of speculative fiction, from science fiction to the stories of Borges. Metaphysical fiction is a genre in its infancy, but a promising one for all that. I have argued that thinking about cosmic loops serves several more academic purposes, however. They demonstrate, that we can make sense of loops of ground in a different way from the usual examples of loops achieved through only a few steps, and the conceivability and perhaps possibility of them are supported in ways different from other arguments I know of to support failures of asymmetry and transitivity. This should give us additional reason, were additional reason needed, to

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daniel nolan  admit the conceivability and consider seriously the possibility, that grounding need not be transitive (and to a lesser extent, reason to take non-symmetry seriously, if we think that some cosmic loops of ground are not counterexamples to transitivity). Finally, through exploring options for recovering local transitivity (and so local asymmetry and irreflexivity, should we want them), we can see that confidence about grounding relations between familiar items should not lead us to overconfidence about general principles of ground, no more than experiencing the local asymmetry of the direction of time should lead us to assert dogmatically that cosmic temporal loops are impossible. Those who want to reject the possibility of cosmic loops, let alone those who reject the coherence of them, would be well served to defend the principles they think rule out such loops, rather than just taking those principles to be obvious or analytic. And this applies just as much to cosmic loops of part-to-whole, or cosmic loops of any other relation, as it does to cosmic loops of grounding. Metaphysics, with its hope to be a completely general investigation of what there is, should be particularly wary of the perils of overgeneralization.5

References Barnes, E. 2018. “Symmetric Dependence”, in R. Bliss and G. Priest (eds), Reality and its Structure: Essays in Fundamentality. Oxford: Oxford University Press, pp. 50–69. Bliss, R. 2011. “Against Metaphysical Foundationalism”. PhD thesis, University of Melbourne. Borges, J.L. 2000 [1949]. The Aleph and Other Stories. London: Penguin. Chalmers, D. 2002. “Does Conceivability Entail Possibility?” in T. Gendler and J. Hawthorne, Conceivability and Possibility. Oxford: Oxford University Press, pp. 145–200. Cobreros, P., Egré, P., Ripley, D., and van Rooij, R. 2015. “Vagueness, Truth and Permissive Consequence”, in T. Achourioti, H. Galinon, K. Fujimoto, and J. Martinez-Fernandez (eds), Unifying the Philosophy of Truth. Dordrect: Springer. Fine, K. 2001. “The Question of Realism”. Philosopher’s Imprint 1: 1–30. Fine, K. 2010. “Some Puzzles of Ground”. Notre Dame Journal of Formal Logic 51.1: 97–118. Gödel, K. 1949. “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy”, in P.A. Schlipp (ed.) Albert Einstein: Philosophical Scientist. Library of the Living Philosophers, La Salle, IL: Open Court Press, pp. 555–62. Hyde, D. 1997. “From Heaps of Gaps to Heaps of Gluts”. Mind 106.424: 641–60. Jenkins, C.S. 2011. “Is Metaphysical Grounding Irreflexive?” The Monist 94.2: 267–76. Mortensen, C. 1989. “Anything is Possible”. Erkenntnis 30.3: 319–37. Nolan, D. 2011. “The Extent of Metaphysical Necessity”. Philosophical Perspectives 25.1: 313–39. Parsons, J. Unpublished. “The Earth and the Aleph”. http://www.joshparsons.net/draft/aleph/. Accessed 16 January 2016. Restall, G. 1994. “On Logics Without Contraction”. PhD Thesis, University of Queensland. Rucker, R. 1982. Infinity and the Mind. London: Paladin Books.

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Thanks to Sara Bernstein, Ross Cameron, Alex Sandgren, and two anonymous referees for feedback.

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 cosmic loops Sanford, D. 1993. “The Problem of the Many, Many Composition Questions, and Naive Mereology”. Noûs 27.2: 219–28. Schaffer, J. 2012. “Grounding, Transitivity and Constrastivity”, in F. Correia and B. Schnieder (eds), Grounding and Explanation. Cambridge: Cambridge University Press, pp. 122–38. Slaney, J.K. 1988. “Vagueness Revisited”. Australian National University, Automated Reasoning Project Technical Report, TR-ARP-15/88. van Inwagen, P. 1993. “Naive Mereology, Admissible Valuations, and Other Matters”. Noûs 27.2: 229–34. Yablo, S. 1993. “Is Conceivability a Guide to Possibility?” Philosophy and Phenomenological Research 53: 1–42.

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5 Metaphysical Interdependence, Epistemic Coherentism, and Holistic Explanation Naomi Thompson

1 Introduction This paper develops an argument for metaphysical interdependence; an alternative to orthodox foundationalist accounts of metaphysical structure as characterized by grounding relations. Friends of metaphysical interdependence take facts to be related in networks of grounding such that there might be no foundational facts, and that a given fact can appear in its own grounding ancestry. Grounding is an explanatory relation, and the need to recognize holistic explanations (and in particular, holistic metaphysical explanations) generates a requirement for an account of grounding with a holistic structure. Metaphysical interdependence is such an account. After briefly introducing the notion of ground in §2, §3 outlines both the core of the foundationalist approach, and that of metaphysical interdependence. §4 develops an analogy between metaphysical interdependence and coherentism in epistemology. §5 argues that grounding is to be thought of as an explanatory relation. In §6, the view that grounding is an explanatory relation is considered against the backdrop of different approaches to explanatory structure. In §7 I respond to some perceived objections to holistic explanation. §8 concludes this chapter.

2 Grounding I take grounding to be a relation of metaphysical dependence, which obtains between facts.1 Grounding is said to be an explanatory relation, such that when some fact [A] 1 This point is contentious amongst friends of grounding, and I make no attempt to defend it here. I talk of grounding as obtaining between facts merely in order to simplify the discussion, and not because I think there are conclusive arguments for thinking that grounding relations do not relate entities of other ontological categories. I take it that what I say here could also be applied to cases of grounding between entities of other ontological categories with only minor adjustments.

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 interdependence, coherentism, and holistic explanation grounds a further fact [B], [A] explains [B]. Like explanation, grounding is a onemany relation, such that some fact may have a number of grounds. Following Fine (e.g. 2012: 50) I take [A] to be a partial ground for [C] if [A], on its own or with some other grounds, is a full ground of [C]. A full ground for [C] is sufficient, by itself, to ground [C]. It is generally assumed that grounding claims can be expressed using a variety of different locutions. They can be signified with a sentential operator such as ‘because’, or with a relational formulation such as ‘[A] grounds [B]’ or ‘[B] depends on [A]’. For ease of expression I’ll generally use the relational formulation, but it shouldn’t be assumed that anything follows from this choice. Grounding claims seem each to involve an explanatory element—it is the way that the painting is received that explains its being beautiful, it is the non-moral features of an action that explain an action’s being morally permissible, and so on. Grounding is usually considered a primitive relation; it can’t be analysed in other terms. Along with citing putative examples of grounding, a favourite recourse for the friend of grounding when attempting to clue us in to what the notion is supposed to be is to point to the explanatory character of ground (see e.g. Fine, 2001; 2012). This tactic is taken to be particularly useful when defending the notion against sceptical attacks on its intelligibility.2 A quick look to the relevant literature reveals the ubiquitousness of the idea that grounding and explanation are closely connected. Dreier (2004: 35) says that the ground for some fact is the ‘most illuminating explanation’ of that fact; Raven (2012: 689) says ‘a fact’s grounds explain it by its holding in virtue of them’, and Trogdon (2013: 97) says ‘in causal explanations the explanans and explanandum are connected through a causal mechanism, while in metaphysical explanations they’re connected through a constitutive form of determination, that of grounding’. Orthodoxy has it that grounding is transitive (if [A] grounds [B] and [B] grounds [C], then [A] grounds [C]); irreflexive (nothing grounds itself); hyperintensional (necessarily co-referring terms cannot be substituted salva veritate); non-monotonic (if [A] grounds [C], it doesn’t follow that [A] and [B] ground [C]); and asymmetric (if [A] grounds [B], [B] doesn’t also ground [A]). Note that these properties of grounding are also generally taken to be properties of explanation. In fact, it is standard to claim that grounding inherits these properties from the properties of explanation, since grounding is an explanatory relation (see e.g. Raven, 2015: 327). Grounding relations are taken to describe the structure of reality, in the sense that ontological dependence is to be cashed out in terms of grounding. In the literature, one conception of the structure of reality dominates: metaphysical foundationalism. Orthodoxy has it that grounding relations form a well-founded partial order. In §3, I briefly outline the foundationalist conception of metaphysical structure, and introduce my preferred alternative: metaphysical interdependence.

2 Those mounting such attacks include Daly (2012) and Wilson (2014). Defences which appeal to the explanatory nature of grounding include Audi (2012a; 2012b); Barnes (2013); Trogdon (2013).

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naomi thompson 

3 Foundationalism and Interdependence Metaphysical foundationalists hold that facts are related in non-repeating chains of grounding, terminating in a collection of fundamental or foundational facts, which are not themselves grounded in anything further. We can characterize metaphysical foundationalism in terms of its commitment to two theses (where x and y are facts): Well-foundedness: For all x, x is either grounded by some foundational fact or facts, or is itself a foundational fact. Asymmetry: For all x and all y (where x = y) if x grounds y then y does not ground x.3 Well-foundedness guarantees that each fact is ultimately grounded in some foundational fact or facts, and asymmetry guarantees that grounding hierarchies run only in one direction; from the more fundamental to the less fundamental. The higher up the chain of grounding a fact appears, the further it is from the foundational facts that ultimately ground it. (I assume here that all facts are part of the grounding hierarchy. Anybody who wishes to resist that assumption might take the universal quantifiers in the definitions above to be restricted to range over facts which they think are part of that hierarchy.) Metaphysical foundationalism is roughly analogous to a foundationalist approach to epistemic justification, where justification is inferred along linear chains of beliefs from basic beliefs at the end of the chain which are the source of justification. The most prominent alternative picture of how beliefs are justified is a coherentist approach, whereby justification emerges when beliefs form a coherent network. At the heart of the coherentist’s approach is the idea that the structure of justification is one of mutual support. A set of facts or beliefs is coherent just in case every element in the set is supported by all the other elements taken together (Lewis, 1946). Support might be understood in a weak probabilistic sense, such that P is supported by Q if the probability of P is raised if we assume that Q is true. Alternatively, we might define coherence in terms of logical consequence; a coherent set must be consistent, and every member of the set must follow by logical deduction from the rest (see Olsson, 2017). An analogous picture is plausible in the metaphysical case. Grounding between facts might be such that each fact is supported by all the other facts taken together, rather than (as in foundationalism) being supported by a set of foundational facts. If grounding relations are taken to hold with metaphysical necessity (as is standard), then probable relations will have little role to play in either the metaphysical foundationalist or the interdependence picture. Instead, we can focus on something 3 That x and y are distinct facts is built into my definition of asymmetry here so as not to make any assumptions about the reflexivity of grounding; so that those (e.g. Jenkins, 2011) who do not wish to rule out the possibility that ground might be a reflexive relation are not thereby forced to deny that ground is asymmetric. This is sometimes called antisymmetry.

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 interdependence, coherentism, and holistic explanation closer to logical deduction. It is common for foundationalists to claim that once the foundations are settled, the rest of reality follows—a complete story can be told in terms of the foundations alone. Friends of metaphysical interdependence might claim that any element of the system can be deduced from all the rest taken together, and that we can’t tell a complete story without considering the system as a whole. In addition, support has an explanatory dimension. Just as the metaphysical foundationalist takes the fundamental facts to explain or to account for all the rest, the friend of metaphysical interdependence can take each fact in the system to be supported, in this explanatory sense, by all the other facts taken together. Facts are related in web-like networks of ground such that each fact in the network is partially grounded by other facts in the network. Metaphysical interdependence is thus most similar to versions of coherentism that focus on inferential connections between component beliefs. These beliefs often form a linear order within the system, but a given belief might appear in its own reason ancestry. By the transitivity of partial ground, each fact in the interdependent network is partially grounded by every other fact in the network, and itself. The grounds for some fact [A] might be the further facts [B], [C], and [D], but [D] might itself be grounded by [E], [F], and also by [A]. There might therefore be no fundamental facts, but the facts in the network enter into mutually supporting grounding relations. The friend of metaphysical interdependence thus denies both well-foundedness and asymmetry. Note that a weak version of interdependence requires only that there be at least one counterexample to both well-foundedness and asymmetry. In that case, grounding structures might be hybrids featuring chains of ground that bottom out in foundational facts alongside small pockets of interdependence. Such a case would be much less closely analogous to the coherentist position sketched above than a strong version of interdependence where there are no foundational facts. Though I think a weak version of interdependence deserves attention, my discussion here concerns the stronger version of the view. For our purposes then, we can assume that the friend of interdependence endorses non-well-foundedness; the view that there are no foundational facts. Non-well-foundedness is a commitment usually shared with metaphysical infinitists (see e.g. Cameron, 2008; Morganti, 2009), who hold that linear chains of ground extend infinitely in some direction.4 Metaphysical interdependence requires that asymmetry also be rejected. If [A] grounds [B], [B] might (either fully or partially) also ground [A]. In order to motivate my claim that asymmetry should be rejected, I’ll mention two examples which purport to demonstrate that grounding is not asymmetric, the first involving full grounding, and the second partial grounding (see Rodriguez-Pereyra, 2015 and Thompson, 2016 for more detailed examples). First, consider the following true propositions: A = and B = . Assume that both propositions are true. It is very

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Unfortunately I do not have the space here to discuss versions of infinitism in any detail.

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naomi thompson  plausible to suppose that propositions are true in virtue of the relationship between their constituents and the world (thus, e.g. the fact that is true is grounded in the fact that snow is white). In this case, the fact that A is true is grounded in the fact that B is true, and the fact that B is true is grounded in the fact that A is true. If we accept that this is an example of grounding, we must accept that full grounding is not asymmetric. Second, consider the relationship between the qualities of mass, density, and volume in a homogeneous fluid. A natural way to describe that relationship is in terms of grounding; the volume of the fluid seems to have the value it does in virtue of the values of the mass of the fluid and the density of the fluid. But each of the parameters seems to have the value it does in virtue of the other two parameters; the three parameters are interrelated. If grounding is transitive, then facts about the value of each of the parameters partially ground facts about the value of the other two, and itself. If we accept this example, we must accept that partial grounding is not asymmetric. Once we have at least cast doubt on the orthodox view that grounding must be asymmetric, we can consider arguments for metaphysical interdependence. Three such arguments are given in Thompson (2016). I’ll briefly outline two of them. First, metaphysical interdependence is the only theory capable of reconciling competing intuitions about certain cases of grounding. Take, for example, the grounding between facts about an organism and its facts about its organs. It seems, for example, that the fact that the heart pumps blood around the body depends on the fact that the organism exists and has a properly functioning circulatory system. But the fact that the organism exists and has a properly functioning circulatory system depends on the fact that the heart pumps blood around the body. More generally, in the case of what Schaffer (2010: 47) calls integrated wholes (which are to be distinguished from mere aggregates, such as heaps), there are good reasons to think that the parts are grounded in the whole. Consider, for example, a circle; any divisions (e.g. its semi-circles) are ‘arbitrary partition[s] on the circle’ (Schaffer, 2010: 47). But there are also good reasons for thinking that wholes are always grounded in their parts. Just as atoms might compose a table, semi-circles might compose a circle, and so the fact that the circle exists can be explained by the fact that the semi-circles exist; the existence of the circle seems to depend on the existence of the semi-circles. Metaphysical interdependence can simultaneously account for both of these seemingly competing intuitions about dependence. Second, we cannot rule out the possibility that the world is gunky—that everything has proper parts. It is also possible that the world is junky—that everything is a proper part of something. Assuming that parthood relations entail grounding relations,5 we cannot rule out the possibility of an infinitely extending grounding chain in either

5

See e.g. Cameron (2008); Schaffer (2010).

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 interdependence, coherentism, and holistic explanation direction. Metaphysical foundationalists require that grounding chains terminate, whether they terminate in multiple foundational facts as in priority pluralism (which is incompatible with gunky worlds) or a single totality fact as in priority monism (which is incompatible with junky worlds). The foundationalist must therefore argue (if grounding relations are taken to hold with metaphysical necessity) that one or other of gunk and junk is metaphysically impossible.6 Metaphysical interdependence does not require that there be any foundational facts, and so is compatible with gunk, junk, both, or neither (this also makes interdependence more attractive than infinitism, which requires that there be infinite extension of grounding chains in at least one direction). With our account of metaphysical interdependence on the table, I motivate metaphysical interdependence via an analogy with coherentism about epistemic justification in §4. The rejection of asymmetry and of well-foundedness is held in common by friends of metaphysical interdependence, advocates of coherentism, and defenders of the holistic approaches to explanation in general which I discuss in the final sections of the paper.

4 Epistemic Coherentism In §3, I highlighted an analogy between metaphysical interdependence and epistemic coherentism. Both structures are non-well-founded and involve relations of mutual self-support. Coherentists think that no belief is the source of its own justification, but rather that justification is an emergent feature of coherent sets of beliefs. Friends of metaphysical interdependence think that no fact is ungrounded. The analogy with coherentism isn’t perfect, but an understanding of how beliefs might work together to support one another via inferential connections might help make clear how facts support one another in a system of ground characterized by metaphysical interdependence. The example I describe below focuses on explanations for beliefs. Justificatory explanations are one type of explanation, and so the example might also help to motivate the more general claim I make in this paper, that holistic explanations can be good explanations. Here’s the example: Aimee notices that her neighbour, Bob, seems a little upset and withdrawn. She wonders what could explain his behaviour, and realizes that she hasn’t seen Bob’s partner, Chris, in a week or so. She then remembers hearing raised voices coming from Bob’s house one evening, about a week ago. She hypothesizes that Bob’s behaviour is due to him and Chris having split up. With that explanation in mind, she reasons that the raised voices she heard were Bob and Chris, and that the reason she

6 Even if the foundationalist denies that grounding is necessary in this way, the inability to rule out the possibilities of gunk or junk in the actual world poses the same problem.

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naomi thompson  hasn’t seen Chris lately is that Chris and Bob have split up. On this basis she reasons that Bob is indeed upset, and that he’s upset because he and Chris have split up. In the above example, Aimee’s belief that Bob and Chris have split up is explained by her observations that she hasn’t seen Chris lately, that she heard raised voices a week or so ago, and that Bob seems upset. In turn, it is Aimee’s belief that Bob and Chris have split up that lends support to her belief that Bob really is upset, and explains why Chris hasn’t been around lately, and why voices were raised. This is a holistic system of explanation, characterized by mutual support relations between explanans and explanandum. It’s important to note that without taking each belief in this system to be supported by all the other beliefs in the system, this explanation of Bob’s behaviour wouldn’t seem like a good explanation. Without further argument one might maintain that holistic explanations can be plausible in epistemic cases such as that of the justification of our beliefs, but are implausible when it comes to metaphysics, and to grounding. I think explanation should be understood in general terms, such that holism about explanation in one area should strengthen the case for holism in others. In §5, I argue that grounding is an explanatory relation, and in §6 and §7 that grounding explanations can be holistic explanations.

5 Explanation and Ground What precisely is the relationship between ground and explanation? There seem to be two options. Either the relationship is one of identity; grounding just is a relation of metaphysical explanation, or it is the weaker relationship of tracking; explanations track grounding relations. Support for both views can be found in the literature.7 In this section I offer two considerations in favour of the former view, the first based on a problem for the tracking view, and the second based on the epistemology of ground. Assume that explanations track grounding relations. This idea has some precedent with respect to causation; we generally think of causal explanations as ‘tracking’ causal relations in the world (see e.g. Salmon, 1984; Lewis, 1986; Woodward, 2003). A question then arises as to the nature and the mechanism of this tracking relation. Kim (1994: 26) argues that explanations track dependence relations. More precisely, Kim says that ‘the relation that “grounds” the relation between an explanans, G, and its explanatory conclusion, E, is that of dependence; namely G is an explanans of E just in case e, the event to be explained depends on g, the event evoked as explaining it’. Kim thus takes dependence relations to ground explanations.

7 Defenders of the former view include Dasgupta (2014); Fine (2012); Litland (2013); Raven (2012); and Rosen (2010). Defenders of the latter view include Audi (2012a); Schaffer (2012); and Trogdon (2013).

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 interdependence, coherentism, and holistic explanation Let’s suppose then that the relationship between a grounding relation and an explanation that tracks it is that of grounding. Kim distinguishes between the relata of the dependence relation (which in the above quote are events) and the relata of the explanatory relation. Since we are assuming that the relata of the grounding relation are facts, we won’t make a corresponding distinction; explanatory relations and grounding relations both have facts as their relata. We can suppose then that when [A] grounds [B], there is a corresponding explanatory relationship between [A] and [B], and that the relationship between the facts that [A] grounds [B] and that [A] explains [B] is one of grounding; [[A] grounds [B]] grounds [[A] explains [B]]. Here’s the worry. That the relationship between ground and explanation is itself one of grounding is not viciously circular, but it is problematic because it renders the connection between explanation and ground explanatorily redundant. Friends of grounding rely on the close connection between explanation and grounding in order to elucidate the relatively opaque notion of primitive metaphysical grounding with the far more familiar notion of explanation (see e.g. Audi, 2012a; Fine, 2012; Raven, 2015; Trogdon, 2013). If an appeal to explanation is to shed light on the notion of ground, part of what must be understood is how ground and explanation are related. Here we are told that the relationship between ground and explanation is in fact one of ground, but ground was what we were seeking elucidation of in the first place! If the connection between ground and explanation is to illuminate the notion of ground, we need an account of that connection not itself cashed out in terms of ground. So if not ground, then what? Merely modal notions like supervenience and entailment are too coarse-grained to respect the sense in which it is the grounding relations that back the explanations, and not the other way around. Making sense of the dependence of the explanation on the grounding relation requires some kind of hyperintensional account of tracking, and so the friend of the tracking conception must come up with some alternative to grounding which meets this condition. In the absence of such an account, we have reason to prefer a view whereby grounding is an explanatory relation, and so there is no mystery as to how an understanding of explanation might help elucidate ground. A second reason for thinking that grounding is a relation of explanation concerns the epistemology of ground. An underexplored question in the grounding literature is that of how we come to know what grounds what. It is generally assumed that we can know about grounding by recourse to our explanatory intuitions (see e.g. Fine, 2001; 2012). Here’s one reason for thinking that explanatory intuitions clue us in to grounding relations: grounding is hyperintensional, and knowledge of hyperintensional notions requires a way of knowing which is sensitive to hyperintensional distinctions. Explanatory knowledge is a paradigm example. We can explain to someone why it costs a fortune to see Bob Dylan in concert in terms

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naomi thompson  of Dylan’s fame, but not (unless they know that Dylan and Zimmerman are the same person) why it costs a fortune to see Robert Zimmerman in concert in terms of Dylan’s fame. Similarly, understanding that Socrates grounds {Socrates}(but not that {Socrates} grounds Socrates) requires an epistemology that is sensitive to fine-grained distinctions between necessary co-existents. If grounding is an explanatory relation, we have a neat explanation both of the hyperintensionality of grounding, and of how we could come to know about the grounding relations (explanations are precisely the kinds of things we can come to know). If, on the other hand, explanations merely track grounding relations, it is an open question how we can come to know what grounds what. Adopting a weaker account of the connection between explanation and ground generates a requirement for an epistemology of ground. Friends of grounding might be able to provide such an epistemology, but until they do it seems safer to assume that if we can know the grounding facts, it’s because grounding just is an explanatory relation. Neither of the above arguments provides conclusive proof that we ought to adopt the view that grounding just is an explanatory relation, but they provide reason to think that the alternative account leaves some important questions unanswered. My aim here is merely to support the claim that explanatory considerations can legitimately be brought to bear on our account of grounding. I suspect that an account of the tracking view that answered the questions raised above would also legitimize this sort of argument, but I think we have reason for now at least to set that view aside, and to proceed as though ground just is an explanatory relation. Before continuing, I wish to respond to one perceived concern. In the next sections, I argue that considerations about the structure of explanation push us towards accepting metaphysical interdependence over foundationalism. But friends of grounding don’t just say that grounding is an explanatory relation. They say that grounding is related to explanation of a distinctively metaphysical sort (see e.g. Fine, 2012: 37). It might be that metaphysical explanation functions very differently from the more familiar explanatory notions. Were that the case, discussion of explanation generally might not be relevant here. In response, note that if we are to be able to use the connection between grounding and explanation as it is generally assumed that we can (to shed light on the features of grounding generally, as well as to settle questions about what grounds what), what we mean by explanation in this context must be at least fairly familiar; not too far removed from our ordinary understanding of what an explanation amounts to. We couldn’t use an unfamiliar notion of explanation to shed light on anything. In the absence of a properly developed theory of metaphysical explanation independent from our theory of grounding, assuming that metaphysical explanation is divorced from our ordinary conception of explanation would only serve to undermine the project of highlighting connections between the two notions (see Daly, 2012; Thompson, forthcoming). I therefore assume that metaphysical explanation is not different in

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 interdependence, coherentism, and holistic explanation kind from explanation in general (and so, for example, will exhibit the same formal features).

6 Explanatory Considerations In this section I argue that a foundationalist conception of the structure of explanation is inferior to the sort of holistic account of explanatory structure favoured by friends of metaphysical interdependence. I discuss two problematic features of the foundationalist account, and give two examples of structures of metaphysical explanation best described in accordance with holism.

6.1 Foundationalism The idea that explanatory chains terminate is a familiar one. Take, for example, the idea that higher level psychological facts are grounded in and explained by biological facts, which are themselves grounded in and explained by chemical facts, in turn grounded in and explained by physical facts, themselves dependent on lower level microphysical facts. Eventually, some argue, we reach a level of facts for which no further explanation can be given (or at least we will reach this level when physics is complete). Advocates of this sort of conception of the structure of explanation think that explanations terminate; there is a point at which (relative to a given fact) the explanatory project is complete. There are some facts that don’t require further explanation, or that are ungrounded. When evaluating this account of the structure of explanation we might first consider theoretical virtue.8 In evaluating competing theories, facts that cannot be explained are called brute facts. Brute facts carry a theoretical cost; they represent something that a theory leaves unexplained. Other things being equal, a theory that carries a commitment to fewer brute facts is to be considered superior because it has more explanatory power—it leaves fewer things unexplained. On a simple assessment then, metaphysical foundationalism does much worse than interdependence, because it carries a commitment to as many brute facts as there are fundamental facts. Metaphysical interdependence (at least in the strong form under consideration here) denies that there are any brute facts at all; each fact is (partially) explained by every other fact in the system. Arguments from theoretical virtue are notoriously difficult to evaluate, and a friend of a foundationalist way of thinking about explanation might even take a nonfoundationalist view according to which there are no brute facts to be a reductio of the idea that the number of brute facts in a theory is to be minimized. But I think this would be a mistake, for the reasons mentioned above; brute facts weaken a theory. If

8

There is some precedent for this—see e.g. Cameron (2008).

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naomi thompson  we can have a theory according to which there are no brute facts, so much the better! There is something unsettling about the idea that there are some facts which simply obtain, and that’s all there is to say about it. I’ll mention two ways to make this point a little more concrete. First, note again that brute facts are not explained by the theory of which they are a part. A foundationalist structure does not allow for the possibility that there might be metaphysically explanatory connections at the fundamental level of explanation, because all grounding chains terminate in brute facts. Applied to our above example, that means that the facts of fundamental physics are explanatorily independent of one another (at least in terms of the sort of explanation relevant to grounding). This restriction on grounding between fundamental physical facts in fact goes against our best current physics, which points to the presence of holism and/or non-separability at the quantum level (see e.g. Healey, 2016). This is naturally cashed out in terms of grounding (see e.g. Schaffer, 2010; Ismael and Schaffer, forthcoming). Metaphysical interdependence is the only theory of grounding (perhaps other than monist foundationalism) suited to characterize this sort of metaphysical dependence. A second unsettling feature of brute facts is that they represent apparent counterexamples to the principle of sufficient reason (PSR); the principle stating that every fact has an explanation. Bliss (2013: 415) argues that in requiring that every fact be ultimately explained by some unexplained explainer (the brute facts) metaphysical foundationalists reveal an implicit commitment to the PSR. Bliss contends that this invites difficult questions about the modal status of the fundamental facts and their ability to act as the requisite sort of explainers. At a minimum, unexplained explainers should presumably be non-contingent, but foundationalists do not usually claim that all foundational facts are thereby necessary facts. Foundationalists seem both to be committed to the PSR and routinely to violate it.

6.2 Interdependence An alternative approach to explanation in general involves thinking of explanation as a holistic phenomenon. Explaining some fact, belief, or event is a matter of connecting it with other facts, beliefs, or events in such a way that there can be a mutual reinforcement between an explanation and what it explains (see Quine and Ullian, 1978: 120). Holism in diverse areas of thought is enjoying something of a resurgence (e.g. sociology, politics, ecology, psychology, physics, and medicine). Holistic approaches to explanation are more often encountered in daily interactions then in philosophical writing,9 and so I’ll illustrate what I have in mind with a couple of examples. These I take to be examples of holistic metaphysical explanations, but it is not just grounding explanations that force us to think of explanations as 9 Exceptions include discussions of holism about meaning, of quantum mechanics, and of living organisms.

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 interdependence, coherentism, and holistic explanation having a holistic structure.10 More generally, there are reasons to think that holistic explanations can be good explanations (see e.g. the example in §4 above) and so there is nothing ad hoc about taking explanation to have this structure in the grounding case. This matters if, as I suggested above, we are to appeal to our understanding of explanation in general to elucidate grounding. A first example of the relevant sort of explanatory structure is present in structuralist approaches to mathematics. According to mathematical structuralists, mathematical objects are ontologically dependent on one another and on the mathematical structure of which they are a part (see e.g. Shapiro, 1997). The following provides a good characterization of the view: The number 2 is no more and no less than the second position in the natural number structure; and 6 is the sixth position. Neither of them has any independence from the structure in which they are positions, and as positions in this structure, neither number is independent of the other. (Shapiro, 2000: 258)

According to the mathematical structuralist, mathematical objects depend, for their existence and their identity, on the other objects that are part of the structure. The identities of those objects are determined ‘by their relationships to other positions in the structure to which they belong’ (Resnik, 1982: 95). An obvious candidate for understanding the relevant sort of dependence is in terms of grounding; facts about the identity and nature of any given mathematical object are explained by, and grounded in, facts about the structure of which that object is a part, and in facts about the structure as a whole. If grounding is an explanatory relation, the nature of the number 2 is to be explained in terms of the natural number structure, and so it both helps explain the nature of other numbers in the structure, and is itself explained in terms of the nature of those other numbers which make up the structure. That structure itself is to be explained in terms of the numbers that are a part of it. Mathematical structuralism can only be adequately described by appeal to holistic explanation and to metaphysical interdependence. Consider another example. Structural realism is a now-popular form of scientific realism which holds that rather than asserting that the nature of things is correctly described by our best scientific theories, the realist emphasis should be on the structural content of those scientific theories. The motivation for the position is that it is structural content that is retained across theory change (Ladyman and Ross, 2007: 93). Structural realists of a metaphysical variety take structure and relations not to be merely derivative of the entities or structural nodes they relate, but to be more ontologically fundamental than has traditionally been assumed by scientific realists (Ladyman, 2014). Esfeld and Lam (2010) develop a version of metaphysical structural

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I use the terms ‘metaphysical explanation’ and ‘grounding explanation’ synonymously throughout.

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naomi thompson  realism that they term ‘moderate structural realism’ and which holds that relations require relata, but that it is not the case that the relata necessarily have intrinsic properties over and above the relations they bear to one another (Esfeld and Lam, 2010: 13). In other words, there are objects, but those objects are wholly characterized by the relations in which they stand. It follows from this characterization of moderate structural realism that there is a mutual dependence between relations and relata—the objects are characterized by the relations that relate them, and the relations themselves are characterized by the objects that stand in the relations. There is, therefore, . . . a mutual ontological as well as conceptual dependence between objects and structure (relations): objects can neither exist nor be conceived without relations in which they stand, and relations can neither exist in the physical world nor be conceived as the structure of the physical world without objects that stand in the relations. (Esfeld and Lam, 2010: 13–14)

Explaining facts about the nature of a given object is a matter of citing facts about the relations that object bears to other objects, facts about which are themselves to be explained in terms of the relations they bear to further objects (and to the object which was our starting point). Since facts about the structure through which the objects are related themselves depend on facts about the objects themselves, a moderate structural realist picture has it that giving an explanation will be a matter of pointing towards a mutual dependence between explanans and explanandum. The relevant sort of explanation here is a grounding explanation; facts about objects are grounded in facts about relations, and vice versa. Moderate structural realism thus gives us a case of symmetric metaphysical explanation, and therefore of metaphysical interdependence. These two examples strengthen the case for thinking that explanation, and in particular metaphysical explanation, is at least sometimes a holistic affair. A defence of the strong version of metaphysical explanation under discussion here requires the stronger claim that all metaphysical explanations are holistic explanations. I make the case for this in §7, after first dispelling an objection to the idea that any explanations are holistic.

7 Holistic Explanation There is an obvious and immediate objection to the idea that explanation could be a holistic phenomenon; explanations are asymmetric, and holistic systems licence symmetric explanation. But there are good reasons to think that not all explanations are, in fact, asymmetric. The examples given above each provide some reason to resist the assumption that explanation is asymmetric. Numerous other examples are available. To mention just two: recent developments in quantum mechanics have led many to believe that some quantum states can only be explained holistically (see e.g. Teller, 1986; Healey, 2016); and Achinstein (1983) gives a number of examples of identity explanations (i.e. explanations that identify two things, such as water and

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 interdependence, coherentism, and holistic explanation H2 O) which seem to require us to accept that explanation is non-symmetric. Note too that it is a well-documented feature of Hempel’s influential (e.g. 1965) DeductiveNomological (DN) account of explanation (albeit usually invoked as a criticism) that it licences instances of symmetric explanation. These are reasons to think that our familiar understanding of explanation includes at least some instances of symmetric explanation. It is in fact a difficult task to identify a basis for the intuition that explanations must be asymmetric. Attempts to locate that asymmetry in the asymmetry of causation have been called into question (see e.g. Persson, 2001), and in any case there are many rivals to causal theories of explanation. In particular, metaphysical explanation is generally assumed to be non-causal.11 An alternative way to account for the intuition that explanation is asymmetric is to claim that explanation is an epistemic phenomenon, and symmetric explanations are unlikely to advance our understanding. On this epistemic basis, we generally object to symmetric explanations. This indeed is the position of van Fraassen (e.g. 1980), recent champion of the pragmatic theory of explanation. Van Fraassen argues that ‘asymmetries of explanation result from a contextually determined relation of relevance . . . [we] account for specific asymmetries in terms of the interests of questioner and audience that determine this relevance’ (1980: 130). According to van Fraassen, explanations are only explanatory in a context, where that context is determined by the interests and the background commitments of whoever is seeking the explanation. In most cases, context dictates that asymmetric explanations are satisfying, but sometimes the context will be such that holistic explanations are required. We have seen some compelling examples already, but another case might help bring out the point. In order to argue for his claim that explanatoriness is dependent on context, van Fraassen (1980, §3.2) amends an example used to criticize Hempel’s DN account of explanation. The example involves deriving the length of the shadow s cast by a flagpole from the height h of the flagpole, the angle θ of the sun above the horizon and laws l about the rectilinear propagation of light. According to Hempel’s theory, we can deduce, and thus explain s by appeal to h, θ, and l. However (so the criticism goes), we can also deduce, and thus explain, h from s, θ, and l. But our explanatory intuitions are such that the direction of explanation only runs one way—s should be explainable in terms of h, but s shouldn’t come out as an explanation of h—lengths of shadows don’t explain heights of flagpoles. Van Fraassen adapts the example and constructs a story according to which the context is such that we do take the length of the shadow to explain the height of the

11

Note that there is no tension here with the claim that grounding is an explanatory relation. Not all explanations are grounding explanations, and so there may be some features of other varieties of explanation not shared with grounding explanations (though it is important that grounding explanations are familiar enough from our ordinary understanding of explanation to be illuminating).

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naomi thompson  flagpole. The flagpole was designed to have height h in order that the shadow s would be cast on a particular spot at a particular time.12 Van Fraassen’s point is that as a response to a particular explanatory request in a particular context, it is both appropriate and satisfying to give an explanation in terms of the length of the shadow. But as a response to a slightly different explanatory request, it would be equally appropriate and satisfying to give an explanation of the length of the shadow in terms of the height of the flagpole. Local explanatory asymmetries are the consequence of the context-sensitivity of explanation, but are not built in to what it is to be an explanation. We can now make two points about explanation and asymmetry. The first is that if we understand the asymmetry of explanation in terms of its connection to understanding and its relevance to the explanation seeker, there is no principled restriction on explanation such that explanations must always go in one direction. Holistic systems of explanation are certainly not ruled out, and are only to be considered unacceptable if they fail to advance the epistemic position of the explanation seeker; if they fail to make something intelligible, or to advance an agent’s understanding. We have seen a number of examples above which demonstrate that holistic explanations at least sometimes advance an agent’s epistemic position. Second, the context sensitivity of explanation allows us to recognize that though an entire explanatory system might have a holistic structure, it is very rarely appropriate to cite the whole system in response to a specific explanation request. Accepting that explanations can be holistic doesn’t require us to give up on the idea that local explanations very often only work in one direction. In this way we can in fact maintain that all explanatory systems have a holistic structure, as is required by the strong version of metaphysical interdependence. In some cases (such as in the examples above) the context dictates that providing a satisfactory explanation requires citing enough of the explanatory system that its holistic structure is evident. In others, requests for explanation are limited enough that a satisfying explanation cites only a seemingly asymmetric portion of the structure. The claim that it is generally appropriate to cite only a portion of an explanatory system is far from unique to holistic explanations. In providing an adequate causal explanation of some event, we are only required to cite information about some portion of the causal history of that event (see e.g. Salmon, 1984; Lewis, 1986). The causal history of each event can (presumably) be traced all the way back to the Big Bang, but in very few contexts is an explanation which mentions the Big Bang appropriate. The cause that really explains depends on our interests (Lipton, 1990: 249). So, even if giving a maximally complete explanation would involve describing a holistic system, and so we ought to think of explanations as having a holistic structure, local cases of providing an explanation are generally far more restricted. Consider

12

Actually van Fraassen’s example involves a tower, but that need not concern us here.

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 interdependence, coherentism, and holistic explanation again the case of coherentism in epistemology. When we ask a coherentist why she holds a given belief, she will offer support for that belief in terms of other beliefs to which the questioned belief is closely connected in her belief system. Though it is an aspect of her view that justification for the disputed belief depends on the entire belief system, she could hardly be expected to communicate the entire system in response to a request for justification (any more than a foundationalist is to be expected to follow his or her chain of beliefs right down to the foundation when giving reasons for a particular questioned belief). The same is true when providing a grounding explanation. At this stage, one might object again that this is all very well for ordinary cases of explanation, but our concern here is supposed to be with metaphysical explanation. One might worry that there is no place for a discussion of context when our concern is with this supposedly more objective notion of explanation, and argue as follows: Metaphysical explanation is not supposed to be about getting somebody to understand something—it’s about characterizing reality’s structure. Perhaps it’s acceptable to take ordinary or scientific explanations to have a holistic structure and to explain the illusion of asymmetry in terms of our explanatory interests, but metaphysical explanations are different; they’re divorced from our explanatory interests, and so if they appear asymmetric it must be that the relevant structure is asymmetric! I have already discussed some cases where it seems clear that metaphysical explanation is not asymmetric (e.g. in structuralist approaches to mathematics and science), but I’ll make a couple more points in favour of holistic metaphysical explanation. First, note again that in distancing metaphysical explanation from ordinary explanation, the friend of grounding is playing a dangerous game. The connection between grounding and explanation is key to elucidating the somewhat opaque notion of grounding, as well as to evaluating particular grounding claims. In order for that connection to play the required role, grounding must be related to a notion of explanation familiar enough that our explanatory intuitions are deemed relevant, and that we can understand grounding in terms of it. That familiar notion of explanation is connected to understanding, and is constrained by context. But for the friend of grounding who wishes to resist that cautionary note and insist that metaphysical explanation is not connected to understanding and that context has no role to play, we can remind them that it is hard to locate any preference for asymmetric explanation outside of the epistemic constraints on explanation in general. If metaphysical explanation really is non-epistemic, those reasons to worry about symmetric explanation don’t apply. In order to resist the possibility that metaphysical explanations might be holistic, one must both resist the above putative examples of symmetric grounding and holistic metaphysical explanation, and come up with a nonepistemic account of the alleged asymmetry of (metaphysical) explanation. I have argued that the supposed asymmetry of explanation is tied to the epistemic character of explanation, and that that epistemic character is consistent with a view whereby explanation can have a holistic structure. Not only can holistic explanations

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naomi thompson  be informative (and so it is a mistake to think that only asymmetric explanations can increase understanding), but it is consistent with holding that explanatory structures are holistic that context dictates that many local requests for explanation will elicit a response which cites only a fraction of the holistic structure, and which runs only in one direction.

8 Concluding Remarks Foundationalism has been the dominant view of metaphysical structure since the inception of the contemporary debate, but there are good reasons to challenge the foundationalist orthodoxy. I have described some of those reasons here. In particular, that in accepting that holistic explanations are good explanations, we break down a significant barrier to serious consideration of theories such as metaphysical interdependence, which are alternatives to metaphysical foundationalism.13

References Achinstein, P. (1983). The Nature of Explanation. Oxford: Oxford University Press. Audi, P. (2012a). A Clarification and Defense of the Notion of Ground. In F. Correia & B. Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality (pp. 101–21). Cambridge: Cambridge University Press. Audi, P. (2012b). Grounding: Toward a Theory of the In-Virtue-Of Relation. Journal of Philosophy, 109, 685–711. Barnes, E. (2013). Explanation and Fundamentality. In M. Hoeltje, B. Schnieder, & A. Steinberg, Varieties of Dependence (Basic Philosophical Concepts Series) (pp. 211–42). Munich: Philosophia Verlag. Bliss, R. (2013). Viciousness and the Structure of Reality. Philosophical Studies, 166, 399–418. Cameron, R. (2008). Turtles All the Way Down: Regress, Priority and Fundamentality. The Philosophical Quarterly, 58(230), 1–14. Daly, C. (2012). Scepticism about Grounding. In F. Correia & B. Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality (pp. 81–100). Cambridge: Cambridge University Press. Dasgupta, S. (2014). On the Plurality of Grounds. Philosophers’ Imprint, 14, 1–28. Esfeld, M. & Lam, V. (2010). Holism and Structural Realism. In R. Vanderbeeken & B. D’Hooghe (eds), Worldviews, Science and Us: Studies of Analytical Metaphysics. A Selection of Topics from a Methodological Perspective (pp. 10–31). Singapore: World Scientific. Fine, K. (2001). The Question of Realism. Philosopher’s Imprint 1, 1–30. Fine, K. (2012). A Guide to Ground. In F. Correia & B. Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality (pp. 37–80). Cambridge: Cambridge University Press.

13 Thanks to Darragh Byrne for helpful comments and discussion, and to two anonymous referees for detailed and thought-provoking comments.

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 interdependence, coherentism, and holistic explanation Healey, R. (2016). Holism and Nonseparability in Physics (ed. E. Zalta). Retrieved March 2016 from The Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/archives/spr2016/ entries/physics-holism. Hempel, C. (1965). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press. Ismael, J. & Schaffer, J. (forthcoming). Quantum Holism: Nonseparability as Common Ground. Synthese. Jenkins, C. (2011). Is Metaphysical Dependence Irreflexive? The Monist, 94, 267–76. Kim, J. (1994). Explanatory Knowledge and Metaphysical Dependence. Philosophical Issues, 5, 51–69. Ladyman, J. (2014). Structural Realism (ed. E. Zalta). Retrieved August 2015 from The Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/archives/spr2014/entries/structuralrealism. Ladyman, J. & Ross, D. (2007). Every Thing Must Go: Metaphysics Naturalized. Oxford: Oxford University Press. Lewis, C. I. (1946). An Analysis of Knowledge and Valuation. LaSalle: Open Court. Lewis, D. (1986). Causal Explanation. In Philosophical Papers, Volume II. Oxford: Oxford University Press. Lipton, P. (1990). Contrastive Explanation. Royal Institute of Philosophy Suppliment, 27, 247–66. Litland, J. (2013). On Some Counterexamples to the Transitivity of Grounding. Essays in Philosophy, 14(1), 19–32. Morganti, M. (2009). Ontological Priority, Fundamentality and Monism. Dialectica, 63(3), 271–88. Olsson, E. (2017). Coherentist Theories of Epistemic Justification (ed. E. Zalta). Retrieved November 2017 from The Stanford Encyclopedia of Philosophy (spring 2017 edn): https:// plato.stanford.edu/archives/spr2017/entries/justep-coherence/. Persson, J. (2001). Why is there Explanatory Asymmetry? Explanatory Connections (ed. M. Kiikeri & P. Ylikoski). Retrieved from: http://www.helsinki.fi/tint/matti/. Quine, W. & Ullian, J. (1978). The Web of Belief (2nd edn). New York: McGraw-Hill. Raven, M. (2012). In Defence of Ground. Australasian Journal of Philosophy, 90, 687–701. Raven, M. (2015). Ground. Philosophy Compass, 10(5), 322–33. Resnik, M. (1982). Mathematics as a Science of Patterns: Epistemology. Noûs, 16, 95–105. Rodriguez-Pereyra, G. (2015). Grounding is Not a Strict Order. Journal of the American Philosophical Association, 1(3), 517–34. Rosen, G. (2010). Metaphysical Dependence: Grounding and Reduction. In R. Hale and A. Hoffman (eds), Modality: Metaphysics, Logic, and Epistemology (pp. 109–36). Oxford: Oxford University Press. Salmon, W. (1984). Scientific Explanation and the Causal Structure of the World. Princeton, NJ: Princeton University Press. Schaffer, J. (2010). Monism: The Priority of the Whole. Philosophical Review, 119, 31–76. Schaffer, J. (2012). Grounding, Transitivity, and Contrastivity. In F. Correia & B. Schnieder (eds), Metaphysical Grounding: Understanding the Structure of Reality (pp. 122–38). Cambridge: Cambridge University Press. Shapiro, S. (1997). Philosophy of Mathematics: Structure and Ontology. Oxford: Oxford University Press.

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naomi thompson  Shapiro, S. (2000). Thinking about Mathematics. Oxford: Oxford University Press. Teller, P. (1986). Relational Holism and Quantum Mechanics. British Journal for the Philosophy of Science, 37(1), 71–81. Thompson, N. (2016). Metaphysical Interdependence. In M. Jago (ed.), Reality Making. Oxford: Oxford University Press. Thompson, N. (forthcoming). Grounding, Metaphysical Explanation, and the Structure of Reality. Proceedings of the Aristotelian Society. Trogdon, K. (2013). An Introduction to Grounding. In M. Hoeltje, B. Schnieder, & A. Steinberg (eds), Varieties of Dependence (pp. 97–122). Munich: Philosophia Verlag. van Fraassen, B. (1980). The Scientific Image. Oxford: Oxford University Press. Wilson, J. (2014). No Work for a Theory of Grounding. Inquiry, 57(5–6), 1–45. Woodward, J. (2003). Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.

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6 Buddhist Dependence Graham Priest

1 Introduction: Orientation Many issues in Western philosophy were discussed with great sophistication in the Eastern philosophical traditions. A prime example of this is metaphysical dependence.1 This is absolutely central to Buddhist metaphysics.2 Indeed, there is a wide variety of views about, in particular, the structure of metaphysical dependence. In this essay, I will explain some of these views, and some of their ramifications. The aim is neither to give a scholarly account of any of these views, nor to argue for or against any one of them. Rather, the point of the essay is to open the eyes of philosophers who know little of the Eastern philosophical traditions to important possibilities of which they are likely to be unaware. In Section 3 of this essay, I will explain three Buddhist positions concerning metaphysical dependence: those of Abhidharma, Madhyamaka, and Huayan.3 In Section 4, I will turn to some ways in which these positions engage with some Western debates. But first, for those readers whose knowledge of the history and development of Buddhist philosophy may be incomplete, I will explain enough of this in Section 2 to situate what is to follow.

1 In contemporary Western philosophy, the topic is discussed under a variety of names, such as ontological dependence and grounding. Moreover, there seems to be little unanimity as to whether there is just one relationship here, or, if not, how the different varieties of the species are related. For general discussions, see Tahko and Lowe (2015), and Bliss and Trogdon (2014). I use the term metaphysical dependence as a catch-all term, to cover any sort of relationship concerning how some things depend for whatever form of being they have on other things. More fine-grained distinctions are unnecessary for our purposes. 2 I certainly do not want to suggest that the topic is unimportant in other Asian traditions, such as the Vedic and Daoist ones. However, it is better for people who know more about these traditions than I do to write about these matters. 3 Again, I do not want to suggest that there are not relevant and interesting matters in other parts of the tradition, such as Yog¯ac¯ara and Tiantai; but one can do only so much in one essay.

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graham priest 

2 A Little History and Geography Buddhist thought started with the historical Buddha, Siddh¯artha Gautama. His dates are uncertain, but he flourished around 450 bce; and his ideas were developed in a canonical way for the next 500 years or so. The philosophical part of this development was called Abhidharma (higher teachings). There were many Abhidharma schools. The only one to survive to this day is Therav¯ada (Way of the Elders). Around the turn of the Common Era, novel ideas emerged, which were critical of the older tradition. This generated a new kind of Buddhism: Mah¯ay¯ana. The foundational philosopher of this kind of Buddhism was N¯ag¯arjuna. Dates are, again, uncertain; but he flourished around 200 ce. He founded the version of Mah¯ay¯ana Buddhism called Madhyamaka (Middle Way). Buddhist thought died out in India around the twelfth century, but by that time it had spread to the rest of Asia; Theravada going South East, and Mah¯ay¯ana going North West into central Asia, and thence, across the Silk Route, into East Asia. It entered China around the turn of the Common Era, where it met the indigenous philosophical traditions: Confucianism and Daoism. Daoism, in particular, exerted a crucial influence on Chinese Buddhist thought.4 This resulted in the emergence of distinctively Chinese forms of Mah¯ay¯ana Buddhism, around the sixth century. Some of these, such as Chan (Jap: Zen) are still extant. But perhaps the most philosophically sophisticated of these flourished in China for only a few hundred years (though it still has a presence in Korea and Japan), many of its ideas being incorporated into other forms of Buddhism (and indeed, into Neo-Confucianism). (Skt: Avatam This was Huayan . saka; Kor: Hwaeom; Jap: Kegon; Eng: Flower Garland) Buddhism, named after the s¯utra it took to be most important. The most influential philosopher in this tradition was Fazang, traditionally dated as 643–712.5

3 Metaphysical Dependence in the Buddhist Traditions With this background, let us turn to our three views concerning metaphysical dependence.

3.1 Well-founded Buddhism It is common to all Buddhisms that the world of our common experience is a world of dependent origination, prat¯ıtyasamutp¯ada. Nothing is permanent: things come into existence when causes and conditions are ripe, and go out of existence in the same way. Now, how should one think of a person in this context?6 4 Buddhism (Mah¯ ay¯ana) entered Tibet relatively late in the piece, in the eighth century. The indigenous Tibetan views did not have an impact of such magnitude. 5 For good introductions to the history of Buddhist thought, see Mitchell (2002), Siderits (2007), and Williams (2009). 6 For what follows, see Siderits (2007), chs 3 and 6.

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 buddhist dependence The understanding of a person that developed in the Abhidharma literature was as follows. Consider a car. This comes into existence when its parts are put together. The parts interact with each other and the environment; they wear out and are replaced; and they finally fall apart entirely. Persons are just like that. True, their parts (skandas), unlike the car’s, are both material (r¯upa) and mental. But otherwise the story is the same. Of course we can think of this dynamically evolving bunch of parts as a single thing, a person; we can even give it a name, say ‘Bertrand Russell’; but this is just a matter of convenience. The Abhidharma philosophers could see nothing special about people in this way. Anything with parts, like our friend the car, is exactly the same. Indeed, what anything in our common world of experience is, depends on what its parts are and how we think about them. So take the car, again, as an example. This depends on its wheels, engine, chassis, and so on. The engine depends on its combustion chambers, fuel-injection system, and so on. If we keep decomposing in this way, do we come to things where no further decomposition is possible? The Abhidharma philosophers thought that the answer was obviously: yes. If something is a conceptual construction, there must be something, dharmas, out of which it is constructed. You can’t make something out of nothing. This would seem to be the point when Asa˙nga (fl. 4th century ce), in a late Abhidharma text, says: Denying the mere thing with respect to dharmas such as r¯upa and the like, neither reality nor conceptual fiction is possible. For instance, where there are the skandhas of r¯upa etc., there is the conceptual fiction of the person. And where they are not, the conceptual fiction of the person is unreal. Likewise if there is a mere thing with respect to dharmas like r¯upa etc., then the use of convenient designators concerning dharmas such as r¯upa and the like is appropriate. If not then the use of convenient designators is unreal.7

There was some dispute about the nature of the dharmas. (A common view was that they are tropes of some kind.) But, as all agreed, they are just as impermanent as anything else; what distinguishes them is the fact that they are what they are independently of anything else (parts, concepts, each other). They have svabh¯ava (self-being). The Abhidharma philosophers described the picture as one of two realities.8 There is the fundamental reality composed of dharmas—ultimate reality (param¯arthasatya); then there is the conceptual reality constructed out of this—conventional reality (sam . vr.ti-satya). Clearly, the whole picture paints a story concerning ontological dependence. Where does it lie in the taxonomy of the Introduction to this volume? It is obviously some 7

Bodhisattvabhumi, 30–2. Translation by Mark Siderits. The Sanskirt word is satya. This can mean either truth or reality. It is standard to translate the word as truth. Of course if there are two realities, there are also two (sets of) truths: one about each of the realities. But in the present context, and others that we will come to soon, the best translation is ‘reality’. 8

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graham priest  kind of foundationalism, the foundational elements being the dharmas. Does it endorse anti-reflexivity, anti-symmetry, and transitivity? There is, as far as I know, no explicit discussion of these matters in the texts, but let us extrapolate. The Abhidharma philosophers would probably have endorsed transitivity. If the car depends on it its engine, and the engine depends on its fuel injector, the car depends on its fuel injector. Moreover, a whole would appear to depend on its parts, in a way that the parts do not depend on the whole.9 So the dependence relation would seem to be anti-symmetric. Since anti-symmetry entails anti-reflexivity, we have that as well. So this puts us in case 2 of the taxonomy laid out in Section 2 of Chapter 0 in this volume.

3.2 Non-well-founded Buddhism We now turn to Madhyamaka. Madhyamaka entirely rejected the notion of the dharmas. Nothing has svabh¯ava. Everything is what it is by relating to other things. The Madhyama philosophers accepted the Abhidharma view that the relations in question could be mereological and conceptual, but also added a third important dimension: causal. (Thus, persons are what they are, for example, because of their relations to their parents, their genetic structure, etc.) Everything depends on other things in some or all of these ways. That is, all things are empty (´su¯ nya) of self-being.10 In much of his enormously influential text, the M¯ulamadhyakamak¯arik¯a (MMK, Fundamental Verses of the Middle Way) N¯ag¯arjuna mounts the case that nothing has svabh¯ava.11 He does this by running through all the things one might suppose to have it (causation, consciousness, space, and so on), and rejecting each one. Many of the arguments are reductio arguments. We assume that something has svabh¯ava and show that this cannot be.12 We will not consider the arguments in any detail here. More to the point in this context, one might expect N¯ag¯arjuna to have rejected the distinction between the two realities. But he does not (MMK XXIV: 8–10): The Buddha’s teaching of the Dharma Is based on two truths: A truth of worldly convention And an ultimate truth. Those who do not understand The distinction between these two truths Do not understand The Buddha’s profound truth.13

9

By ‘part’ here, I mean proper part, i.e. a part distinct from the whole. For a discussion of this and what follows, see Siderits (2007), ch. 9, and Williams (2009), ch. 3. 11 It must be said that this is a highly cryptic text, and there can be significant differences as to how to understand its claims. I try not to go beyond a general consensus in what follows. 12 The arguments themselves are often by cases, though the cases are not the ones familiar to Western philosophy—true and false—but the four delivered by the catus.kot.i (Eng: four corners)—true, false, both, and neither. 13 Translations from the MMK are from Garfield (1995). In this context, ‘Dharma’ means correct doctrine. 10

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 buddhist dependence Conventional reality is the world of our familiar experience. But if there are no things with svabh¯ava, what is ultimate reality? Though hardly explicit in the MMK, the view that emerged in Madhyamaka was that ultimate reality is what is left if one takes the things of conventional reality, and strips off all conceptual overlays: emptiness (Skt: ´su¯ nyat¯a; Chin: kong ) itself. One might well think that this ultimate reality provides some foundational bedrock.14 It does not. According to Madhyamaka, everything is empty, including emptiness itself. In perhaps the most famous verse of the MMK (XXIV:18), N¯ag¯arjuna says: Whatever is dependently co-arisen That is explained to be emptiness. That, being a dependent designation, Is itself the middle way.

Emptiness, as the verse says, is a dependent designation. That is, emptiness depends on something. Conventional reality clearly depends on ultimate reality. But what does ultimate reality depend on? It is hard to extract a clear answer to this question from the MMK; let us set it aside for the moment. We are now in a position to see how the Madhyamaka view fits into the taxonomy described in Section 2 of Chapter 0 in this volume. In general it takes over the Abhidharma view, but simply rejects its foundationalism. That is, it endorses Exendability. We are therefore in case 1.

3.3 Buddhist coherentism Let us now turn to Huayan.15 This, like all Chinese Buddhisms is Mah¯ay¯ana, and so inherited Madhyamaka thought. But whilst Madhyamaka held that all things depend on some other things, the Huayan universalized: all things depend on all other things. How did they get there? Come back to the question of what ultimate reality depends on.16 As we have noted, Chinese Buddhism was indebted to Daoism. According to a standard interpretation of this, behind the flux of phenomenal events, there is a fundamental ineffable principle, dao , which manifests itself in the flux. To Chinese Buddhist eyes, it was all too natural to identify the flux with conventional reality, and the dao with ultimate reality. That is exactly what happened. Moreover, just as one cannot have manifestations without whatever it is of which they are a manifestation, one cannot have something whose nature it is to manifest, without the manifestations. So conventional reality depends on ultimate reality, and ultimate reality depends on conventional reality: they are two sides of the same coin. In his Treatise on the Golden

14 In which case, we still are in case 2 of the taxonomy described in Section 2 of Chapter 0 in this volume, but G is true. Ultimate reality is the unique foundation. 15 For the following, see Williams (2009), ch. 6. 16 It must be said that these thoughts were available, in principle, to Madhyamaka, but no one ever articulated them.

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graham priest  Lion, Fazang explains the point in this way.17 Imagine a statue of a golden lion. The gold is like ultimate reality. The shape is like conventional reality. One cannot have the one without the other. By this time in the development of Buddhist thought, the objects of phenomenal reality are called shi , and ultimate reality is referred to as li , principle. Hence we have the Huayan principle of the mutual dependence of li and shi: lishi wuai . The matter is put this way by the Huayan thinker Dushun (557–640) as follows: Shi, the matter that embraces, has boundaries and limitations, and li, the truth that is embraced [by things], has no boundaries or limitations. Yet this limited shi is completely identical, not partially identical, with li. Why? Because shi has no substance [GP: svabh¯ava]—it is the selfsame li. Therefore, without causing the slightest damage to itself, an atom can embrace the whole universe. If one atom is so, all other dharmas should also be so. Contemplate on this.18

But if every shi depends on li, then by the transitivity of dependence, every shi depends on every other shi. Hence we have the Huayan thesis of the dependence (interpenetration) of every shi on every other shi: shishi wuai . Chengguan (738–839?), another Huayan thinker, puts the matter thus: Because they have no Selfhood [GP: svabh¯ava], the large and the small can mutually contain each other . . . Since the very small is very large Mount Sumeru is contained in a mustard seed; and since the very large is the very small, the ocean is included in a hair.19

We therefore arrive at this: all things, whether li or shi, depend on each other. The situation is depicted in what is arguably the most famous image in Huayan: the Net of Indra. A god has spread out a net through space. At each node of the net there is a brightly polished jewel. Each jewel reflects every other jewel, reflecting every other jewel, reflecting . . . to infinity. Fazang puts the metaphor thus: It is like the net of Indra which is entirely made up of jewels. Due to their brightness and transparency, they reflect each other. In each of the jewels, the images of all the other jewels are [completely] reflected . . . Thus, the images multiply infinitely, and all these multiple infinite images are bright and clear inside this single jewel.20

Each jewel represents an object. And it is the nature of each jewel to encode every other jewel, including that jewel encoding every other jewel, and so on. So where is the Huayan picture in the taxonomy described in Section 2 of Chapter 0 in this volume? Clearly, this is coherentism, C, and we are in category 13 (since there is more than one object).

17

The Treatise is translated into English as pp. 409–14 of Chan (1969). Quoted in Chang (1972), pp. 144–5. The character translated as ‘identical’ is better translated in this context as ‘interpenetrating’. See Priest (2015). 19 20 Quoted in Chang (1972), p. 165. Quoted in Liu (1982), p. 65. 18

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 buddhist dependence

4 Western Connections So much for the three Buddhist positions. As is clear, they are significantly different. This is a striking feature of the tradition compared with Western philosophy, which, for all its variety views, has been almost entirely foundationalist.21 For all that, there are many interesting connections between the Buddhist views, and debates and problems to be found in Western philosophy. In this section of the essay, I want to turn to some of these. There is certainly no attempt to be comprehensive here: I have just chosen some of the most obvious connections. I will structure this section by three subsections mirroring those in Section 3.

4.1 Mereology So let us return to the Abhidharma picture. Clearly, this is some kind of mereological atomism, with the atoms being the dharmas—whatever they are. Why should one be an atomist? The Abhidharmikas, as I noted, produced no real arguments for this: they just seemed to think it obvious. But it isn’t. Just consider the real line, and let its parts be all the nonempty sub-intervals. One is a part of another if it is a proper subset. Then any part has parts, since any interval can be divided into a left and a right part. The picture is perfectly coherent. So how might one argue that reality is not like that? One famous answer was given by Kant, in the Second Antinomy of his Critique of Pure Reason, and goes like this: Let us assume that composite substances are not made up of simple parts. If all composition then be removed in thought, no composite part, and (since we admit no simple parts), also no simple parts, that is to say, nothing at all will remain, and accordingly, no substance will be given. Either, therefore, it is impossible to remove in thought all composition, or after its removal there must remain something which exists without composition, that is, the simple. In the former case the composite would not be made up of substances; composition, as applied to substances, is only an accidental relation in independence of which they must still persist as self-subsistent beings. Since this contradicts our supposition, there remains only the original supposition, that a composite substance is made up of simple parts.22

Kant’s argument is both dark and tangled—and, it should be remembered, he is going to argue that it does not work (since the simple is a noumenon, and so the categories cannot be applied to it). However, in nuce, it would appear to be this.23 Given any substance, it is always possible to decompose any compound part, at least in thought. This is because the fact that something is arranged (composed) in a certain way is always a contingent one. Now, take any substance, and suppose that it is not composed of simples. Decompose it through and through. Nothing will be left, which is impossible since, in that case, the substance would have had no substance.

21 22

See Bliss and Priest (2017), from which much of the above material comes. 23 A434 = B462ff. Translation from Kemp Smith (1933). See Priest (2002), p. 90.

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graham priest  But the argument would not seem to work—even setting Kantian scruples about the noumenal. Take a substance, say the table on which I write. It is composed of cells of wood. These are composed of molecules, which are composed of atoms, which are composed of protons and electrons, which are composed of quarks, which . . . Whether this regress does eventually terminate, we may never, in fact, know. But there is nothing logically absurd about supposing that physics will find indefinitely smaller and smaller particles (or maybe better, more and more fundamental kinds of thing). The table is a substantial entity for all that. Of course, none of this shows that atomism is false: merely that, at least as far as this argument goes, there is no particular reason to suppose it true. But let us grant its truth, at least for the sake of argument. Another Abhidharma claim is that it is only the atoms which are ultimately real. The table, for example, has no being over and above its atoms. It is simply a bunch of atoms ‘arranged table-wise’. Again, I know of no very focused Abhidharma arguments for this view,24 but it does comport with a certain intuition. Suppose I have a hydrogen atom composed of a proton and electron, how many objects do I have: two or three? Say ‘three’ if you like, but the hydrogen atom itself would seem to be, in the words of David Armstrong, an “ontological free lunch”: no addition to being.25 Still, the atom would seem to have some kind of reality, unlike ghosts and phlogiston. How are we to understand this? It is here that the Abhidharma distinction between the two satyas kicks in. The table has a conventional reality, but not an ultimate one. But how are we to understand this? Recall that for the Abhidharmikas, the conventionally real objects are conceptual constructions. That is, we have a concept, table, which we use to organise our thinking about the world. Recall, also, that in mereology there is a debate concerning the question of compositionality: when does a bunch of parts ‘fuse’ to form another object?26 There are two extreme answers. The first is never: mereological nihilism. This seems too extreme. In some sense, I am a perfectly good object, partite though I be. The other is always: unrestricted composition. Every bunch of objects fuses to form an object. This seems equally counter-intuitive. What sort of object is one whose parts are: the number π , the rings of Saturn, and the Buddha’s left earlobe? The most natural answer is a middle way, sometimes: special composition. But when? Abhidharma provides a simple and natural answer to this: when the objects fall under some concept. So tables and people are in; the bizarre object of the last paragraph is not. Of course, it is always possible to gerrymander a concept (e.g. simply by listing a bunch of objects). The concepts must be ones which we actually employ to find our way around the world (which does not entail that they have to be ‘common sense’ ones; 24 The nearest I know is to be found in the Malindapañha dialogue, part of which is translated in Radhakrishnan and Moore (1957), pp. 281–4. 25 26 Armstong (1997), p. 12. See Varzi (2015) for discussion and references.

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 buddhist dependence the concepts of science also satisfy this rubric). The objects of conventional reality are, then, those non-atoms delivered by the mereological principle of conceptually constrained special composition. This picture—whether or not it is correct—at least provides, at once, a natural answer to the question of what, exactly, a conceptual construction is, and an answer to the question of compositionality.

4.2 Causation Let us turn next to the Madhyamaka picture. Madhyamaka took over the Abhidharma picture, with a couple of very significant changes. First, and perhaps most importantly, it ditched the dharmas, the things with svabh¯ava. The picture is quite coherent. Come back to our model of the subsets of the real line; but now restrict the intervals in question to those which are definable, say in the first-order language of real number theory. (This gets rid of most of them, since there is only a countable number of first-order definitions.) It is still true that every interval has sub-intervals, but now every interval is also linguistically/conceptually isolable. Reality for a Madhyamaka is like that.27 Neither is this an argument for idealism.28 True, things get to be in the domain in virtue of there being certain concepts. But there is more to idealism than this. For idealism holds not only that objects are conceptually dependent, but also claims an ontological priority for the conceptual. This most certainly is not the case in Madhyamaka. For concepts are as empty of svabh¯ava as anything else. They are what they are in virtue of other things. What other things? Whilst, again, one does not find a clear answer in the MMK, it is easy enough to produce one with the help of the contemporary philosophy of language.29 What makes the concept dog the concept it is, rather than, say, the concept cat? The fact that it relates in a certain way to the canine creatures wandering the world. (If it related to feline creatures in the same way, it would mean cat instead.) What exactly that relationship is, we might argue about; but all that matters here is that the concept depends for its identity on being related to things in the world in this way.30 And so an argument for the emptiness of all things emerges. Things in the world depend on language and vice versa. But the picture is more complicated than that. As noted, Madhyamaka takes over mereological and conceptual dependence from Abhidharma, but adds a third kind of dependence: causal. And this brings us to the second Madhyamaka break with Abhidharma. It is absolute Buddhist orthodoxy that everything in the world is in a state of prat¯ıtyasamutp¯ada, coming into existence when caused to do so, and going out of existence when caused to do so. Just as much as Madhyamaka, then, Abhidharma

27

In particular, we have another argument for the emptiness of ultimate reality. For as N¯ag¯arjuna says, emptiness is a “dependent designation”—thing denoted. 28 Though there was another school of Indian Mah¯ ay¯ana that was idealist: Yog¯ac¯ara. 29 30 e.g. Putnam (1973): “meanings ain’t in the head”. See Priest (2013), and (2014), §13.5.

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graham priest  philosophers took it that the dharmas were caused to exist and to cease to exist. They just did not take these causal relations to be (partly) constitutive of the nature of a dharma. The Madhyamaka did. (The first chapter of the MMK is a long analysis of causation.) This might certainly look like a mistake. It is fairly standard to distinguish between causal dependence and metaphysical dependence.31 Causation determines when something comes into existence, but not what it is. But not so fast. What makes me the very person I am? Answer (in part): the way my parents treated me, the education I had, my professional experiences, and so on. These are causal factors. It might be thought that people are special in this way. Not so. What makes something an oak tree? The fact that it grows out of an acorn, delivers acorns, and so on. If it grew out of an onion, and delivered, not acorns, but goldfish, it would not be an oak tree. So maybe it’s just biological entities that are like this? Again, no. Take an electron. This is the kind of thing which repels particles of the same kind, which is annihilated by positrons, and so on. If it were attracted by other particles of the same kind, and annihilated by neutrons, it would not be an electron. Causation, it would seem, can determine the nature of things, quite generally. One might certainly contest the above considerations, but they have a certain persuasiveness. So let us turn to another matter: the vexed issue of what to make of the notion of ultimate reality and its relationship to conventional reality, once the notion of svabh¯ava has gone out of the window. A distinctive view of the matter was given by Candrak¯ırti (fl. first half of the seventh century), one of the most authoritative commentators on N¯ag¯arjuna, as follows: The Buddhas, who have an unmistakable knowledge of the nature of the two truths, proclaim that all things, outer and inner, as they are perceived by two kinds of subject (deluded consciousness on the one hand and perfectly pure wisdom on the other), possess a twin identity . . . They say that the object perceived by authentic primordial wisdom is the ultimate reality, whereas the object of a deluded perception is the relative truth.32

That is, there is only one reality, but it has a dual nature, a double aspect. When perceived correctly, its ultimate aspect is seen. When perceived incorrectly—that is, by ordinary benighted beings like you and me—only its conventional aspect is seen. But if these are both objective aspects of the one reality, what makes the one any better (more ultimate) than the other? Come back to Kant again. According to his transcendental idealism, our perceptions (‘intuitions’)—say of a table—are the product of two things: a raw sensory input and a mental imposition: the forms of space and time, and the concepts of the understanding. The empirical object, then, has these dual aspects, and one of these involves conceptual imposition. Candrak¯ırti’s account of reality may be thought of in the same way. (Though one should not push the analogy too far. There is no suggestion in Candrak¯ırti that 31 32

See e.g. the first few sentences of Tahko and Lowe (2015). Padmakara Translation Group (2004), p. 192.

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 buddhist dependence the concepts are universal and a priori. So much the better for Candrak¯ırti.) The difference between Candrak¯ırti and Kant concerns neither the dual nature, nor the conceptual overlay, but in our access to the conceptually naked. Seeing such a thing is an impossibility for Kant. Our perceptual apparatus just doesn’t work that way. But it is what you would see if, per impossible, you were able to do this. For Candrak¯ırti there is no such impossibility. Difficult it may be; impossible it is not. It is exactly what training in certain meditative practices gives you. Here is a serious and important difference between our two philosophers; I do no more than note it here. More importantly, and to return to our question of the previous paragraph, the one aspect of reality is more ultimate than the other, precisely because it dispenses with an extrinsic conceptual overlay.

4.3 The missing link So let us turn finally to the Huayan picture. This moves from the claim that all things depend on some other things to the claim that all things depend on all other things. The crucial move here is to find something on which all things depend, and which depends on all things. Transitivity then does the rest. In the Huayan story, it is li (an intellectual descendent of dao) that plays this role. Are there other things which might plausibly be thought to do so, so that the move in the argument does not need to be underpinned by specifically Buddhist ideas? As a first approach, come back to causation. Everything, physics tells us, is causally derived from the Big Bang. Everything depends for what it is, then, at least in part, on this. That gives us half the story we need. What of the other half? Could the Big Bang depend for its identity on the things it produces? That is not so obvious. And even if it is, in fact, the case, we have to worry about not just things in space and time, but abstract objects, such as numbers—assuming there to be such. For these, we do not have even one-way dependence on the Big Bang. As a more promising candidate for a link, take the object which is the mereological sum of everything: the whole of what is, W. The existence of this would seem to be delivered by our account of special composition. We certainly have a conception of such a totality: it does not seem to be at all gerrymandered. Now, a natural view is that a whole depends on its parts. (Maybe not necessarily the very parts it has now. Arguably the parts of a car can change while it remains that very car. But you could not have a car without parts.) So W depends on all its (proper) parts. What about dependence in the other direction: do the parts depend on the whole? One can certainly make a case for this in some cases. Thus, Aristotle argued that a hand, for example, would not be a hand unless it were integrated into the functioning whole of a body.33 Aristotle’s claim has been generalized by Schaffer, who argues

33

See Parts of Animals, esp. 640b 34–641a 10.

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graham priest  that any object depends on W.34 At root, one might think of the whole as a single functioning entity: we just normally fail to appreciate the deep inter-dependences. Schaffer, it is true, holds that such dependence is anti-symmetric. So he would not endorse the claim that the dependence also goes the other way. However, he gives no argument for this, but simply assumes anti-symmetry. The considerations suggesting dependence in the other direction still obtain. Given these, W depends in the objects that are its parts, and these depend on W.35 A completely different route to a missing link comes from another direction.36 Any object is an object. It could not be the very thing it is unless it were an object. Hence its nature depends on a certain relationship with the property of being an object, or objecthood, to make the reference to universals explicit.37 Now, if one is a Platonist about universals, there is no hope of getting a dependence in the other direction. Plato’s forms epitomize beings with svabh¯ava. But if one is an Aristotelian about universals, the matter is different. For Aristotle, there can be no uninstantiated universals. The universal of being human depends on the humanity of Socrates, and so Socrates, the humanity of Plato, and so Plato, and so on. And the universal objecthood depends on objects. We have, then, the symmetric dependence relations we need. We may recast the whole matter in Heideggerian terms. The driving question behind Heidegger’s thought is exactly ‘What is being?’, and to be for Heidegger is exactly to be an object.38 And being is that in virtue of which beings are. As Heidegger puts it in Sein und Zeit: What is asked about in the question to be elaborated is being, that which determines beings as beings, that in terms of which beings have always been understood no matter how they are discussed.39

Beings, then, depend on being. But Heidegger is an Aristotelian about the matter. Being is always the being of some object. Again as he puts it: If we think of the matter just a bit more rigorously, if we take more heed of what is in contest in the matter, we see that Being means always and everywhere: the Being of beings.40

So being depends on beings as well. We have our symmetrical dependence. 34 Schaffer (2010). Though Schaffer is careful to restrict his concern to just the physical. He also uses a version of the causal argument from the Big Bang. This delivered an entangled quantum state, in which every object is dependent on the whole. 35 I note that this is exactly what the Huayan accepted. For them, any whole depends on its parts, and any part depends on the whole. See Jones (2009). 36 I note that there is also at least one more candidate for the required linking concept: nothingness. I have explored that matter in Priest (2014), ch. 13. As we are about to see, the universal of oneness, that is, of being an object, could also play this role, though this had not occurred to me when I wrote the book. 37 The relationship between a universal and its instantiations is not exactly the same as that between a whole and its parts, but it is very similar. For a gentle introduction to the matter, see Garrett (2006), pp. 37ff. 38 For a general discussion of the matter, see Priest (2014), ch. 4. 39 40 Stambaugh (1996), pp. 4f. Stambaugh (2002), p. 69.

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 buddhist dependence I note that, for Heidegger, one cannot say what being is. (For to do such would be to treat it as a being, which it is not.) Being shows itself in the way that beings present themselves—to those with the eyes to see it. I note that at this point we are not so far away from the dao which cannot be described, but which manifests itself in “all under heaven”.41

5 Conclusion So ends our somewhat whistle-stop tour of some Buddhist views on ontological dependence, and some of their Western connections. Most of this has been written with Western philosophers who know little of Eastern traditions in mind; but I hope that some of it will be of interest to those who know of Buddhist philosophy, but, perhaps, less of Western philosophy. I have done nothing here to try to evaluate the views we have met, or determine their truth. The exercise has been one of urban geography. To use a metaphor I have used before:42 Philosophy is like a city. It has relatively self-contained suburbs, such as metaphysics, ethics (each with their own neighborhoods). But only relatively: the connections spread in a network over the city, sometimes in the most surprising of ways. Nor is this a finished city: remarkable new buildings are going up all the time. All I have done in this essay is to describe one of the Eastern neighborhoods, and explore some of the connections which cross the city’s Berlin Wall. Of course, a philosopher can live quite happily in just one half of the city—or even just one of its suburbs—the whole of their thinking lives. But their philosophy cannot but be richer and deeper, the more they know of the city. Such is the spirit in which this piece is written.

References Armstrong, D. M. (1997), A World of States of Affairs, Cambridge: Cambridge University Press. Bliss, R. L. and Priest, G. (2017), ‘Metaphysical Grounding, East and West’, pp. 63–85 of S. Emmanuel (ed.), Buddhist Philosophy: a Comparative Approach, Wiley-Blackwell, 2017. Bliss, R. L. and Trogdon, K. (2014), ‘Metaphysical Grounding’, in E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/grounding/. Chan, W. T. (ed.) (1969), A Sourcebook in Chinese Philosophy, Princeton, NJ: Princeton University Press. Chang, G. C. C. (1972), The Buddhist Teaching of Totality: the Philosophy of Hwa Yen Buddhism, London: George Allen & Unwin Ltd. Garfield, J. (1995), The Fundamental Wisdom of the Middle Way, New York, NY: Oxford University Press. Garrett, B. (2006), What is this Thing Called Metaphysics?, Abingdon: Routledge. 41 As the famous opening lines of the Daodejing put it, “The Dao that can be described in language is not the constant Dao; the name that can be given it is not the constant name”: Lynn (1999), p. 51. 42 Priest (2011).

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graham priest  Jones, N. (2009), ‘Fazang’s Total Power Mereology’, Asian Philosophy 19: 199–211. Kemp Smith, N. (1933), Immanuel Kant’s Critique of Pure Reason, 2nd edn, London: Macmillan & Co. Liu, M. W. (1982), ‘The Harmonious Universe of Fazang and Leibniz’, Philosophy East and West 32: 61–76. Lynn, R. J. (1999), The Classic of the Way and Virtue: A New Translation of the Tao-te Ching of Laozi as Interpreted by Wang Bi, New York, NY: Columbia University Press. Mitchell, D. (2002), Buddhism: Introducing the Buddhist Experience, Oxford: Oxford University Press. Padmakara Translation Group (2004), Introduction to the Middle Way: Candrak¯ırti’s Madhyamak¯avat¯ara with a Commentary by Jamgön Mipham, Boston, MA: Shambala. Priest, G. (2002), Beyond the Limits of Thought, 2nd edn, Oxford: Oxford University Press. Priest, G. (2011), ‘Why Asian Philosophy?’, pp. 211–21 of G. Oppy and N. Trakakis (eds), The Antipodean Philosopher. Volume 1: Public Lectures on Philosophy in Australia and New Zealand, Lanham, MD: Lexington Books. Priest, G. (2013), ‘Between the Horns of Idealism and Realism: The Middle Way of Madhyamaka’, ch. 13 of S. M. Emmanuel (ed.), A Companion to Buddhist Philosophy, Chichester: Wiley-Blackwell. Priest, G. (2014), One, Oxford: Oxford University Press. Priest, G. (2015), ‘The Net of Indra’, pp. 113–27 of K. Tanaka, Y. Deguchi, J. Garfield, and G. Priest (eds), The Moon Points Back, Oxford: Oxford University Press. Putnam, H. (1973), ‘Meaning and Reference’, Journal of Philosophy 70: 699–711. Radhakrishnan, S. and Moore, C. (eds) (1957), A Sourcebook in Indian Philosophy, Princeton, NJ: Princeton University Press. Schaffer, J. (2010), ‘Monism: The Priority of the Whole’, Philosophical Review 119: 31–76. Siderits, M. (2007), Buddhism as Philosophy, Aldershot: Ashgate. Stambaugh, J. (trans.) (1996), Being and Time, Albany, NY: State University of New York Press. Stambaugh, J. (trans.) (2002), Identity and Difference, Chicago, IL: University of Chicago Press. Tahko, T. E. and Lowe, E. J. (2015), ‘Ontological Dependence’, in E. Zalta (ed.), The Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/dependence-ontological/. Varzi. A. (2015), ‘Mereology’, in E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato. stanford.edu/entries/mereology/. Williams, P. (2009), M¯ah¯ayana Buddhism: The Doctrinal Foundations, 2nd edn, London: Routledge.

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7 Bicollective Ground Towards a (Hyper)Graphic Account Jon Erling Litland

1 Introduction Most authors on grounding hold that grounding is left-collective: there are some truths γ0 , γ1 , . . . such that, without any one of the γi grounding φ on its own, taken together the truths γ0 , γ1 , . . . nevertheless ground φ. (A standard example is the grounding of a conjunctive truth in its conjuncts.) Could grounding also be right-collective? In the simplest case: could a truth φ ground some truths γ0 , γ1 , . . . taken together without the truth φ grounding any of the truths γi on its own? More generally, let us say that grounding is bicollective if it is both left- and right-collective.1 If bicollective ground is intelligible an interesting kind of metaphysical coherentism becomes a live option. Just like an epistemological coherentist may say that it is a mistake to ask, about a particular belief, what makes it justified, a metaphysical coherentist may say that it is a mistake to ask, of a particular truth, what grounds it. In the epistemological case we should rather ask of some beliefs, taken together, what makes them justified; in the metaphysical case, we should rather ask, of some truths, what grounds them. A considerable advantage of this version of metaphysical coherentism is that one does not have to countenance circles of ground in order to be a metaphysical coherentist.2 The intelligibility of bicollective ground was first argued for by Dasgupta (2014b) in the course of defending various structuralist theses. Recently, Litland (2016) showed how some sense can be made of the notion by developing a logic of bicollective ground using Fine’s truthmaker semantics. While the truthmaker semantics is by far 1 A note about terminology. Dasgupta (2014b) speaks of grounding being “irreducibly plural” and Litland (2016) speaks of grounding being “many–many”. I believe the present terminology is better; the issue is not whether there are grounding operators that take many (or a plurality) of arguments on the right; the issue is whether grounding is collective (non-distributive) on the right. The point is purely terminological—nobody has been confused on this point. 2 Compare the discussion of “reciprocal” essence in (Fine 1994, pp. 65–6).

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jon erling litland  the most developed approach to the logic of ground,3 it is nevertheless problematic as a semantics for ground.4 These problems, as we will see, are particularly pronounced in the case of bicollective ground. A different—in many ways more natural—approach to the logic of ground is (hyper)graph-theoretic.5 The main contribution of this paper lies in showing how to extend the (hyper)graph-theoretic account of ground to the bicollective case. (Along the way we correct some minor infelicities in previous presentations of the graphtheoretical account of ground.) We also—on the philosophical side—sketch how bicollective ground is naturally applied to mathematical structuralism.

1.1 Overview We begin in §2 by introducing the central notion of immediate strict full ground. In §3 we develop some ways of making sense of the characteristic non-distributivity of bicollective ground and argue that mathematical structuralists should avail themselves of bicollective ground. In §4 we rehearse the truthmaker semantics for bicollective ground and point out some problems that arise in the bicollective case. In §5 we recall the graph-theoretic account for the left-collective case and argue against Fine’s principle of Amalgamation. The main contribution of the paper comes in §6 where we develop the graph-theoretic account of bicollective ground. We discuss how to define acyclic graphs, mediate ground, the notions of partial ground, and what it is for two collections of truths to be ground-theoretically equivalent. We conclude with some questions for future research (§7).

2 Notions of Ground The central notions of ground for the graph-theoretic approach are strict full mediate (