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Unlimited ontology and its limits

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Unlimited ontology and its limits

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Content Unlimited Ontology and Its Limits Maegan Fairchild August 2018 A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHILOSOPHY) In the marshes the buckbean has lifted its feathery mist of flower spikes above the bed of trefoil leaves. The fimbriated flowers are a miracle of workmanship and every blossom exhibits an exquisite disorder of ragged petals finer than lace. But one needs a lens to judge of their beauty: it lies hidden from the power of our eyes, and menyanthes must have bloomed and passed a million times before there came any to perceive and salute her loveliness. The universe is full of magical things patiently waiting for our wits to grow sharper. -Eden Philpotts, A Shadow Passes (1919) Acknowledgments This isn’t the first time I’ve tried to start writing my Acknowledgments section. I’ve written notes after cohort dinners, after inspiring (but grueling) meeting-marathons with my committee, after hours of working in coffee shops with friends, and after late nights and long talks at yet another Pacific APA. But, like many of the notes I’ve jotted over the past six years, those first drafts are all buried in long-lost digital folders or (worse!) ”organized” in a box somewhere under my desk. So, I’ll have to make do with what I can remember now, accepting that I’ll never be able to adequately thank all of the people for all of the moments that have made this dissertation possible. First, to my incredible family, Jim, Tierney, and Macey Fairchild: everything good I’ve ever done is because of you and for you. Thank you. I’m sorry I’ve been so far away for so long, but I hope y’all will be proud of what I’ve tried to do with my time way out here in California. (You too, Bella.) And for making this time worth it all, I owe so much to my committee. I feel so very lucky to have had the chance to work with each of them, and am so grateful for all of the time and energy they’ve invested in me. I couldn’t have asked for a more supportive and inspiring team. Above all, I want to thank Gabriel Uzquiano, without whom this dissertation (and my career at USC more generally) could never have happened. Our first conversation on my visit as a prospective student was a huge part of why I wound up choosing this program, and each of our meetings since has made me more glad that I did. He has always approached my ideas with kindness, excitement, and respect, and is willing to share his praise as generously as he does his time. He has always taken my work seriously; no matter how scrambled my thoughts were, he inevitably found something in the storm worth saving, while patiently guiding me back to smoother waters. Among the many things I’ve learned from Gabriel is a deep appreciation of the delicate interaction between philosophy and formalism, and the corresponding thrill of unravelling some new philosophical insight by (ever-so carefully, ever-so cautiously) attending to the lessons and limits of logic. For years, he has been just as dedicated and careful a mentor as he is a philosopher, and will forever be a model of the sort of advisor I hope to someday be. John Hawthorne couldn’t have joined our department at a better time for me. He arrived just as I was starting to properly dive in to my own larger projects, and his guidance made that not only less terrifying, but far more fun than I ever could have expected. Talking with John about iii Fairchild Chapter 0. Acknowledgments philosophy is a blast – such a blast, in fact, that sometimes you don’t realize until hours later that you’re going to have to sweep your whole project off the floor and start again. In the midst of all of the fun, though, he is also incredibly sensitive to how difficult philosophy is. (Usually meetings with John end with him laughing encouragingly at my dismay and saying “it’s hard, this!” .) Although his ability to find the crucial thread in any philosophical knot helped shape this project at every turn, it is his ability to approach intractably difficult problems with playfulness that has most formed how I now think about philosophical research, and for that I am especially grateful. Of all my committee members, Andrew has probably seen me in some of my most floundering philosophical moments. In the summer between my second and third year, I met with him for hours every week, combing through Hartry Field’s Saving Truth From Paradox in preparation for my Area Exam. Often I’d show up utterly stumped by the most recent reading, and Andrew would sit in Jones Coffee Roasters with me for three, four, or five hours at a time, until it all finally clicked. And, if we both went bleary-eyed before I got it, he’d write me long and careful emails before the end of the day, filling in the pieces I’d missed. Andrew taught me an approach to philosophy that leaves no stone unturned, and requires the grueling but rewarding work of slowing down and working through cases til you’re sure it all works out. Teaching me to turn that attention and dedication to my own work required huge amounts of attention and dedication from Andrew as a mentor, for which I am so grateful. I still have far to go, but without his support I never would have been able to take this project as far as I have. Jeff is as eager and thoughtful a mentor as he is philosopher; he is always quick to remind me that finding a healthy balance between personal and professional demands is hard — but crucial — and has invariably been one of the most caring and open members of my committee. When it comes to philosophy, Jeff has an incredible ability to help me get from a place of utter despair about a project to giddy, bouncing excitement about taking it even further. Every chapter in this dissertation at one time or another escaped the trash bin because of Jeff’s excitement about its potential. Of course, those same chapters often wound up in the trash in the first place because of a devastating objection (or two or three or four) from Jeff. This has been the life-cycle of all of my favorite projects, though, and each is so much better for it in the end. I have pages of email exchanges with Jeff concerning daunting holes in this project that I’m sure I’ll spend years trying to patch, and because of him, I can’t wait to try. And, finally, I am so, so grateful to Shieva Kleinschmidt. Not only for her unwavering support of my wildest philosophical pursuits and invaluable guidance through the most tangled thickets of this dissertation, but also for her constant mentorship in every area of my life. She is not only one of the most perceptive and dedicated mentors in our department, but also one of the most careful and courageous metaphysicians I know of. I have learned so much of what it is to be a philosopher and an educator from Shieva; she was the first and last professor I TA’d for, and I can’t think of a better capstone. I feel very lucky to have had the chance to work with her and to be her friend during my time here, and I look forward to many more years of both. I hope (and this is big for iv Fairchild Chapter 0. Acknowledgments me!) that she gets a dog before I do. (Which is to say: extremely soon.) Ultimately, in one way or another, I owe thanks to everyone who has been on the faculty at USC while I’ve been here, for all of the time and energy they have put in to guiding me as a student, teacher, and scholar. Beyond the members of my committee, I owe special thanks to Robin Jeshion, Scott Soames, Ralph Wedgwood, and Kenny Easwaran for giving me a foundation in my first year courses, for pulling me out of my shell so I could make the most of graduate school, and for continued mentorship in the years that followed. I am also grateful to Janet Levin and Steve Finlay, for their guidance and support when I TA’d for them. Outside of the department, I also owe a huge debt of gratitude to Barry Schein for stepping in to save the day as my outside committee member. Like so many, I owe a special thanks to Mark Schroeder. Every time I’ve stumbled, Mark has been there to help me back on my feet and plot out my next steps. I honestly don’t know how to add to the many paragraphs of acknowledgments that have been written about Mark’s profound and formative impact on so many young philosophers, so I’ll just say this: without him, I wouldn’t have made it far enough to write an Acknowledgments section at all. Thank you, Mark, for believing in me, and thank you for insisting that I believe in myself. And, finally, here’s the part of the acknowledgments that I am certain I’ll never properly do justice to: there is no way that I can thank the graduate students at USC enough for all that they have done for me. I am constantly astounded by the brilliance and kindness of my peers, and have learned so much more from them in the past years than I’ll ever be able to say. First, I am so thankful for the very best cohort I could ever have asked for: Mike Ashfield, Renee Bolinger, WooRam Lee, and Jonathan Wright. I am proud to have spent grad school alongside them, and hope there are many more barbecues in our future. Still, none of us would have settled in at all without being welcomed by a truly fabulous community of older students. I am especially grateful to Rima Basu, Erik Encarnacion, Caleb Perl, Kenneth Silver, and Aness Webster for years of mentorship, friendship, and really great philosophy. I’ve grown so much as a philosopher because of the many conversations I’ve had with my peers, and with every incoming cohort the list grows longer: I’m especially grateful for all that I’ve learned from conversations with Alex Dietz, Jennifer Head, Joe Horton, Nicola Kemp, Tanya Kostochka, Matt Leonard, Elli Neufeld, and Christa Peterson. And, of course, there are still so many more people whose conversations in the grad lounge, in coffeeshops, in seminars, and in Spec Society have been so important for shaping my work over the years. I truly wish I’d spent more time talking to each of you, and look forward to continuing to learn from you in the future. On a more personal note: I’m a planner by nature, but you can’t plan for everything, and sometimes when you least expect it, the sky will fall. I’ll never have words enough to thank the friends who, when the sky fell on me, all put their lives on hold (in so many big and small ways) to help put me back together. Many of the people I have listed so far are among the very best friends I’ve ever had, and I didn’t really appreciate the extent of that until this year. I’ll also never have words enough to thank the faculty who kept pushing me and kept believing in me, even when I v Fairchild Chapter 0. Acknowledgments didn’t think I could do it. I genuinely don’t know where I would be now without the support of the philosophy community in this department and beyond, but I know I couldn’t have completed this dissertation otherwise, and so for that I am speechlessly grateful. For this and so many other reasons, I’d like to dedicate this dissertation to all of the graduate students I’ve shared my time at USC with. Thank you – each of you – for so many great conver- sations, for all the many things you’ve taught me, for making this department a community I’m burstingly proud to be a part of, and for turning Los Angeles into a home I’ll be so very sad to leave. You guys are incredible, and I can’t wait to read your work for many, many years. I love y’all, abundantly. vi Contents Acknowledgments iii 1 Introduction 1 1 Varieties of Plenitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Dimensions of Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Non-Coincident Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Coincident Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Moving Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 The Barest Flutter of the Smallest Leaf: Understanding Material Plenitude 11 1 Bad Eggs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.1 Another taxonomical strategy: Sortalish Properties . . . . . . . . . . . . . . . 16 2 A structural solution : Neutral Properties . . . . . . . . . . . . . . . . . . . . . . . . 18 3 The consistency problem for plenitude . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 Problems for Merely Modal Plenitude . . . . . . . . . . . . . . . . . . . . . . 22 4 Non-local entailment, otherworldly necessity, and global plenitude . . . . . . . . . . 25 5 Ground Floor Humility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6 Promises of Plenitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 8.1 Initial Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 8.2 Constructing a Global Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.3 Global Plenitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 A Paradox of Matter and Form 39 1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2 Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.1 Weaken Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.2 Abandon Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4 Arbitrariness and the Long Road to Permissivism 49 1 Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.1 The Stakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 1.2 Clarifying the Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 vii Fairchild Contents 2 Arbitrariness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.1 Anthropocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.2 Epistemic Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.3 Methodological Complaints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3 Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1 Remarks on Parity and Significant Differences . . . . . . . . . . . . . . . . . . 64 3.2 Parity at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4 Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1 Pessimistic Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 The “Top Down” Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3 The Nitty Gritty Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 References 75 viii 1 Introduction The world is crazier and more of it than we think, Incorrigibly plural. I peel and portion A tangerine and spit the pips and feel The drunkenness of things being various. Louis MacNeice, “Snow” Much of human inquiry aims at building an inventory of the material universe. Some contributions to the record are more surprising than others: for example, the ‘pink see-through fantasia’ is a species of sea cucumber, recently discovered in the Gulf of Mexico, whose tangled digestive tract is visible through its rosy balloon-like body. Other additions to the list are less alien than transparent sea-cucumbers, but are all the more incredible for their familiarity. (There are, for example, many thousands of species of moss and almost twice as many known species of flatworm.) When we reflect on the astonishing variety of the inventory so far, it is hard to see why some have the sense that the metaphysician’s question – what is there? – should have only unsurprising answers. The vantage point of a metaphysician is different, and her methods aren’t those of the botanist or marine biologist, but her project is ultimately similar: to fill out a complete picture of the world, squishy bits and all. Still, some philosophers believe that when the botanists and biologists (and physicists, art his- torians, and sociologists) have finished their inventory of the world, the result will be mostly right from the perspective of metaphysics. After the sciences have finished their inquiry, there will be no more surprises lurking in the metaphysical deep. These are the conservatives in the literature on material object ontology: what exists, they say, is roughly what we ordinarily take there to be. Other philosophers do think that the metaphysician’s final inventory will be surprising, but only because the attempted inventory of the sciences has already gone off the rails ontologically. According to these eliminativists, strictly speaking, there are no familiar ordinary objects at all; no sea cucumbers or flatworms, only the fundamental particles that seem to make them up. Finally, there are the permissivists. Permissivists hold that the material world contains vastly more than common sense and the sciences together recognize. In addition to flatworms, electrons, orchestras, and lawn furniture, there may be all sorts of other extraordinary things. As with the other sciences, this extraorindariness may come in degrees: there might be strange but ultimately sensible objects, like something composed out of my left shoe and my right shoe (a pair) or a ring 1 Fairchild Chapter 1. Introduction that can be destroyed with a small scratch (the papal signet ring, for example). But there might be utterly unfamiliar things as well, like the scattered object composed out of all of the flatworms in North America, or the Los Angeles Philharmonic Orchestra on Tuesdays in June, or the thing that exists only when my neighbor’s lawn chair is painted orange. Which of these strange objects the world contains will depend on the details of our permissivism. And, unsurprisingly, there are a number of ways to be permissive about what there is. Perhaps the most familiar variety of permissivism is mereological universalism, a thesis about which composite objects there are: for any things, there is something composed out of them (or more technically: every plurality has a fusion). So, for example, not only is there something made up of these five pieces of wood (the table), there’s also something made up of all of the furniture in this room, and even something else made up of this table and your right thumb. Universalism is a variety of what I will call radical permissivism: it not only extends the inventory of the world beyond that of common sense, but purports to “max out” ontology along a particular dimension. The family of views this dissertation concerns is analogously liberal: material plenitude says that every material object is co-located with a multitude of other material objects, each of which can survive a different range of changes. More specifically, it says that there is an object corresponding to every consistent “modal profile” . Very roughly, an object’s modal profile specifies its modal persistence conditions; or the changes or circumstances that it can and cannot survive. Plenitude is often motivated by a certain reaction to the puzzles of material constitution.Consider: A glassblower sits in her workroom admiring her newest creation; a vase in the shape of a rearing horse. Were she now to take issue with the arrangement of the horse’s mane, the angle of one of its legs, or the size of the mouth of the vase, she could gently reheat the piece and make small changes without destroying it. But were she to reheat the glass completely and fashion an elephant, instead, she would destroy the vase, though wouldn’t thereby destroy the gob of molten glass that made it up. Pluralists about material constitution say that the vase and the gob of glass that make it up are distinct; serious pluralists insist that this is so regardless of whether the gob actually outlives the vase. According to serious pluralism, distinct material objects can occupy the same region of space for the duration of their existence.We say that these permanently coinciding objects have different ‘modal profiles’; they are able to survive through different circumstances, and have different properties ‘essentially’ and ‘accidentally’ . (For example: the vase has its rough (though not exact) shape essentially, the gob of glass has that shape only accidentally. The gob may have its component matter essentially, while the vase may be able to survive loss of some parts (a hoof, a tail) and so has those parts only accidentally.) But, having admitted that there are distinct coincident objects corresponding to different modal profiles, it seems that it would be objectionably arbitrary to stop with just the vase and the gob. Why should a world rich enough to contain coincident objects contain only those objects corresponding to familiar modal profiles, and not relevantly similar (but nonetheless unfamiliar) ones? Why not 2 Fairchild Chapter 1. Introduction something coincident with the vase which cannot survive even very slight changes to its shape? Why not also something is created when a bouquet of flowers is first put in the vase, but cannot survive their replacement?Having acknowledged that the world is varied in the ways the serious pluralist suggests, and absent any satisfying answers to these questions, we’re driven to the view that there isn’t any stopping point – no line in the sand cordoning off the profiles that correspond to bits of the world from those that don’t. Thus, on pain of unacceptable arbitrariness, we seem to be led to the conclusion that there are coincident objects witnessing the full range of modal variation. In short: there is an object for every consistent modal profile. Although serious pluralism opens the door, it is clear that plenitude will take us much further than pluralism alone. In fact, it seems to be the height of ontological decadence; the plenitude-loving permissivist long ago left the desert behind for wilder landscapes. It is primarily on grounds of anti-arbitrariness considerations like these that philosophers have found varieties of plenitude so appealing, but it promises other advantages as well. If we take mere- ological universalism as our paradigmatic variety of permissivism, we have reason to expect that permissivist pictures in general will be both more powerful and more elegant than their conservative alternatives: more powerful, in that they promise to provide resources for addressing or dissolving longstanding puzzles in metaphysics, and elegant, in that they are usually characterized by sim- ple, general principles.However, as I’ll emphasize in much of what follows, we should be extremely cautious about our temptation to generalize from the case of mereological universalism to other varieties of permissivism. Whether and how an abundant ontology of coincident objects equips us to address familiar problems in metaphysics will depend heavily on the details, and, as we’ll see, pinning down the details of plenitude is neither straightforward nor ‘simple’ . This dissertation is first and foremost an exploration of material plenitude: its varieties, its limits, and its foundations. Although plenitude is a popular position in contemporary metaphysics, comparatively little has been done to examine the view in detail. My aim here is to show that when we do so, we find that the world through the lens of plenitude is much more rich and complex than we might have expected. This chapter serves as a broad introduction to plenitude and to the core themes of the coming chapters. In Sections 1 and 2, I’ll introduce three varieties of plenitude and trace out some important boundaries for our investigation of the target views. In particular, I’ll focus on ways that some varieties of plenitude may not deliver the unconstrained abundance with which it is sometimes associated: plenitude is silent on more questions than we might expect. In the remainder of the dissertation, I’m concerned with three questions: (1) What is material plenitude?, (2) What is it not? (That is, what are the limits of plenitude?), and (3) Why should we believe it? As we’ll see in the next section, the first question is slightly misleading: there are a number of different ways to make the slogan-form of material plenitude precise. Although I’ll suggest below that some may do a better job of living up to the heuristic ambitions of plenitude than others, 3 Fairchild Chapter 1. Introduction the card-carrying plenitude-lover has a number of membership options. However, it turns out that it is sometimes much harder to pin down a precise formulation of plenitude based on the target idea than we might expect. The devil is in the details of how we understand ‘consistent modal profiles’: in Chapter 2, I argue that one very natural way of understanding modal profiles faces two serious obstacles (the bad eggs problem and the consistency problem. There, I develop and defend a version of plenitude that I argue is capable of overcoming both, but as a result is in some ways more ‘humble’ than the decadent ontology it yields would suggest. The arguments I consider in Chapter 2 also reveal that we have to be extremely careful what other principles of abundance we associate with plenitude. This same theme emerges again in Chapter 3: there, I am instead interested in a plenitudinous version of hylomorphism (Simple Hylomorphism) inspired by work in Fine (1982), according to which (for example) for any property the vase has, there is something coincident with it that has that property as a form. I argue that (given an abundant theory of properties) Simple Hylomorphism is subject to a Russellian argument. In the face of paradox, something in the simple account has to give: I argue that on the strength of the anti-arbitrariness considerations in favor of the relevant principle of plenitude (Existence), we should instead weaken the conditions of individuation for hylomorphic compounds. (As we’ll see, this yields a much more mysterious picture of material objects than we may have anticipated!) The cumulative lesson of these chapters is that, although the boundaries might be different for different varieties of plenitude, we shouldn’t expect any version of plenitude to deliver an ontological free-for-all. Rather, investigation in to the limits of plenitude helps to reveal substantive constraints on any adequate theory: by pushing ontology ‘as far as we can’ along some dimension or other, we illuminate the boundaries of the material world. Finally, in Chapter 4, I examine the credentials of the arguments that led us here: the arguments from arbitrariness. I argue that a number of ways of making these arguments more precise fail to support the varieties of radical permissivism we’re interested in. I think we can do better, and propose what I take to be the best framework for understanding the arguments from arbitrariness. However, the proposed framework reveals that the permissivist who hopes to rest her liberal ontology on an aversion to arbitrariness must either bolster the foundations with substantive metaphysical theses, or recognize that those foundations are much less stable than they’re usually taken to be. The upshot is that while I think we should endorse a plenitudinous metaphysics of material objects – and should do so on pain of arbitrariness – there is much more work to be done to say exactly why a more moderate metaphysics would be unacceptable. In keeping with the theme of the previous chapters: the road to plenitude will be longer than we might have expected. 1 Varieties of Plenitude I want to begin with a brief note about how I’ll be using the label ‘plenitude’ . My target here is the family of theses corresponding to the slogan “there is an object for every consistent modal profile”, 4 Fairchild Chapter 1. Introduction but given the variety of views in the family and the proximity of these views to other varieties of permissivism, it will be helpful to draw some initial distinctions. First, as I’ve said, different ways of spelling out the notion of ‘consistent modal profiles’ will yield different varieties of plenitude. There are also some ways of making the slogan more precise that clearly don’t live up to the heuristic ambitions of plenitude: for example, a precisification of the slogan according to which the only ‘consistent modal profiles’ are those that correspond to familiar objects hardly counts! Thus, it will help to focus our attention if in addition to the slogan, we also rely on the motivations we started with: plenitude concerns the extent of modal variation between coincident material objects. Different varieties of plenitude involve cashing this out in different ways, but all have in common an attempt to capture the idea that having admitted some such variation between coincidents, we should admit it ‘all’ . Perhaps the most familiar contemporary version of plenitude comes from Hawthorne (2006). We’ll say that a modal occupation profile is a (partial) function from worlds to filled regions of spacetime, and that an object corresponds to a modal occupation profile if for each world w, it occupies exactly the regions f(w) there. What I’ll call occupational plenitude then says: Occupational Plenitude. There is an object corresponding to every modal occupa- tional profile. Occupational Plenitude guarantees that there is something that exists coincident with the gob of glass exactly when it is shaped like a horse-vase, something that exists exactly when the horse’s mane is just so, and something else that coincides with the vase only when it has this very bouquet of flowers inside, and so on. But it still may not deliver the variety we’d hoped for. Here’s just one example. Hawthorne suggests that Occupational Plenitude can help us to ac- commodate things like restaurants in our ontology, which are distinct from the buildings they occasionally coincide with: For example, a restaurant might be (...) coincident with a building at a time but not identical to it. From within the relevant framework, one reminds oneself that the per- sistence conditions of a restaurant are not that of the building, and so, whether or not the actual occupation profile of the restaurant is that of the building, the former is not identical to the latter. 1 The same restaurant might at one time coincide with one building, and when that building is destroyed, might survive to coincide with another. They have different modal profiles: the building has its structure and location (perhaps) essentially, and the restaurant does not. But although presumably restaurants must at some point in their career be coincident with a building, we might think that they are created when a certain legal step is taken – irrespective of whether the building(s) with which they will eventually coincide have been built. Suppose further that restaurants never 1 Hawthorne (2006, 112) 5 Fairchild Chapter 1. Introduction coincide with legal documents, individuals, or groups of people – they only ever coincide with buildings. When a restaurant is not spatially coincident with any building, it lacks a location (or maybe: an exact location). Suppose now that I go to the Pasadena Chamber of Commerce and file of the relevant paperwork, giving me sole ownership of the town’s first coffeeshop-slash-burrito joint: the Sleepy Burrito. The Sleepy Burrito is created the, and can (like most restaurants) continue to exist through the con- struction and demolition of a number of different buildings. Although this is controversial, if there are periods during which there is no building with which the Sleepy Burrito coincides, I wouldn’t be tempted to say that the Sleepy Burrito is temporally gappy. Rather, it persists through those periods without exactly occupying any particular region of spacetime. (Or, to make it more vivid, suppose that the Sleepy Burrito is a “pop-up restaurant” or a food truck, and is only open on Thursdays. Even in this case, it still persists from Friday until Wednesday – it doesn’t pop out of existence. Maybe we even want to grant that on Saturday, it is located in Southern California, or even in Pasadena. You can imagine yourself saying: “There’s this hip new pop-up restaurant in town that you should try; you should find out where it will be this week. ”) Occupational Plenitude does guarantee that there is an object — say, a concrestaurant — that is correctly described by the modal occupation profile which picks out at each world exactly the regions occupied by the restaurant when it is coincident with some building or other. However, the concrestaurant and the restaurant seem to have different modal persistence conditions; the restaurant can pre-date the construction of and survive the destruction of any building with which it is ever coincident. If this is the right way to think about restaurants, then the concrestaurant and the Sleepy Burrito have the same modal occupation profile – they have the same modal patterns of spatiotemporal occupation – but they differ modally in other ways, as well. Intuitively, they have different ‘modal profiles’ . (Again this may be more vivid in the pop-up case: there are things that the Sleepy Burrito survives that the concrestaurant can’t survive – like weekends, for example.) To be clear, I don’t take this to be a problem for Occupational Plenitude. Occupational Plenitude is a partial thesis about what there is that plenitude-lovers should be happy with – but cases like this provide motivation to look for other ways of understanding plenitude. We needn’t look far: the initial case for plenitude was formulated not in terms of differences in possible spacetime paths, but in terms of differences in properties had essentially and accidentally (or, as Fine (1982, 98) puts it, differences in “existence-conditions”). Similar arguments for coincident abundance are phrased in terms of essences or forms. For example, Sosa (1987): We are supposing a snowball to be constituted by a certain piece of snow as constituent matter and the shape of (approximate) roundness as constituent form. That particular snowball exists at that time because of the roundness of that piece of snow. More, if at that time that piece of snow were to lose its roundness, then at that time that snowball would go out of existence. Compare now with our ordinary concept of a snowball the concept of a snowdiscall, 6 Fairchild Chapter 1. Introduction which we may define as an entity constituted by a piece of snow as matter and as form any shape between being round and being disc-shaped. (...) The crucial point now is that there are infinitely many shapes o 1 , ..., o n ..., between roundness and flatness (of a piece of snow), and for each i, having a shape between roundness and o i would give the form of a distinctive kind of entity to be placed beside snowballs and snowdiscalls. It follows that whenever a piece of snow constitutes a snowball, it constitutes infinitely many distinct entities all sharing its place with it. It follows also that none of us can so much as wiggle a finger without destroying, and creating, infinitely many things. 2 Given how central this way of talking is to the motivations for plenitude, it is natural to ask what varieties of plenitude we get by focusing instead on essential properties, ‘forms’, and the like. As we’ll see in Chapters 2 and 3, unlike Occupational Plenitude, it isn’t at all straightforward to make sense of the views that correspond to ‘maxing out’ material ontology along these dimensions. 2 Dimensions of Abundance One sometimes gets the sense from contemporary discussions of material object ontology that radical positions – like eliminativism and permissivism – are the “easy” way out of many of our ontological tangles, and that the real difficulty of metaphysics lies elsewhere. For example, Schaffer (2009): So do not be alarmed. Permissivism only concerns the shallow question of what exists. One can and should still be restrictive about the deep question of what is fundamental, and one still owes an account of how these very many things exist in virtue of what little is fundamental. 3 But a core theme of the chapters to follow is that this impression is misleading; that making sense of the contours and credentials of varieties of radical permissivism is far from a trivial exercise. My overall aim is to argue for sensitivity to the limitations of views that seem otherwise to be uninhib- itedly liberal, and demonstrate how understanding varieties of permissivism can reveal substantive constraints on any theory of the material world. (Who ever thought cataloging a jungle would be easy?) Since we’re mostly concerned with plenitude, it will be helpful by way of ground clearing to begin by pointing out some dimensions of abundance that the varieties of plenitude I’ve introduced so far are silent on, as well as some of the ways that these varieties might ‘reach beyond’ the target idea. As a thesis about the range of modal variation between coincident objects, there are two sorts of questions that we shouldn’t expect plenitude to answer for us. First: the target idea itself won’t say anything about non-coincident abundance: many familiar permissivist theses are independent of plenitude, and aren’t always easily recovered by either beefing up plenitude or our background 2 (Sosa, 1987, 178-179) 3 (Schaffer, 2009, 361) 7 Fairchild Chapter 1. Introduction metaphysics. Second, plenitude needn’t say anything about every dimension of coincident abun- dance: although plenitude guarantees a rich range of modally different coincident objects, insofar as we are willing to allow that there are non-modal dimensions of variation between coincident objects, plenitude may be silent on those. (We saw with Occupational Plenitude above a way that some versions of plenitude may be silent on some modal differences, as well.) In Sections 2.1 and 2.2, I briefly discuss two examples. 2.1 Non-Coincident Abundance As I propose to understand it, our target idea is silent on a number of permissivist theses that are often regarded as much more modest – for example, mereological universalism. This point is sometimes lost because a number of the most visible versions of plenitude on offer pack in very nearby commitments (eg. that every filled region of spacetime contains an object). But as I’m using the label, plenitude is an importantly separate thesis: not about composition at all, but about coincidence. It is helpful, I think, to distinguish between superabundant and purely modal plenitude principles. Put extremely roughly: superabundant plenitude principles are not ‘purely’ modal, in that they are not trivially satisfied by models according to which there is exactly one possible world. Coherent purely modal principles, on the other hand, are trivially satisfied even in these models. Such principles say only that there are coincidents witnessing the full range of modal variation, whatever that might be. Occupational Plenitude, for example, is a superabundant principle. Consider a simple one- world model: in this world, there are exactly two material objects O1 and O2 which respectively exactly occupy the disjoint regions of spacetime r and s. This isn’t a model of Occupational Plenitude: even supposing that regions r and s have no further subregions, Occupational plenitude demands that there be a further material object exactly occupying the fusion of r and s. (Even so, Occupational Plenitude is technically silent on parthood, and so doesn’t entail mereological universalism. However, there are independently plausible background assumptions (for example, about links between the locative properties of objects and their mereological properties) that can bridge the gap.) Occupational Plenitude therefore guarantees not only an abundance of coincident objects, but an abundance of non-coincident objects as well – it doesn’t just add material objects to our ontology “wherever we’ve already got some”. Once again, this is no count against Occupational Plenitude (or against any other superabundant plenitude principle). At the end of the day, we will want simple, powerful theories that describe as much of the material world as possible. However, since my goal here is to better understand a particular family of permissivist views, it will be useful to be as clear as possible in advance about the contours of the target idea. This will be especially important in Chapter 4, when we turn to the motivations for plenitude: as we’ll see there, despite the structural similarities between the arguments, we needn’t assume that our grounds for endorsing mereological universalism will be the 8 Fairchild Chapter 1. Introduction same as our grounds for going plenitudinous. Thus, we do better not to prematurely conflate the ideas. 2.2 Coincident Abundance You might (like I do) find it implausible to think that Statue is a ‘precise’ object: surely, for some bits of matter, its indeterminate whether Statue has those bits as parts. But surely also there is something in the vicinity of matter that is ‘precise’ in this sense; something that has all of Statue’s matter determinately. If that is right, in the same way that we should be pluralists about the instantiation of modal profiles, we should be pluralists about ‘determinacy profiles’: there are at least two instantiated in the vicinity of Statue. On reasoning from arbitrariness considerations that seem initially perfectly parallel to those that support plenitude, we should endorse something like fuzzy plenitude: ‘there is an object corresponding to every consistent determinacy profile. ’ Without amendment, the versions of plenitude we’ve been considering so far are silent on this kind of abundance. Focus again on Occupational Plenitude: there are loads of modal occupation profiles picking out regions in the vicinity of Statue. The most natural thing to say if we are tempted by this picture is that there is some region that Statue occupies, it is just indeterminate which (given that it is indeterminate for some of Statue’s parts whether they are parts of Statue). Similarly, Statue does have one of these modal occupation profiles – it is just indeterminate which. So, consider Statue’s modal occupation profile – we’ll call it f. Statue has f indeterminately, but we could (by appeal to similar cases) convince ourselves that there could be something that has that very same occupation profile determinately. And by apparent parity of reasoning with earlier cases, it would arbitrary to exclude this kind of “precisely located” object. But again: Occupational Plenitude only entails one thing per modal occupation profile, and so doesn’t guarantee both Statue and its determinate companion. Although we don’t yet have other varieties of plenitude firmly in hand, it should also be clear that any version of modal plenitude without a built-in mechanism for accommodating indeterminacy will face a similar limitation. Which is fine: this is a non-modal dimension of variation between coincidents! The point, once again, is just that this is a separable sort of abundance. The kind of material plenitude we’re interested in has a reputation for unconstrained decadence. This isn’t totally undeserved - plenitude obviously delivers a pretty luxurious ontology. However, it is also helpful to highlight some dimensions of material abundance that plenitude itself doesn’t deliver. My hope is that the observations above will provide some preliminary motivation to look more carefully at permissivism, and support a call for more care and caution in the commitments we attribute to (or claim as) plenitude-lovers. 9 Fairchild Chapter 1. Introduction 3 Moving Forward I said in section one that this dissertation concerns three questions: (1) What is material plenitude?, (2) What is it not? (That is, what are the limits of plenitude?), and (3) Why should we believe it? I won’t here be providing complete answers to any of these questions; however, my hope is that the partial answers I do provide will not only illuminate the target idea, but will provide a springboard for investigation into other more radical varieties of permissivism. Throughout, I am also concerned with ‘unlimited’ ontologies more generally. Like many others, I am tempted by the thought that we should ‘max out’ ontology wherever possible. However, this kind of ‘maximalism’ faces a host of problems – many of which are analogous to those faced by plenitude. Thus, in each chapter, the questions I tackle for plenitude are all meant to point to much more general lessons for permissivism: How do we formulate a principle of abundance that is compatible with our ‘ground floor’ meta- physical commitments? In some cases (for example, universalism) it seems easy – in others (like plenitude) it is far from straightforward, and as I argue in Chapter 2, getting things right requires careful attention to the details. How, in the face of paradox, do we avoid compromising our com- mitment to the non-arbitrariness of existence principles? Simple hylomorphism is a paradigmatic example of a natural ‘maximalist’ picture, but crashes in predictable ways. If my suggestion in Chapter 3 is right, sometimes consistent maximal positions won’t be the most fine-grained or varied pictures of the world, but rather those that allow us to avoid drawing certain sorts of arbitrary dis- tinctions. And, finally: how far does a commitment to non-arbitrariness really get us? The answer in Chapter 4, unsurprisingly, is that it will depend on the details: we cannot avoid doing difficult metaphysics by running to the jungle. 10 2 The Barest Flutter of the Smallest Leaf: Understanding Material Plenitude The barest flutter of the smallest leaf creates and destroys infinitely many things, and ordinary reality suffers a sort of ‘explosion’ . (Sosa, 1999, 133) We start small: although the ring on my finger coincides with the quantity of metal that makes it up, the metal can survive things that my ring cannot. Unlike my ring, the quantity of metal can survive being recast into a coin, an earring, or a part of a computer chip. The ring, on the other hand, can survive having portions removed for resizing, while the very same quantity of metal cannot. These differences – in what changes the ring and hunk of metal can survive – are differences in their modal properties. The ring has its shape essentially (it must have that shape if it exists at all), while the quantity of metal has that shape only accidentally (it still might have existed with a different shape). 1 This is one of many familiar examples that motivate pluralism about material constitution: the view that there might be distinct coincident things that differ in their modal properties. I, like other pluralists, think that wherever my ring is, there are at least two material objects. Pluralism is among the most popular responses to the paradoxes of material constitution, but may not be as innocent as it seems at first. Having distinguished the ring from the metal, it seems to many that we lack principled grounds for not recognizing further distinctions between coincidents. The resulting picture is radical: the material world is in some sense full to the brim with coincident objects. 2 According to defenders of material plenitude, in addition to the ring and the metal there is something that would be destroyed if this engraving were to wear off completely, something else that couldn’t have been given to me by anyone but you, and something further that could survive being re-cast into an earring but not into a coin. (Perhaps: a signet ring, a friendship token, a piece 1 I am using these terms stipulatively as shorthand for certain familiar modal notions: x hasF essentially iff necessarily, ifx exists,Fx. Similarly,x hasF accidentally iffFx, but possiblyx exists and is notF . See Fine (1994) for reasons to think that these modal notions don’t capture everything we might want to capture about the metaphysics of essence and accident. 2 A note about coincidence: for reasons that will become clear in Section 2, I hope to remain neutral throughout on how exactly to define ‘coincidence’, and in particular, on whether by ‘coincidence’ we mean mere spatial coincidence (sharing of location) or material coincidence (sharing of some or all material parts). Although coincidence is central to the views I’ll be discussing, the issues I raise will arise in some form whichever notion we invoke. 11 Fairchild Chapter 2. Understanding Material Plenitude of heirloom jewelry.) 3 For any change at all, the thought goes, there are coincidents that differ with respect to whether they survive it. Sosa’s fluttering leaf destroys multitudes. My aim in this paper is to develop and defend a novel formulation of material plenitude. As I’ll argue, it turns out to be extraordinarily tricky to pin down a coherent statement of the view. Straightforward attempts to do so are either inconsistent or fail to adequately capture the target idea. Making progress requires us to engage in more delicate metaphysics than we might have expected, and along the way reveals substantive constraints on the material world. Even armed with only the rough gloss of plenitude I’ve given so far, it is clear that the picture is ontologically decadent to an extreme. However, its proponents argue that this decadence is justified (even inevitable!) when we take seriously worries about arbitrariness and anthropocentrism in our metaphysical theorising. Why think that there is something coincident with the quantity of metal on my finger that can’t survive change of shape, but deny that there is something further that can’t survive change of location? The cases seem (at least to the plenitude-lover) to be metaphysically on a par, and differ only in that we ordinarily recognize objects of the first sort but not the second. But it seems that after we’ve bought seriously into pluralism, we should be suspicious of those who, as Yablo (1987) puts it, “insist on the credentials of the things we recognize against those which others do, or might” . 4 The force of anti-arbitrariness considerations has compelled many philosophers to endorse plen- itude, despite its radicalism. Plenitude has been defended in some form by, among others, Yablo (1987), Sosa (1999, 178), Fine (1999), Hawthorne (2006), Leslie (2011), Inman (2014), Jago (2016), and Kurtsal (ms). 5 Even opponents of plenitude have engaged with it as a serious contender in debates about material object metaphysics. (See, for example, Bennett (2004) and Korman (2015).) Plenitude not only promises to deliver a response to the paradoxes of material constitution that avoids intolerable arbitrariness, but has also been put to work in other ways: Bennett (2004) argues that pluralists must endorse plenitude not just to avoid arbitrariness, but to have an adequate answer to the grounding problem. Leslie (2011) argues that material plenitude allows us to dissolve a family of ‘paradoxes of essentialism’ involving ‘tolerant’ essences. Dasgupta (2016a) proposes a solution to Parfit’s Non-Identity problem in ethics that relies crucially on material plenitude. Sider (forthcoming) suggests that plenitude might provide the right framework for theorizing about Hasslangarian social structures. But despite its importance, plenitude isn’t well understood beyond its slogan form. The target idea implicit in much of the discussion is something very much like the picture Dasgupta (2016a) 3 Nothing hangs on these suggestions. Strangeness is no barrier to existence on the plenitude lover’s picture (eg. there is also something coincident with my ring which cannot survive my computer updating its operating system), but it is still worth noting that the modal properties of familiar objects are sometimes stranger than we recognize. 4 Yablo (1987, 307). This kind of argument from arbitrariness for permissive ontologies is extremely pervasive. See, for example, Sosa (1987, 178), Sosa (1999, 178), van Inwagen (1990, 126), Sider (2001, 156), and Hawthorne (2006, esp. 109), van Cleve (2008), as well as Thomasson (2015, 214-215) discussing Bricker (forthcoming). For resistance to this line of argument, see Korman (2015, Ch. 8) and Fairchild and Hawthorne (forthcoming) for further discussion. 5 The more radically permissivist views developed in Thomasson (2015) and Eklund (2008) will also yield something like the kind of material plenitude I discuss here, although the motivations in each case are somewhat different. 12 Fairchild Chapter 2. Understanding Material Plenitude calls ‘unlimited essentialism’: “On this view, there is a dazzlingly large number of distinct entities coincident with Statue, one for each subset of its non-modal properties! There is an entity that is essentially in my office, which is destroyed when I take it elsewhere; an entity with its value essentially, which is destroyed when its value rises; an entity with its position relative to Saggitarius essentially, which is destroyed as we rotate around the sun; and so on. ” 6 The thought looks deceptively simple, but it is harder to pin down a precise formulation of plenitude based on this target idea than we might expect. For example, one thesis in the neighborhood of the passage above is: Exact Essence. For any subset of o’s nonmodal properties, there is something coinci- dent with o that has exactly those properties essentially. But Exact Essence has easy counterexamples. For example, the statue Statue has the non-modal property being statue-shaped. But nothing has that as its only essential property. Anything that is essentially statue-shaped is also essentially statue-shaped or green. (Recall that essential properties, in the sense I intend, are closed under entailment.) Likewise, any object x has the property being identical to x essentially. Still, we also want to distinguish plenitude from another important idea: Just the Essentials. For any subset of o’s nonmodal properties, there is something coincident with o that has those properties essentially. Just The Essentials, unlike Exact Essence, merely requires that every subset of o’s nonmodal prop- erties is had essentially by something coincident with it. But that is a low ontological bar! Suppose there could be a world where every object is a ‘modal minimum’ – an object that has all of its (non-modal) properties essentially. Such a world satisfies Just The Essentials, but is a far cry from a modally plenitudinous world. So (albeit for different reasons) Just the Essentials also misses the mark as an attempt to capture the target idea behind plenitude. We can make things a little more precise by introducing the ideology of ‘modal profiles’ . Very roughly, an object’s modal profile specifies the changes it can and cannot survive. We’ll say that a modal profile M based on a set of properties S is a partition of S into two subsets E and A. An object has M if it has every property in E essentially and every property in A accidentally. 7 Dasgupta’s target in the passage above, then, is something like: Non-Modal Plenitude. For any material object o and any modal profile M based on 6 Dasgupta (2016a, 2). 7 This conception of modal profiles broadly follows the strategy in Yablo (1987) and Bennett (2004). Hawthorne (2006) offers another way of understanding modal profiles: as partial functions from worlds to filled regions of space- time. It is an interesting further question how these two conceptions of modal profiles (and the resulting varieties of plenitude) might come apart. 13 Fairchild Chapter 2. Understanding Material Plenitude all of o’s nonmodal properties, there is something coincident with o that has M. Non-Modal Plenitude seems initially to capture a lot of what we wanted from the target idea. However, challenges remain. I think these challenges are most helpfully presented as two problems, though as we’ll see they are very tightly connected. The first is: on pain of incoherence, any adequate formulation of plenitude will require some restriction to keep troublesome properties – the “bad eggs” – out of the ‘bases’ of modal profiles. That is; there must be some restriction on the membership of the set S of properties partitioned by M. Non-Modal Plenitude, for example, restricts the bases of modal profiles to non-modal properties, thereby avoiding the result that (for example) there is something coincident with my ring that is accidentally essentially shaped like so. 8 However, in Section 1 I show that this restriction fails, and consider a more refined proposal drawn from Bennett (2004). I argue that this too runs into trouble, and propose a very different sort of strategy. I’ll call this challenge the bad eggs problem. However, we face a further challenge even after we’ve answered the bad eggs problem. The formulation of Non-Modal Plenitude above requires that there be an object corresponding to every partition of the properties in S (whatever they are). But there are some partitions of apparently innocent properties that yield impossible modal profiles; for example, nothing has being red as an essential property and being colored as an accidental property. Partitions like this correspond to modal profiles that are in some sense ‘inconsistent’; the instantiation of these profiles is ruled out already on general metaphysical grounds. So, any adequate formulation of plenitude will have to solve the consistency problem by identifying a minimal restriction to consistent modal profiles. 9 Both problems have been acknowledged in some form by many philosophers writing on plenitude. For example, Yablo (1987) discusses a version of the bad eggs problem at length, and Bennett (2004) presses something like the consistency problem as the final outstanding worry for plenitudinous pluralism. 10 Both also acknowledge the stakes of giving a satisfying response: for plenitude to retain any of its initial appeal, the resulting constraints on modal profiles will have to be more minimal than the restrictions imposed by more conservative metaphysicians. 11 Although these challenges have been recognized in the literature, my first aim in this paper is to suggest that we have nonetheless failed to appreciate the depth and consequences of the obstacles facing any attempt to formulate a viable version of plenitude. In Section 1 and Section 2, I develop the bad eggs problem, and argue that the strategy of characterizing the bases of modal profiles by appeal to taxonomical distinctions between properties (for example, the modal/non-modal distinc- tion) won’t work. I then propose a solution which relies on a purely structural observation about 8 Given that metaphysical possibility is transitive, if something is essentially F, it is essentially essentially F. 9 Note that I am here using ‘consistency’ in a non-standard way. Some of the problematic profiles are not logically inconsistent but rather in some sense metaphysically inconsistent. 10 See, for example, Yablo (1987, 296-300) and Bennett (2004, 357). 11 For example, Bennett contrasts the plenitudinous bazillion-thinger, who thinks that there are very many consistent modal profiles, with the so-called plenitudinous two-thinger, who claims to accept the letter of plenitude but holds that there are very few possible modal profiles (eg. the ones corresponding to the objects we ordinarily recognize). Part of the challenge of the consistency problem as I understand it is ruling out views like plenitudinous two- thinger-ism. 14 Fairchild Chapter 2. Understanding Material Plenitude modal profiles. In Section 3, I argue that the consistency problem runs deeper than standard pre- sentations suggest, and raise trouble for what I take to be the most promising version of plenitude suggested by existing literature. Finally, in Section 4, I turn to my second aim; to develop and defend a version of plenitude capable of addressing both challenges. As I argue there and further in Section 5, these considerations lead us to the view I call global plenitude. The idea behind plenitude suggests that the resulting picture of the material world will be radically full but ultimately straightforward – there seems to be little subtlety in an overflowing ontology. However, it is my third and ultimate goal in this paper to show that global plenitude carries with it a rich and complex picture of the material world – far richer than anyone seems to have expected. For this reason, many of the proposed applications of plenitude may require a more delicate touch than we thought. Many of the arguments I consider here also show that we have to be extremely careful what other principles of abundance we associate with plenitude – I return to this in Section 6. Moreover, since we are led to global plenitude by attempts to give minimal responses to very general problems for plenitude, this discussion reveals not only an attractive formulation of the target idea, but also substantive constraints on any adequate formulation of plenitude. 1 Bad Eggs Central to the plenitudinous picture is the idea that many of an object’s properties are had essentially by something coincident with it. For example, for nearly every change, there is something hereabouts that cannot survive it: something coincident with me is essentially sitting, and destroyed when I stand, something is essentially typing, and destroyed when I pause. Plenitude similarly purports to guarantee that nearly every change is also survived by some of my coincidents. Very many of my properties are had accidentally by something coincident with me: something here is only accidentally living, and survives my last breath, something else is has its origins accidentally, and might have had different parents than me. But this can’t go for all properties: certain properties can’t be had essentially and others can’t be had accidentally, even by the permissive lights of the plenitude lover. For example, consider modal properties like being essentially statue-shaped and accidentally wearing a scarf. Nothing can be accidentally essentially statue-shaped, and nothing can be essen- tially accidentally scarfed. On the first, as observed above, given that metaphysical possibility is transitive, no thing has any of its essential properties merely accidentally. The argument for the second observation is more subtle, but notice that for o to essentially be accidentally F would be for o to be accidentally F wherever it exists. Since being accidentally F entails being F , o should therefore beF wherever it exists. But being accidentally F also entails possibly existing while failing to be F . So o must be possibly not F and not possibly not F – a contradiction. 12 These properties seem to cause trouble for plenitude because coincidents can’t freely vary with respect to their modal status. By way of illustration, compare an obviously false formulation of 12 See Spencer (2017) for an argument modeled on Fitch’s Paradox of Knowability that generalizes this last kind of case. Notice that other properties cause very similar problems: being actually seated, possibly redheaded, etc. 15 Fairchild Chapter 2. Understanding Material Plenitude plenitude that invokes no property restriction at all: Naive Plenitude. For any material object o and any modal profile M based on all of o’s properties, there is something coincident with o that has M. Naive Plenitude entails that for any property whatsoever, coincidents can vary with respect to its modal status. That is, for any property F of o, there is something coincident with o that has F accidentally, and something coincident with o that hasF essentially. But, as the cases above reveal, this is incoherent for modal properties like being essentially F and being accidentally G. Non-Modal Plenitude does better than Naive Plenitude on this count, by restricting the properties in the bases of modal profiles to only the non-modal properties. Unfortunately for Non-Modal Plenitude, some ‘bad eggs’ aren’t obviously modal properties, and so aren’t uncontentiously ruled out by this restriction. Consider identity properties like being Statue. This isn’t a paradigmatic modal property (at least on a superficial gloss of what it is for a property to be modal) 13 , but if it is allowed into a modal profile based on Statue, Non-Modal Plenitude is straightforwardly false. Nothing with the property being Statue differs modally from Statue in any way. Similarly, properties like being human aren’t clearly modal properties, but nonetheless have modal import. For example, being human might require being essentially human. If that’s right, nothing can be accidentally human, since (as before) nothing can be accidentally essentially human. And so, just like with modal properties, we can’t consistently suppose that coincidents freely vary with respect to the modal status of these properties. 14 In the following section, I consider a more refined proposal drawn from a suggestion in Bennett (2004). This proposal expands the class of restricted properties to so-called ‘sortalish’ properties, thus excluding kind and sortal properties as well as properties that depend on modal, kind, and sortal properties. Ultimately, I argue that this distinction fails to avoid a further family of counterexamples, and suggest that this should make us pessimistic about the general strategy behind both responses to the bad eggs problem. In Section 2, I turn to a different approach: rather than identifying the bad eggs by relying on a metaphysically contentious taxonomy of properties, we might instead appeal to a purely structural observation about the role the ‘good eggs’ play in the target idea. 1.1 Another taxonomical strategy: Sortalish Properties Recent appeals to non-modal plenitude trace back to a version of plenitude proposed by Karen Ben- nett in “Spatiotemporal Coincidence and the Grounding Problem” . There, she invokes a restriction to what she calls ‘non-sortalish’ properties: 13 One related difficulty with this response to the bad eggs problem is that it requires a conception of properties as more fine-grained than functions from worlds to sets of individuals. On the coarse-grained picture, there is no helpful distinction between ‘modal’ and ‘non-modal’ properties. 14 The staunch defender of Non-Modal Plenitude may insist that the characterization of modal properties implicit here is too narrow minded, and that we should think of anything with a modal entailment as a modal property. On that picture, identity properties and kind properties are genuinely modal. The worries I raise for Bennett’s non-sortalish proposal below apply to this suggestion as well. 16 Fairchild Chapter 2. Understanding Material Plenitude “The story is really very simple. It is this: every region of spacetime that contains an object at all contains a distinct object for every possible way of distributing ‘essential’ and ‘accidental’ over the non-sortalish properties actually instantiated there. ” 15 The restriction to ‘non-sortalish’ properties excludes “(i) persistence conditions, particularly modal properties like being essentially shaped about like so, (ii) kind or sortal properties, and (iii) properties that things have partially in virtue of their instantiation of properties in categories (i) or (ii). ” 16 Bennett herself notes that this is only intended as a rough gloss of what it is for a property to be ‘sortalish’, and her initial aim in introducing the term is importantly different than the use we’ll now put it to. 17 Still, it will be informative for us to first consider the proposal at face value. Restricting the bases of modal profiles to include only non-sortalish properties seems to improve in many ways on Non-Modal Plenitude. For example, Bennett-style plenitude accommodates the worries above about properties like being human, which is plausibly a kind or sortal property. But other problem cases are harder to pin down: consider as a warm-up the property being Madeline and wearing a yellow hat. This is neither a modal nor a sortal property, so it might be initially tempting to say that there is something coincident with Madeline that has the property being Madeline and wearing a yellow hat essentially. But since Madeline can survive removal of her hat, nothing essentially hat-wearing can be identical to her, and so nothing can have that modal profile. One response is, of course, that the property being Madeline and wearing a yellow hat partly depends on Madeline’s possession of certain modal or sortal properties, and so counts as ‘sortalish’ by Bennett’s third condition. But what seems to be doing the work in this case is not the modal import of the property (as with the cases above). Rather, it is that the property can’t be had at all by anything distinct from Madeline. This problem seems to be much more general. For example, consider a property like being God’s favorite thing. This isn’t an identity property, but nonetheless, only one thing can be God’s favorite, and so there cannot be coincident objects that differ with respect to whether they have that property essentially or accidentally. (Since there cannot be distinct things that have it at all.) 18 Something similar goes for many other properties: for example, being one of Maria’s fifteen favorite things. On the face of it, this is a non-sortalish property. Suppose that Fido is one of Maria’s fifteen favorite things. Any modal profile based on Fido’s non-sortalish properties would require the object with that profile to have the property being one of Maria’s fifteen favorite things, and so a non-sortalish version of plenitude threatens to deliver the unacceptable result that (many) more than fifteen things share the property being one of Maria’s fifteen favorite things. Call any property like this a ‘capped’ property. 15 Bennett (2004, 354) 16 Bennett (2004, 341) 17 Bennett’s reason for introducing the ‘sortalish’/‘non-sortalish’ distinction was to characterize the grounding problem more precisely, capturing the observation that the grounding problem concerns all of the alleged differences between coincident objects, not just the modal differences. Though this is closely related to the bad eggs problem in ways that will become clear in the next section, it is important to note that Bennett isn’t explicitly taking on the same question we’re now concerned with. 18 Perhaps also God’s favor doesn’t depend on any modal or sortal properties of the object. 17 Fairchild Chapter 2. Understanding Material Plenitude ‘Capped’ properties reveal that the bad eggs challenge for plenitude isn’t just about determining which properties can consistently be had either essentially or accidentally. In principle, capped properties can vary in this respect: perhaps one of Maria’s favorite things is essentially so, while another could live on among the less favored. Capped properties constrain the modal profiles of objects that have them in a different way: if something is one of Maria’s fifteen favorite things, it must have one of fifteen modal profiles. Of course, it is always open to the devoted defender of the non-sortalish strategy to argue that any such property is in fact implicitly modal, or sortal, or depends in some way on modal and sortal properties. I am pessimistic that this will be successful for a class of problem cases as heterogeneous as this. More worryingly, it seems largely orthogonal to making progress on understanding material plenitude. Surely, the intelligibility of plenitude doesn’t hinge on having the distinction between non-sortalish and sortalish properties precisely in hand. Where does this leave us? We need a characterization of the properties to be excluded from the bases of modal profiles that is informative enough to make progress understanding the target view. We might proceed as we have so far - searching for the right taxonomical line in fits and starts - but this doesn’t strike me as especially promising. Thankfully, we can make significant progress without giving a precise explication of which properties are the ‘bad eggs’ . Instead, we can work with a purely structural observation about the target idea. Having done so, we’ll see why we should be pessimistic about identifying all of the troublesome properties before we have a better handle on other features of plenitude. 2 A structural solution : Neutral Properties The taxonomical strategy, though tempting, faces serious challenges. The problems we’ve encoun- tered so far should at least make us pessimistic about the prospects of identifying some independent similarity all of the troublesome properties share. Instead, we might try a different sort of approach entirely. Rather than relying on an antecedent characterization of the bad eggs, we can pick out the good eggs by appeal to the structural role they’re meant to play in plenitude. Return briefly to the initial picture. Plenitude is motivated in part by the broad-strokes obser- vation that coincident objects share their circumstances, but differ with respect to whether they can survive changes to those circumstances. 19 The statue and the clay have the same shape, but differ with respect to whether they have it essentially. The ring and the hunk of metal are made up of the same matter, but differ with respect to whether they are made up of that very matter essentially. We captured this idea at the outset with a bit of technical terminology, describing coincidents as instantiating different ‘modal profiles’ that are ‘based on’ a set of shared properties. With this in mind, we can capitalize on a purely structural observation about the role of the ‘good eggs’ in our formulation of plenitude: they’re properties that are shared by coincident objects. 19 Or, more carefully: they differ with respect to whether they could exist under other circumstances. 18 Fairchild Chapter 2. Understanding Material Plenitude Many of the troublesome properties we identified in previous sections were troublesome precisely because we couldn’t coherently suppose that an abundance of coincident objects shared them. 20 Let us then focus on exactly the properties that are completely neutral with respect to coinci- dence: A property F is neutral iff necessarily, for all x and y, if x and y coincide, Fx iff Fy. If we help ourselves to some uncontroversial facts about coincidence, we can already begin to see how this will help. On any plausible definition of coincidence, coincident objects must share their shape and location properties, but clearly won’t share identity or capped properties. More contentiously, by the plenitude-lover’s lights, many modal and ‘sortal’ properties won’t be shared by coincident objects: being human, being essentially shaped like so, being accidentally located at r won’t be neutral. 21 Much more needs to be said here (especially on the last point) but it will helpful to have the corresponding proposal in hand first. Here is the most straightforward formulation of plenitude in light of the current suggestion: Simple Plenitude. Necessarily, given any material object o and any modal profile M based on all ofo’s neutral properties, there is something coincident with o which hasM. Unlike the proposals we’ve considered thus far, Simple Plenitude doesn’t require a tendentious taxonomy of properties into modal and non-modal, sortal and non-sortal, etc. 22 But it may still look somewhat suspicious. After all; plenitude is a thesis about what coincident objects there are – doesn’t the appeal to neutrality threaten circularity? Insofar as our goal is to articulate and understand a coherent formulation of plenitude, I think any apparent circularity here is harmless. Although exactly which properties are neutral will turn in part on facts not built in to the structural definition above, the consequences we uncover using only the structural characterization will hold for any candidate theory of coincidence we might adopt in the background, and thus will constrain any adequate formulation of plenitude. To make sense of the content of plenitude, we don’t (yet) need an independent characterization of neutrality. Thus, we can understand Simple Plenitude (and the revisions to follow) as a kind of schematic principle, highly sensitive to the details of the background metaphysics, but informative enough to trace out the contours of the target idea. 23 20 In some sense, this is exactly how Bennett’s appeal to non-sortalish properties was meant to function in the context of her discussion of the grounding problem: to pick out the properties shared by coincidents. Happily for our purposes we can jettison the elusive distinctions and work only with the structural characterization. 21 Something roughly like this strategy emerges in Yablo (1987, 306-308). However, Yablo puts the idea to a very different use. He argues that categorical properties (given a certain version of plenitude) are exactly the neutral properties, and aims to show that these in turn just are what he calls the cumulative properties. Cumulative properties are properties that can “build up the essences in which they figure”, unlike restrictive properties – such as identity and kind properties – that “ exercise an inhibiting effect on certain of [their] colleagues.” (299) This argument, as well as the picture that Yablo ultimately proposes, requires that neutral properties be in some sense modally independent. While I take one of his core observations on board – that neutrality is the idea we need to fix on plenitude – the further independence requirement packs in implausibly strong commitments about coincidence. 22 And thus, doesn’t rest on a hyperintensional conception of properties. 23 Notice that my proposed solution is not alone in relying on the details of the background metaphysics; all of the 19 Fairchild Chapter 2. Understanding Material Plenitude The structural definition is far from empty, as we’ll see in what follows. It is already enough, for example, to distinguish plenitude from opposing metaphysical pictures. Given only that coincidence entails co-location, anything coincident with my car shares the property of being inside of a garage. The conservative ontologist will accept that much, but deny the corresponding consequence of Simple Plenitude: that there is something coincident with the car that (for example) is essentially inside of a garage. Still, we do need some assurance that neutrality is enough to solve the problem at hand. I’ve already pointed out that identity properties and capped properties more generally won’t turn out to be neutral; but what about the trouble caused by broadly modal properties? Some cases look straightforward: since being located at r is neutral, Simple Plenitude seems to guarantee that acci- dentally being located at r is not. (Suppose that I am located at r. Given Simple Plenitude, there is something coincident with me that is essentially located at r and something coincident with me that is only accidentally located at r). So, Simple Plenitude won’t then require there to be something essentially accidentally located at r. Similarly, being essentially shaped like so won’t be neutral, and so Simple Plenitude avoids the incoherent result that there is something accidentally essentially shaped like so. So far, so good. But the plenitude-lover should still be able to allow for neutral properties that are had essentially if they are had at all. For example, it seems that plenitude is in principle compatible with the following metaphysical thesis: Location. Necessarily, if something is located, then it is essentially located. 24 Having a location is clearly a neutral property, if coincidence entails co-location. Thus by Location, being essentially located is also neutral. So, given Simple Plenitude, there is something that is accidentally essentially located. 25 More worryingly, consider the following logical truth: Self-Identity. Necessarily, everything is self-identical. Thus, being self-identical is (trivially) a neutral property. Given Simple Plenitude, we’re led to the absurd conclusion: there is something that is accidentally self-identical. (And, for that matter, something that is accidentally essentially self-identical.) Should we conclude from these arguments that we were wrongly optimistic about neutrality? strategies considered so far would have required us to answer further substantive metaphysical questions before producing a list of the putative ‘good’ eggs. 24 Although I think that the target idea is in principle compatible with theses like Location, and thus that a formulation incompatible with Location has overstepped, I also think that some of the most interesting versions of plenitude will deny this particular thesis. 25 There are many examples like this, though some are more contentious than others. Consider, for example, Materiality. Necessarily, if something is a material object, then it is essentially a material object. If everything coincident with a material object is a material object (and so being a material object is neutral), we get the same problem. 20 Fairchild Chapter 2. Understanding Material Plenitude Have some ‘bad eggs’ gotten through our net? I think not. Although these are counterexamples to Simple Plenitude, I want to argue that the lesson is not that neutrality is too permissive for our purposes – we needn’t find some more restrictive characterization of the properties that form the bases of modal profiles. Rather, we’ll make more progress if we understand the problem as lying elsewhere. We’ve assumed in formulating Simple Plenitude and its predecessors that plenitude entitles us to say that for any property in the base of a modal profile, there are coincidents which vary with respect to whether they have that property essentially or accidentally. This has led us to run together the ‘bad eggs’ question (how should we characterize the property base of a modal profile?) with another question: which properties are such that coincidents can differ with respect to their modal status? The answer to that question rests on a solution to the second of the challenges facing the plenitude-lover: the consistency problem. In what follows, I’ll take for granted the appeal to neutrality as a working hypothesis in answer to the bad eggs problem, and show how any residual troubles can be addressed by an adequate solution to the consistency problem. My aim in the next two sections is to provide such a solution. 3 The consistency problem for plenitude Bennett (2004) considers the following sort of case, which turns out to be a counterexample to Simple Plenitude: by Simple Plenitude, there is something coincident with the blue coffee mug on my desk which is essentially blue and only accidentally colored. 26 But such a thing would have to possibly be blue and not colored. Since that is metaphysically impossible – nothing can be blue without being colored – Simple Plenitude is false. 27 Cases like this are easy to come by. Any neutral determinable and one of its determinants will generate this sort of difficulty for Simple Plenitude, but so too will pairs of properties like being colored and being spatially extended, or being located in r and being located in a subregion of r. Similarly, Simple Plenitude doesn’t rule out modal profiles according to which being blue and being round are both had essentially, but being blue and round is had only accidentally. The problem is simply that many neutral properties necessarily entail other neutral properties, and nothing can have a property essentially while possibly lacking some property entailed by it. The sense of entailment here is just standard property entailment: A property F entails G iff necessarily, for all x, if Fx then Gx. We can generalize this to say when a set of properties jointly entails a property: 26 In fact, many such somethings – many modal profiles based on the neutral properties there will require this pattern of modal properties. 27 Bennett’s target isn’t Simple Plenitude, but instead a view she calls ‘wild bazillion-thingism’ . The challenge, says Bennett, is not just to solve this consistency problem, but to do so without winding up with a more ‘chaste’ view than hoped. Similar arguments appear in Yablo (1987), and have been echoed in Leslie (2011), Dasgupta (2016a), and Jago (2016). Although the problem has received a lot of attention, it is hard to find explicit proposals for how to address it. 21 Fairchild Chapter 2. Understanding Material Plenitude A setF of properties entails G iff necessarily, for any x, if x has every property inF, then Gx. We can define a very natural property of modal profiles in terms of property entailment. Recall that a modal profile M based on a set S of properties is a partition of S into subsets E and A. Here is a first pass: A modal profileM based on a setS of properties isclosed ∗ iff for any subset of properties F of S and any G in S, ifF entails G, then if every property inF is in E, G is in E. In other words, if some properties, the F s, are had essentially according to M, then any property jointly entailed by theF s is also had essentially according toM. The troublesome profiles described above fail this closure condition. But if we restrict our attention to closed* modal profiles, we avoid them. However, this condition won’t yet suffice to handle the problem posed by neutral properties had essentially if at all. So far, closure ∗ only guarantees that if the property being self-identical is inE, then the property being essentially self-identical will be inE. Nothing yet captures the requirement that being self-identical must be in E. So, we should supplement closure* with a further condition: A modal profile M based on a set S of properties is closed iff (i) for any subset of propertiesF of S and any G in S, ifF entails G, then if every property inF is in E, G is in E and (ii) if F entails being essentially F , F is in E. Closure accommodates the further observation that when having some neutral property entails having that property essentially, no consistent modal profile can partition that property into A. Thus, the following looks promising: Merely Modal Plenitude. Necessarily, given any material object o and any closed modal profile M based on all of o’s neutral properties, there is something coincident with o which has M. 3.1 Problems for Merely Modal Plenitude Merely Modal Plenitude is promising, but – like many promising things – is false. Closure un- der property entailment isn’t a stringent enough constraint to guarantee the consistency of modal profiles. There are two problems: first, closure doesn’t guarantee what we should think of as ‘meta- physical consistency’ . That is, some closed modal profiles aren’t possibly instantiated by anything. But also: metaphysical consistency doesn’t even guarantee what I want to call ‘local instantiability’ . Roughly what this means is that the fact that a modal profile m based on some object o is possibly instantiated is no guarantee that it can be instantiated by something actually coincident with that object – even by the plenitude-lovers lights! 22 Fairchild Chapter 2. Understanding Material Plenitude In this section, I introduce a family of counterexamples to Merely Modal Plenitude that turn on these challenges. The lesson, I argue, is that consistency of modal profiles is not a merely combinatorial matter - it depends on coordination between how things stand at the actual world and how they might have been. Finally, in Section 4, I argue that we can solve both problems by replacing closure with a stronger condition. Very roughly, the new condition I’ll propose (non-local closure) looks not just at which patterns of properties are possible, but at how those patterns are spread through modal space. Here’s a first pass at an objection to Merely Modal Plenitude: recall that being blue is among the neutral properties of my blue coffee mug. So too is the property being such that p, where p is some proposition true at exactly this world. And of course, being such that p doesn’t entail being blue – you and me and my green coffee mugs witness that. So, there is a closed modal profile M according to which being such that p is had essentially, and being blue is had accidentally. Although it is closed, nothing can have that modal profile: M requires its bearer to be blue and such that p, and to possibly fail to be blue while still being such that p. But by stipulation were the world to be otherwise in any way (eg. if something actually blue weren’t blue) p would be false, and nothing would be such that p. So, contra Merely Modal Plenitude, there can’t be anything coincident with my blue coffee mug that has modal profile M. It is tempting to dismiss this case because of quibbles about the properties involved. Although I argued above that the restriction to neutral properties captured our target idea, you might think that cases like this reveal that we might not have discriminated carefully enough. Properties like being such that q are trivially shared by coincidents in q-worlds. Perhaps we had something in mind that was more hyperintensional; for example, properties that are shared by coincidents in virtue of coinciding, or in virtue of occupying some region. 28 I’m inclined to think the target idea behind plenitude doesn’t rest on anything so fine-grained, but if my objection can be avoided by moving to a more discerning characterization of neutrality, perhaps I’ve overstepped. 29 However, the same counterexample can be re-run another way: Flimsy. On my kitchen table near the fruit bowl, there is Flimsy. Flimsy is a ‘modal minimum’ – an object that has all of its properties essentially. (Remember, the plenitude- lover should think there are many things like Flimsy, one coincident with every material object.) In the fruitbowl near Flimsy, there is something red – say, an apple. Once again: being near Flimsy and being red are both neutral properties of the apple, even in the more refined sense suggested above. And again, being near Flimsy doesn’t entail being red – there are bananas, oranges, and pears in my fruit bowl, too. By Merely Modal Plenitude, there is something coincident with the apple which is essentially near Flimsy and accidentally red. But there can’t be any such thing – had anything been otherwise (eg. had anything red failed to be red) there wouldn’t have been Flimsy. 28 See Jago (2016) on region-focused properties. 29 Thanks to Mark Jago for discussion of this point. 23 Fairchild Chapter 2. Understanding Material Plenitude The amended Flimsy case avoids the worry about triviality, but shares something important in common with the first pass case. Both rely on a property instantiated at exactly one world: in the first, being such that p, and in the second, being near Flimsy. But in fact the structure of the problem doesn’t require even that. Consider another counterexample to Merely Modal Plenitude: Whimsy. Suppose that on my kitchen table there is also Whimsy. Whimsy is isn’t as fragile as Flimsy; it can survive some things being otherwise. Whimsy, suppose, actually has a blue half (B) and a green half (G), but had anything been otherwise, Whimsy would have been entirely green. Consider Whimsy’s green half, G. By Merely Modal Plenitude, there is something coincident with G which essentially spatially overlaps Whimsy and is accidentally green. (This is because overlapping Whimsy doesn’t entail being green; witness B.) Nothing coincident with G can essentially overlap Whimsy and be accidentally green. That would require it to possibly overlap Whimsy while being non-green, but had anything been otherwise, anything overlapping Whimsy would be green. Postpone for a moment the hard question of why we should think anything like Whimsy is possible. If there could be, then we have a new sort of counterexample that doesn’t rely on perfect modal fragility. What’s more, in this case, the relevant modal profile is metaphysically possible - but still not, in some sense, instantiable here. The condition that a modal profile be closed ensures that whenever a propertyF is had essentially according toM andG is had accidentally according toM, it is possible that something beF without being G. As we saw in above, this is exactly what we need the kinds of counterexamples standardly associated with this problem. But in all of my cases, the troublesome profiles are closed – it is possible for something to be such that p without being blue, to be near Flimsy without being red, to be near Whimsy without being red, and so on. The recipe for a case like this is very general: Let F and G both be neutral properties of o at w. Suppose that F and G have the following modal patterns of instantiation: at every world w 0 distinct from w, every F is G. However, at w, there are some F s that are not G. Now let M be an closed modal profile based on o’s neutral properties such that F is in E and G is inA. 30 By Merely Modal Plenitude, there is somethings coincident witho inw that is essentially F and accidentally G. Such an s would have to be F and G in w, but at some w 0 be F and not G. However, by stipulation, at all w 0 distinct from w, every F is a G. So, there can be no such s, contra Merely Modal Plenitude. Notice that this nowhere relies on the supposition that F is instantiated in exactly one world. In cases where F is instantiated at some worlds distinct from w, the modal profile M is still possible: there might be things at those worlds which are essentially F and accidentallyG. In fact, the core of the argument doesn’t even rely on our restriction to ‘neutral’ properties. Any restriction we might plug into Merely Modal Plenitude that allows in properties 30 We can convince ourselves there is such a modal profile M as follows. Let N be an closed modal profile based on o, and now construct M from N by placing F (and everything entailed by F ) in E, and G in A. Since F doesn’t entail G, if N was closed then M is. 24 Fairchild Chapter 2. Understanding Material Plenitude behaving like F and G will be subject to counterexamples of this form. 31 4 Non-local entailment, otherworldly necessity, and global plenitude The need for a consistency condition more discerning than standard property entailment is forced on us by the nature of modal profiles themselves, and in particular, by the conditions of accidentality. Recall that to have a property accidentally is to have it and to possibly lack it – accidental property possession (unlike essential property possession) requires the cooperation of two worlds. So, consider any modal profile based on an object o in a world w such that A is nonempty – any modal profile other than the modal minimum. Any such modal profile will require that, for each property G in A, it is possible for something at a world other than w to have every property in E and lack G. At bottom, the trouble is that entailment closure can only assure us that the required pattern of properties is possible, but what we need instead is assurance that the right pattern of properties is possible elsewhere. 32 In this section I propose a formulation of plenitude that builds on these lessons to address the problems raised above. First, we’ll need some new terminology: A setF of properties non-locally entails G at w iff it is otherworldly necessary that for all x, if x has every property inF, then Gx. Where It is otherworldly necessary that P at w iff at all worlds w 0 distinct from w, P . The corresponding condition on modal profiles is: A modal profile M based on a set S of properties is closed under non-local entailment iff (i) for any subset of properties F of S and any G in S, ifF non-locally entails G, then if every property inF is in E, G is in E and (ii) if F entails being essentially F , F is in E. I want to argue that the lesson of the cases above is that closure under non-local entailment (or ‘non-local closure’) is the right notion of consistency for modal profiles. We should flag one thing, first. Notice that closure under non-local entailment is world-relative 31 Leslie (2011) suggests a constraint on the bases of modal profiles that also builds in a consistency constraint. She requires that the properties be “strongly modally independent, so that each (...) can be possessed either essentially or accidentally without requiring that the other four be possessed essentially, accidentally or even at all, and likewise for any combination of the properties.” The resulting version of plenitude runs into the same problem I’ve raised here: strong modal independence guarantees metaphysical possibility, but not local instantiabiliy. 32 Although Kurtsal (ms) doesn’t commit to a particular conception of modal profiles or a corresponding notion of consistency, her formulation of modally full plenitude suggests that she may instead have in mind something more like sets of properties had either essentially or possibly. The resulting formulation of plenitude will be importantly different from the one I describe here. Although it will also require some notion of consistency for profiles, the challenges will be distinct. 25 Fairchild Chapter 2. Understanding Material Plenitude – a modal profile M may be closed under non-local entailment at one world and not at another. (The modal profile in the Whimsy case has exactly this feature.) But this shouldn’t be surprising – after all, plenitude was never meant to be the view that every metaphysically possible modal profile was instantiated (presumably the modal profile of Pegasus is possible, but it is no part of plenitude that there is something instantiating that modal profile). Rather, plenitude is the idea that every metaphysically possible modal profile that is (in some sense) compatible with the actual matters of fact is instantiated by something. So, on reflection, it should be no surprise that whether a modal profile is consistent in the right sense will depend both on how things are and how they might have been. Incorporating non-local closure into our template delivers the following version of plenitude: Global Plenitude. Necessarily, given any material object o and any non-locally closed modal profile M based on all of o’s neutral properties, there is something coincident with o which has M. Consider again the second counterexample, involving being near Flimsy and being red. Although the modal profile M according to which the latter is had essentially and the former is had accidentally is entailment closed, it isn’t closed under non-local entailment at the actual world w. If we ignore w and look through all of the rest of modal space, we see that trivially everything near Flimsy is red (because elsewhere, nothing is near Flimsy). In the third counterexample, although there are things near Whimsy at other worlds, they are all red – so, being near Whimsy non-locally entails being red. 5 Ground Floor Humility There is also some good circumstantial evidence that we are on the right track with Global Plenitude. In this section I describe what I take to be a desideratum of any adequate version of plenitude, and suggest that Global Plenitude meets it. I’ve argued above that Merely Modal Plenitude is subject to a certain family of counterexam- ples that arise when we suppose that neutral properties are distributed through modal space in a particular way. We can thus say something more general about Merely Modal Plenitude: it lacks a feature I’ll call ground floor humility. Very roughly speaking, a plenitude principle is ground floor humble if it is compatible with any reasonable hypothesis about the distribution of neutral proper- ties through modal space. My aim in this section is to suggest that unlike Merely Modal Plenitude, Global Plenitude is ground floor humble. Both Merely Modal Plenitude and Global Plenitude can be thought of as generative principles. Broadly put, generative principles generate a domain from a ‘ground floor’ . For example, we might think of set-theoretic comprehension principles as generating the universe of sets from a ‘ground floor’ of ur-elements, or of unrestricted mereological composition as generating a domain of composite 26 Fairchild Chapter 2. Understanding Material Plenitude objects from a ground floor of individuals. In our case, the ground floor for both Merely Modal Plenitude and Global Plenitude is given by the distribution of neutral properties across modal space. The arguments in Section 3.1 revealed that there are some hypotheses about the distribution of neutral properties that Merely Modal Plenitude isn’t compatible with – and so it clearly isn’t ground floor humble. (And worse: the hypotheses that Merely Modal Plenitude is incompatible with are hypotheses the plenitude-lover should accept.) But how could we go about showing that a plenitude principle is ground floor humble? One problem is that the idea is hard to even pin down precisely. It is at least intuitively clear what is meant by ground floor humility, but to get more precise, we have to make sense of the notion of “any reasonable hypothesis about the distribution of neutral properties”, and it isn’t obvious how to do so. Here is a sketch of a promising general strategy: we introduce the notion of a ‘ground model’ (which fixes some distribution of neutral properties) and show that any ground model can be ex- panded to a model satisfying Global Plenitude. Thus, if the result holds for a sufficiently permissive conception of ground models, we’ll have shown that Global Plenitude is ground floor humble. In the appendix I develop a version of this proposal in detail, but sketch the idea briefly below. Let a ground model G be a pair M = (W,D) of a set of worlds W and a family of sets of ground individuals D w for each w∈ W . (That is: a ground model is just a standard variable domain Kripke model.) A ground property is a function from worlds to sets of individuals in those worlds. (In the appendix, I use the label S-property instead.) I define a procedure for producing a global expansionM+ of a ground modelM. Very roughly, for every worldw, every ground individual x inw, and every partitionE,A ofx’s ground properties that is non-locally closed at w, we add a new individual y, which coincides with x in w. In the second stage of the construction, we ensure that for every property f inA, the new individualy also exists in a world w 0 where it coincides with a ground individual that has every property in E and lacks f. (Ultimately, this will amount to having added an individual for every non-locally closed modal profile.) Since the procedure assumes nothing about the ground model, we guarantee that every ground model has a global expansion. I show that the neutral properties in the resulting model are exactly the ‘expansions’ of the ground properties. (This is mostly intuitive; in every world, each group of coincidents corresponds to exactly one ground individual, and so the ground properties are exactly those that don’t distinguish between coincidence classes.) Importantly, then, every ground model corresponds to a different distribution of neutral properties through modal space – a different hypothesis about what properties distinguish between coincidents. I then prove the following result: Theorem. Every global expansion of a ground model is a model of global plenitude. These formal results are significant for us in two ways. The first and most important is that it should reassure us that global plenitude can resist the sorts of problems that I’ve levied at its predecessors. For my purposes here, it is enough that we take an instrumental attitude towards the 27 Fairchild Chapter 2. Understanding Material Plenitude result in the appendix: that it is humble in this way is evidence that it won’t be felled by the kind of counterexamples we’ve seen so far. The secondary significance is that, although it is a further (and substantive) project to argue that the formal result I’ve proven guarantees that Global Plenitude has the elusive theoretical property I’ve called ground floor humility, it does constitute significant progress in that direction. I think it is also worth emphasizing that ground floor humility is an independently attractive and philosophically important property of generative principles. Defending principles that are hum- ble about the ground floor entitles us to a certain kind of epistemic humility that is not usually associated with abundant ontologies, but is clearly desirable in metaphysical theorizing. For an extreme illustration of why humility is a virtue for generative principles, compare a toy principle of mereological composition: Light Fusion. For any disjoint xxs, there is some y weighing less than a pound that fuses them. While there are models where Size holds, any model with a sufficiently heavy ground floor will violate Light Fusion. Thus, the defender of Light Fusion is committed to a further metaphysical claim: that the ground floor isn’t ‘too heavy’ . Global Plenitude, on the other hand, does not rest on any further contentious assumptions about what the possible patterns of neutral properties are. Although she is committed to the claim that material object ontology is modally full in a particular way, the plenitude-lover can remain appropriately cautious about what exactly that fullness amounts to. Relatedly, plenitude lovers of a certain stripe might also take the foregoing as evidence that plenitude is in some sense ‘innocent’, or that the proposed profligation of ontology is ‘cheap’, as witnessed by its conservativeness over a large body of modal truths. There is a deep and interesting connection between metaontological minimalism – metaontological views according to which exis- tence is ‘cheap’ or ‘easy’ – and abundant ontologies. 33 For the theorist approaching plenitude from this direction, ground floor humility is an extremely attractive feature of a theory, and bolsters their claim that the expanded ontology does nothing to clutter the modal landscape. 6 Promises of Plenitude We started out with the goal of making a vague idea precise, and saw that there were serious obstacles to doing so. Cutting our way through the thicket has led us to Global Plenitude. Of course, questions about the details remain: global plenitude neither tells us what the neutral properties are nor does it provide any account of how they’re spread across modal space. I’ve suggested that the fact that Global Plenitude leaves these questions largely open is a virtue, and better characterizes the commitments of the target idea. 33 For extensive discussion of Metaontological Minimalism, see Linnebo (2012). For a recent example of this connection at work, see especially Thomasson (2015). 28 Fairchild Chapter 2. Understanding Material Plenitude More importantly, however, we came to Global Plenitude by considering minimal responses to fully general problems for the plenitudinous idea. Thus, Global Plenitude captures constraints on any adequate formulation of plenitude. Whatever else a plenitude lover hopes to pack into their preferred account, our observations about neutrality and consistency will constrain the resulting view. What then do we learn about the target idea? One major upshot of the discussion so far is that, although plenitude is usually associated with utterly unconstrained abundance, we’ve learned on closer inspection that this abundance will be somewhat tempered by the nature of modal profiles themselves together with our choice of background modal theory. Given that, we might well wonder: do the constraints of Global Plenitude allow us to make good on all of the initial promises of plenitude? Ultimately, I think so, though unsurprisingly things turn out to be much more subtle than we might initially have expected. Here is just one case study. Plenitude offers an appealing diagnosis of certain paradoxes involving gradual changes. For example, consider the case of a trunk, owned by a certain Theseus, made from six light-wood planks. Over time, we remove the light wood planks, and replace them one-by-one with darker wood. (We focus on a trunk for simiplicity, in place of its more unweildy nautical cousin.) Familiar questions about whether the trunk survives these changes seem to dissolve easily against the backdrop of plenitude: there are many cube-shaped things at t 1 , including some that survive replacement of the first plank but not the second, some that survive replacement of three planks but not four, and some that survive the entire series. On one plenitudinous diagnosis, the difficulty of survival questions has to do with linguistic indeteriminacy surrounding which of these cube-shaped things our word ’trunk’ picks out. This is just one concrete illustration, but there are more complex puzzles involving the ways that ordinary objects can tolerate changes to their parts with a similar structure. In each it is available to the plenitude-lover to point to the abundance of coincident objects, and observe that among them are objects with these parts but not those essentially, others with those parts but not these essentially, and so on. 34,35 However, a lesson of our progress so far is that this sort of strategy has to be employed with care. In the trunk case, we say that there are very many things at t 1 , among them are: the cube that has a...e essentially as parts, and can survive replacement of plank f, the cube that has a...d essentially as parts and can survive the replacement of planks e and f, the cube that has a...c as parts, and so on, for any combination of planks. Naively, it might seem as though this argument relies on an appeal to a much more general principle: 34 Note that this strategy only goes through if properties like having the xxs as parts are neutral. This, finally, will turn on how we understand coincidence: if we understand coincidence as mere co-location and it is possible for co-located objects to nonetheless be mereologically disjoint then mereological properties won’t in general be neutral. On such a picture, plenitude has very little to say about cases like the Trunk of Theseus. 35 Leslie (2011) proposes this sort of solution to Chisholm’s paradoxes of essence, arguing that once we recognize the abundance of instantiated modal profiles, the paradox dissolves. 29 Fairchild Chapter 2. Understanding Material Plenitude Part Variety. For any disjoint xxs and yys that are proper parts of z, something coincident with z has the xxs essentially as parts and the yys accidentally as parts. But the counterexamples we’ve seen provide us with the template for an argument against Part Variety. As long as perfectly fragile objects – ‘modal minimums’ like Flimsy – are parts of composite objects, Part Variety will fail. An object like Flimsy cannot be essentially a part of something while other more resilient objects are accidentally parts of it. The defender of Global Plenitude will be hard pressed to deny that perfectly fragile objects are sometimes proper parts of things. Fragility follows from Global Plenitude as stated: Fragility. There is something that is perfectly fragile. Given any object o, there will be a non-locally closed modal profile based on o’s neutral properties such that every neutral property of o is partitioned in to E. Since, as we have seen, o’s neutral properties include properties equivalent to being such that p, where again p is true at exactly one world-time, this suffices to guarantee that some thing coincident with o is perfectly fragile. 36 Universal Composition guarantees that such objects are sometimes proper parts of things: Universal Composition. For any xxs, there exists a z such that z fuses the xxs. Although Universal Composition isn’t similarly entailed by Global Plenitude, it does seem to fit with the general background picture: mereological universalism is often motivated by the same concerns for anti-arbitrariness that drove us to plenitude. 37 Given both, there will be composite objects that have perfectly fragile objects as parts, and so Part Variety will fail. The upshot is that applications of plenitude to familiar metaphysical puzzles, though useful, can’t straightforwardly go via prima facie attractive principles like Part Variety. Even given a plen- itudinous ontology, we can’t cavalierly assume that there are extraordinary objects answering to any old pattern of essential and accidental properties. Instead, we will often need to take the particular cases carefully in hand, and examine them against the backdrop of the rest of our metaphysics. There is much more to be said here: there is a wealth of interesting questions about the mereo- logical pictures available to the plenitude-lover, and the kinds of principles of variety we might be able to consistently pair with the view. However, my aims in this section have been more modest: I hope to have suggested that while Global Plenitude can make good on many of the promises of the target idea, it doesn’t license naive appeal to any general principles of abundance. Although the proposed ontology is luxurious, we still must attend to the ledger. 36 Alternative versions of plenitude that replace neutrality with some more restricted class of properties may avoid this result, but as with the Whimsy case before, we can construct a fusion of objects whose modal lifespans pattern the right way to generate a counterexample to Part Variety. The details of this will depend on the details of the replacement proposal. 37 Though see Chapter 4 for some wrinkles. 30 Fairchild Chapter 2. Understanding Material Plenitude 7 Conclusion Plenitude provides a dramatic picture of the material world: small changes – the flutter of a leaf, or the loss of an atom – shape reality just as radically as the collapse of a star or construction of a new skyscraper. Still, the thought at the heart of the ontological drama seemed simple at first; that metaphysics doesn’t privilege some modal profiles over others. We’ve seen that it is harder to make something sensible out of that simple idea than we might have expected. I’ve argued here that we can make significant advances on understanding the target idea by considering very general structural observations about neutrality and accidentiality. In particular, I’ve argued that the intelligibility of plenitude doesn’t rest on contentious distinctions between kinds of properties, but also that plenitude is constrained in surprising ways by what it is for an object to have a property essentially and accidentally. As a result, we find not only an attractive (and in some ways, humble) version of plenitude, but also substantive constraints on any adequate theory of the material world. 38 38 This paper has benefited greatly from the feedback of many people. I am especially grateful to Gabriel Uzquiano, Jeffrey Russell, Andrew Bacon, John Hawthorne, Shieva Kleinschmidt, and Mark Schroeder for feedback on earlier versions of this paper. I am also grateful to Jeremy Goodman, Wade Hann-Caruthers, Mark Jago, Irem Kurtsal Steen, Matt Leonard, Joshua Spencer, and audiences at the Graduate Women in Metaphysics Conference and at UCSB for helpful discussion of these issues. 31 Fairchild Chapter 2. Understanding Material Plenitude 8 Appendix To show that Global Plenitude is ground floor humble, we’ll show that any ground model can be expanded to a model of Global Plenitude. First, I introduce the notion of a ground model G, and then show how to construct a global expansion G+. I then show that any such G+ is a model of Global Plenitude. 8.1 Initial Definitions A ground model G is a quadruple <W,I,d,S >, where ◦ W is a nonempty set of worlds. ◦ I is a nonempty set of ground individuals. ◦ d is a function from W to P (I). For notational ease, let d(w) = D w , the domain of ground individuals at w. ◦ S is the set of all functions from W to P (I) such that f(w)⊆D w . We interpret S as the set of properties in the ground model. It will be helpful later on to be able to refer quickly to all of x’s S-properties at a given world, so we’ll use the shorthand S x,w . That is, S x,w ={f∈S :x∈f(w)} In constructing a global expansion of G, we’ll be interested in a particular family of bipartitions of S x,w for each x, w. These are the partitions of S x,w that are closed under non-local entailment. To define non-local closure, we’ll need two further definitions: first, that of the essentialization of a property, and second, that of non-local entailment. We say that for any properties h and f in S, h is the essentialization of f iff h is the function such that for all x, w, x∈ h(w) iff x∈f(w 0 ) for all w 0 such that x∈D w 0. (I will at times make use of the shorthand f ess to refer to the function that is the essentialization of f.) And we define non-local entailment as follows: A setF of properties non-locally entails a property g at w iff at all w 0 distinct from w, ∀x, if∀f∈F, x∈f(w 0 ), then x∈g(w 0 ) And thus, a bipartition P of S x,w into E and A is closed under non-local entailment iff (i) for any subsetF of S x,w , ifF non-locally entails g at w, then ifF⊆E, then g∈E and (ii) if f entails h and h is the essentialization of f, f is in E. Notice regarding condition (ii) that ifh is the essentialization off,h entailsf, so iff also entailsh,f ish. Thus, (ii) also says that E must contain every property in S x,w that is its own essentialization. 32 Fairchild Chapter 2. Understanding Material Plenitude 8.2 Constructing a Global Expansion To construct a global expansion G+ from a ground model G, we will first expand the domain of each world. We proceed in three steps. Step 1. Build a set D pre w from each D w . For eachx∈D w and each non-locally closed partitionP ={E,A} ofS x,w , add a triple (w,x,{E,A}) to D pre w . (We use a triple to encode the ground individual and partition in question.) D pre w is D w together with the set of every such triple for every ground individual in D w Step 2. Choose witnesses. From our definition of non-local entailment, we know the following: given a partition P ={E,A} of some S x,w that is non-locally closed at w, for any property f in A, there is some individual z in some world w 0 distinct from w which has every property in E at w 0 and lacks f at w 0 (that is: for all g∈E, z∈g(w 0 ) and z / ∈f(w 0 )). Argument. Suppose for a contradiction that for some P ={E,A} of some S x,w that is non-locally closed at w, and for some f ∈ A, there is no such z. Then,∀w 0 6= w, and∀z∈ w 0 , if z∈ g(w 0 ) for all g∈ E, then z∈ f(w 0 ). But then by the definition of non-local entailment, E non-locally entails f at w, thus P is not non-locally closed. Contradiction. We will say therefore that A pair (z,w 0 ) is a witness to the non-local closure (at w) of a partition P of S x,w iff z has every property in E at w 0 and lacks some f in A at w 0 . Or, for short, we say that (z,w 0 ) is a witness for (w,x,{E,A}). We now choose a function Wit from the set of pairs of the form ((w,x,{E,A}), f) where f∈ A to I×W , such that each ((w,x,{E,A}), f) is assigned to some pair (z,w 0 ) such that (z,w 0 ) is a witness for (w,x,{E,A}) and z / ∈f(w 0 ). It is worth noting two things about witnesses. First, although non-local closure guarantees that corresponding to (w,x,{E,A}) and f∈A, there is some witness, there may be many. Thus, there will not always be a unique candidate function to choose as Wit. Second, it may be that the same (z,w 0 ) is assigned to both ((w,x,{E,A}), f) and ((w,x,{E,A}), g). Step 3. Build a set D + w from each D pre w . In the final stage of the domain construction, we use the function Wit to expand each D pre w to D + w as follows: For eachw 0 , for every triple (w,x,{E,A}) and everyf∈A such that the pair ((w,x,{E,A}), f) is in Wit −1 (D w 0×{w 0 }) (every pair such that Wit assigns it to something (z,w 0 ) for some z in w 0 ), we add the triple (w,x,{E,A}) to D + w 0. 33 Fairchild Chapter 2. Understanding Material Plenitude So, for every w, D + w is the union of the set of all such triples with D pre w . 8.2.1 A Global Expansion A global expansion G+ of a ground model G =<W,I,d,S > is a quintuple <W,I + ,d + ,S + ,C >, where ◦ W remains unchanged from the ground model. ◦ I + is the union of all D + w for all w∈W . ◦ d + is a function that assigns each w to D + w . This much is straightforward, thoughS + andC are slightly more complex. The former is a privileged subset of properties in the new model, corresponding to expansions of the properties S in the ground model, the later is a binary relation to be interpreted as the coincidence relation. To characterize C, we’ll first define the set S + . The set S + is a subset of the set of functions from W to P (I + ). In particular, it is the set of all expanded properties f + , where for each f∈S, we define f + as follows: f + (w) =f(w)∪{(w,x,{E,A}) :x∈f(w)}∪{(w 0 ,y,{E 0 ,A 0 }) :y∈Wit −1 (f(w)×w)} That is: at each world w, the expansion f + of f includes not only every x∈ f(w), but also every triple added for some x∈f(w) in Step 1, and also every triple added in Step 3 for a witness (x,w) such that x∈f(w). Nothing else is in f + (w). Intuitively, each property in the ground model corresponds to a property in the global expansion that has as its extension at each world all of the same old objects as well as their ‘corresponding’ new objects. S + is just the set of all such properties. We retain the same shorthand as above, and use S + x,w to denote the set of all of x’s S + properties. (Which, notice, will now be a proper subset of all of x’s properties.) We can now define a binary relation C on I + , to be interpreted as the coincidence relation. Let R: W→ P (I + ×I + ) be the function such that (u,y)∈ R iff u∈ D + w and y∈ D + w , y∈D w , andu is a triple added fory in either Step 1 or Step 3 of the construction. That is: either u is a triple of the form (w,y,{E,A}) for some partition{E,A} of S y,w or u is a triple (w 0 ,z,{E 0 ,A 0 }) such that Wit((w 0 ,z,{E 0 ,A 0 }),f) = (y,w). Now, let R 0 be the reflexive closure of R. Let R 00 be the symmetric closure of R 0 , and let R 000 be the transitive closure of R 00 . Finally, C is R 000 , the resulting equivalence relation. In short,u andy will coincide inw iffu =y,y is a ground individual andu was added toD + w for y in the construction of G+ (and vice versa), or u and y were added for the same ground individual in w. 34 Fairchild Chapter 2. Understanding Material Plenitude 8.3 Global Plenitude To show that an arbitrary global expansion G+ is a model of global plenitude, we need to show two claims. Claim 1. A property is in S + iff it is a neutral property. That is,f∈S + iff for all w, if x and y coincide in w, x∈f(w) iff y∈f(w). and Claim 2. For everyw, everyx∈D + w , and every non-locally closed partitionP ={E,A} ofS + x,w , there is somey such that (x,y)∈C(w), andy has every property inE essentially and every property inA accidentally at w. Recall that to say that y has every property inE essentially and every property inA accidentally at w is to say that for everyg∈E , y∈g(w) in every w such that y∈ D + w , and for everyf∈A , y∈f(w) and there is some w 0 such that y∈D + w and y / ∈f(w 0 ). Proof of Claim 1. We first require a result (Lemma 1) about coincidence, and then will show the biconditional Claim 1 by showing the left to right direction (Lemma 2) and then the right to left (Lemma 3). Lemma 1. Let y be an individual in I + . For all w∈ W , there is at most one x∈ D w such that (x,y)∈C(w). Proof. We show first that given x,x 0 in D w , if (x,y)∈R(w), and (x 0 ,y)∈R(w), then x =x 0 . Let y = (w 0 ,z,{E,A}) for some non-locally closed partition P ={EA} of S z,w 0. We consider two cases. (a) If w = w 0 , then y was added in Step 1 of the construction, and so the only individual in D w that bears R to y is z. Thus, x =z and x 0 =z, so x =x 0 . (b) Ifw6=w 0 , theny was added in Step 3 of the construction, and for somef∈S,Wit((w 0 ,z,{E,A}),f) = (x,w), and for some g∈ S, Wit((w 0 ,z,{E,A}),g) = (x 0 ,w). So, for every h∈ E, x∈ h(w) and x 0 ∈h(w). Let j∈ S be the function where for all w∈ W , j(w) = D w ∩z. Thus, z∈ j(w 0 ). Note that j = j ess . So, by the definition of non-local closure, j∈ E. So, x∈ j(w) and x 0 ∈ j(w). So, x =z, x 0 =z, and x =x 0 . So, given x,x 0 in D w , if (x,y)∈R(w), and (x 0 ,y)∈R(w), then x =x 0 . However, this is preserved when we take the reflexive closure of R to get R 0 , when we take the symmetric closure of R 0 to get R 00 , and finally when we take the transitive closure of R 00 to get R 000 . So, given x,x 0 in D w , if (x,y)∈C(w), and (x 0 ,y)∈C(w), then x =x 0 . We will make use of Lemma 1 frequently in what follows, beginning with the left-to-right direc- tion of Claim 1. Lemma 2. Iff∈S + then for all w, if x and y coincide in w ((x,y)∈C(w)), x∈f(w) 35 Fairchild Chapter 2. Understanding Material Plenitude iff y∈f(w). Proof. Let x,y ∈ D + w for some w. Then, there is z 1 ,z 2 ∈ D w , such that (x,z 1 )∈ C(w) and (y,z 2 )∈ C(w). (The argument for this is similar to Lemma 1 above. Notice that in the definition of R 00 , every object in D + w for any w is R 00 -related in w to some ground individual, so every object is therefore related by C to some ground individual in w.) If (x,y)∈ C(w), then since C is an equivalence relation, (z 1 ,z 2 )∈ C(w). So, z 1 = z 2 , since by Lemma 1 distinct ground individuals never coincide. Sincef is in S + , there is some f∈ S such thatf =f + . By definition of f + , if (x,y)∈C(w), then x∈f + (w) iff z 1 ∈f + (w) iff z 2 ∈f + (w) iff y∈f + (w). Lemma 3. If for all w, if x and y coincide in w ((x,y)∈C(w)), x∈f(w) iff y∈f(w), thenf∈S + . Proof. We show that iff is neutral, then there is some function f ∈ S such thatf = f + . By construction of S + , this suffices to show thatf∈S + . We first suppose for conditional proof thatf is neutral. We now define a functionf| : W→ P (I) such that for every w and every x∈ D w , x∈f|(w) iff x∈f(w). That is:f| is just the restriction off to ground individuals. So,f|∈S. We now just want to show that for all w and all y∈D + w , y∈f(w) iff y∈f| + (w). Let w∈ W , y∈ D + w , and let x be the ground individual in D w such that (x,y)∈ C(w). Then, y∈f| + (w) iff x∈f| + (w), by the definition off| + . And x∈f| + (w) iff x∈f|(w), also by the definition off| + . Further, x∈f|(w) iff x∈f(w), by definition off| above. Becausef is neutral and x and y coincide in w, x∈f(w) iff y∈f(w). Proof of Claim 2. We will show Claim 2 via two Lemmas. First, in Lemma 4, we show that for any world and and any individual x in w in a ground model G, and for any non-locally closed partition{E,A} of x’s S properties at w, there is an individual in G + that coincides with x, and has every property in E + essentially and every property in A + accidentally. In Lemma 5, we show that for any world and any individual x in w in a global expansion G + , and any non-locally closed partition{E,A} of x’s S + properties at w, there is an individual in G + that coincides with x and has every property inE essentially and every property inA accidentally. Lemma 4. Let x∈D w and let{E,A} be a partition of S x,w that is non-locally closed at w in G. Then, in any global expansion G + of G, there is a y in D + w such that (x,y)∈C(w), S + x,w =S + y,w , and Ess(y) =E + . Where Ess(y) is the set of all of y’s essential S + properties, and E + is the set of all f + ∈ S + for every f∈E. Proof. Let y = (w,x,{E,A}). Then, by the construction of G+, y∈ D + w , and by definition of C, 36 Fairchild Chapter 2. Understanding Material Plenitude (x,y)∈C(w). By Claim 1, S + x,w =S + y,w . By construction, E + ⊆Ess(y). All that we need to show now is that Ess(y)⊆E + , or equivalently, that A + ⊆Acc(y) at w. For every property g + ∈A + , we must show that y∈g + (w) and that there is some w 0 such that y∈D + w 0 and y / ∈g + (w 0 ). The first conjunct follows from the observation that A + ⊆S + y,w . For the second conjunct: if A + is empty, we are done. If not, let g∈A, and for some z in D w 0, let (z,w 0 ) = Wit(y,g) (recall that y = (w,x,{E,A})). Then z / ∈ g(w 0 ), so z / ∈ g + (w 0 ). And since by the definition of C (y,z)∈C(w 0 ), then y / ∈g + (w 0 ), because again by Claim 1 coincidents share all of their S + properties. So, g + ∈ Acc(y) at w. Thus, for any g∈ A at w, g + ∈ Acc(y) at w, so A + ⊆Acc(y) at w. Lemma 5. Let x∈D + w and let{E,A} be a non-locally closed partition of S + x,w . Then, there is a y in D + w such that (x,y)∈C(w), S + x,w =S + y,w , and Ess(y) =E . (Note that it follows that Acc(y) =A , where Acc(y) is the set of all of y’s accidental S + properties at w.) Proof. As above, for everyf inE , definef| : W→ P (I) such that for every w and every z∈ D w , z∈f|(w) iff z∈f(w). (Again,f| is justf restricted to ground individuals.) LetE| be the set of all such restrictionsf| for everyf inE . ThenE|⊆S z,w . Similarly, for everyg∈A , defineg|. Then A|⊆S z,w , and{E|,A|} is a bipartition of S z,w . We now show that{E|,A|} is a non-locally closed partition of S z,w in G. Suppose that{E|,A|} is not non-locally closed at w in G. Then there is some function g / ∈E| such that the setE| non-locally entails g at w. That is, for every w 0 6=w and every u∈D w 0, if for everyf| inE|, u∈f|(w 0 ), then u∈g(w 0 ). Now, by the definition off|, for all w 0 6=w and all ground individuals u∈D w 0, if u∈f(w 0 ) for everyf∈E , then u∈f|(w 0 ) for everyf in E . And, by the definition of g + , for all u∈ D w 0, if u∈ g(w 0 ), then u∈ g + (w 0 ). So, for all w 0 6= w and all u∈ D w 0, if u∈f(w 0 ) for everyf∈E , then u∈g + (w 0 ). By Lemma 1 and the argument for Lemma 2 above, for any w 0 6= w, given any x∈ D + w 0, there is a unique ground individual z∈D + w 0 such that (z,x)∈C(w 0 ). By Claim 1, if x∈f(w 0 ) for every f∈E , then z∈f(w 0 ) for everyf∈E , because coincidents share all of their S + properties. But by the above, for any such z, if z∈f(w 0 ) for everyf∈E , then z∈g + (w 0 ). However,{E,A} is non-locally closed in S + , so it follows that g + ∈E . But g =g + |, so g∈E|. Contradiction. Thus,{E|,A|} is a non-locally closed partition of S z,w in G. By Lemma 4, there is a y in D + w such that (y,z)∈C(w), S + y,w =S + z,w , and Ess(y) =E| + . By the definition ofE| ,E| + =E (y). So, Ess=E . 37 3 A Paradox of Matter and Form In the face of the puzzles of material constitution, some philosophers have been moved to posit a distinction between an object’s matter and its form. 1 The puzzles are familiar by now: it seems that, by Leibniz’s Law, the statue must be distinct from the lump of clay that makes it up, because the lump can survive squashing while the statue cannot. My favorite knit hat must be distinct from its yarn, because the yarn can survive unravelling, but the hat (sadly) cannot. The matter that makes up the oak tree outside my window is distinct from the tree itself, because the matter can survive being fashioned into a table after the tree has been destroyed. On the other hand, it is hard to see how these things could differ from each other when they appear so intimately related.After all, the statue and the lump seem to share their material parts, occupy the same regions, have many of their non-modal properties in common, and so on. Hylomorphism purports to address both sides of this puzzle. Very informally; according to hylomorphists, objects both have matter — the chunky stuff that makes them up — and embody forms — a non-chunky component that somehow unifies, moulds, or structures their material parts. Thus, although the statue and the lump share their matter, the statue, unlike the lump, embodies the property of being statue shaped. This is meant to allow us to accommodate the application of Leibniz’s Law while at the same time making the distinction between the statue and the lump somewhat less mysterious: although their difference in form explains their different modal properties, they nonetheless are made of all the same chunky stuff, so it is no wonder that they are so intimately related. 2 Although hylomorphists agree that there is a difference between merely instantiating a property (as the lump does) and having it as a form (as the statue does), they differ on the details. Some hylomorphists say that properties are formal parts of the objects that embody them, others say that they are non-mereological constituents of objects, and still others say that forms are instead some kind of non-constituent constraint on objects. 3 Although these are important differences, my 1 Among the most vigorous defenders of this kind of contemporary hylomorphism are Koslicki (2008) and Kit Fine (1982, 1999, 2007, 2008). For slightly different approaches to hylomorphism, see Evnine (2016) and Sattig (2015). 2 Though see Sidelle (2014) for a recent critique of this strategy. 3 Koslicki and Fine both take forms to be mereological parts of embodiments, Rea (2011) takes them to be non- 39 Fairchild Chapter 3. A Paradox of Matter and Form plan here is not to focus on the details of any particular account. I am instead interested in the minimal version of hylomorphism that emerges when we take seriously the difficulty of saying which properties are eligible as forms — and thus, which embodiments there are. 4 For a theory to be viable as a response to the puzzles of material constitution, it must have a permissive enough conception of forms to generate all of the objects we ordinarily recognize. When- ever some matter instantiates the property being statue shaped, we want the account to guarantee that there is a further object — a statue — which embodies that property. The difficulty is finding some principled stopping point: it seems that it would be intolerably arbitrary to say that being statue-shaped is eligible as a form, but that a range of other complex shape properties aren’t. 5 To avoid arbitrariness, it seems that we should avoid positing any restriction on forms, which will in turn lead us to an abundant ontology of embodiments. 6 One standard complaint about this picture is that the super-abundance of material objects is too extraordinary to accept. 7 I want to raise a different and prior worry: that the most natural and attractive way of developing this rough picture (what I’ll call “simple hylomorphism”) is already inconsistent. Simple hylomorphism is subject to problem analogous to Russell’s Paradox: I show that, on pain of contradiction, we’ll have to surrender something from the simple account. However, it isn’t immediately obvious what we should give up; despite the close parallels, we cannot treat the problem straightforwardly as an instance of Russell’s Paradox. Standard responses to the set- theoretical argument turn out to be surprisingly unhelpful here. A bit of vocabulary, first: I follow ? in calling an object which embodies some property a “qua-object” . A qua-object has both a form and a base. Following Fine (1999) and Fine (2008), I’ll denote a qua-object with base a and form F by writing a/F. Simple hylomorphism is given by the following pair of principles: Existence. Given any property F and object a such that F(a), there is some thing b such that b is a/F. Uniqueness. For any properties F and G and objects a, b, a/F = b/G iff a = b and F is the same property as G. 8 mereological constituents, while Johnston (2006) talks instead of principles of unity governing (but not composing) embodiments. 4 Some hylomorphic theorists answer this challenge: for example, Koslicki (2008, 190) proposes an existence principle that says that only kinds (not properties in general) give rise to embodiments. 5 This may be an oversimplification of the example. You might think that for statues the relevant property is more complex than being statue shaped, perhaps also involving a relation to the intentional action of a creator. Since nothing hangs on this example in what follows, I follow Fine (1982) in appealing to the simpler presentation. However, see Evnine (2009:206), where this point is developed as a problem for Fine’s account, and Thomasson (2003) for further discussion of this sort of view of artifactual kinds. I am grateful to an anonymous referee at Thought for this observation. 6 See Sosa (1999) for this route to a super-abundant (“explosive”) Aristotelian ontology. Worries about arbitrariness also play an important role in motivating other abundant ontologies; eg. in Yablo (1987:307) and Sidelle (2002:118- 119). For recent discussion of arguments from arbitrariness, see Korman (2015). 7 See, for example, Koslicki (2008: 83). 8 Exactly how we understand property identity will not be relevant, as long as we suppose that if F and G are the same property, something is F iff it is G. That is, we will require only coextensiveness for the argument below. I 40 Fairchild Chapter 3. A Paradox of Matter and Form Existence is the principle of plenitude that reflects the now-familiar aversion to arbitrariness, and says that for any instantiated property, there is a qua-object that embodies it. Uniqueness gives the individuation conditions for qua-objects: qua-objects are the same just in case they have the same bases and embody the same property. This guarantees, among other things, that the matter- qua-being statue-shaped and the matter-qua-being lumplike are distinct, despite having the same material basis. Although Uniqueness is suggested by the identity conditions explicitly proposed in ? and Fine (1999), something like it seems to be presupposed in most contemporary versions of hylomorphism. 9 1 The Problem The structure of the argument is analogous to the argument in Russell’s Paradox of Sets, and can be presented in four steps: (i) There is a property N which an object instantiates iff it embodies a property that it does not instantiate. (ii) Some thing m instantiates N. (iii) By (i), (ii), and Existence, there is a qua-object m/N. (iv) (iii) is inconsistent with Uniqueness. A liberal conception of properties gives us (i). Roughly, according to the liberal conception, corre- sponding to any intelligible condition there is a property had by exactly the things that satisfy that condition. 10 Although a defense of this background picture of properties is beyond the scope of this chapter, I’ll briefly revisit it in Section 2.1. We can argue for (ii) in a number of ways, since all we need is a qua-object a/F that doesn’t instantiate F. One straightforward argument depends on the assumption that qua-objects are distinct from their bases, so any qua-object that embodies a property had only by its base will satisfy (ii). Schematically: if there is at least one object a, the liberal conception of properties guarantees that return to this in 2.2. 9 Although Fine does not typically make the range of F explicit, if we read his principles unrestrictedly as I have them here, Existence follows from a stronger principle of Fine’s (also called Existence) in ?, 100 and Fine (2008, 112). Similarly, Uniqueness is part (i) of Identity in?, and is a consequence of the plural principle (R3) in Fine (1999, 66). It is worth emphasizing that Uniqueness isn’t an idiosyncrasy of Fine’s view, though he states it most explicitly. It seems to fall out of the informal characterization of hylomorphism; we talk of “the” property or quality that an object embodies, assume that object have a single formal part, and so on. 10 If we wanted to put this more rigorously using the language of second-order logic, we interpret X as ranging over properties and define properties intensionally. Then the liberal conception of properties corresponds to the assumption that properties obey: Full Property Comprehension. ∃X∀x(Xx↔φ(x)) where φ doesn’t contain X. In this language, N is: Nx :∃y∃F (x =y/F∧¬Fx) 41 Fairchild Chapter 3. A Paradox of Matter and Form there is a property F had only by a. By Existence, there is a qua-object a/F, and if the distinctness assumption holds, a/F isn’t F (because only a is F, and a/F isn’t a). How plausible is the distinctness assumption? On the one hand, a large part of the initial appeal of simple hylomorphism is that in the paradigm puzzle cases, it allows us to accommodate the modal differences between ordinary objects and their matter by providing a framework capable of distinguishing them. So, for example, the hylomorphist can offer an especially attractive explanation of why the matter-qua-being statue shaped is more modally fragile than the matter itself. On the other hand, the most obvious cases with the right structure to support (ii) – namely, where a qua- object embodies a property had only by its base – seem much more implausible. For example, if o and o-qua-being identical to o are distinct, then o-qua-being identical to o embodies a property it doesn’t instantiate (since only o has that property). But o-qua-being identical to o doesn’t seem to differ modally from o, so we lack our usual grounds for distinguishing a qua-object from its base. Happily, for the argument above to work, we need only an object that is contingently the unique F. Given the plausible principle that a/F exists only when a is F, then if Michael is contingently God’s (uniquely) favorite angel, the qua-object Michael/being God’s favorite angel is more modally fragile than Michael himself. (And thus, plausibly distinct from Michael.) Michael/being God’s favorite angel doesn’t enjoy the same exalted status as Michael, and so embodies a property that it doesn’t instantiate. 11 More interestingly, we can justify (ii) even without the distinctness assumption. The argument is slightly less straightforward, but requires nothing beyond the principles of simple hylomorphism. If there are at least two things a and b, the theory of properties guarantees that there is a property F had by only a, and a property G had by only a and b. 12 By Existence, there is a/F and a/G, and by Uniqueness, these are distinct. In the absence of the distinctness assumption, we’re free to identify either a/F or a/G with a, but we cannot identify both with a. Ultimately, we can show that however this goes, there will still be something that fails to instantiate its own form, and so there will be something that instantiates N. 13 The next two steps of the argument follow immediately: (iii) is just an application of Existence. Call the object from (ii) m, then since Nm, Existence gives us m/N. Step (iv) of the argument is similarly straightforward, and reminiscent of Russell’s Paradox. The qua-object m/N either instantiates N or it doesn’t: (I) If m/N doesn’t instantiate N, then there is some property that it embodies which it does instantiate. But this is just what it is for something to be N. So if m/N doesn’t instantiate 11 Thanks to Jeremy Goodman for suggesting this route. 12 We could interpret F as “being a” and G as “being a or b”, but again the argument would work even if F and G are properties contingently had by only a and only a and b, respectively. 13 The simple case is if a/F isn’t a. Then a/F fails to be F, and we are done. But if a/F is a, then a/G isn’t. There are two such cases: either a/G is distinct from both a and b, or a/G is b. In the first case, a/G fails to be G, and we are done. In the latter case, a/G is G. However, there is a further property had only by b: Hx = b. Existence gives b/H, which by Uniqueness is distinct from a/F and a/G. So, if a/G is b, then a/H isn’t – and again, we have something which doesn’t instantiate the property it embodies. 42 Fairchild Chapter 3. A Paradox of Matter and Form N, then m/N does instantiate N. 14 (II) If m/N does instantiate N, then m/N must fail to instantiate some property that it embodies. But by Uniqueness, the only property m/N embodies is N: so if m/N instantiates N, then m/N doesn’t instantiate N. 15 On pain of contradiction, we can’t hold on to the minimal package. It seems that are only two salient routes for responding to the puzzle. Short of abandoning the liberal conception of properties, we must either give up Existence – to block the construction of the Russell object entirely – or surrender Uniqueness. Both routes are parallel to responses to Russell’s paradox of sets, but as we’ll see, some of the corresponding moves look much less plausible in this setting. 2 Responses Before exploring these two responses, I want to pause to head off the temptation to aim our attentions elsewhere. This argument relies on the liberal theory of properties assumed in the background. This is what guarantees that there is a property (N) that a qua-object has just in case it doesn’t instan- tiate any property it embodies. The important feature of this view for our purposes is that it is allows impredicative conditions to determine genuine properties, meaning roughly that we allow property-determining conditions to contain quantifiers ranging over properties. A weaker conception of properties – for example, one that regarded only predicative conditions as intelligible – wouldn’t guarantee that N is a genuine property, and so the argument would never get off the ground. But weakening our (otherwise consistent) theory of properties in light of the problems for simple hylomorphism would surely be an overreaction. For those who already take issue with the liberal conception of properties, the minimal theory may be safe. Intuitively, however, this argument doesn’t show us that the property involved is somehow pathological. Instead, it seems to cast 14 More rigorously, we trivially have (m/N)→m/N =m/N∧¬N(m/N) and by existential generalization ∃y∃F (m/N =m/F∧¬F (m/N) So, by the definition of N, ¬N(m/N)→N(m/N) 15 More rigorously, by the definition of N above: N(m/N)→∃y∃F (m/N =y/F∧¬F (m/N)) By existential instantiation, m/N =a/G∧ (m/N) Thus, by Uniqueness, m = a and G is the same property as N. So, G is at least coextensive with N. But then, ¬G(m/N)→¬N(m/N) So N(m/N)→¬N(m/N) 43 Fairchild Chapter 3. A Paradox of Matter and Form suspicion on the object that embodies the property. Something has gone wrong in the theory of embodiments, not in the theory of properties on which it relies. 2.1 Weaken Existence Instead, we might say that although the properties involved in the argument are genuine properties, not all properties are eligible as forms. Given an appropriately restricted alternative to Existence, we could avoid the “Russell-like” qua-object in (iii) (namely, m/N). But such a principle would have to be independently motivated, and we already have good reason to be suspicious of any such restriction. Simple hylomorphism was initially attractive on the same grounds that plenitudinous pictures typically are: it seems that there is no satisfying, non-arbitrary alternative to Existence. Does this argument point us towards any new candidates? We might hope that the analogy with Russell’s paradox could help here. For example, the lesson of the argument in the set-theoretic setting is sometimes taken to be that some properties specify collections “too large” to be sets. The analogous diagnosis here is that N is unsafe because it is too large, and so we should restrict the range of F in Existence to “small enough” properties. But this is clearly hopeless: such a restriction looks painfully ad hoc in this setting, and renders the theory too weak to do its intended job. The existence of a statue shouldn’t depend on the number of statue shaped lumps of clay, and yet given the size diagnosis, a world with too many statute-shaped lumps would be a world without statutes. Maybe this isn’t the most promising connection for our purposes – perhaps other ways of weak- ening the set-theoretic analog of Existence will inspire less ad hoc alternatives. One of the most familiar responses to Russell’s Paradox is to embrace the iterative conception of sets. On the it- erative conception, we think of sets as being “built” in “stages” . At each stage of the cumulative hierarchy, we can only form new sets from sets that have already been built at earlier stages. The analogous conception of the hylomorphic domain is quite attractive: we begin with “mere matter” and all of the properties had by mere matter, and then build our first stage of qua-objects. From there, we can introduce “second stage” qua-objects which embody the properties had by those at the first stage, and so on. This amounts to insisting that Existence is restricted in two ways. The first way is reasonably intuitive; the alternative existence principle can only deliver qua-objects that have lower-stage objects as bases. The more surprising restriction that comes with the iterative pic- ture is the one we actually require to avoid the argument: qua-objects can only embody properties that are instantiated only by lower-stage objects. (So, for example, the closest thing to the Russell object we get on this picture is a level-n qua-object m that embodies the property of being a level n-1 qua-object that doesn’t have the property it embodies. But there is no contradiction in m lacking that property.) Again, what is plausible in the set-theoretic case is too weak to be plausible here. The iterative conception of material objects seems to gut simple hylomorphism of its explanatory power. Simple Hylomorphism is supposed to help us explain how (for example) the lump and the statue can share 44 Fairchild Chapter 3. A Paradox of Matter and Form the property being statue shaped, but the latter and not the former embodies it. On the iterative conception, nothing can have the property it embodies, because it can only embody “lower stage” properties. It seems that the connection to the set-theoretic case doesn’t suggest any adequate, non-arbitrary alternative to Existence. A more radical response is to regard the argument as forcing arbitrariness upon us. This is where Fine (2007) lands, albeit for different reasons. He argues that for some domains (including the domain of the material) what exists may “inevitably be an arbitrary matter” . Fine suggests that this is because embodiments might not be subject to a general existence axiom after all; which embodiments there are might depend instead on which objects we (through human activity) introduce or recognize. 16 If we are comfortable with this kind of relativity, then there may be room to overcome our commitment to ‘anti-arbitrariness’ and accept some restriction to Existence. 17 Still, it would be at least surprising to find that arbitrariness or relativity in material object ontology is inevitable on pain of inconsistency. The credentials of the idea that admitting arbitrariness should be a last resort seem strong. Thankfully, we haven’t yet been brought to our last resort. 2.2 Abandon Uniqueness The second reaction to the puzzle is to abandon Uniqueness and leave Existence untouched. 18 Although this route may seem initially unpromising, my aim in this section is to suggest that for the hylomorphist who is reluctant to give up Existence, it is worth taking seriously. But how weak would an adequate restriction of Uniqueness have to be? In argument in Section 1, we appealed to Uniqueness where in fact we might have appealed to something much weaker. Consider the following apparently innocuous consequence of Uniqueness: Extension For any F and G, if a/F = b/G, then for all c, Fc iff Gc. We can re-run the argument in defense of step (iv) using only Extension. We only needed to appeal to Uniqueness once, in showing that if m/N instantiates N, then m/N doesn’t instantiate N (II). Briefly, that argument can now go as follows: If m/N instantiates N, then by the definition of N, there is some y and some property G such that m/N = y/G and m/N doesn’t instantiate G. But then by Extension, G and N must be coextensive. So, if m/N doesn’t instantiate G, m/N doesn’t instantiate N. Thus, it won’t do us any good to abandon Uniqueness unless our alternative permits counterexamples to Extension. 16 Fine (2007, 163-165) Interestingly, he illustrates this picture by appeal to the cumulative hierarchy. While I think the Finean proposal might be used to fill out the iterative proposal discussed in the previous paragraph, they still amount to different responses to the problem. It seems that the iterative proposal can be developed without anthropocentrism – the problem there is one of inadequacy, not arbitrariness. Fine’s proposal, on the other hand, is only able to help us with the Russellian argument if the “inevitably arbitrary” procedure by which qua-objects are generating somehow blocks step (iii). It isn’t obvious to me that the picture he has in mind will prevent us from “introducing” a Russell-object. 17 Though as we’ll see in the next chapter, depending on how the proposed Finean picture is developed, it might be better to describe this reaction not as admitting arbitrariness, but as admitting that there is some non-arbitrary (non-parity-violating) restriction, after all. 18 For a defense of the analogous strategy in response to Russell’s paradox of propositions, see ?. 45 Fairchild Chapter 3. A Paradox of Matter and Form Although it isn’t easy to see how we could come to terms with such permissive individuation conditions, it doesn’t seem that the loss of Uniqueness (and with it, Extension) would be much of an impairment to the hylomorphic picture. Our grounds for accepting these principles in the first place were already shaky. We’ve seen that a viable hylomorphic response to the puzzles of material constitution must be able to accommodate the distinctions we’re led to by putative applications of Leibniz’s Law, and so will have as a consequence that reality is (in some sense) more fine-grained than it looks. However, that isn’t yet a positive motivation for Uniqueness itself. We have no reason to expect that the fineness of grain required to deliver a satisfying answer to the target puzzles must be quite so extreme. Full-fledged Uniqueness is ripe with unsettling consequences that haven’t gone unnoticed, even by those who take it as their starting point. For example, Fine (1999) points out that in the plural extension of the hylomorphic theory, given two stacked wooden blocks a and b, we shouldn’t distinguish the tower a,b/being on top of from b,a/being beneath, because to do so would be to cut things too finely. Instead, he proposes an alternative individuation condition according to which embodiments are the same just in case “the state of a, b...standing in the relation R is the same as the state of a’, b’... standing in the relation R’. ” The intuitive idea here, I take it, is that although the relations come apart, what they require of the object that embodies them is the same. 19 In general, failures of Uniqueness can be made palatable by reflecting on the difference between embodying and merely instantiating a property. When an object embodies a property, we say that the object is “shaped”, “structured” or “qualified” by that property. Or, again from Fine: “ ...we might think of the form F in the matter-form combination m/F as a kind of mould to which the matter m is meant to conform. ” 20 I want to suggest that cases where Uniqueness fails are cases where distinct properties nonetheless impose the same “mould” on the objects that embody them. An individuation condition that appropriately respects the hylomorphic conception of embodiment should allow these cases. On this way of thinking, the initial argument is just more evidence that Uniqueness is too strong. The only lingering concern is that this route will run afoul of the arbitrariness constraint. But that risk seems less pressing here. Abandoning Uniqueness doesn’t seem to compel us draw any arbitrary lines: properties are all on a par with respect to the theory, in that they are all eligible as forms. We don’t have to take a stand on when properties are and are not embodied, since there aren’t any cases where an instantiated property fails to be embodied. Rejecting Uniqueness simply allows that for certain properties, differences in extension may not always correspond to a difference in what is required of an object that embodies them. Whether there is a difference between something embodying this property and that one may – unsurprisingly – be sensitive to the base and property in question. 21 19 Fine (1999, 66). He writes: “ ...under this criterion, the same rigid embodiment may involve two distinct principles [or] forms. ” To be clear, though: Fine’s case isn’t obviously a counterexample to Extension, but can smooth our path in that direction. 20 Fine (2008, 112). 21 I don’t mean to move past this issue too quickly, as it is an extremely important one: In the next chapter, we’ll 46 Fairchild Chapter 3. A Paradox of Matter and Form 3 Conclusion Of course, this discussion is far from conclusive. The second route leaves many questions unanswered: exactly how widespread are failures of Uniqueness? Is there any general principle of individuation capable of replacing it, or are we bound to proceed by cases? These questions all merit further investigation, but like the questions left open in Chapter 2, will be better addressed with a more developed version of hylomorphism in hand. Nor do I take myself to have shown that the second route is conclusively preferable to the first. My goal here was more modest; I hoped to show that – having noted the inconsistency of simple hylomorphism – there is space to amend the theory without giving up an antecedent commitment to avoiding arbitrariness. The result, however, is a more mysterious picture of the material world, and a version of plenitude that is again more humble than we might have expected. Whichever way we turn, the tension between avoiding arbitrariness and maintaining a fine-grained conception of material objects is an interesting one, and presents an unexplored choice point for contemporary defenders of hylomorphism. 22 turn to the notion of arbitrariness at work in support of theses like Global Plenitude and Existence. There, I’ll propose a framework that will help us to say why (for example) restricting Existence seems objectionably arbitrary in a way that restricting Uniqueness does not. 22 Thanks to Andrew Bacon, Jeremy Goodman, John Hawthorne, Shieva Kleinschmidt, Michaela McSweeney, Jeff Russell, and participants in the 6th SoCal PhilMath+PhilLogic+FoM Workshop for helpful discussion and feedback on earlier versions of this paper. I am especially grateful to Gabriel Uzquiano for extensive discussion and comments on multiple drafts. This chapter appears as Fairchild (2017) in Thought: A Journal of Philosophy. 47 4 Arbitrariness and the Long Road to Permissivism socks half hidden under a dirty mat quilt decorated with green leaves – the sunlight specifying these but not other objects, setting boundaries, sure of itself, not arbitrary. Louise Gluck, “Dawn” For the most part, we agree that metaphysics doesn’t admit of arbitrariness. But what does that mean? And what follows from our commitment to avoiding arbitrariness? Considerations of arbitrariness play important roles in a number of different such disputes. As we’ve already seen, it is supposed to be on grounds of arbitrariness that we are led to radical theses about mereological composition (namely, mereological universalism) and material coincidence (namely, material plenitude). Again, both are varieties of permissivism, according to which there are vastly more material objects than we ordinarily take there to be. Universalism is the thesis that given any plurality of objects, there is some further object composed of them. Plenitude is (more or less) the thesis that wherever there is some material object there is an abundance of coincident material objects. In each case, the thought is that once we have admitted some familiar composite or coincident objects, we have no principled grounds for excluding those with bizarre mereological or modal profiles – on pain of arbitrariness, we must accept them all. We’ve seen in Chapters 2 and 3 two examples of varieties of plenitude motivated in this way, and have examined the obstacles we face we try to take considerations of anti-arbitrariness super- seriously. But, so far, we’ve only been working with a rhetorical version of the idea. Thus, my first aim in this chapter is to provide a framework for understanding arbitrariness considerations in metaphysics, and in particular, in disputes about ontology. My second aim is to explore whether the argument from arbitrariness, as I propose to understand it, really is the proper foundation for one or both varieties of permissivism (that is, universalism and plenitude). As I’ll argue, the permissivist who hopes to rest her liberal ontology on an aversion to arbitrariness must either bolster the foundations with substantive metaphysical theses, or recognize that those foundations are much less dialectically stable than they’re usually taken to be. In Section 1, I lay out the territory surrounding the line of argument I’m interested in, and show 49 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism how the stakes are in some ways higher than we might expect. In Section 2, I investigate several different ways we might understand the connection between arbitrariness and permissive ontologies, and argue that none really works as an argument for the target views. I suggest in Section 3 that the best framework for understanding the arbitrariness arguments for permissivism relies on appeal to parity principles. However, I argue that even this is not sufficient to motivate the varieties of radical permissivism that interest us here: permissivists must also be committed to a schematic principle I call homogeneity. Section 4 explores three approaches to supporting homogeneity, and raises further worries for each route. Although I am here raising challenges for the argument from arbitrariness, my ultimate goal is to provide strategies for defending it by better clarifying what is at issue. The argument, like the views that it is meant to motivate, requires more careful attention than we might expect. 1 Set Up As we saw in Chapter 1, there are a lot of different routes to motivating varieties of permissivism –they have powerful applications to longstanding puzzles (eg. the puzzle of material constitution), and seem to provide comparatively more simple and elegant accounts of the world. 1 But by far the most pervasive idea in motivating both varieties of permissivism is an appeal to arbitrariness. In support of universalism, we hear speeches like the following: “Of course there are composite objects: that table, for example, is made up of some suitably arranged atoms. But why should that collection of atoms compose something, but not – say – the collection of chairs in this room? Even though the chair-fusion isn’t the sort of complex object we usually talk about, it seems objectionably arbitrary to recognize only the fusions that correspond to familiar objects. On pain of arbitrariness, we should recognize them all. ” And, in favor of plenitude, we hear something similar: “Of course there are coincident objects; statues, for example, are distinct from the lumps of clay that make them up. Unlike lumps, statues have certain features of their shape essentially, and so can’t survive being squashed. (That is, statues and lumps of clay have different modal profiles.) But consider desk-statues, which are just like statues, except that they also have features of their location essentially, and so can’t survive being moved around. This isn’t the sort of thing we usually talk about, but why should we accept that there is something that cannot survive a dramatic change in shape – like a statue – but not something that cannot survive a dramatic change in location, like a desk statue? It seems, again, objectionably arbitrary to accept only the objects corresponding to familiar modal profiles. On pain of arbitrariness, we should recognize 1 Though as we’ve seen in previous chapters, some varieties of permissivism are far from simple. 50 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism them all. These considerations are sometimes called “arguments from arbitrariness,” and are often understood as some of the most persuasive grounds for permissivism. 2 But despite the rhetorical effectiveness of these speeches, it isn’t obvious on a closer look what the intended argument amounts to. (Some opponents are even less impressed: Hirsch (2002) accused proponents of these arguments of being “perilously close to carrying out a burlesque battle with the English language. ”) Here, for example, is an evocative passage from Sidelle (2002): Another theoretical idea often invoked in criticism of ordinary (and other) views is a proscription against arbitrary distinctions. Arbitrariness, or its appearance, can show up in judgments about which portions of the world do, and which do not, contain objects, and in judgments about how things persist through change – what changes are ‘substantial’, and how things move through time. For instance, we commonly think that cells arranged in certain ways constitute cows, but that no object is constituted by this paper and my eye. But one may wonder whether there is any difference here which can, in an appropriate way, substantiate such a distinction, especially when science reveals how much space there is between small particles making up cows. What of our judgment that something ceases to exist when a cow dies, but not when a hoof is clipped, or it catches a cold? In each case, it seems that something persists, but some properties change. Or why does a car become larger when bumpers are attached, but not when a trailer is? The point is not that these questions have no answers, but that the failure, or absence, of obvious answers is often presented as grounds for rejecting a theory – so, conversely, a positive desideratum for a theory is to avoid arbitrariness, and to have explanations for those distinctions that might be challenged as doing so. 3 Among the threads evident in this passage already are conceptions of arbitrariness as a broadly epistemic complaint (“showing up in our judgments”), as a complaint about worldly distinctions in the absence of “appropriately” substantiating differences, and as a constraint on metaphysical theory choice. Each of these ways of thinking about arbitrariness, though closely related, will turn out to support very different motivations for permissivism. Of course, as I said above, this is just one line of argument for an apparently independently attractive view: why should we bother wading through this particular rhetorical tangle? One reason is that appeals to arbitrariness don’t just appear in these sorts of speeches, but support premises in other important arguments for permissivism. For example, in the well known Argument from Vagueness, a similar thought plays a crucial role. In the presentation of the argument in Sider (2001), the second premise is that in no continuous series is there a sharp cut-off in whether 2 Again, see for example, Cartwright (1975, 158),Van (1986, 145), Yablo (1987, 307), van Inwagen (1990, 66-69, 126), Sosa (1987, 178), Sosa (1999, 178), Bennett (2004), Hawthorne (2006, vii, 105), ?, 323-333, Leslie (2011, 281), Thomasson (2015, 214-215), Fairchild (2017, 34), and Uzquiano (forthcoming). For replies and criticism, see eg. Korman (2010) and Korman (2015). 3 Sidelle (2002, 119-120) 51 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism composition occurs. The justification he offers crucially appeals to arbitrariness: (...) there would seem to be something ‘metaphysically arbitrary’ about a sharp cut-off in a continuous series of cases of composition. Why is the cut-off here, rather than there? Granted, everyone must admit some metaphysically ‘brute’ facts, and it is a hard question why one brute fact seems more or less plausible than another. Nevertheless, this brute fact seems particularly hard to stomach. 4 Similar appeals to arbitrariness are also pervasive in other areas of metaphysics. And so, beyond the ontological payoff of getting a handle on the notion of arbitrariness, my hope is that we’ll illuminate the range of available frameworks for understanding complaints about arbitrariness in metaphysics more generally. The plan for the remainder of the paper, then, is to clarify the challenge facing the permissivist in developing an adequate argument from arbitrariness, and to discuss these and other candidate frameworks for understanding the road from arbitrariness to universalism or plenitude. Ultimately, I’ll argue that considerations of arbitrariness (even when made more precise) are less successful at motivating these varieties of permissivism than we often take them to be. I hope to show that we can do better, but as I’ll explain in Section 4, there is a long road ahead. In particular, I’ll suggest that although we often think of conservative ontologies as those that require us to do ‘nitty-gritty metaphysics’, in order to find the right ‘stopping point’ in ontology, it will turn out that a full-fledged defense of permissivism requires either a much more developed metaphysics of material objects, or of what we are doing when we do metaphysics. 1.1 The Stakes One other thread from the Sidelle passage above is worth unspooling before we begin: there is more than a passing analogy between the way that arbitrariness considerations motivate mereological universalism and material plenitude. Even in the sample speeches above, the arguments look ex- traordinarily similar: they rely on broadly anti-eliminativist premises (rejection of nihilism about constitution in the former case and the rejection of monism about coincidence in the latter) together with what seems to be a very general commitment to non-arbitrariness. Indeed, this considerations of ’arbitrariness’ are usually levied at a very general level in defense of pictures in ontology that are radically abundant along many dimensions: Sidelle’s passage is one such example (pointing us to an abundance of coinciding entities and an abundance of composite entities), but maybe even more vivid is Hawthorne’s motivation for Occupational Plenitude (which, again, entails synchronic, diachronic, and modal abundance). If we take the analogy seriously, it seems that the arbitrariness arguments for universalism and plenitude may stand or fall together (why should we think that restrictivism about universalism is objectionably arbitrary, but resist modal plenitude?). (Ultimately I’ll argue in Section 4 that they need not, but as we’ll see, that isn’t 4 Sider (2001, 124).I’ll return to some of these ideas in later sections. 52 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism obvious or straightforward.) Thus, the impression one gets from these arguments is that considerations of arbitrariness may support arguments against restrictivism – that is, moderate positions in ontology – across the board. If taken to an extreme, this could have far reaching ripples. For example; Irem Kurtsal Steen has recently argued that the very same considerations of arbitrariness which motivate universalism and plenitude should motivate us to accept a hybrid ontology of perduring and enduring entities. 5 If these arbitrariness arguments have such general force, then not only does it seem that the motivations for mereological universalism and material plenitude hang together, but we risk being led all the way to something like maximalism. Maximalism, very roughly put, is the thesis that anything that can exist, does exist. Here’s a gloss from Matti Eklund: What maximalism says is that for any type of object such that there can be objects of that type given that the empirical facts are exactly what they are, there are such objects. The qualification about the empirical facts being exactly what they are is there to rule out that maximalism should be committed to the existence of phlogiston or Vulcan. The ontological decadence of maximalism consists in its willingness to countenance all sorts of metaphysically weird sorts of objects – like incars, or like unintuitive abstract objects – as existing. 6 The thought is that this kind of maximalism “minimizes arbitrariness”, and insofar as we base our commitments to universalism and plenitude on a commitment to minimizing arbitrariness, we have reason to take maximalism seriously. For example, Sider (2007) writes: And—perhaps contrary to appearances—maximalism is indeed a reasonably attractive hypothesis. Maximalism is tempting (to the degree that it is) because it minimizes arbitrariness. If maximalism is false, and some consistent objects are present while others are missing, there’s a why-question without an answer: why do these objects, but not those, exist? Whereas if maximalism is true, we have a nicely rounded picture of the world, and fewer why-questions go unanswered. Maximalism is attractive for the same reason that plenitudinous views about material ontology are attractive. The more general the maximalism, the more it minimizes arbitrariness. 7 As Sider goes on to note, like any theoretical virtue, there is more to theory choice than min- imizing arbitrariness (or maximizing parsimony, etc). (“Of course, this may be taking things too far—there’s more to epistemic life than minimizing arbitrariness.”) But the standard appeals to non- arbitrariness in ontological disputes don’t seem to involve treating arbitrariness as a comparative vice, and weighing it against other theoretical virtues. 8 (And if they did, it isn’t clear they would 5 Kurtsal (ms). 6 Eklund (2008, 391) 7 Sider (2007, 223) 8 Except, perhaps, the end of the Sidelle passage above. 53 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism be half so compelling.) Instead, the rhetoric is that arbitrariness has no place in metaphysics, full stop, and thus that any form of restrictivism along this or that dimension of ontology is untenable. If that is what is supposed to be happening in the arbitrariness arguments, maximalism isn’t just an option on the table for those who are especially skittish about arbitrariness. Rather, it is the consequence of the very natural generalization of our usual arguments for this or that permissive ontology. And, as should already be apparent from Eklund’s gloss, maximalism isn’t for the faint of heart! I won’t here be arguing that taking arbitrariness seriously requires us to accept maximalism (or even that it requires us to accept both universalism and plenitude). However, I raise this now to point out two questions worth having on our radar as we proceed: first, to what extent to the motivations for universalism and plenitude hang together? (What must the complaint of arbitrariness look like for it to be principled to, as many do, endorse universalism and not plenitude? Is the reverse combination motivationally stable?) And, relatedly, do the very same concerns about arbitrariness that lead us to comparatively modest positions like universalism motivate something as extreme as maximalism? What are the limits of this line of argument? We’ll see in Section 4 that there are routes that forestall the rush to maximalism, and offer opportunities to drive a wedge between the arguments for different varieties of permissivism – for example, plenitude and universalism. However, not all paths from arbitrariness to permissivism this feature. This, I think, is yet another reason it is important to be extra clear about the com- plaint of arbitrariness. In addition to better understanding an important notion, and finding stable foundations for widely held views in metaphysics, part of what is at stake is understanding whether we should on the same grounds accept plenitudinous views along various other dimensions. Cards on the table: I quite like universalism, plenitude (no surprises there), and maximalism. In a way, the aim of this chapter is to make my own life much harder, by turning the microscope on what strikes me as the most compelling argument for my preferred positions in metaphysics. Fine – in the name of intellectual honesty, we do better to investigate the credentials of our own views! And, as we saw in the previous chapter, thoughts about arbitrariness aren’t just important for motivating views like plenitude: in many cases, they’re our main resource for making sense of the contours of the target view. And finally, while I like (something like) maximalism, I think that the threat of being driven to maximalism for the wrong reasons hasn’t been sufficiently appreciated. There is, as the Sider passage above emphasizes, an important connection between permissivism and arbitrariness. Still, we should take care in how we exploit that connection. 1.2 Clarifying the Challenge I first want to clarify the challenge the permissivist faces in making sense of the arbitrariness arguments. We often characterize the terrain of contemporary ontology in terms of attitudes about so-called ordinary objects – the objects recognized by common sense (or maybe, some combination of common sense and the special sciences). For example, Dan Korman (2015) characterizes his 54 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism preferred position (conservatism) as the view that there are more or less the objects we ordinarily take there to be: there are electrons, tigers, minivans, and mountains.He contrasts conservatism with the two other major players: eliminativism, according to which there are none or hardly any of the objects we ordinarily take there to be, and, of course, permissivism, which on his characterization says that there are all of there ordinary objects, but also huge numbers of extraordinary unfamiliar ones as well. But another way of carving up the landscape more closely resembles Peter van Inwagen’s tax- onomy of answers to the Special Composition Question, which asks: when do some things compose something? Any answer to the SCQ must be either Moderate or Extreme. There are exactly two Extreme answers: Universalism and Nihilism. According to Universalism, composition “always” happens; it happens, so to speak, automatically. (...) According to Nihilism, composition never happens (...). “Moderate” answers hold that sometimes, under certain conditions, two or more things compose something, and that sometimes two or more (non-overlapping) things do not compose anything. Moderate answers differ from one another about what the conditions under which composition occurs are. 9 Universalism and Plenitude are analogous in this way. Not only do they entail the existence of certain extraordinary objects in addition to the common-sense stock of ordinary ones, but they are each “extreme” answers to their respective questions. (That is, the SCQ on one hand and something like “When are there objects corresponding to a modal profile?” on the other.) On the face of it, they both purport to “max out” ontology along some dimension. Thus, it will be helpful to distinguish between what I’ll call moderate permissivism, which is a family of views that merely add to common sense, and radical permissivism, which is a family of views that purport to “max out” ontology – the “always” answers to their respective questions. 10 The way I propose to think of things, Korman-style conservatives and moderate permissivists will both count as metaphysical moderates. (I will occasionally use the word “restrictivist” in place of “moderate”, where it seems more helpful.) So, here is the particular challenge that the sort of motivation we’re looking for is going to have to live up to: arguments that undermine particular versions of conservatism, or which motivate expanding our ontology in certain local ways (by recognizing incars, or certain scattered fusions, and the like) won’t necessarily do the job I’m interested in. My aim is to find the structure of an argument that supports going “all the way” to one or more varieties of radical permissivism. As we’ll see, motivating truly radical ontologies – rather than just bigger ones – turns out to be a distinctively difficult task. It is also helpful to note that even an understanding of arbitrariness that meets this challenge 9 Inwagen (1993, 684) 10 Again, as we saw in Chapter 2, it is extremely difficult to make sense of the dimension(s) along which plenitude is an ‘extreme’ and consistent position. 55 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism won’t thereby weight the scale fully in favor of permissivism. Both versions of van Inwagen’s “ex- treme” ontologies – in the permissive and eliminativist directions – are touted by their proponents as gold-star methods for avoiding arbitrariness. For example, see again Sidelle (2002) on Universalism and Nihilism: These views share their fundamental ‘leading idea’, that any distinctions between (ma- terially filled) portions of the world which do, and which do not, contain objects would be ultimately arbitrary – so they both threat all such regions alike. Universalism is then more impressed with the seemingly obvious fact that there are objects (...). 11 In what follows, I’ll only be focusing on radical permissivism, and so will be spotting myself starting assumptions about the existence of mereologically composite objects and distinct, coincident objects. But I want to flag that what I say below should, for the most part, apply to attempts to motivate varieties of radical eliminativism as well. 2 Arbitrariness In ordinary usage, ‘arbitrariness’ is usually connected with personal whim. Etymologically, this is unsurprising: the word comes from the Latin arbiter, and meant originally in English “to be decided by one’s liking; dependent upon will or pleasure; at the discretion or option of any one. ” In more contemporary usage, “arbitrary” means “derived from mere opinion or preference; not based on the nature of things; hence, capricious, uncertain, varying. ” 12 We call decisions, distinctions, selections, beliefs, and edicts “arbitrary” when they have as their foundation someone’s personal whim – take, for example, the student who complains that his professor’s grading scheme is ‘arbitrary’ by insisting that your exam scores depend only on how much they like you. One thought in the neighborhood of our ordinary concept of ‘arbitrariness’, then, has to do with the epistemic standing of conservatism or conservative beliefs: that it is a matter of mere epistemic whim that the conservative believes that there are statues and not desk-statues, or that certain collections of atoms compose something but that collections of chairs do not. But what might this sort of epistemic whimsy consist in? It is not as if a commitment to moderate metaphysics characteristically involves a kind of ontological wishful thinking: after all, it seems that we do have some reason to believe that there are ordinary objects, and perhaps even some reasons to believe that there aren’t extraordinary ones. In Sections 2.1 and 2.2, I consider two epistemic complaints that we might be tempted to levy here, by way of filling out the idea of ‘epistemic whim’: the first has to do with the charge of anthropocentrism, while the second concerns violations of ‘parity constraints’ on our beliefs. I’ll argue that both fail to support an argument that can meet the challenge we’ve set for ourselves, though for different (and, I think, illuminating) reasons. In Section 2.3 I consider the methodological 11 Sidelle (2002, 129-130) 12 arbitrary (n.d.) 56 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism version of the appeal to non-arbitrariness, before turning in Section 3 to a more broadly metaphysical approach. 2.1 Anthropocentrism It clearly isn’t fair to charge moderate metaphysicians with having no reasons for their belief in restricted composition. But we might nonetheless be tempted to charge them with a different sort of epistemic failing: that their reasons for believing that there are atom-fusions but not chair-fusions just aren’t good ones. One familiar version of this complaint in discussions of permissivism is that conservatives, in one way or another, illegitimately weight contingencies of human activities, biology, and interests. For example, this may be part of Yablo’s warning about parochialism: Metaphysics aspires to understand reality as it is in itself, independently of the con- ceptual apparatus observers bring to bear on it. Even if we do not ourselves recognize essentially juvenile or mature entities, it is not hard to imagine others who would; and to someone who, in addition to the statue and the piece of clay, discerned a statue- cum-shards, not everything coincident with the statue would be fragile. Conversely, we recognize things essentially suitable for playing cribbage, or cutting grass, which others do not, or might not have. To insist on the credentials of things we recognize against those which others do, or might, seems indefensibly parochial. 13 Some versions of this complaint, then, target moderate metaphysicians who rest their conviction in restrictivism on the felt strength of ordinary judgments about what things there are, or on appeals to the fact that we usually recognize fusions of atoms but not fusions of chairs. But some presentations of this kind of complaint go further and invoke ideas about epistemic ‘luck’, and so resemble debunking arguments in other areas of philosophy. 14 The following passages from Sider (2001) and Hawthorne (2006) have been interpreted as suggesting this sort of argument: 15 [According to conservatism,] the entities that exist correspond exactly with the categories for continuants in our conceptual scheme: trees, aggregates, statues, lumps, persons, bodies, and so on. How convenient! It would be nothing short of a miracle if reality just happened to match our conceptual scheme in this way. Or is it rather that the world contains the objects it does because of the activities of humans? This is an equally unappealing hypothesis. 16 13 Yablo (1987, 307) 14 Especially given this, it is maybe tendentious that I am considering these lines of thought under the heading of arguments from arbitrariness, since they may seem to be importantly distinct kinds of motivations. (Since I consider this only to set it aside, there’s a sense in which I agree!) But two replies to support my inclusion of it here: first, anecdotally, this is the first port of call in conversation about the “arbitrariness” of metaphysical moderatism, so it is worth examining more carefully. Second, this isn’t a totally unfamiliar use of the notion of ‘arbitrariness’ . See, for example, Schoenfield (forthcoming): “Here’s how I’ll think of things: To regard a belief as formed arbitrarily is to regard which belief one ends up adopting with respect to P as independent of whether P. ”. 15 Both are quoted in Korman (2015, 95) as “debunking arguments specifically targeting conservatives”, advanced in defense of permissivism. However, see Fairchild and Hawthorne (in press) for a disclaimer. 16 Sider (2001, 156-157) 57 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism Isn’t it anthropocentric to suppose that the ontology of the world matches (more or less) exactly what human speakers have words for? Barring a kind of anti-realism one of us should tolerate, wouldn’t it be remarkable if the lines of reality matched the lines we have words for? The simplest exercises of sociological imagination ought to convince us that it is something of a biological and/or cultural accident that we draw the lines that we do. If we are to be charitable towards ourselves without being unduly chauvinistic, it seems that we should posit ever so many more objects than we habitually talk about, in order not to credit ourselves with too much luck or sophistication in hitting ontological targets most of the time. 17 The rough thought behind the debunking line is that, having reflected on the ways that our ontological beliefs seem to be contingent on our social, cultural, and biological circumstances, we find that we might easily have believed radically different things about what there is. This may leave us with the impression that, supposing that the conservative is right, and our ordinary ontological beliefs are true, then this is so only by accident, “miracle”, or luck – a kind of luck that it is tempting to think is incompatible with knowledge. Korman (2015) discusses this kind of argument in great detail, and argues that it is ‘epistemically unstable’ for the permissivist, since familiar and tempting arguments for permissivism rely just as much on the epistemic good-standing of our ontological beliefs. Fairchild and Hawthorne (in press) reply at length on behalf of permissivism – the upshot of that discussion is that, like Korman, we are not optimistic about this line of argument for the permissivist (though for somewhat different reasons; see esp. our Sections 2 and 3). However, here I just want to make the very brief observation that even the best versions of any complaints appealing to anthropocentrism (or otherwise targeting our ordinary ontological beliefs) will target only very specific versions of restrictivism. The charge that our ordinary beliefs are “too lucky” to constitute knowledge, or that our justifications for common-sense conservatism are in bad standing, will only affect conservatives who tie their views in some way to the “ontology of common-sense” . But recall the challenge we’re interested in: we need more than just an objection to particular metaphysical moderates; an argument for radical permissivism requires that we go much further. Whatever fault of anthropocentrism common-sense (conservative) moderates might be guilty of, there doesn’t seem to be anything anthropocentric about someone who believes that every plurality has a fusion except for the collection of chairs in this room. And, so, even if we are licensed to levy some family of epistemic complaints against particularly anthropocentric-seeming proposals, there is no reason to think that belief in any moderate position will be in that same sort of bad 17 Hawthorne (2006, 105). See also Shoemaker (1988, 209). 58 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism standing. 18 So, complaints of anthropocentrism won’t get us all the way to radical permissivism. 19 2.2 Epistemic Parity A much better model for an epistemic complaint against moderate metaphysics comes from the way we usually talk about “arbitrary choices” . Given a choice between two options A and B, when we have equally good reasons for choosing option A as for choosing option B, our choice of A rather than B is typically said to be “arbitrary” . (So, for example, when I offer you a chance to select one of two identical candy boxes – assuming you know no further relevant information about them – your selection is bound to be arbitrary.) Similarly, when we have equally good reason to believe that p and that q, and p and q are incompatible, our belief that p is in some sense arbitrary. This idea is made particularly explicit in McSweeney (in press), where she argues that when we have equally good reason to believe incompatible theories, we aren’t justified in believing either one. She is there concerned with theories about what is fundamental, but we can adapt the epistemic principle she motivates for our purposes: Epistemic Non-Arbitrariness. For theories T and T’, if we have no reasons to favor T over T’ (and vice versa), and T and T’ are incompatible, then we should not believe T and we should not believe T’ . One thought, then, is that this is exactly the situation we are in with respect to certain groups of theories about composition and coincidence: any moderate position will involve “drawing a line” somewhere on the ontological ruler, and you might think that for a great many candidate ‘ticks’ on the ruler, we’ve got equally good reason to draw the line at tick A as at tick B. Thus, committed moderates violate Epistemic Non-Arbitrariness. Notice that this complaint, unlike the complaint of anthropocentrism, at least has the right sort of structure to live up to the challenge. Even really bizarre forms of moderate permissivism that no one has ever endorsed may nevertheless be epistemically on a par. Despite having the right sort of structure, this isn’t going to be enough to get us to radical permissivism. Even granting the (very controversial) premise that this is the sort of position we are in with respect to every form of moderate metaphysics, it is perfectly consistent for the moderate metaphysician to nonetheless 18 Though see Thomasson (2015) for discussion of a related argument from Bricker (forthcoming) that does crucially appeal to parochialism in defense of certain radically permissive pictures. His complaint, roughly, is not that particular theories are objectionably anthropocentric, but that the virtues we appeal to in metaphysical theory choice provide only parochial grounds for believing theories. So, we do better epistemically to accept something much closer to maximalism. This line has more in common with the arguments I consider in the following sections. 19 There is also a nearby complaint that is less purely epistemic: that (barring “anti-realism”), there is something distinctively objectionable about the metaphysical hypothesis that what the world contains is roughly what we ordinarily take there to be. (See eg. discussion of the How Bizarre! Complaint in Fairchild and Hawthorne (in press)). But the same general sort of limitation applies there: this kind of challenge only straightforwardly targets particular versions of moderate metaphysics. Also, as an aside: if, as some of the quoted passages suggest, this complaint is supposed to be a premise in an argument to the effect that there must be everything we (or creatures sufficiently like us) might think or talk about, I still suspect that this will fall short of radical permissivism, at least along some dimensions. There are presumably modal profiles (if not pluralities) that correspond to objects that it isn’t possible for creatures like us to recognize. 59 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism hold that some moderate metaphysics must be right (even if they can’t know which). Here is one toy comparison, by way of illustration. 20 Consider the question: how many things are there in the universe? There may be many numbers m such that there is no n such that we have better reason to believe there are n exactly things in the universe than that there are exactly m things. But it would be absurd for me to conclude on this basis that there is no k such that k is the number of things in the universe. This sort of position is often important in metaphysics, given our impoverished epistemic state with respect to many metaphysical questions. For example, David Lewis takes a similar position regarding restrictions on the possible sizes of spacetime. He points out that while there must be some constraint, we might be “incurably ignorant” about what it is: My hope, notice, is just that some such break exists. I do not claim to make the worlds, and I do not claim to have some way of finding out all about them, therefore I will not be at all troubled if I cannot say just what break is right. My thesis is existential: there is some break, and the correct break is sufficiently salient within the mathematical universe not to be ad hoc. If study of the mathematical generalisations of ordinary spacetime manifolds revealed one salient break, and one only, I would dare say that it was the right break (...). If study revealed no suitable breaks, I would regard that as serious trouble. If study revealed more than one suitable break, I would be content to profess ignorance – incurable ignorance, most likely. 21 In many domains, we have very general reasons to be confident in ruling out extreme options while simultaneously acknowledging that we are in dire epistmeic straits with respect to particular moderate theses. So, while the charge of Epistemic Arbitrariness might constitute an important complaint against defenders of particular moderate positions, it won’t be enough to support a positive argument for radical permissivism. One final thing worth noting on this line is that the security I’ve suggested that the moderate can enjoy does rely in a certain way on our ignorance. If, in fact, all moderate positions turn out to be epistemically on a par, then although the moderate can in this way hang on to her rejection of radical eliminativism and radical permissivism, she won’t be able to endorse a specific moderate proposal. Thus, by her lights, we’re incurably ignorant (as Lewis suggests) when it comes to central ontological questions. We might think that this is a major limitation of moderatism, but I’m not confident it is damning enough a burden to constitute support for radical permissivism. 22 20 Thanks to Gabriel Uzquiano for this example and to Jeff Russell for this way of putting it. 21 Lewis (1986). Thanks to Jeff Russell for pointing me to this passage. 22 After all, the permissivist may have to declare widespread ignorance on similar grounds: in a later section, I briefly discuss the Problem of the Many as it arises in a universalist setting, and analogous issues come up there. Even if exactly one collection of atoms in the vicinity of my friend’s cat Eliot makes up Eliot, there may not be any collection such that I have more reason to believe that it is that collection than any of many others. Personally, I’m more comfortable with ignorance about Eliot’s exact whereabouts than I am with widespread ignorance about what there is, but that preference doesn’t yet constitute an argument against this defense of moderatism. Relatedly, there may be especially good dialectical reason for the permissivist to be careful with this Epistemic Non-Arbitrariness principle. Applied too generally, a principle of this form might tell in favor of agnosticism about 60 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism 2.3 Methodological Complaints Before we turn away from broadly epistemic complaints, there is one final theme from the passages above that I want to address. One complaint we might levy against moderate metaphysics doesn’t stem from some kind of general epistemic failure on the part of those who endorse varieties of restrictivism, but rather from a methodological disagreement. We might conceive (as the end of the Sidelle and Sider passages suggest) of arbitrariness as a kind of methodological vice to be minimized or avoided in theory choice, as much as possible. For example, we might try to motivate radical permissivism by pointing to a general method- ological disposition to minimize the distinctions we draw as theorists, and only “draw lines” when given truly outstanding reason to do so – in the case of ontology, absent such reason, we’ll default to some form of radicalism as a methodological starting-place. I think it is helpful to think of this per- spective as analogous to those who take parsimony super-seriously: the hard-core pasimony-driven metaphysician will only accept objects into her ontological theory under extreme duress. But, just as an announced preference for desert landscapes would be unsatisfying without some kind of fur- ther explanation, this methodological default isn’t very satisfying on its own as an explanation for why we’re uncomfortable with restrictivism. And, insofar as it is only a methodological disposition, we’re given only a temporary foundation for radical permissivism: although we might be optimistic that no outstandingly good reason to draw a line will come along, nothing I’ve said so far gives us any foundation for that optimism. (Though in later sections, I will sketch a picture that may help us do a little better.) A similar approach treats anti-arbitrariness as a more comparative theoretical virtue. This sort of metaphysician might adopt as a global methodological guide that we ought to minimize unexplained distinctions in our theorizing as much as possible. Insofar as any form of moderate metaphysics appears to involve drawing unexplained distinctions, we see to have reason to prefer more radical positions. For example, see Horgan (1993): (...) An adequate metaphysical theory – like an adequate scientific theory – should itself be systematic and general, and should keep to a minimum the unexplained facts that it posits. In particular, a good metaphysical theory should avoid positing a plethora of quite specific, sui generis, compositional facts. ” 23 But it isn’t clear that applying this methodological guide fully generally will lead us to per- varieties of radical eliminativism and radical permissivism!. 23 Horgan (1993, 695). He goes on to say, like the Sider passage from Section 1, that “Even though explanation must presumably bottom out somewhere, it is just not credible – or even intelligible – that it should bottom out with specific compositional facts which themseleves are utterly unexplainable and do not conform to any systematic general principles. Rather, if one bunch of physical simples compose a genuine physical object, but another bunch of simples do not compose any genuine object, then there must be some reason why, it couldn’t be that these two facts are at the explanatory bedrock of being.” This kind of proposal differs from the “minimize unexplained distinctions” guideline: it allows that there are certain areas where “bruteness” is acceptable. (See also Dasgupta (2016b) on this.) I’m sympathetic to this proposal, and am tempted to see the discussion in Sections 3 and 4 as setting up the framework the permissivist needs for sorting the “acceptable” from the “unacceptable” bruteness. 61 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism missivism at all. That is, it isn’t clear whether radical permissivism yeilds a theory that does a better job of minimizing unexplained distinctions than its competitors when we turn to the other consequences of the view. For example, although universalism avoids positing unexplained distinctions between the plu- ralities that compose and those that don’t, it seems to require us to posit unexplained distinctions elsewhere in our metaphysics. Consider the Problem of the Many: my friend’s cat Eliot is made up of some atoms, but (given universalism) there are also a number of things made up of only slightly different collections of atoms. We want to say there is exactly one cat in the vicinity, but this seems to require us to posit an unexplained distinction between the various collections of atoms. What could explain why this fusion, but not any of the others, is a cat? Until we have a compelling answer, it seems that we’ve avoided unexplained distinctions in one arena only to incur them in another. 24 This is not to say that the permissivist can’t say something satisfying here, but only that insofar as we are motivated by concerns about comparative virtues, it isn’t immediately obvious that the scorecard looks vastly better for radical permissivism. 25 3 Parity Ultimately, I think that the most promising complaint in the vicinity of “arbitrariness” does crucially appeal to violations of parity and unexplained distinctions, but is not a complaint that concerns how metaphysicians settle their beliefs. Instead, the complaint I am most interested in is a complaint that concerns what reality is like according to the moderate: roughly, that any version of restrictivism requires there to be some parity-violating distinction in the world. As believers and as choosers, when we make an arbitrary decision, we draw a distinction between options where there is no difference relevant to the choice at hand; no difference with the right sort of significance to account for our decision. Similarly, for there to be an “arbitrary” line in the world is for there to be a distinction the absence of a relevantly significant difference. (And so to say that some bit of the world doesn’t admit of arbitrariness is to say that it obeys this kind of parity constraint: there are no distinctions (of a certain kind) without (the right sort of) differences.) This is much more in line with what many people in the literature seem to have in mind at the end of the day. For example, Dan Korman places something like parity at the center of his characterization: The argument from arbitrariness turns on the claim that there is no difference between 24 Without taking us too far afield, I also want to acknowledge that there are other responses to this case that may do better on this count. However, it seems that this is a part of a much more general pattern for permissivism: for example, in Chapter 4, I discuss an attempt to avoid paradox by allowing occasional violations of a certain uniqueness condition on matter/form compounds, but it is far from clear that we’ll be able to pin down a satisfying explanation distinguishing those that obey it and those that do not. 25 Thanks to Shieva Kleinschmidt for pressing me on this as a problem for permissivists (or, at least, those motivated by ‘anti-arbitrariness’ construed as a general constraint on theorizing. See also Kleinschmidt (2013) for a related case against arguments that the PSR (rather than a weaker explanatory demand) is required to guide good theory choice. 62 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism certain of the familiar kinds that we intuitively judge to exist and certain of the strange kinds that we intuitively judge not to exist that could account for the former’s but not the latter’s having instances. In short, there is no ontologically significant difference between the relevant strange and familiar kinds. 26 I’ll follow Korman in making use of the idea of ‘ontologically significant differences’ as a kind of placeholder. 27 However, unlike Korman, I don’t think it will ultimately be most fruitful to understand the demand for parity in terms of familiar and unfamiliar kinds. Instead, I want to suggest that we can sharpen things by framing them in same terms as the questions that radical pictures are meant to be “always” answers to. (“When do pluralities compose?”, “When are profiles instantiated?”) That is: we should focus on parity principles governing the correspondences that each radically permissive picture purports to “max out” . For example, the two principles of interest to the universalist and plenitude-theorist are Compositional Parity and Profile Parity, respectively: Compositional Parity. For any pluralities the xs and the ys, if there is no relevant (or “compositionally significant”) difference between the xs and the ys, then if the xs compose something, then the ys do. So, the only way that collection of atoms in the vicinity of this cup could compose something while the collection of chairs in this room could fail to compose something is if there were some compositionally relevant difference between the collections. Similarly, Profile Parity says: Profile Parity. For any modal profiles m and n, if there is no relevant (or significant) difference between m and n, then if m corresponds to an object, n does. Again, I am hoping (in this chapter) to remain mostly neutral about the various ways that we might understand modal profiles, which makes Profile Parity somewhat more difficult to illustrate. But the thought here is still familiar: the only way for it to be that there is something coincident with the lump of clay that has its shape essentially (and so would be destroyed by squashing) but that there isn’t something that has its location essentially (and so would be destroyed by being moved elsewhere) is if there were some relevant difference between these profiles. In Section 3.2, I’ll say how I think that focusing on these sorts of parity principles can help us better understand the structure of the arbitrariness arguments. But first, I want to make good on the promise to say a bit more about my use of the placeholder notion of relevant or significant 26 Korman (2010, 123). 27 Admittedly, the placeholder is somewhat distracting. I’ll say more about it in Section 3.1, but here is some temporary reassurance: first, we are familiar with a similar placeholder in moral theorizing. Given a pair of actions where one is permissible and the other impermissible, or two creatures where one is a moral agent and the other is not, we’ll seek a morally significant difference between the cases. This seeking might reveal that we don’t share sensibilities about what suffices, or have different views on whether there should be any further difference in this case – so we can make some progress even with the placeholder. Second, this idea shows up as a placeholder in lots of the literature on composition. See, for example, Merricks (2005, 28): “After all, lest restricted composition seem arbitrary, there should be something special about the product of atoms that compose an object. That is, there should be something about that product that differs relevantly from the ersatz “product” of atoms that compose nothing at all.” 63 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism differences. 3.1 Remarks on Parity and Significant Differences First, as I’ve stated these two parity principles, there’s clearly a way of understanding “relevant” or “significant” differences that makes them trivial. Suppose, for example, that the conservative is right that the collection of atoms in the vicinity of this cup does compose something, but that the collection of chairs in this room does not. Here is one difference we can point to between the collections: the atoms compose something, and the chairs don’t! If that different counts as “compositionally significant”, then moderate metaphysics trivially avoids any complaint about parity violations. The best solution here is likely to invoke some notion of explanation or “accounting for” in our understanding of “significant differences”, as Korman does in the quoted passage above. But exactly how to do that in a non-tendentious way is going to be delicate. So, for now, I want to avoid packing any heavy-duty commitments about explanation into our preliminary formulation of the parity principles, and take it as common ground that these sorts of differences won’t count as answering a challenge from parity. 28 There is another worry nearby. How useful could it really be to focus on these parity principles without filling in the placeholder notion? After all, it seems that this just highlights the sense in which we are in serious danger of a dialectical standstill: moderates and radicals alike agree that these domains obey parity. They disagree about precisely what the placeholder suppresses: which differences are (compositionally, etc.) significant. I want to sharply distinguish two tasks. The first is to find an argument that will move committed metaphysical moderates. I think that this is an extraordinarily hard (and important) task, but it isn’t the one I aim to take up here. (In part because I somewhat suspect that such an argument won’t go via considerations of arbitrariness.) Instead, my aim here is to get more clear on the motivations that I and other permissivists (and, perhaps, eliminativists) point to as our own reasons for rejecting moderate theories in favor of extreme ones. Even if our progress on that front turns out to be only schematic, my hope is that we’ll have landed at a better understanding of the foundations for and credentials of radical permissivism. What I hope to show in the next section is that, even generously spotting ourselves this placeholder, it is also an extraordinarily hard task to find a path “all the way” to radical permissivism that looks good even by our own lights. So, although we may not gain much ground against the moderate by focusing on these schematic principles, we can nonetheless make progress understanding what is required for radical permissivism by thinking about what principles with this shape can do for us. I turn to this project in the next section. 28 On this framework, a brutalist in the style of Markosian (1998) rejects Compositional Parity. Markosian (2014) should maybe be understood as accepting Compositional Parity and instead rejecting something like the following Parity principle: for any regionsr ands, ifr contains an object ands does not, there is some significant difference between r and s. 64 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism 3.2 Parity at Work I want to look first at two familiar argumentative strategies for expanded ontologies that rely on parity principles. We have already seen the first strategy at work. Case-based arbitrariness arguments involve identifying some case from our stock of recognized existents, and pairing it with some relevantly similar but contested case. So, for example, in the toy speech with which we began, the plenitude- lover pointed out that we recognize things that have their rough shape essentially, but that there isn’t any metaphysically interesting difference between having a certain shape essentially and having a certain location essentially. And so, by Profile Parity, given that there are statues that sometimes sit on desks, there must be desk statues as well. But, at best, this sort of strategy only extends our ontology by fits and starts. Granted, it may be especially rhetorically effective for motivating some weird and surprising versions of moderate permissivism. But my complaint here is in keeping with the theme so far: a convincing argument for moderate permissivism need not provide any support for radical permissivism. And while we might get the sense from these sorts of exercises that we can “keep going”, these local arguments don’t yet provide us any reason to trust that expanding our ontology bit-by-bit will take us all the way. A more promising (related) strategy that similarly invokes parity principles focuses not just on local considerations about specific pairs of cases, but instead on continuous series of cases (analogous to Sorites series we consider when thinking about vagueness). On this strategy, the permissivist argues from a recognized case of existence to contested ones by constructing a series where each adjacent pair of cases is such that there is no metaphysically significant difference between them. (And thus: any “stopping point” in such a series would be parity-violating.) The long game, then, is to take baby steps all the way to the target variety of radical permissivism. Consider an example adapted from Sosa (1987) and Sosa (1999): a snowball, lets suppose, is a ball made of snow that is essentially perfectly round – it can’t survive any degree of squashing. There are snowballs, but there doesn’t seem to be any metaphysically interesting difference between snowballs and things that can survive just a little bit of squashing. Such a small difference, it seems, shouldn’t make a difference to existence. 29 So (by parity), if there are snowballs, there are these marginally more resilient things as well. And as Sosa pointed out, for any of the infinitely many “degrees of squashing” between being round and being flattened, we can argue incrementally in the same way that there is something made of snow that there is something made of snow that can survive exactly that degree of squashing (but no more). Thus, consideration of these sorts of series leads us to recognize infinitely many things, just by taking small jumps between very similar cases. It is clear, then, that we can motivate extraordinarily liberal ontologies in this way – certainly some liberal enough to make conservatives uncomfortable! 29 This is the thought crucial to the vagueness argument discussed in Section 1. See also the discussion of Alteration Parity in Farichild and Hawthorne (forthcoming). 65 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism Again, we still lack more than a rhetorical sense that we’ll make it all the way to radical permis- sivism. In general, for the series strategy to meet the challenge, we require a further assumption: that any form of moderate ontology will involve drawing a distinction between adjacent pairs in some such chain. This point is probably most familiar from the Lewis-Sider argument from vague- ness for universalism (and diachronic plenitude): crucial to that argument is the premise that if any version of restricted composition is true, then we can construct a continuous series of cases from a case where composition occurs to a case where it doesn’t. But this assumption seems illegitimate in many of the cases we care about, for a variety of reasons. First, as in the Lewis-Sider argument, a really natural way to construct a series running from putative cases of composition to putative cases of non-composition is to take adjacent pairs of pluralities where each subsequent plurality is just like the one preceding, except that it has one additional member. But there are compelling versions of restricted composition which don’t involve drawing a line between adjacent pairs in this kind of series: consider, for example, a version of moderate permissivism according to which only pluralities of finitely many things compose, but pluralities of infinitely many things are “too many” to compose. Even according to Finitary Composition, no adjacent pair in a series like the one I’ve described will differ in what matters for composition. 30 Sider suggests that we can set this kind of restrictivism aside, writing that “no one will want to claim that the jump from finitude to infinity is what makes the difference between composition and its absence. ” This might be right as a description of standard conservatives, but again our aims are higher, here: Finitary Composition strikes me as an extremely compelling moderate position – one that we’ll have to be able to rule out to rest easy in our commitment to radical permissivism. I agree with Sider that we have grounds to do so, but the point I want to make here is just that it won’t be challenged by an application of parity to this sort of continuous series. For other varieties of permissivism, it isn’t even clear how to go about constructing the right sort of series. Some versions of plenitude (for example, Occupational Plenitude) lend themselves to this, but many others do not. For example, the two versions of plenitude I have devoted the most time to here seem much less amenable to this treatment: “distributional” varieties plenitude like global plenitude from Chapter 2, and hylomorphic varieties of plenitude like the one discussed in Chapter 3. If we understand profiles in a broadly property-theoretic way, for example, as specifying the properties an individual has essentially and those it has accidentally, it is much more difficult to see how we should think about chains of “relevantly similar” pairs of modal profiles. The snowball example above is especially vivid because we focused on incremental ‘degrees’ of squashing, but it is much harder to see what sort of continuous chain of property-theoretic modal profiles could get us to (for example) an object that is coincident with me, but might have been coincident with an oak tree. So, ultimately, although both the case and chain-based applications of parity are powerful ar- gumentative strategies for permissivists, and may leave us with the strong impression that we can 30 See Sider (2001, 123). 66 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism go all the way to radical permissivism, neither yet supports the conclusion that we can “go all the way”. 4 Homogeneity To make sense of the motivational foundations of radical permissivism, I think we do better to focus on a further commitment: the assumption that the domains in question are homogeneous with respect to any of the sorts of differences that could account for a difference between cases of existence. That is, radical permissivists are committed to principles like Compositional Homogeneity and Profile Homogeneity: Compositional Homogeneity. For any pluralities the xs and the ys, there is no relevant difference between the xs and the ys. Profile Homogeneity. For any profilesm andn, there is no relevant difference between m and n. These are both still highly schematic, but even so it is clear that homogeneity principles are incredibly strong, and furthermore, seem to be carrying all of the weight in the background of the arbitrariness arguments. Another thing is clear: these principles are going to be incredibly hard to provide independent support for. This is, I think, where the hard work really begins. In what remains of this chapter, my aim is to provide a preliminary agenda for that project. I’ll sketch three approaches to supporting one or both homogeneity theses, and explore some of the distinctive advantages and obstacles facing each strategy. Each draws out themes we’ve seen in the previous chapters, and will offer different routes to answering some of the questions left open by the work we’ve done so far. 4.1 Pessimistic Induction One especially tempting route to motivating the homogeneity of some domain is to proceed by a kind of pessimistic induction on existing moderate proposals. We look, as we have throughout the long history of this debate, at the most promising candidates for relevant differences in that domain – being sufficiently unified, being intentionally created, participating in a life, or even figuring in our best scientific theories – and having found them all lacking in one way or another, conclude that there must not be any such differences between (eg.) pluralities or profiles after all. 31 As I suggested above, I think there is something really unsatisfying about approaches that lean 31 After arguing for universalism “by elimination”,?, 145 expresses this kind of pessimism. One caveat, though: often the problem raised for proposed restrictions on composition is that they fail extensionally as characterizations of the domain of common sense. (Either because they rule out things common sense recognizes, or rule out things it doesn’t.) But by the permissivist’s lights, that isn’t likely to be a count against the ontological significance of the relevant features. So, in finding past proposals lacking, that had better not be the standard we’re holding them to. 67 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism on this sort of pessimism. Not only do I prefer to be an optimist when I can, but I think that we should hope to do better when it comes to providing support for radical permissivism. It is also not clear to be that there really are sufficient grounds of this kind for many of the varieties of radical perissivism we’re interested in here. There is, of course, a huge body of literature on candidate differences between pluralities in support of moderate theories of mereological composition, and it may be tempting to regard the familiar difficulties with these proposals evidence that no better moderate theory of composition is waiting around the corner. But even if we are tempted to conclude on these grounds that there is nothing more promising in the offing where composition is concerned, we certainly shouldn’t also conclude on this basis that other varieties of moderate metaphysics are similarly unpromising. (For example, in part because of the variety of ways we might understand modal profiles, the terrain surrounding Profile Homogeneity is much less well explored.) 32 4.2 The “Top Down” Approach The basic thought behind what I’ll call the Top Down Approach is that, in general, “ontological significance” will be a very high bar. We shouldn’t expect very many features to carry that weight – so, we should expect many domains to be homogeneous! This idea is admittedly extremely rough: in this section I will do what I can to give a better sense of it, with the caveat that making the idea fully precise will be well beyond the scope of this chapter. My aim, instead, is to give a better sense of how this kind of approach to metaphysics leads us to permissivism and some of the distinctive challenges it gives rise to. I see at least two paths through this approach. One way of thinking that might lead us to take the “Top Down” approach to homogeneity is inspired by a picture of metaphysics as a kind of “maximally general” sort of inquiry, where the ontologist is tasked with (among other things) providing a framework for understanding the full range of possible domains of inquiry. As such, many of the features that loom large in other more narrow fields – being a groundhog, being indivisible, being finite, being a moral agent, being intentionally created – won’t turn out to matter for answering ontological questions. In physics, we have a sense of the sorts of differences between objects or systems that might be physically significant - that might make a difference to whether the objects will behave the same way, or whether two systems are physically equivalent, for example. Similarly, as we saw above, we’re familiar with the general idea (even if we disagree on the details) that certain things might be moral difference makers (like consciousness or freedom) and others might not (like shape or flavor). We similarly have a sense of the sorts of things that can be relevant difference-makers in logic and mathematics. However, we tend to think of those domains, though, as operating at a level of “generality” where many things that are significant in other domains won’t make a difference. 32 This may not be quite right: as I’ve set things up, any form of pluralism about material constitution without plenitude amounts to a form of moderatism analogous to restricted composition. Thus, the extensive literature on the grounding problem for pluralism (although conducted in different terms) might be understood as providing exactly this sort of explanation. In a slightly different setting, Dasgupta (2016a) attributes this sort of reason to many contemporary essentialists, saying that they are “skeptical that any principled distinction can be drawn [between the sets of properties that constitute the essential properties of an entity, and those that don’t]. ” 68 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism It doesn’t matter whether we have a collection of fundamental particles or groundhogs for whether that collection forms a set. On the proposed way of thinking, ontology is similar in ambition, and so many things that matter when we “zoom in” won’t be relevant for whether something is a case of existence or not. 33 Another route to the thought that ontologically significant differences are hard to come by, and thus to radical permissivism, instead goes via ‘deflationist’ slogans: that “existence is cheap” or “easy”, or that “nothing much is required” for existence. As Linnebo (2012) puts it: Meta-ontological minimalism is accordingly the view that the key concepts of ontology have a minimal character. Not surprisingly, this view tends to result in very generous ontologies. For the less that is required for existence, the more objects there will be. As I understand these slogans, it falls out of the picture that the features (of pluralities, profiles, etc) that can “make the difference” between existence and non-existence are hard to come by. (One nice thing about thinking about things this way is that we needn’t be tempted to say other more controversial deflationist things: eg. that objects themselves are ‘thin’ .) Notice, also, that the Top Down Approach is compatible with other sorts of picture thinking that push in a very different di- rection. Where the deflationist says that ’existence is easy’, another sort of metaphysician will insist that ‘existence is hard’: maybe all that matters is being perfectly fundamental, or being ’the Uni- verse’ . This picture again motivates the idea that many domains are homogeneous, but corresponds instead to a kind of widespread radical eliminativim. As expected, the motivational scaffolding behind the arbitrariness arguments is the same whether we’re arguing for radical eliminativism or radical permissivism. Whatever our path to the Top Down Approach, if we take this approach at face value, it looks like it will give us reason to be radical along many dimensions. Thus, the kind of maximalism we worried about at the outset turns out to be a consequence of one way of implementing this kind of approach. particular, the version of the approach that says “very few things are ontologically significant – in fact, all that matters at the end of the day is (an appropriately careful notion of) consistency” . (Exactly how coherent we can make this thought isn’t entirely clear, but the observation I’m interested in here is just the connection to the arbitrariness arguments.) But, interestingly, there are other ways to implement this idea, which will lead to different sorts of pictures. For example, we might instead think that (say) consistency and “materiality” are all that matters. Again, if we can make sense of it, that yields a kind of material maximalism: similar to maximalism in spirit, but without yielding a bloated ontology of abstracta, mere possibilia, and so on. We can thus answer one of the questions we started with: given the right background sensibilities an aversion to arbitrariness may lead to maximalism, but it isn’t a forced march, and care with the path reveals alternatives to mainstream maximalism that are worth exploring. 33 This analogy is far from perfect, and may hurt more than it helps, but: compare our answers to the questions “What matters for whether something is a tiger?” and “What matters for whether something is a mammal?” (and “What matters for whether something is alive?”). 69 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism A few last remarks on some of the dangers of the Top Down Approach: first as I’ve noted (and probably demonstrated), it is far from clear how to say something very sensible or satisfying about it. Maximalism and its cousins are also notoriously difficult to state coherently, and in some cases, it isn’t clear that there is a unique consistent view in the vicinity. More worryingly, in some cases trying to ‘max out’ along one or more dimensions while holding fixed other natural metaphysical assumptions leads us directly in to paradox. We saw a case of exactly this kind in Chapter 3, resulting in part from a commitment to an abundant theory of properties as well as a liberal theory of embodiments. As we’ve seen, in order to avoid disaster in these settings, we either need to give up the corresponding homogeneity principle (which requires a serious revision of our sensibilities, on the Top Down Approach), or make adjustments elsewhere in our metaphysics. In Chapter 3, I proposed one sort of adjustment we might try to make elsewhere in order to hang on to our commitment to avoiding arbitrariness; as there, these adjustments will sometimes have to be quite dramatic. The lesson here is that really tidy maximalist positions are very difficult to make sense of, especially if we are tempted by maximalism in its most radical form. But, if we’re hoping to motivate permissivism on fully general grounds by taking the Top Down Approach to homogeneity, these are open questions we will have to take up. If we want to root permissivism in such a global strategy, we’ll have to make sense of its limits. 4.3 The Nitty Gritty Approach Permissivists of another stripe are more cautious in their approach to homogeneity principles. Rather than beginning from a more global picture like the one above, they arrive at homogeneity principles by first rolling up their sleeves to do some nitty-gritty metaphysics. Put extremely roughly: whether some or other domain is “homogenous” depends on what differences are significant there. Those attracted to this approach allow that getting our hands dirty with the metaphysics might reveal that what matters for composition, modal persistence, temporal persistence, set formation – and so on – may differ. We might, for example, root our commitment to Compositional Homogeneity in reflections on mereological composition. Having done some nitty-gritty metaphysics of composition, we find that (given what composition is, or what composite objects are) the domain of pluralities in fact turns out to be homogeneous with respect to whatever differences we have found to be relevant to composition. Just like moderates, radical permissivists motivated in this way will say something about “what is required for composition to occur”; it is just that it will turn out that these requirements are satisfied by every plurality. (Perhaps because, as people often say, “nothing is required” for composition.) But again: this is neither purely a matter of reflecting on particular cases, nor on global or commitments about what matters for ontology – rather, it is importantly domain-specific. This Nitty Gritty Approach is illustrated especially vividly by defenses of radically permissive theories of sets. Just as we asked when some things compose, we’re also interested in when some things form a set. Again, “always” is an attractive answer, in large part because candidate “some- 70 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism times” answers seem to involve violations of parity. The relevant homogeneity principle is: Set Homogeneity. For anyxs andys, there is no (set-theoretically) relevant difference between the xs and the ys. Of course, Set Homogeneity gets us in to trouble in well known ways: Russell’s Paradox is often taken to show that a particular plurality doesn’t form a set, and so (barring brutalism) there must be a set-theoretically relevant difference somewhere. But as I remarked in Chapter 3, the credentials of this idea are strong: one reason they are so strong is that we seem to be led to Set Homogeneity by reflection on what sorts of things sets are. 34 For example, Linnebo (2010) takes this approach in his defense of radical permissivism about sets, suggesting that to answer the question “we must go beyond [the claims of ordinary singular set theory] and analyze the concepts of plurality and set” . Reflection on the nature of sets leads to the observation that pluralities seem to be “on a par” with respect to what matters for set formation. He writes: Since a set is completely characterized by its elements, any plurality xx seems to provide a complete and precise characterization of a set, namely the set whose elements are precisely xx. What more could be needed for such a set to exist? 35 In light of this, I want to make two final observations about the Nitty Gritty Approach to homogeneity theses. First, look again to a remark from Linnebo about what a restrictivist about sets might do to motivate a moderate position. . In arguing that the most salient competing “sometimes” answer – that some pluralities are “too many” to form a set – is committed to “committed to an arbitrary boundary between pluralities that do and do not form sets”, he writes: The main challenge will be to motivate and defend the threshold cardinality beginning at which pluralities are too large to form sets. Why should this particular cardinality mark the threshold? Why not some other cardinality? (...) One answer is that it is somehow “written into” the concept of a set that every set must have fewer elements than this threshold cardinality. ” 36 But, he says, no such idea seems to be “written into” the concept of a set. The interesting lesson here, I think, is that to motivate the ‘non-arbitrariness’ of their position both the moderate and the radical must look to the “concept of a set” to find support for the heterogeneity or homogeneity of pluralities. In general, we typically think of the burden of doing “nitty-gritty metaphysics” as resting on the moderate alone. Moderates, not radicals, must provide some positive account of what is required for composition, or for modal persistence, such that existence is restricted in such-and-such a way. Put differently, they owe us an account of what differences are (and are not) compositionally or metaphysically significant, motivated by their account of the phenomenon 34 It is also worth noting again that not every instance of the Top Down Approach from Section 4.2 delivers Set Homogeneity: material maximalism, for example, likely does not. 35 Linnebo (2010, 147) 36 Linnebo (2010, 152-153). 71 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism in question, such that their restrictivism falls out as a consequence. But again: on the proposed approach to homogeneity principles, radical permissivists take on a very similar burden. The Nitty Gritty Approach thus sets a task that is quite far from what we seemed to be getting ourselves in to when we first encountered the arbitrariness arguments. The impression we took from the appeals to arbitrariness in Section 1 is that arbitrariness considerations are intended to have force on very general (and uncontroversial) grounds. If only we have recognized the virtues of non- arbitrary theories, the thought goes, we’ll be driven immediately to radicalism! But if instead our best grounds for endorsing (say) compositional homogeneity invoke substantive commitments about the nature of composition or composite objects, then these appeals to the virtues of anti-arbitrariness were misleadingly cavalier. One final and closely related thing worth emphasizing is that, as I discussed in Section 1.2, it also seemed at the outset as though the motivations for mereological universalism and modal plenitude were perfectly analogous, and so it seemed that varieties of permissivism might stand or fall together. But the proposal that we find support for homogeneity in local considerations will allow a wedge here: it may well turn out that the motivations for universalism and plenitude come apart. At the end of the day, it will depend on the details of the metaphysics. This should be especially welcome news to those who balked at (any of the varieties of) maximalism, and in particular, those who hold the very familiar combination of universalism and pluralist non-plenitude. On many metaphysical pictures, compositional homogeneity is extremely plausible, but profile homogeneity isn’t – the nitty gritty approach not only leaves the space to drive a wedge between the two theses, but gives us something of a strategy for doing so. Relatedly, this approach also provides opportunities to take seriously under-explored combinations of views: for example, the combination of plenitude and moderatism about composition. We wondered at the beginning whether a commitment to avoiding arbitrariness would lead us to something like metaphysical maximalism. It seems, at least so far, that the answer is “no” (or, better: not obviously). In Section 4.2, we saw that maximalism comes out as a consequence of one way of spelling out the relationship between anti-arbitrariness and varieties of permissivism, but even on the global approach, it isn’t a forced march. In this section, I’ve laid out a different approach that paves the way for an even more cautious defense of one or more varieties of permissivism, but requires more substantive local metaphysical work than we might have thought. 5 Conclusion We have found that a number of attempts to make something out of the arbitrariness arguments won’t cut it as foundations for radical permissivism, even if they make for effective arguments against conservatism or other moderate forms of permissivism. While I don’t want to suggest that I’ve provided an exhaustive discussion of all of the ways we might think about arbitrariness, the frameworks considered here point to a general problem for motivating permissivism in this way. 72 Fairchild Chapter 4. Arbitrariness and the Long Road to Permissivism When we look at what I have suggested is the best structure for understanding the way that anti- arbitrariness considerations motivate permissivism (via a commitment to instances of parity and to homogeneity theses) we find that the motivations for permissivism depend on much more substantive commitments than we might have expected from the speeches we started with. In Section 4, I’ve tried to give a sense of what those commitments might be, though there is clearly more work to be done. And so, by trying to get more clear about the commitments that were hiding beneath an effective rhetorical strategy, we have illuminated exciting future directions for exploring and defending radical permissivism. The strategies described in Sections 4.2 and 4.3 both carry significant challenges. If we think these considerations of arbitrariness have force on very general grounds, for “top down” reasons, we are going to have to make sense of something like maximalism. If we want to avoid that, we’re going to have to do some very nitty-gritty metaphysics of material objects. The arguments from arbitrariness are thus not entirely hopeless, but ultimately, it seems that the road to radical permissivism is going to be much longer than we might have expected. 37 37 Thanks to Mark Balaguer, Renee Bolinger, Liam Kofi Bright, Naomi Dershowitz, John Hawthorne, Nicola Kemp, Shieva Kleinschmidt, Tanya Kostochka, Matt Leonard, Michaela McSweeney, Jeff Russell, Mark Schroeder, Irem Kurtsal Steen, Dan Korman, and Gabriel Uzquiano, and Jonathan Wright for comments and discussion of these issues. I am especially grateful to audiences at Rutgers Metaphysical Mayhem, the University of Rochester, the University of Michigan, Cornell University, and UNC Wilimington for helpful feedback on earlier versions of this paper. Some of the material here overlaps with material in Fairchild and Hawthorne (in press). 73 References arbitrary (Oxford English Dictionary Online ed.). (n.d.). Oxford University Press. Retrieved 2018-06-06, from http://www.oed.com/view/Entry/10180 Bennett, K. (2004). Spatio-temporal coincidence and the grounding problem. Philosophical Studies, 118(3), 339–371. Cartwright, R. (1975). Scattered objects. In K. Lehrer (Ed.), Analysis and metaphysics (pp. 153–171). Reidel. Dasgupta, S. (2016a). Essentialism and the nonidentity problem. Philosophy and Phenomenological Re- search. Dasgupta, S. (2016b). Metaphysical rationalism. Noˆ us, 50(2), 379–418. Eklund, M. (2008). The picture of reality as an amorphous lump. In T. Sider, J. Hawthorne, & D. W. Zim- merman (Eds.), Contemporary debates in metaphysics (pp. 382–96). Blackwell. Evnine, S. J. (2016). Making objects and events: A hylomorphic theory of artifacts, actions, and organisms. Oxford University Press UK. Fairchild, M. (2017). A paradox of matter and form. Thought: A Journal of Philosophy, 6(1), 33–42. Fairchild, M., & Hawthorne, J. (in press). Against conservatism in metaphysics. Philosophy. Fine, K. (1982). Acts, events, and things. Language and Ontology. Proceedings of the 6th International Wittgenstein Symposium(1), 97 -105. Fine, K. (1994). Essence and modality. Philosophical Perspectives, 8, 1–16. Fine, K. (1999). Things and their parts. Midwest Studies in Philosophy, 23(1), 61–74. Fine, K. (2007). Response to kathrin koslicki. Dialectica, 61(1), 161–166. Fine, K. (2008). I—kit fine: Coincidence and form. Aristotelian Society Supplementary Volume, 82(1), 101–118. Hawthorne, J. (2006). Metaphysical essays. Oxford University Press. Hirsch, E. (2002). 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Abstract (if available)

Abstract According to serious pluralism about material constitution, there are distinct material objects that occupy the same region of space for the duration of their existence. We often say that these permanently coinciding objects have different ‘modal profiles’: they are able to survive through different circumstances and differ in which properties they have essentially and accidentally. But having admitted that there are distinct coincident material objects corresponding to different modal profiles, it seems to many that it would be objectionably arbitrary to grant anything short of a ‘full’ abundance of coincident material objects. We seem to be led -- on pain of arbitrariness -- to ‘material plenitude’: the radical view that there is a material object corresponding to every consistent modal profile. ❧ This dissertation is primarily an exploration of material plenitude: its varieties, its foundations, and its limits. I am concerned with three questions: (1) What is material plenitude?, (2) What is it not? (that is, what are the limits of plenitude?), and (3) Why should we believe it?. I provide a partial answer to each question, and argue that the cumulative lesson of this exploration is that we shouldn’t expect any variety of plenitude to straightforwardly deliver an ‘ontological free-for-all’. Still, investigations into the foundations and limits of plenitude will help to reveal substantive constraints on any adequate theory: by understanding views that push ontology ‘as far as we can’ along some dimension or other, we illuminate the boundaries of the material world.

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Creator Fairchild, Maegan (author)

Core Title Unlimited ontology and its limits

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Philosophy

Publication Date 07/25/2018

Defense Date 05/08/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag arbitrariness,hylomorphism,material constitution,metaphysics,OAI-PMH Harvest,ontology,plenitude

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Uzquiano, Gabriel (committee chair), Bacon, Andrew (committee member), Hawthorne, John (committee member), Kleinschmidt, Shieva (committee member), Schein, Barry (committee member)

Creator Email maeganfairchi@gmail.com,mmfair@umich.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-30128

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Legacy Identifier etd-FairchildM-6455.pdf

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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