the double lives of objects: an essay in the metaphysics of the ordinary world

The Double Lives of Objects

The Double Livesof Objects

An Essay in the Metaphysicsof the Ordinary World

Thomas Sattig

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Preface

The ordinary world is populated with such objects as persons, tables, trees, andmountains. This volume defends a novel philosophical picture of ordinaryobjects, perspectival hylomorphism. The picture has a metaphysical part, quasi-hylomorphism, or q-hylomorphism, concerning the nature of ordinary objects,and a semantical part, perspectivalism, concerning the functioning of discourseabout ordinary objects. The thesis, in a nutshell, is that ordinary objects leaddouble lives: they are compounds of matter and form; and since their matter andform have different qualitative profiles, ordinary objects can be described differ-ently from different perspectives.Perspectival hylomorphism carves a middle way between the two accounts that

have dominated traditional metaphysics of material objects, namely, classicalmereology and Aristotelian hylomorphism. It is a fundamentally classical-mereo-logical framework with an Aristotelian twist. By combining some of theirstrengths, perspectival hylomorphism diminishes the distance between the twotraditions. More importantly, however, it exhibits powers beyond the reach of itscompetitors. Neither the classical-mereological conception nor the Aristotelianconception divides an ordinary object into components with different lives. Thepossibility of qualitative divergence among a double-layered object’s componentsis unique to perspectival hylomorphism.Why believe that ordinary objects lead double lives? A philosophical account

of ordinary objects should aim to preserve our common-sense conception of thelatter. The task of saving the appearances, however, has proven difficult. For ourfamiliar worldview faces a range of hard problems: it is riddled with paradox andclashes with plausible principles from metaphysics. The orthodox position incontemporary discussions is that these problems show our familiar worldview tobe defective and in need of substantial revision. What recommends perspectivalhylomorphism is that it does a better job than its rivals in preserving our folkconception of the world in the face of a range of such problems. The unified typeof response in the proposed framework is compatibilist: seemingly inconsistentjudgements about ordinary objects are really consistent because they manifestdifferent perspectives on the same double-layered objects.This volume has a straightforward structure: first the theory is developed, then

it is applied. In Chapters 1 and 2, perspectival hylomorphism is introduced inits simplest version, which undergoes various refinements and extensions in

subsequent chapters. Chapter 1 contains the metaphysics: q-hylomorphism.Chapter 2 contains the metaphysical semantics: perspectivalism.Chapter 1 opens with a review of the classical-mereological and the Aristoteli-

an accounts of ordinary objects, thus setting the stage for the introduction ofq-hylomorphism. While q-hylomorphism follows classical mereology in viewingcomplex material objects as mereological sums of smaller material objects, itdenies that ordinary objects are material objects, where a material object is anobject with a spatiotemporal location in a basic, non-derivative sense. Moreover,while q-hylomorphism follows Aristotelian hylomorphism in distinguishingbetween an ordinary object’s matter and form, it construes forms as having avery different nature and at least a partly different function than Aristotelianforms. An ordinary object is a double-layered compound of a material object anda complex fact about this material object, which fact contains properties thatrealize an ordinary kind, such as person or table. The material object is charac-terized as the ordinary object’s matter, and the complex fact as the ordinaryobject’s individual form. The most significant aspect of this q-hylomorphicaccount is that the qualitative profile of an ordinary object’s matter and thequalitative profile of the same object’s form may diverge. In short, there may behylomorphic divergence.In Chapter 2, the metaphysical account is combined with a perspectival

semantics of discourse about ordinary objects. The starting point is a psycho-logical thesis: we may conceive of ordinary objects from different perspectives.We may take the sortal-sensitive perspective and think of ordinary objects interms of properties that realize ordinary kinds. Or we may take the sortal-abstractperspective and think of ordinary objects in a primarily spatiotemporal way,regardless of which specific kinds they belong to. The next step is to link thispsychological thesis with a semantical one: to a type of perspective on objectscorresponds a mode of predication, a certain way of predicating a property of anobject. By adopting the sortal-sensitive perspective on an ordinary object, aspeaker employs the formal mode of predication when describing the object.By adopting the sortal-abstract perspective on an ordinary object, a speakeremploys the material mode of predication when describing the object. Whenwe ask what an object is like formally, we ask which properties are contained inthe object’s individual form, emphasizing the specific kind to which the objectbelongs. When we ask what an object is like materially, we ask which propertiesare instantiated by the object’s underlying matter, abstracting from the object’skind. The key feature of perspectivalism is that it allows perspectival divergence: ashift in perspective, and hence in mode of predication, may yield a shift in truthvalue. Perspectival divergence is based on hylomorphic divergence: one and the

viii preface

same object may have a given property from one perspective and lack it fromanother, because form and matter may encode different properties. In short,ordinary objects lead double lives.In Chapters 3–8, perspectival hylomorphism is applied to a range of problems

that threaten our common-sense conception of objects. Some of the problemsconstitute a threat from within, suggesting that our conception is internallyinconsistent. Some constitute a threat from without, suggesting that our concep-tion clashes with compelling metaphysical principles. Some of the problems havebeen staples in the history of metaphysics, some have appeared more recently,and some appear here for the first time. While Chapters 1 and 2 are presupposedby the rest and thus form the obligatory starting point, Chapters 3–8 can be readselectively and in a different order.Chapter 3 is about paradoxes of coincidence that arise from temporal coun-

terexamples to the platitude of common sense that distinct ordinary objectscannot fit into the same place at the same time. Chapter 4 is about paradoxesof fission and of intermittent existence, which arise from compelling counter-examples to the platitude that an ordinary object cannot have two exact spatiallocations at the same time nor have two temporal beginnings. Chapter 5 is aboutthree problems: a modal paradox of coincidence that arises from a modalcounterexample to the principle that distinct ordinary objects cannot fit intothe same place at all times at which they exist, the related grounding problem,concerning how modal properties of objects are grounded in non-modal prop-erties, and the problem of specifying sufficient conditions of transworld identity.Chapter 6 is about the problem that the common-sense conception of objectsseems to make the actual world indeterministic on mundane, a priori grounds.Chapter 7 is about problems arising from trying to make sense of ordinaryobjects’ indeterminate mereological, spatial, and temporal boundaries, andabout the related problem of the many, concerning how to get the intuitivenumber of ordinary objects right. And Chapter 8 is about the problem thataccording to common sense, ordinary objects cannot undergo variationin shape that transgresses the limits associated with certain kinds to whichthey belong, whereas according to a compelling metaphysical picture of ordinaryobjects’ shapes in relativistic spacetime, they do undergo such radical variation.Responses to these problems that rest on a single-layered account of ordinary

objects, as proposed by classical mereology and Aristotelian hylomorphism, tendto be incompatibilist, forced to view the problems as uncovering a genuineinconsistency and to reject one or more compelling premises. Moreover, stand-ard responses are disunified, using disparate keys to unlock different problems.Perspectival hylomorphism scores higher on both counts, offering a unified,


preface ix

compatibilist response to the mentioned problems, which reconciles their seem-ingly inconsistent premises. The key that unlocks each problem is perspectivaldivergence: since ordinary objects are double-layered compounds permittinghylomorphic divergence, we may correctly describe the same object in differentways from different perspectives, employing different modes of predication.Many philosophical mysteries about ordinary objects dissolve once we realizethat they lead double lives.No attempt is made in this volume of saving ordinary objects from all philo-

sophical threats having been identified in the literature. The focus is on thevirtues of perspectival hylomorphism; and there are problems on which thisposition has no bearing. Nor is the volume designed to make a conclusive casefor perspectival hylomorphism. Some rivals may have been missed and somemisrepresented. The aim is to argue that when it comes to saving the world as weknow it perspectival hylomorphism has a clear advantage with respect to asignificant range of problems over its most salient rivals. Assuming that anequilibrium between metaphysics and common sense is desirable, this is a strongreason for taking the unorthodox position seriously.Most of the ideas presented in this book were developed during my time at

Washington University in St. Louis. A large portion of the first draft was writtenwhile I held a Research Fellowship from the Alexander von Humboldt-Founda-tion at Humboldt University in Berlin. I completed the book at the University ofTuebingen.I am grateful to a number of people for valuable comments on the material

in this book: Ralf Bader, Yuri Balashov, Philipp Blum, Eric Brown, Ralf Busse,Marta Campdelacreu, Fabrice Correia, Tom Crisp, Aurélien Darbellay, ShamikDasgupta, Matti Eklund, Kit Fine, John Gabriel, Cody Gilmore, KatherineHawley, John Hawthorne, John Heil, Geert Keil, Kathrin Koslicki, ThomasKroedel, Dan López de Sa, Jonathan Lowe, Matthew McGrath, GiovanniMerlo, Ulrich Meyer, Christian Nimtz, Eric Olson, Josh Parsons, Laurie Paul,Jan Plate, Tobias Rosefeldt, Sven Rosenkranz, Benjamin Schnieder, PeterSchulte, Moritz Schulz, Wolfgang Schwarz, Ori Simchen, Alex Skiles, RoySorensen, Wolfgang Spohn, Alexander Steinberg, Jim Stone, Amie Thomasson,Achille Varzi, Barbara Vetter, Robbie Williams, Tim Williamson, ChristianWüthrich, Stephen Yablo, Elia Zardini, Dean Zimmerman, and several anonymousreferees. I also express collective thanks to my audiences at numerous talks at whichI presented this material.


x preface

Portions of this book are based on previously published work, in which earlierversions of some of the present ideas were formulated. I am grateful to the editorsand publishers for their permission to reuse material from the following articles:

‘Compatibilism about Coincidence’, Philosophical Review, 119 (2010): 273–313; copyrightCornell University Press, by kind permission of Duke University Press.

‘The Paradox of Fission and the Ontology of Ordinary Objects’, Philosophy and Phenom-enological Research, 85 (2012): 594–623; by kind permission of John Wiley and Sons.

‘Vague Objects and the Problem of the Many’, Metaphysica, 14 (2013): 211–23; by kindpermission of Springer Science and Business Media.

‘Mereological Indeterminacy: Metaphysical but Not Fundamental’, in K. Akiba andA. Abasnezhad (eds), Vague Objects and Vague Identity: New Essays on Ontic Vague-ness. Springer (2014), 25–42; by kind permission of Springer Science and BusinessMedia.

‘Pluralism and Determinism’, Journal of Philosophy, 111 (2014): 135–50; by kind permis-sion of the Journal of Philosophy.

preface xi

Contents

List of Figures xiv

1. Q-Hylomorphism 11.1 Classical Mereology and Aristotelian Hylomorphism 11.2 Material Objects, Sortals, and K-paths 131.3 Q-Hylomorphism about Ordinary Objects 22

2. Perspectivalism 322.1 Representing Ordinary Objects 322.2 Modes of Predication and Q-Hylomorphism 432.3 Metaphysics, Metaphysical Semantics, and Common Sense 67

3. Coincidence 753.1 Paradoxes of Coincidence 753.2 Incompatibilism about Coincidence 793.3 Compatibilism about Coincidence 88

4. Discontinuity 1044.1 Paradoxes of Fission 1054.2 Compatibilism about Fission 1154.3 Paradoxes of Intermittent Existence 127

5. Modality 1345.1 A Modal Paradox of Coincidence 1355.2 The Grounding Problem 1495.3 Transworld Identity and Sufficiency 154

6. Determinism 1666.1 Weak and Strong Qualitative Determinism 1666.2 The Problem of Cheap Indeterminism 1706.3 Material Determinism and Formal Branching 184

7. Indeterminacy 1907.1 Indeterminacy De Dicto and the Problem of the Many 1917.2 Fundamental Indeterminacy De Re and Coincidence 1957.3 Derivative Indeterminacy De Re 200

8. Relativity 2198.1 The Problem of Relativistic Change 2198.2 No Easy Way Out 2288.3 Compatibilism about Relativistic Change 234

Bibliography 247Index 255

List of Figures

3.1 The piece of paper and the paper plane 943.2 Tibbles and Tib 954.1 The material basis of fission 1194.2 Bilocation 1204.3 Coincidence 1224.4 Non-local persistence 1234.5 Intermittent existence 1335.1 Louis, Miles, and eternal recurrence 1565.2 Formal role-switching 1616.1 Purely formal qualitative branching 1857.1 Indeterminate mereological boundaries 2097.2 Indeterminate temporal boundaries 2178.1 A standard case of relativistic change in shape 2228.2 An extreme case of relativistic change in shape 2268.3 The chair’s kind-dependent trajectory in F 2318.4 The chair’s kind-dependent trajectory in F* 2328.5 F-bound chair-path iF 2428.6 F*-bound chair-path iF* 242

1

Q-Hylomorphism

Ordinary objects lead double lives: they are compounds of matter and form; andsince their matter and form have different spatiotemporal and qualitative pro-files, they may be described differently from different perspectives. This is the gistof perspectival hylomorphism, the philosophical picture of ordinary objects thatwill be presented and motivated in this volume. The present chapter lays thefoundation by developing the metaphysical part of the picture, quasi-hylomorph-ism. The account of ordinary objects to be proposed stands on the shoulders oftwo classical approaches. It is with these that the story begins.

1.1 Classical Mereology and AristotelianHylomorphism

There is, let us assume, a basic sense of having a spatiotemporal location.A material object is located in space and time in this basic sense, and has variousnon-derivative physical properties, such as shape and weight. Let us also assumethat there are composite material objects, which have smaller material objects astheir spatial parts at the different times at which they exist. What is the nature of acomposite material object?

1.1.1 Classical mereology

The position that dominates contemporary metaphysics of material objects and isnow most immediately associated with David Lewis is that composite materialobjects are mereological sums, fusions, or aggregates, as construed by classicalmereology, where the mereological sum, or aggregate, or fusion, is the only typeof whole there is.1 The two central principles characterizing mereological sums

1 Classical mereology was developed by Stanislaw Leśniewski in the 1920s. Notable proponents,in addition to Lewis (1986, 1991), include Goodman and Quine (1947). Simons (1987) calls thisfamily of systems ‘classical extensional mereology’.

are the principle of unrestricted composition, or universalism, and the principleof uniqueness of composition, or extensionality. Universalism concerns theexistence of mereological sums. Extensionality concerns their identity. We canthink of universalism as a condition concerning how a whole is generated from aplurality of objects. And we can think of extensionality as an explanation of whata given whole, generated in this way, fundamentally is. According to universal-ism, whenever there are some objects, there is at least one whole that theycompose. Given the material objects a, b, and c, there is a new object, a + b + c,the sum of a, b, and c. Any plurality of objects compose a further object, nomatter how the composing objects are arranged or what kinds they belong to.Moreover, according to extensionality, a whole x is identical with a whole y just incase x and y have the same parts. So the identity of a whole depends solely onwhich objects it is composed of, irrespective of any further qualitative facts aboutthese objects. For example, the identity of the sum a + b + c depends only on itsbeing composed of a, b, and c. Since a mereological sum fundamentally dependsonly on which things it is composed of, not on what kinds these things belongto or on how they are related, a mereological sum is an unstructured whole.(More on mereological structure below.) We can say, furthermore, that when theidentity of an object, x, is explained in terms of other objects, the ys, then the ysare ontologically prior to x. A mereological sum’s parts are then ontologicallyprior to the whole.2

There are several versions of the classical-mereological conception of compos-ite material objects, depending on whether the objects are cut into parts alongtheir temporal dimension as well as along their spatial dimensions—that is,depending on whether they have temporal as well as spatial parts. According tothree-dimensionalism, or endurantism, material objects lack temporal parts,whereas according to four-dimensionalism, or perdurantism, they have temporalparts. Four-dimensionalists standardly apply a temporally unrelativized notion ofparthood—parthood simpliciter—to material objects, whereas three-dimension-alists standardly apply a temporally relativized notion of parthood—parthood ata time—to material objects.3

Here is a brief sketch of the standard four-dimensionalist, classical-mereological picture of complex material objects. First, various temporallyunrelativized mereological notions may be defined in terms of the primitivenotion of parthood simpliciter. For example,

2 See Fine (1995: 283; 2010: 582).3 For details, see Lewis (1986), Sider (2001a), Hawley (2001), and Sattig (2006).

2 q-hylomorphism

x is a proper part of y =df x is a part of y and x is not identical with y.x and y overlap =df some object z is a part of x and a part of y.The xs compose y =df every x is a part of y, and every part of y overlaps an x.4

Second, four-dimensionalist mereological sums may be characterized by thefollowing atemporal versions of the principles of unrestricted composition, oruniversalism, and uniqueness of composition, or extensionality:

Unrestricted composition (universalism): For any plurality of material objects, the xs, thereis a material object that is composed of the xs.

Uniqueness of composition (extensionality): For any composite material objects a and b, ais identical with b iff for any pluralities of xs and ys, if a is composed of the xs and b iscomposed of the ys, then the xs are the same as the ys.

According to standard four-dimensionalism, temporally longer-lived sums aregenerated from temporally shorter-lived objects, just as spatially bigger sumsare generated from spatially smaller objects. Just as the spatially small is onto-logically prior to the big, so the temporally short-lived is ontologically prior to thelong-lived. A spatially and temporally extended mereological sum is an unstruc-tured whole, divisible into spatial and temporal parts in any which way.This specification of mereological existence and identity conditions in purely

atemporal terms stays quiet about a material composite’s temporal profile, whichconcerns the composite’s properties and relations at various times. Focusing onan object’s mereological profile over time, standard four-dimensionalists viewthis profile as derived from the atemporal mereological profile of the object’sinstantaneous temporal parts: a has b as a part at t iff a’s temporal part located at thas b as a part simpliciter. Notice that this account of an object’s temporalmereological profile allows a material object to change in its parts over time: ahas different parts at different times iff a has different temporal parts, located atdifferent times, with different absolute parts.A three-dimensionalist version of the classical-mereological account of com-

plex material objects may be obtained by taking the notion of parthood at a timeas primitive (in the four-dimensionalist framework, this is a derived notion) andby temporally relativizing the above definitions and principles in the followingstraightforward way:

x is a proper part of y at t =df x is a part of y at t and x is not identical with y.

x and y overlap at t =df some object z is a part of x at t and a part of y at t.

4 As an alternative to taking the parthood relation as primitive, Kit Fine has proposed aformulation of classical mereology in a more general framework that takes the operation ofsummation as primitive instead (2010: Section V).

q-hylomorphism 3

The xs compose y at t =df every x is a part of y at t, and every part of y overlaps an x at t.

Unrestricted composition (universalism): For any plurality of material objects, the xs,existing at a time t, there is a material object that is composed of the xs at t.

Uniqueness of composition (extensionality): For any composite material objects a and b, ais identical with b iff for any times t and t* and for any pluralities of xs and ys, if a iscomposed of the xs at t and b is composed of the ys at t*, then the xs are the same as the ys.

On the three-dimensionalist picture, spatially bigger sums are generated fromspatially smaller objects, but temporally longer-lived sums are not generatedfrom temporally shorter-lived objects. No ontological priority is assigned to theshort-lived. Accordingly, while spatially extended objects are composed of spatialparts, temporally extended objects are not composed of temporal parts.Notice, further, how inflexible this three-dimensionalist variant of extension-

ality is with respect to a material object’s temporal mereological profile (which ishere viewed as underived). Since sameness of the parts of composite materialobjects a and b is necessary for the identity of a and b, a material object cannotchange in parts over time; the parts go where it goes. If a material object a iscomposed of the xs at any time of its existence, then a is composed of the xs at alltimes of its existence.5 Second, since sameness of the parts of composite materialobjects a and b is sufficient for the identity of a and b, a material object cansurvive radical scattering; it goes where the parts go. If the xs compose materialobject a at any time, then they compose a when the xs are spatially close together,but also when the xs are scattered across the universe.Friends of the classical-mereological conception of complex material objects

typically hold that ordinary objects, such as persons and tables, are just compositematerial objects construed as mereological sums of smaller material objects.Among the many mereological sums of material objects that exist, by universal-ism, only very few are ordinary objects, in virtue of instantiating properties andrelations that make them instances of certain ordinary kinds, such as person ortable. So there are sums that are familiar and useful to us, such as tables, and hencecount as ordinary objects, and there are sums that are too spatiotemporallyscattered to be recognized by ordinary folks, such as the sum of my left arm andthe moon. While ordinary mereological sums have properties and relations thatrealize ordinary kinds, such as table, the identity of a table does not depend on anytable-realizers. In general, the identity of an ordinary object construed as a mere

5 The doctrine that sameness of parts is necessary for identity is known as mereologicalessentialism. This doctrine was popular among a number of 18th-century philosophers, includingLeibniz (1982), Butler, and Reid (see the excerpts in Perry 1975). More recently the doctrine wasdefended by Chisholm (1976: App. B) and Van Cleve (1986).

4 q-hylomorphism

sum does not depend on the instantiation of any kind-determining properties.Ordinary objects are not fundamentally characterized by any specific kinds; theyhave a kind-independent nature. The identity of a table depends solely on whichmaterial objects are its parts, irrespective of whether these parts are arrangedtablewise. Such an arrangement is not constitutive of the table’s nature.Given a four-dimensionalist version of the classical-mereological account of

composite material objects and a three-dimensionalist version, we need to dis-tinguish the thesis that ordinary objects are four-dimensionalist sums from thethesis that they are three-dimensionalist sums. To most friends of classicalmereology, the first thesis has seemed far more plausible than the second.Ordinary objects are typically capable of change in parts over time and incapableof surviving massive scattering. This expected mereological variability and unityof ordinary objects is incompatible with the three-dimensionalist version ofextensionality stated above. The four-dimensionalist version, by contrast, allowsfor a derivative notion of temporary parthood that secures compatibility withmereological change and unity. This asymmetry, and related considerations, hasmoved most friends of the classical-mereological approach to adopt the four-dimensionalist package.6

Concluding this brief review, the classical-mereological analysis of ordinaryobjects may be summarized as follows:

Classical mereologyAccording to the classical-mereological conception, an ordinary object is an unstructuredmereological sum of material objects, whose identity depends only on which objects are itsparts, irrespective of which kinds these objects belong to and of how they are arranged.

1.1.2 Aristotelian hylomorphism

Aristotelian, or neo-Aristotelian, hylomorphism is an alternative conception ofparthood and composition.7 As I understand this family of views, they have atleast in common the rejection of the classical-mereological thesis that theunstructured mereological sum is the only type of whole there is, recognizing astructured type of whole completely absent from classical mereology. A type ofwhole can be characterized by various principles, among them a principleconcerning how a whole is generated from a plurality of objects, and aprinciple concerning the conditions of identity for wholes.8 Universalism and

6 Though see Thomson (1983) for a three-dimensionalist alternative. See Koslicki (2008:chapter 2) for a valuable overview of various positions.

7 See Koslicki (2008) for an extensive discussion of different versions of hylomorphism.8 Fine (2010: 569–70) speaks of formal and material principles governing a composition oper-

ation. Among the formal principles are those providing conditions of application, or existence, and

q-hylomorphism 5

extensionality are the existence principle and the identity principle, respectively,by which unstructured mereological sums are (at least partly) characterized. Thetask of outlining Aristotelian hylomorphism may likewise be approached bycharacterizing a type of whole, though a structured one, in terms of these sortsof principle.Aristotelian hylomorphists agree that there is a type of whole that is generated

from a plurality of objects just in case these objects are arranged in a certain wayand belong to certain kinds. There is, to put the idea with a familiar phrase, a typeof whole that is generated from a plurality of objects under a certain ‘principle ofunity’. A principle of unity is what ‘glues’ some entities together to compose afurther entity. Such a principle of unity is the form of a whole generated in thisway. The plurality of parts that are unified by such a principle is its matter.Following Harte (2002) and Koslicki (2008), we can think of an object’s form asproviding ‘slots’ that are to be filled by objects that belong to certain kinds andthat are arranged in a certain manner. An object’s matter, then, is the things thatfill the slots. This is a condition of existence of a certain type of whole. Theidentity of a whole generated under a principle of unity is taken to depend on thatprinciple—that is, the object’s identity depends on the object’s form. Thisdependence on a form with slots for certain kinds and arrangements of objectsmakes a hylomorphic whole a structured object. Furthermore, the type of wholecharacterized in this way is hierarchically organized. When a new whole isgenerated under a principle of unity from a plurality of objects that are them-selves generated under their own principles of unity, then the new whole has aform with slots filled by objects that have their own forms with slots filled byobjects that may have yet further forms, and so on. In this way, we get objects thatare internally divided into levels, possessing more or less immediate parts. Mereo-logical sums, by contrast, are flat, lacking such an internal division into levels.9

Aristotelian hylomorphists typically intend their conception of mereologicalnotions to apply to a wide range of entities, abstract as well as material ones.Ordinary objects are among the things to which the picture is taken to apply.Thus, ordinary objects are structured wholes: their parts must exhibit a certainmanner of arrangement and be of certain kinds, in order for the whole to exist,and the parts of these parts in turn must be unified. The principle of unity is theform of an ordinary object. Perhaps each specific kind is associated with its

those providing conditions of identity. These are the principles I focus on here. Among the materialprinciples are ones providing conditions under which a whole possesses certain non-mereologicalproperties, including spatiotemporal and physical ones.

9 See Fine (2010: 566–7) on mereological levels.

6 q-hylomorphism

characteristic principle of unity, so that sameness of form is what qualifies objectsas members of a certain kind. A tree, for example, has as its form a principle ofunity associated with the kind tree; perhaps this form is shared by all trees. Theobjects that are unified in this way, namely the trunk, branches and leaves, are thetree’s ‘horizontal’ parts, whereas it has as a merely ‘vertical’ part a certain quantityof wood. Since a tree may lose branches and leaves, its matter is variable overtime, whereas its form is constant. Note that while the classical-mereologicalaccount of ordinary objects is typically combined with four-dimensionalismabout material objects’ spatiotemporal profile, as pointed out earlier, the Aristo-telian-hylomorphist account is typically combined with three-dimensionalism,and hence ordinary objects are here viewed as lacking temporal parts.To get a glimpse of how this picture might be developed, let us briefly consider

Kit Fine’s (1999) theory of rigid and variable embodiment. The theory of rigidembodiment characterizes a type of material whole that is incapable of varying inits parts over time, whereas the theory of variable embodiment characterizes atype of whole that is capable of doing so. Fine’s strategy is to introduce twoprimitive composition operations that generate a material object from a pluralityof objects under certain conditions.10 While these operations are sui generis,various postulates are provided to yield an understanding of how the operationsbehave. I shall here focus on Fine’s postulates concerning existence and identity.The operation of rigid embodiment, designated by ‘/’, generates a whole, a, b,

c, . . . /R, from a plurality of objects, a, b, c, . . . and a condition, corresponding towhat I earlier called a principle of unity, R. Fine’s existence postulate settles whensuch a rigid embodiment exists: the rigid embodiment a, b, c, . . . /R exists at a timet iff R holds of a, b, c, . . . at t (Fine 1999: 66). That is, a rigid embodiment exists ata time just in case a certain plurality of objects exist at the time and are arrangedin the way specified by R at the time. Moreover, Fine’s identity postulate specifiesan identity condition for rigid embodiments: the rigid embodiments a, b, c, . . . /Rand a0, b0, c0, . . . /R0 are the same iff a = a0, b = b0, c = c0, . . . and R = R0 (Fine 1999:66). By this condition, the identity of a rigid embodiment depends on whichobjects are its immediate parts as well as on its form. Rigid embodiments aremereologically unchangeable objects with nothing but atemporal parts.Since ordinary objects are typically capable of change in parts, they are not

strict embodiments, but rather, variable ones, though the notion of a strictembodiment plays a role here, as well. The operation of variable embodiment,designated by ‘//’, generates a whole, /F/, from a principle F, which Fine views as a‘function’ from times to objects (Fine 1999: 69). The various objects picked out by

10 The general framework for dealing with composition operations is provided in Fine (2010).

q-hylomorphism 7

F at various times are described as the ‘manifestations’ of the variable embodi-ment /F/ (Fine 1999: 69). The variable embodiment /F/ exists at a time t iff it has amanifestation at t; and the variable embodiments /F/ and /G/ are the same ifftheir principles F and G are the same (Fine 1999: 70). The identity of a variableembodiment does not depend on any of its particular parts at a any time. What itsidentity depends on is only its principle of variable embodiment, or its form,which may determine different pluralities of parts, or different matter, at differenttimes.For illustration, consider Fine’s example of a car. It is a variable embodiment

/F/, whose form, F, has different manifestations at different times. What are thesemanifestations? According to Fine (1999: 69), they are rigid embodiments. Eachmanifestation of the car’s form at a time is a rigid embodiment generated fromvarious familiar car-constituting objects—an engine, a chassis, wheels, and soon—and their carwise arrangement. These objects are atemporal parts of therigid embodiment picked out by the car’s form at a time t, and so the objects aretemporary parts of the car at t. They are the car’s ‘major’ parts at t. And sincea rigid embodiment with different atemporal parts may be picked out by the car’sform at another time, the car may change in parts over time. Finally, as thecar’s major parts are themselves mereologically changeable variable embodi-ments, the car is a hierarchically structured object.Aristotelian hylomorphists differ on a range of questions, including the fol-

lowing. First, they differ on whether a whole is a composite of matter and form,having the form itself literally as another part, along with its material parts. Fineholds that forms are parts of structured wholes as well as unifiers of these wholes,emphasizing that there is substantive work to be done by this genuinely Aristo-telian feature.11 Mark Johnston, by contrast, holds that forms play a unifying rolebut are not themselves parts of wholes.12 (The choice is relevant to the questionwhether ordinary objects are material objects in my technical sense. If the cardoes not have a form as a part, then the car may be viewed as having a non-derivative spatiotemporal location. But if the car does have a form as a part, and ifthis form is an abstract entity, then the car is likely to have a spatiotemporallocation only in a derivative sense—that is, it will have to inherit its spatiotem-poral location from the location of its matter.13) A second disputed question is

11 See Fine (1999: 67) and Koslicki (2008). I shall address one motivation for this mereologicalaspect of Aristotelian hylomorphism in my discussion of the grounding problem in Chapter 5.

12 See Johnston (1992, 2002, 2006).13 Cf. the existence-postulates and location-postulates in Fine’s theory of rigid and variable

embodiments; Fine (1999).

8 q-hylomorphism

whether forms are individualized, playing a role in the individuation of distinctinstances of the same kind, or whether forms are shared among all instances of akind. Some may view each particular car as having its own form, while othersview all cars as having a common car-form.A third issue concerns which principles of unity are admitted to generate

material wholes. According to Fine, there is no privileged class of properties orrelations to which the operation of rigid embodiment is sensitive, while others areleft out. Likewise, there are no privileged functions from times to objects to whichthe operation of variable embodiment is sensitive. The result is a plenitudinousontology that even outstrips that of classical mereology: ‘for each such object ofthe mereologist, there will correspond a multitude of rigid embodiments, differ-ing in their choice of components or relational principle, and a multitude ofvariable embodiments, differing in their actual and possible manifestations’ (Fine1999: 73). Other Aristotelian hylomorphists incline towards a more restrictiveontology of material objects, maintaining that only a restricted class of principlesof unity have the privileged status of generating structured wholes. The onto-logically privileged complex objects may or may not be seen to be just the objectsrecognized by common sense and science.14

Fourth, while Aristotelian hylomorphists agree that there is a structured typeof whole—or, to speak with Fine, a composition operation generating structuredwholes—there is disagreement over whether this is the only type of whole, or theonly type of composition operation. According to the mereological monist, thereis only a single basic type of whole or composition operation, where a type ofwhole is basic if it is not definable in terms of other types of whole. According tothe mereological pluralist, there are different basic types of whole or compositionoperations.15 Classical mereology is standardly framed as a monist position.Aristotelian hylomorphism could likewise be framed as a monist position, dia-metrically opposed to monist classical mereology.16 Fine, however, is a radicalmereological pluralist, recognizing ‘an infinitude of forms of composition’ (2010:576), including the slim operation of summation, generating unstructuredobjects, as well as the more ‘substantive’ operations of rigid and variable embodi-ment (Fine 2010: 576), generating structured objects.

14 For a restrictivist position, see Koslicki (2008: 171). For a common argument in favour ofplenitude, see Section 1.3.1.

15 These notions are Fine’s (2010: 561–2).16 Koslicki (2008: 167) is at least a mereological monist about material objects.

q-hylomorphism 9

Concluding this rough outline, the Aristotelian-hylomorphist analysis ofordinary objects may be summarized as follows:

Aristotelian hylomorphismAccording to Aristotelian hylomorphism, an ordinary object is a structured whole, whoseidentity depends on its “major” parts’ being arranged in a certain way and on theirbelonging to certain kinds. The principle of unity determining a characteristic manner ofarrangement of certain kinds of object is the ordinary object’s form; the plurality of‘major’ parts is its matter.

1.1.3 Intuitions of mereological structure

Aristotelian hylomorphism about ordinary objects is a bold account that only aminority of contemporary metaphysicians are willing to endorse. I suppose thatthe main target of scepticism is the mysterious nature of structuring compositionoperations, and, correspondingly, of forms of complex objects. What I find mostmysterious about these operations is how they can be sensitive to very specific,high-level kinds of object and manners of arrangement. Suppose that the primi-tive operation of rigid embodiment applies to material objects a, b, c, and d andthe condition that a, b, and c are aluminium legs, that d is a wooden top, and thata through d are arranged in accordance with Mies van der Rohe’s blueprint,thereby generating a particular table (or perhaps only a particular manifestationof a table). The generated table is a structured object possessing a form with slotsfor objects of specific kinds in a specific arrangement. What explains the fact thatit matters to the application of the operation of rigid embodiment that a, b, and care aluminium legs, that d is a wooden top, and that a through d are arrangedaccording to van der Rohe’s design? What is it about aluminium legs that helpsgenerate new objects? Generating a new object is a metaphysically robust job.When a mechanism with this job is tuned to specific, high-level properties andrelations, we expect an explanation of the mechanism in more basic terms—thatis, we expect an explanation in terms of more natural properties and relations.For how can something this fundamental be sensitive to something this deriva-tive? Correspondingly, how can metaphysically deep forms have slots for meta-physically shallow kinds? No answer is provided. These are assumed to beprimitive aspects of the composition operation and its associated forms. Whatholds for rigid embodiment, holds for variable embodiment and for otherstructuring composition operations Aristotelian hylomorphists have postulated:their sensitivity to highly specific and fairly unnatural kinds and manners ofarrangement cries out for an explanation. Without an account in more funda-mental terms, these composition operations remain objectionably mysterious,

10 q-hylomorphism

appearing too stipulative for metaphysicians impressed by the lean elegance ofthe classical-mereological operation of summation to accept.17

The price of Aristotelian hylomorphism, then, is considerable. In order to get asense of why it might be worth paying this price, I shall review how Fine supportsthe approach. Fine’s central motivation for rejecting the classical-mereologicalaccount of ordinary objects in favour of a hylomorphic one is that the account isinsufficient to capture certain intuitions of mereological structure about ordinaryobjects.18 Consider, as a first case, Michelangelo’s David. This statue has variousfamiliar parts, including the left, bent arm. Moreover, the statue occupies thesame spatial region as a certain block of marble, which seems to be distinct fromthe statue, as it was there before Michelangelo created David from it. Therelationship between these two spatially coincident objects will be the subject ofChapter 3. What concerns me here is the following question: Is David’s left armalso a part of the block of marble? It seems not. Intuitively, the block has the samemicroparts as the statue, but the block does not have arms. We admire the statue,not the block. This is so, partly because we admire the realistic portrayal andharmonic composition of its parts. If these were parts of the block, we wouldadmire it too. But we do not.19 This is an intuition of mereological structure. Anobject of a given kind only has parts of certain kinds. Not any way of slicing thespatial region of the object hosts a corresponding part of the object. In the presentcase, the arm is a part of the statue but not of the spatially coextensive block ofmarble. The block of marble, to put it with Fine (1999: 73), is a ‘relativelyunstructured version of the [statue] just as the set {a, b, c, d} is an unstructuredcounterpart of the set {{a, b}, {c, d}}’.The classical-mereological conception of ordinary objects lacks the resources

to handle this intuition of mereological structure. On this conception, an ordin-ary object is an unstructured mereological sum of material objects. For any way ofslicing up the spatial region exactly occupied by an ordinary object at any time,the object has a spatial part that exactly occupies that part of the region,irrespectively of the kind to which the part belongs. The arm is, on this concep-tion, a part of the block of marble just as it is a part of the statue.

17 The worry does not concern arbitrariness. The question is not why a composition operationshould be sensitive to these kinds and arrangements but not to others. Fine does not face a problemof this sort, since there are no privileged kinds and arrangements to which rigid and variableembodiment are sensitive. The worry is, rather, why primitive composition operations should besensitive to specific, high-level kinds and arrangements in the first place.

18 See Fine (1999: 62–5). Fine’s criticism is endorsed by Koslicki (2008: 72–5).19 Cf. Fine (1999: 73, 2003: 198 n.5). Similarly, an organism has a heart as a part (at a time), while

the aggregate of cells constituting the organism does not.

q-hylomorphism 11

For a second case, let us explicitly assume the standard combination of theclassical-mereological account of ordinary objects with four-dimensionalism.Recall that standard four-dimensionalists view an ordinary object’s temporalmereological profile as derived from the atemporal mereological profile of theobject’s instantaneous temporal parts: a has b as a part at t iff a’s temporal partlocated at t has b as a part simpliciter. Now suppose that my car has a certainwheel as a part at time t. Suppose also that there is a spacetime region, R, that hasa part in the present occupied by the car’s wheel as well as a part in the pastoccupied by Socrates. By universalism, there is an R-object that is the mereo-logical sum of all objects contained in R. This object has, among others, the wheeland Socrates as parts simpliciter. Notice that the temporal part of the R-object at tis identical with the temporal part of the wheel at t. Since this temporal part is anabsolute part of the car’s temporal part at t, it follows that the R-object is a part ofmy car at t. But it is hard to accept that an object that contains Socrates as a part isa part of my car at any time.20 As in the case of David, this intuition concerns themereological structure of an ordinary object: the kind to which an object belongsis relevant to whether it is a part. It is a major defect of the four-dimensionalistclassical-mereological conception of ordinary objects that it is blind to this kind-sensitive mereological structure. Note that it will not help to point out thatclassical mereologists are used to having objects in their ontology that ordinaryspeakers fail to recognize—this is a standard problem for any plenitudinousontology. For it is one thing to say that there are highly exotic objects that wenever dreamed of, but quite another thing to say that these are parts of familiarobjects. Since we are experts on ordinary objects, it would be rather surprising ifwe had misrepresented their mereological profile to that extent.Aristotelian hylomorphists have no trouble accommodating the intuitions of

mereological structure under consideration. As we saw, they can view the form ofan object as determining not only a manner of arrangement of other objects, butalso as determining what kinds of object can enter into that arrangement.21

Accordingly, the Aristotelian can say that we can build a table from four legsand a top, but we cannot build a piece of wood from these things, because thekind table has associated forms with slots for legs, whereas the kind piece of wooddoes not. Similarly, a block of marble lacks arms, since its form lacks slots forobjects of the kind arm, and my car does not have an object partly constituted bySocrates as a part, since its form lacks a slot for such a ‘monster’. The ability tocapture these intuitions of mereological structure is a big point in favour of

20 This is a version of Fine’s ‘monster objection’, in Fine (1999: 64–5).21 See Fine (1999: 72, 2010: 576), Koslicki (2008: 169).

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analysing ordinary objects as compounds of matter and form. The Aristotelian-hylomorphist understanding of form as structuring objects is the standard one.As we will see, however, there is an alternative understanding of form.

1.2 Material Objects, Sortals, and K-paths

The metaphysical analysis of ordinary objects to be developed in this essay differssubstantially from both the classical-mereological and the Aristotelian-hylomorphist analyses, and yet stands on their shoulders. The view can bedescribed as a middle way between the two. It is a fundamentally classical-mereological framework with an Aristotelian twist. Or, to locate it by recourseto the received views’ contemporary figureheads, it is a Lewisian theory that takesa Finean turn. It combines some of the classics’ key features, thereby combiningtheir strengths and diminishing the distance between the two traditions. Moreimportantly, however, it exhibits unique powers beyond the reach of its com-petitors. To foreshadow somewhat, the account follows classical mereology inviewing complex material objects as mereological sums of smaller materialobjects, but denies that ordinary objects are material objects. Moreover, it followsAristotelian hylomorphism in distinguishing between an ordinary object’s matterand form, but construes forms as having a very different nature and at least apartly different function than Aristotelian forms. In the remainder of this chap-ter, I shall develop the foundations of this unorthodox, non-Aristotelian variantof hylomorphism about ordinary objects.Ordinary objects will be metaphysically analysed as compounds of material

objects and K-paths, of matter and form. I shall begin with a metaphysicalaccount of material objects.

1.2.1 Material objects

A material object, as I use the label, is an object with a non-derivative spatio-temporal location and with non-derivative physical properties. I shall assumethat there are composite material objects. On the question of the nature ofcomposite material objects I side with the classical-mereological conception,but deny that ordinary objects are identical with such material objects. In whatfollows, I will develop an account of ordinary objects as built up from materialobjects understood in the way of classical mereology.As pointed out in Section 1.1, the classical-mereological conception of com-

posite material objects comes in different versions, a three-dimensionalist one,according to which material objects lack temporal parts, and a four-dimension-alist one, according to which they have temporal parts. The account of ordinary

q-hylomorphism 13

objects to be defended here may be developed on the basis of either a three-dimensionalist version of the classical-mereological conception of materialobjects or a four-dimensionalist version of this conception. I shall spend mostof this chapter developing a three-dimensionalist version of the account in detail.At the end of the chapter, I shall complete my metaphysical groundwork bypresenting a four-dimensionalist alternative, and say a word about the versions’respective role in the bigger picture.Recall that a straightforward three-dimensionalist version of the classical-

mereological account of composite material objects may be stated by taking thenotion of parthood at a time as primitive and by temporally relativizing univer-salism and extensionality in the following way. According to universalism, forany plurality of material objects, the xs, existing at a time t, there is a materialobject that is composed of the xs at t. Moreover, according to extensionality, forany composite material objects a and b, a is identical with b iff for any times t andt* and for any pluralities of xs and ys, if a is composed of the xs at t and b iscomposed of the ys at t*, then the xs are the same as the ys. As we saw, the price ofthis simple and transparent account of the identity of complex material objects isinflexibility regarding a material object’s temporal mereological profile. Sincesameness of the parts of composite material objects a and b is necessary for theidentity of a and b, a material object cannot change in parts over time; the partsgo where it goes. Moreover, since sameness of the parts of composite materialobjects a and b is sufficient for the identity of a and b, a material object cansurvive radical scattering; it goes where the parts go.None of this, however, is worrying when it comes to capturing the familiar

temporal profile of ordinary objects. For extensionality, as stated here, is aprinciple about material objects, not about ordinary objects. On the analysis tobe proposed below, ordinary objects are not identical with material objects,though they are built up from the latter. Ordinary objects do not have aspatiotemporal profile in the basic sense, though they do have such a profile ina derivative sense to be characterized later. To accept extensionality is thus notautomatically to deprive a cat of the ability to survive the loss of a tail, or to allowa cat to survive radical spatial separation of its parts. As we will see, mereologicalvariability and unity of ordinary objects are compatible with extensionality.Extensionality about material objects, even in combination with universalism,will turn out to be harmless by the lights of common sense.22

22 This account of composite material objects is meant to stay neutral on whether matter isatomistic or gunky, and accordingly on whether complex material objects are ultimately composedof partless material atoms or whether they are infinitely divisible into smaller and smaller parts. The

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Given this classical-mereological account of composite material objects, whatare ordinary objects? That is, how are they to be analysed metaphysically? As twofurther preliminaries to answering this question, the notion of a sortal concept, orkind, and the notion of a K-path will enter the stage.

1.2.2 Sortals

Ordinary objects include persons, tables, trees, and mountains. They are objectsfalling under familiar sortal concepts, or kinds.23 What are sortals? Commonnouns are divided into mass nouns and count nouns. While mass nouns, such asstuff, gold, and wisdom, do not vary in grammatical number, count nouns, suchas thing, table, and thought, can take both singular and plural form and can bemodified by a numeral. It is a fairly standard view that a count noun that purportsto apply to things in the physical world expresses a (concrete) sortal concept, orkind, just in case it supplies a criterion for determining where and when a thingfalling under it begins and ends—that is, just in case it supplies a way of locatingits instances in space at a time, and a way of tracking its instances throughqualitative change across time. In short, sortals carve their instances at theirspatiotemporal boundaries.24 By this test, the nouns thing and red thing do notexpress a sortal, while the nouns table and red table do. For the noun thingprovides no way of locating its instances in space and no clue under whatconditions its instances come into and go out of existence, whereas the nountable is associated with such conditions, which include, for example, the neces-sary condition that a table exists at a time only if it is table-shaped at that time.It is, furthermore, standard to distinguish between invariant and variant

sortals.25 A sortal is an invariant sortal of an object just in case the object cannotcease to be an instance of the sortal without ceasing to exist. Variant sortals, bycontrast, apply to their instances only temporarily or only contingently: a sortal isa variant sortal of an object just in case the object can cease to be an instance ofthe sortal without ceasing to exist. Assuming that for any sortal, or kind, K and

metaphysical choices shaping the account will be motivated by their role in the application of theemerging theory of ordinary objects to a range of philosophical problems. These applications do notrequire a stand on the issue of atomism, though further applications of the framework might do.

23 I shall switch freely between talk of sortal concepts and talk of kinds, although concepts areoften thought of as mind-dependent entities and kinds as mind-independent properties.

24 This is more or less the classical account of Strawson (1959). See Locke (1690/1975) and Frege(1884) for precursors.

25 See Wiggins (1980, 2001) for the locus classicus of this distinction, though he calls invariantsortals ‘substance sortals’ and variant sortals ‘phase sortals’. The term ‘substance sortal’ carries toomuch metaphysical weight for my taste; and the term ‘phase sortal’ emphasizes the temporaldimension of variation over the equally important modal dimension.

q-hylomorphism 15

any ordinary object o, o is invariantly a K iff o is a K at all times at which it existsand in all worlds in which it exists, the doctrine of sortal invariance says thatcertain ordinary sortals apply to their instances invariantly.26 As it is often put,the ordinary world is partly individuated by these invariant kinds; it is parsed intopersons, tables, trees, mountains, and so on. This doctrine is part and parcel ofthe common-sense conception of macroscopic objects. While table is an invariantsortal, red table and teacher are variant sortals. Whatever properties make anobject a table, we bring a table into existence by causing these properties to beinstantiated, and a table cannot lose these properties without going out ofexistence. An object need not, however, come into existence by becoming a redtable or a teacher, nor cease to exist by losing these properties. All sortals carvetheir instances at their spatiotemporal boundaries, but the invariant sortalscarve more closely: it is exactly by means of the properties that make an objecta table that we track tables through time, whereas it is not by means of all of theproperties that make an object a red table that we track red tables through time.Note that sortals are not sufficient to delineate the domain of ordinary objects.

In other words, sortals do not fix the pre-metaphysical, conceptual category ofordinary object. It is not the case that something is an ordinary object just in caseit falls under some sortal or other. For we have sortals for concrete things that arenot ordinary objects, and there are ordinary objects for which we lack sortalsaltogether. Characterizing the pre-theoretical category of ordinary object and itsrelation to sortal concepts is far from easy and will be one task of Chapter 2.

1.2.3 K-paths

The notion of a K-path rests on the notion of a property that realizes a kind, orsortal, K, the notion of a property in the sphere of discourse of K, and the notionof a K-state of a material object. I shall introduce these notions in turn.First, each kind, or sortal, K has a certain qualitative content. The latter consists

of the characteristic qualitative properties (and relations) of Ks, the properties bywhich the instances of K are unified, whether the instances are unified by allhaving certain properties in common or merely by exhibiting certain familyresemblances. The kind table has a qualitative content consisting primarilyof functional properties, whatever they may be; the qualitative content oftiger consists primarily of biological properties; the qualitative content of personconsists primarily of psychological properties (or so the Lockeans say); the kindmountain has a primarily geological content; and so on. Note that to specify the

26 I refrain from characterizing modally invariant sortals as essential properties, in order to leavethe door open for a non-modal account of essential properties and essences à la Fine (1994).

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qualitative content of a kind is not sufficient to specify the kind’s applicationconditions. On the present view, instantiating the properties comprising thequalitative content of kind K is not enough for being an instance of K. More isrequired in order to belong to a kind, as we shall see later.Second, for each kind K, there are specific properties (and relations) that

realize the kind K. K-realization will be understood in terms of the notion ofqualitative content and the notion of ground. Grounding will be appealed to invarious places throughout this volume. As taking a stand on recent debates aboutthe nature of grounding lies beyond the scope of this inquiry, I shall confinemyself to a minimal conception in close proximity to Fine’s (2001): when a fact orproposition p grounds a fact or proposition q, then the holding of q consists in theholding of p; q holds in virtue of p’s holding; the holding of p explains the holdingof q. The grounding relation is the tightest explanatory connection between factsor propositions (see Fine 2001: 15–16). When a plurality of facts or propositionsp1, p2, . . . ground a fact or proposition q, then each of p1, p2, . . . partly ground q.

27

Now to kind-realization. The qualitative content of a kind K, �K, is instanti-ated by material objects. (Recall that instantiating �K is not meant to be sufficientfor instantiating K.) The K-realizers are the specific properties whose instanti-ation partly grounds the instantiation of�K. If a material object a instantiates�K,then a property ç partly realizes K if a’s being ç partly grounds a’s being �K.Moreover, if a instantiates �K, then a set or plurality of properties ç1, ç2, . . . , çn,completely realizes K if a’s being ç1, a’s being ç2, . . . and a’s being çn jointlyground a’s being �K. (I shall assume that if ç1, ç2, . . . , çn completely realize K,then each çi partly realizes K.) The K-realizers will typically be different ones indifferent cases. In the case of tablehood, there is a cluster of shapes and decom-positions, such that each property in the cluster partly realizes tablehood; differ-ent tables may have different shapes and parts. In the case of personhood, there isa cluster of mental profiles, such that each profile in the cluster partly realizespersonhood; different persons may have different beliefs and character-traits.Third, for any kind K, there is a range of properties that can meaningfully be

ascribed to Ks—for short, there are K-meaningful properties. A table, for example,can meaningfully be ascribed artefactual as well as physical properties—in addition to having a certain shape, mass, and decomposition, it may befunctionally defective or well designed—though a piece of wood may not mean-ingfully be said to have such artefactual properties in addition to its physical ones.In general, an ordinary kind K is associated with a characteristic range of

27 For further work on the nature of grounding, see Schaffer (2009) and Correia and Schnieder(2012).

q-hylomorphism 17

K-meaningful properties, its sphere of discourse. These are the properties thathave meaningful application to objects falling under the kind.28 The kinds tableand piece of wood have different spheres of discourse. Many properties in thesphere of discourse of K do not realize K. The K-realizers form a sparse group inthe sphere of discourse of K. The property of weighing 10 kg is in the sphere ofdiscourse of table without being a table-realizer; it can be meaningfully applied totables without playing a role characteristic for tables.Fourth, for any kind K, a K-state of a material object is a complex, conjunctive

fact, or state of affairs, about the object that obtains at a particular time.29

A K-state, for some kind K, of a material object a at a time t contains two typesof qualitative profile: a’s K-meaningful intrinsic profile at t and a’s K-realizationprofile at t. The K-meaningful intrinsic profile of a at t contains:

the maximal conjunction of the facts that a exists at t, that a has ç1 at t, that a has ç2 att, . . . , that a has çn at t, such that (i) each çi is an intrinsic qualitative property of a, and(ii) each çi falls in the sphere of discourse of K.30

The K-realization profile of a at t is constituted by two types of fact. To beginwith, the K-realization profile contains:

the maximal conjunction of the facts that a has ł1 at t, that a has ł2 at t, . . . , that a has łnat t, such that ł1, ł2, . . . , łn together completely realize K—that is, the maximal conjunc-tion of the facts about a that jointly ground a’s being �K, where �K is the qualitativecontent of K.

Furthermore, the K-realization profile contains:

the maximal conjunction of the facts that ł1 partly realizes K, that ł2 partly realizes K, . . . ,that łn partly realizes K.

A K-state thus is a temporally brief, intrinsic, K-meaningful, and K-realizingprofile of a material object; all of a material object’s K-meaningful intrinsicproperties at a given time and all of its properties that jointly realize K go intothe object’s K-state at that time. (I shall assume that being K-realizing entailsbeing K-meaningful.31)

28 See Fine (2003: 207).29 I shall make the following minimal assumptions about facts, or states of affairs. Facts form a sui

generis ontological category. They are complex entities whose constituents are structured in a certainway. There are basic and non-basic, or molecular, facts. In particular, there are conjunctive facts.I shall not distinguish between the existence and obtaining of a fact, or state of affairs.

30 An object’s intrinsic properties are, intuitively, the properties that it has purely in virtue of theway it is. See Lewis (1983b: 111–12). I shall not attempt to give a precise definition here.

31 I shall ignore the modal profile of K-states and K-paths for now. This will be a subject ofChapter 5.

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A few points of clarification. Some familiar kinds are presumably completelyrealized by intrinsic properties of material objects, while others are partly realizedby extrinsic as well as intrinsic properties. The kind piece of wood looks like anintrinsically realized kind, whereas table, tiger, and person may be viewed asexamples of partly extrinsically realized kinds.32 So some of the propertiesconstituting a K-state’s K-realization profile might not also constitute its intrinsicprofile—that is, some of the łs might not be çs.Owing to the requirement of K-meaningfulness, a table-state has artefactual as

well as physical facts about a material object as conjuncts, whereas a piece-of-wood state has physical but no artefactual facts about an object as conjuncts. Soeven when a table-state and a piece-of-wood-state are complex facts about thesame material object at the same time, K-meaningfulness alone renders the table-state and the piece-of-wood state distinct, although they will differ further withrespect to their K-realization profiles.Finally, the requirement that K-states contain facts concerning which proper-

ties realize which kinds is an important ingredient in the notion of a K-state. Ithas the effect of ruling out that a qualitative profile of a material object at a time,which contains both K-realizers and K*-realizers, for different kinds K and K*, isboth a K-state and a K*-state. By including facts concerning which propertiesrealize which kind in a K-state, these facts are assigned an individuative force.Thus, if a material object has properties at t, some of which realize K, while othersrealize K*, then the object is in a K-state and also in a distinct K*-state at t. All ofthese features of K-states will be put to work later on, and will receive furtherelucidation in the process. At this stage, my exclusive concern is a statement ofthe basics of the theory.We are now in a position to introduce the notion of a K-path. While a K-state

is the imprint of the kind K on a material object at a particular moment, a K-pathis a series of imprints of K over time, a series of K-states. Intuitively, a K-path isthe life of a K, spanning from K-states that mark the beginning of a K to K-statesthat mark the end of a K. The notion of a K-path, along with that of a K-state, iscentral to this volume and will gradually evolve over its course. My starting pointis the basic account, which will be modified and extended in various ways as wego along.First, some terminology. If a fact is a conjunct of a K-state or a K-path, then the

fact is included in the K-state or the K-path. If a fact that is included in a K-state

32 K-realizers may be spatially and temporally extrinsic. The property of having been craftedwith a certain intention may be an extrinsic, partial table-realizer. The property of having a certainancestral descent might be an extrinsic, partial tiger-realizer. And the property of having a certain belief,as construed by externalists, might be an extrinsic, partial person-realizer.

q-hylomorphism 19

or a K-path has a property ç and a time t as constituents, then the K-state or theK-path contains ç and t, or simply contains the temporal property of being ç at t.If a K-path includes a plurality of facts that contain incompatible properties of acertain type paired with different times, then the K-path includes a change in thistype of property. For example, if a K-path includes the fact that a is composed ofthe xs at t and the fact that b is composed of the ys at t*, where the xs are not theys and t* is later than t, then the K-path includes a change in parts over time.Finally, any material object that is the subject of a K-state in a K-path is also,though derivatively, a subject of that K-path.On the basic account (to be extended in later chapters), a K-path is a series of

K-states with the following properties:

• A K-path is unified by K-continuity. The K-realizing properties in any twotemporally close K-states in a K-path are massively similar. Local property-variation encoded by a K-path is small. Person-states in a person-path, forexample, are psychologically continuous: any two temporally close states inthe path are massively psychologically similar; psychological change fromone moment to the next is gradual. Similarly, any temporally close chair-states in a chair-path contain massively similar chair-shapes and chair-parts.

• A K-path is unified by K-connectedness. The K-realizing properties in anytwo K-states in a K-path, no matter how temporally distant they are fromeach other, are similar to some minimal degree. Global property-variationencoded by a K-path can be extensive but happens within limits. How muchsimilarity is required is a vague matter. Person-states in a person-path, forexample, are psychologically connected: any two states in the path arepsychologically similar to some minimal degree; psychological change overlonger periods of time is limited.33 Similarly, any two chair-states in a chair-path, no matter how temporally distant, contain shapes and parts instanti-ating the same design.

• A K-path is unified by lawful causal dependence. If a material object’s beingin a K-state now and an object’s having been in a K-state yesterday areincluded in the same K-path, then the current K-state causally depends onthe previous K-state. That is, each K-state in a K-path depends for itscharacter on the K-states before it. The causal relation linking K-states isoften called ‘immanent causation’.34

33 Cf. Lewis (1983a: 55–60) on psychological continuity and connectedness.34 The notion goes back to Lotze (1887). The locus classicus is Johnson (1924). For recent

developments, see Swoyer (1984) and Zimmerman (1997).

20 q-hylomorphism

• A K-path is maximal. No segment of a larger conjunction of K-statesinterrelated by K-continuity, K-connectedness, and causal dependence is aK-path. Only the largest conjunction of K-states interrelated in this waycounts as a K-path.35

To deepen our understanding of K-paths, two comments on various condi-tions not included in the basic account are in order. First, and most importantly,the basic account does not include the condition that a K-path ‘trace’ a uniquematerial object, that it have a material object with a matching spatiotemporalboundary as its unique subject. This means that the trajectories of K-paths andthose of their material subjects may diverge. This feature is of central importanceto the present inquiry. Think of the unity conditions of K-paths, the conditionsunder which two K-states belong to the same K-path, as persistence conditions ofK-paths. According to the basic account, the persistence conditions are similarityand causal dependence. (As I will elaborate in Section 1.3, the persistenceconditions of K-paths mirror the persistence conditions traditionally associatedwith K.) Now, the mentioned divergence is one between the persistence condi-tions of K-paths and the persistence conditions of their material subjects. Mater-ial objects need not go where their K-paths go; they need not behave in a K-ishway. According to the classical-mereological analysis of composite materialobjects sketched above, material objects have K-independent, purely mereo-logical persistence conditions: they go where their parts go. One consequence isthat a K-path may have distinct material objects as subjects: there may be distinctmaterial objects a and b, such that a is the subject of some K-states in a K-path,while b is the subject of other K-states in the same K-path. Another consequenceis that a material object may be a subject of distinct K-paths: a material objectmay be a subject of a K1-state, for some kind K1, that belongs to a certain K1-pathand also a subject of a distinct K2-state, for a kind K2 distinct from K1, thatbelongs to a certain K2-path with a different trajectory from the K1-path. Manyspecific ways for K-paths and their material subjects to diverge will be encoun-tered in the following chapters.

35 Is the maximality requirement too strong? Should we not recognize the possibility of anorganism-path that is a segment of a larger organism-path, corresponding, intuitively, to a foetusthat is a proper part of an adult human being? (More on the mereological role of K-paths inSection 2.2.2.) No. Roughly, the organism-realizing properties individuating the organism-pathcorresponding to the fetus are very different from the organism-realizing properties individuatingthe organism-path corresponding to its mother. The organism-states making up the first organism-path are thus different states than those making up the second organism-path. Since the foetus-pathis not a segment of the mother-path, maximality is not violated in this case.

q-hylomorphism 21

Second, the basic account of K-paths does not include the condition that aK-path has a unique K-state at a time. Without this requirement K-paths areallowed to branch out and include distinct, spatially distant K-states obtaining atthe same time in different branches. Another condition omitted from the basicaccount is that a K-path be unified by spatiotemporal continuity in addition toK-continuity, K-connectedness, and causal dependence. Without this require-ment K-paths are allowed to be gappy and include similar and causally connectedK-states whose times are not continuous. The reasons for allowing K-paths totake these striking shapes will become apparent in Chapter 4. The related ques-tion whether a K-path can include K-states obtaining in different possible worldswill be addressed in Chapter 5.

1.3 Q-Hylomorphism about Ordinary Objects

With material objects and K-paths in the picture, ordinary objects may becharacterized metaphysically. I shall present my account and subsequently com-pare it to the traditional accounts of classical mereology and Aristotelianhylomorphism.

1.3.1 Ordinary objects as compounds of material objects and K-paths

Ordinary objects are the objects to which our familiar sortal concepts, or kinds,apply. What unifies the class of ordinary objects conceptually is an issue to betaken up in Chapter 2. I now wish to address the question of the nature ofordinary objects. The view I propose is that an ordinary object is a compoundof a material object and a K-path, for some kind K, such that the material object isa subject, perhaps one of many, of the K-path—that is, the subject of some factincluded in the K-path. For a given material object that is a subject of a table-path, for example, the compound of the material object and the table-path is atable.What is the nature of compounding? That is, what is the nature of the

composition operation that generates an ordinary object from a material objectand a K-path? Having applied the classical-mereological operation of summationand the corresponding conception of wholes as unstructured sums in the char-acterization of composite material objects, I shall invoke this operation again inthe characterization of compounding, and hence refrain from employing anymetaphysically extravagant tools. My account will thus be compatible with themereological monism of classical mereology. Adopting the classical-mereologicalidea that the summation operation applies to pluralities of things independentlyof what they are and of how they are arranged (universalism), and that the

22 q-hylomorphism

identity of a mereological sum depends solely on which things are its parts(extensionality), it is natural to admit not only mereological sums of things ofthe same ontological category, but also sums of things of different categories—that is, transcategorial sums. A restriction of the operation of summation tothings of the same category, or even to things of a particular category, say,material objects, seems ad hoc.An ordinary object will be understood as a compound generated from the

application of the operation of compounding to a material object and a K-path,for some kind K. Compounding is not a primitive composition operation. Itis defined in terms of the primitive operation of summation and the relationof subjecthood holding between a material object and a K-path: the application ofcompounding to a material object a and a K-path i consists in the application ofsummation to a and i under the condition that a is a subject of i. Thuscompounding is more than summation. A K-path and a material object do notmake a compound just by being fused. The material object in the sum also needsto be a subject of the K-path in the sum. Letting �c be the compoundingoperation,36 the condition under which compounds exist may be stated asfollows: for any kind K,

ExistenceIf there is a material object a and a K-path i, such that a is a subject of i, then there is acompound �c(a, i).

Note that although compounding is distinct from summation, the recognition ofcompounding in addition to summation does not carry a commitment to mereo-logical pluralism, since compounding is not a basic composition operation.37

The result of applying the compounding operation to a and i is identical withthe result of applying the summation operation: �c(a, i) = �m(a, i), where �m issummation. A compound is a transcategorial mereological sum of a materialobject and a K-path that has the material object as a subject. Compounds thusshare their identity condition with sums. Their identity depends entirely on whichthings are their parts, irrespective of what these things are and of how they arearranged; compounds are unstructured. The parts of a compound �c(a, i) are itscomponents a and i, as well as the parts of a and i (if i has any parts at all).Assuming that the identity conditions of composite material objects and of factsare settled, the identity condition of compounds may be stated as follows:

IdentityThe compound �c(a, i1) = the compound �c(b, i2) iff a = b and i1 = i2.

36 The �-notation derives from Fine (2010: 566). 37 Cf. Fine (2010: 561–2).

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Notice that since K-paths are not material objects, in virtue of lacking a non-derivative spatiotemporal location, hybrid compounds of K-paths and materialobjects are not material objects either, and hence do not have their parts in thenon-derivative temporally relativized sense employed in characterizing materialobjects earlier. The mereological notions in play in the present account of com-pounds are rather temporally unrelativized notions. Thus, classical-mereologicalparthood and summation simpliciter play their role in the present theory as wellas parthood and summation at a time.38

Recall that a K-path, for any K, is individuated by the qualitative content of theparticular kind K (Section 1.1.3). Since K-paths include facts concerning whichproperties realize which kinds, no K-path is also a K*-path, where K and K* aredistinct kinds. Since each compound has a unique K-path as a part, and sinceeach K-path is individuated by the qualitative content of a unique kind, K, it isnatural to view each compound as belonging to a unique invariant kind, namely,the kind that individuates the object’s component K-path. For instance, a com-pound with a component table-path has the kind table as its unique invariantkind. (This uniqueness will play a role in several applications of the presentframework to be considered later; see Sections 2.2.2, 5.1, and 5.2.)An obvious consequence of this account of ordinary objects as compounds of

material objects and K-paths is that it yields a plenitudinous ontology. First, theaccount yields a plenitude of ordinary objects. Suppose that one material object,a, is both a subject of a piece-of-wood-path, i1, and a subject of a distinct table-path, i2. (Recall that table-paths contain artefactual properties not contained inpiece-of-wood-paths.) By Existence, there is a compound �c(a, i1) and a com-pound �c(a, i2); and by Identity, these compounds are distinct because theircomponent K-paths are distinct. So the table and the piece of wood are twoobjects. Or consider a particular table-path, i. The basic account of K-pathspermits i to have a plurality of material objects as subjects. Suppose, then, thati has distinct material objects a, b, and c as subjects. By Existence, there is acompound �c(a, i), a compound �c(b, i), and a compound �c(c, i); and byIdentity, these compounds are distinct, because their material components aredistinct. So there are three tables. I expect immediate, intuitive worries aboutthese consequences. Does the account entail that ordinary thinkers get the

38 It is common for three-dimensionalists to employ both a temporally relativized and atemporally unrelativized version of the same notion. For example, it is standard to accept asirreducible both existence simpliciter (of abstract as well as material objects) and existence at atime (of material objects), and to accept as irreducible both having a shape simpliciter (of spacetimeregions) and having a shape at a time (of material objects). Similarly for parthood.

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number of ordinary objects wrong? These worries will be addressed in Chapter 2,once the full picture is in front of us.Second, the account yields a plenitude of extraordinary as well as ordinary

objects. Sortal concepts apply to compounds of material objects and complex,qualitative facts about these material objects. Given the application condition ofcompounding, there are many more compounds than the sortal concepts ofordinary thought and talk pick out. For example, incars are things ordinaryfolks have never dreamed of. If a car is present in a garage, there is an incar. Asthe car leaves the garage, the incar shrinks gradually and goes out of existence atthe point at which the car has crossed the garage’s threshold completely.39

According to the present account, incars exist. Suppose that there is a materialobject that possesses car-realizing properties in such an arrangement as to be asubject of a car-path.40 It is easy for this material object also to possess incar-realizing properties in the right arrangement to be a subject of an incar-path.Then there is a compound of this material object and the incar-path. This is anincar. Ordinary objects are compounds. There are many compounds, however,that are not ordinary objects.There is a good reason to appreciate this consequence. Would it not be

astonishing if reality had a privileged domain of objects corresponding exactlyto our rich and varied sortal concepts? Our familiar sortals are realized by vastlydifferent sets of highly specific properties and relations. What is more, the factthat these rich qualitative profiles have been packed into sortals seems to be abiological and cultural accident. The combination of these aspects makes itunlikely that our familiar sortals carve nature at the joints.41 Certain ontologicalanti-realists take this to suggest a distinction between different meanings of ‘thereis’ and ‘exist’, holding that while we ascribe existence in one sense to our ordinaryobjects, extraordinary objects exist in another sense.42 I reject this radical positionin favour of orthodox ontological realism, according to which there is only onekind of existence.43 Ontological realists who are inclined to take seriously com-mon-sense existence claims concerning ordinary objects should view the reason-able doubts about the joint-carving powers of our familiar, specific sortals assuggesting that these sortals represent no more than a fraction of a plenitude of

39 See Hirsch (1976: 361).40 If car-paths invariably include a change in parts, suppose that several material objects are the

subjects of a single car-path.41 Cf. Hawthorne (2006: 109), Hudson (2001: 107), and Sider (2001a: 156–7). For critical

discussion of this complaint, see Korman (2010: 138–41).42 See Hirsch (2002).43 Chalmers (2009) calls this position ‘heavyweight realism’. A discussion of the dispute between

ontological realists and anti-realists lies beyond the scope of this volume.

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unfamiliar objects with the same metaphysical makeup. The present accountyields such a desirable plenitude.Questions of plenitude aside, the most significant aspect of the proposed

analysis of ordinary objects is that the qualitative profile of an ordinary object’smaterial component and the profile of the same object’s K-path may diverge. Asthe relationship between table-paths and their material subjects was summarizedearlier, the material subjects of table-paths need not behave in a table-ish way;specifically, the persistence conditions of material objects differ from the persist-ence conditions of table-paths.44 More precisely, the material object, construed asa mereological sum, instantiates an individual qualitative profile. As the identityof a material object is not dependent on the instantiation of any kind-realizingproperties or relations, this qualitative profile is kind-independent. Moreover, theK-path contains an individual qualitative profile. Since the identity of a K-path isdependent on the instantiation of K-realizing properties or relations, this quali-tative profile is kind-dependent. As the profile of a K-path may diverge from theprofile of any of its material subjects, an ordinary object has components withdifferent lives, a kind-dependent one and a kind-independent one. This diver-gence drives a wedge between a compound’s two layers.More work is required for the point of this qualitative divergence to become

apparent. What I have provided until now is a reasonably fundamental accountof ordinary objects in terms of temporally unrelativized existence and identityconditions of compounds. How does this metaphysical account relate to everydaythought and talk about ordinary objects? We typically describe ordinary objectsas existing at times and as having properties and relations, including spatial andmereological relations, at times. What fundamental metaphysical facts aboutordinary objects make these ordinary statements true? This question will beanswered in the next chapter, where the present metaphysical account of ordin-ary objects will form the basis of a semantical account of ordinary object-discourse, which I call perspectivalism. The qualitative divergence of an ordinaryobject’s components will underlie the key feature of perspectivalism, namely,perspectival divergence.

1.3.2 Classical mereology, Aristotelian hylomorphism, and q-hylomorphism

As announced in Section 1.2, the proposed metaphysical account of ordinaryobjects as double-layered compounds occupies a position midway betweenthe traditional poles of the classical-mereological/Lewisian account and the

44 Further and persistence-unrelated ways for K-paths to diverge from their material subjects willbe encountered as we go along.

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Aristotelian/Finean account of ordinary objects. The three approaches invitecomparison along various dimensions.The present account follows classical mereology in understanding composition

exclusively as summation. However, while viewing composite material objects asmereological sums of smaller material objects, it views ordinary objects as beingmore than complex material objects, as being divided into different components.This dispute with classical mereologists is not a metaphysically substantive one,in the sense that the mentioned disagreement over the nature of ordinary objectsis not a disagreement over fundamental matters of fact—the disagreement doesnot carve nature at the joints.45 To be sure, it is not merely a semanticaldisagreement about the meanings of words. It is a metaphysical disagreementabout the nature of certain derivative objects. It just does not cut to the funda-mental level of reality. Classical mereologists can easily agree that there aredouble-layered compounds in my sense. What we disagree about is whetherordinary objects are such double-layered compounds or rather single-layeredmaterial composites. While not metaphysically substantive, the dispute withclassical mereology is conceptually substantive, in the sense that taking a standon what category of derivative object ordinary objects belong to has far-reachingconsequences for the common-sense conception of objects. This conceptualsignificance plays an important role in this essay and will become apparent inthe chapters to come. (See Section 2.3 for the methodological status of commonsense in the present inquiry.)The division of ordinary objects into different components bears a number of

striking similarities to the Aristotelian form–matter division. The K-path is anon-material part of the object—in addition to the object’s material parts—onwhich the identity of the object depends. The K-path encodes the persistenceconditions of objects of kind K, as will become clearer in Chapter 2, and, as weshall see in Chapter 5, grounds modal properties of these objects. The K-path isinvoked in specifying what makes the object an instance of kind K (seeSection 5.2 for the role of K-paths in solving the grounding problem). Moreover,as will be shown in Section 2.2.2, K-paths are capable of capturing intuitions ofmereological structure, just as forms do in the Aristotelian framework. To mymind, these features of the proposed double-layered account of ordinary objectscry out for a comparison with Aristotelian hylomorphism.46

45 For the notions of metaphysical substantivity and conceptual substantivity, see Sider (2011:section 4.2).

46 Perhaps it is also fair to compare my K-paths with Fine’s primitive functions from times toobjects (see Section 1.1.2), which feature as forms of ordinary objects in his framework.

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However, the similarities are clearly not deep enough for the present accountto qualify as a genuine version of hylomorphism. The main motivation ofAristotelian hylomorphism, as I understand it, is to recognize a structured typeof whole completely absent from classical mereology. Correspondingly, it iscentral to the Aristotelian conception that forms play an object-generating andobject-structuring role. This motivation is not shared by the present approach.Instead, the latter endorses the classical-mereological conception of wholes asunstructured. K-paths are just complex facts that play no deep unifying andstructuring role. The identity of an ordinary object depends on the componentK-path simply because the latter is another part of the object. Moreover, anordinary object’s matter is construed differently. According to the Aristotelianconception, or at least on some variants of it, the object’s matter is the plurality ofits ‘major’ parts, whereas according to the present conception, the object’s matteris itself a whole, an unstructured material object. My dispute with Aristotelianhylomorphists is thus metaphysically substantive, as well as being conceptuallysubstantive. Our metaphysically substantive disagreement concerns the funda-mental question of whether there are genuinely structured wholes. Moreover,taking a stand on whether ordinary objects are structured or unstructuredcompounds of form and matter has far-reaching consequences for the com-mon-sense conception of objects.In a nutshell, the present account’s main motivation is to replace the trad-

itional conception of ordinary objects as single-layered with a conception ofordinary objects as double-layered. Neither the classical-mereological conceptionnor the Aristotelian conception is designed to divide an ordinary object intocomponents with different lives. The possibility of qualitative divergence consti-tutes the main difference from tradition. While the difference from classicalmereology is merely conceptually substantive, the difference from Aristotelianhylomorphism is metaphysically as well as conceptually substantive.So the present theory is a classical-mereological/Lewisian account that takes an

Aristotelian/Finean turn. For the purpose of highlighting this contextualizationof the theory as sharing relevant similarities with genuine hylomorphism of theAristotelian stripe without being a genuine form of hylomorphism, I shall call itquasi-hylomorphism, or q-hylomorphism for short. Accordingly, I shall charac-terize the component K-path of an ordinary object, for some kind K, as theobject’s form, and the component material object as the object’smatter. The formof a table, then, is its component table-path and its matter is its componentmaterial object. The table-path is the form of the table, because it contains a table-realizing profile that grounds the persistence conditions, the modal propertiesand the mereological quasi-structure of tables, as we shall see in following

28 q-hylomorphism

chapters. The table-path is the individual form of the table because it is localized,a distribution of facts across a particular four-dimensional region of spacetime.The material object, by contrast, is the table’s underlying matter. We get to it, as itwere, by stripping away the table’s form; it is kind-independent. Moreover, thequalitative divergence between an ordinary object’s form and its matter will becalled hylomorphic divergence. Strictly, I should speak of quasi-form and quasi-matter, in order to set them apart from genuine, Aristotelian form and matter.Likewise, I should speak of quasi-hylomorphic divergence. For ease of exposition,however, I shall drop the prefixes.Concluding this comparison, the three different views may be summarized as

follows:

Classical mereologyAccording to the classical-mereological conception, an ordinary object is an unstructuredmereological sum of material objects, whose identity depends only on which objects are itsparts, irrespective of which kinds these objects belong to and of how they are arranged.

Aristotelian hylomorphismAccording to Aristotelian hylomorphism, an ordinary object is a structured whole, whoseidentity depends on its ‘major’ parts being arranged in a certain way and on theirbelonging to certain kinds. The principle of unity determining a characteristic mannerof arrangement of certain kinds of object is the ordinary object’s form; the plurality of‘major’ parts is its matter.

Q-hylomorphismAccording to q-hylomorphism, an ordinary object is an unstructured compound of aK-path, for some kind K, and a material object, itself an unstructured mereological sum ofsmaller material objects, which is a subject of that K-path. The K-path is the ordinaryobject’s form; the material subject of the K-path is the ordinary object’s matter.

1.3.3 Three-dimensionalist and four-dimensionalist q-hylomorphism

The basic version of q-hylomorphism as stated so far rests on three-dimension-alism about material objects. I shall close this chapter by indicating briefly howthis account may be placed on a four-dimensionalist foundation instead. Tobegin with, let us review the standard four-dimensionalist characterization ofmaterial objects (in my technical sense). A material object is either an instant-aneous stage or a composite of stages. Composition of stages located at the sametime and composition of stages located at different times are standardly under-stood as classical-mereological—that is, as governed by universalism and exten-sionality (see Section 1.1): any plurality of stages has a fusion, whose identitydepends entirely on which things are its parts. Temporally extended materialobjects thus have temporal as well as spatial parts. The notion of parthood inplay here is a temporally unrelativized notion—parthood simpliciter—to be

q-hylomorphism 29

distinguished from the three-dimensionalist’s temporally relativized notion—parthood at a time. Moreover, since stages are instantaneous, and thereforecannot undergo qualitative change over time, they have their qualitative proper-ties simpliciter.Given these assumptions about the metaphysics of material objects, a K-state,

for any kind K, is the K-meaningful, intrinsic, and K-realizing qualitative profileof a stage. For a stage s located at time t, a K-state of s contains as its K-mean-ingful intrinsic profile the maximal conjunction of the facts that s exists, that s hasç1, that s has ç2, . . . , that s has çn, such that each çi is an intrinsic property of sand each çi falls in the sphere of discourse of K. Furthermore, the K-state ofs contains as its K-realization profile the maximal conjunction of the facts that shas ł1, that s has ł2, . . . , that s has łn, such that the łs jointly realize kind K; andthe maximal conjunction of the facts that ł1 realizes K, that ł2 realizes K, . . . , thatłn realizes K. For example, a chair-state of a stage s at a given time is aconjunctive fact that has all chair-meaningful, intrinsic properties and all chair-realizing properties of s as constituents. Furthermore, exactly as stated inSection 1.2, a K-path is a series of K-states with the following properties: aK-path is unified by K-continuity; a K-path is unified by K-connectedness; aK-path is unified by lawful causal dependence; and a K-path is maximal.On, then, to ordinary objects. They are compounds of material objects and

K-paths. Assuming four-dimensionalism about material objects, there are at leasttwo ways of implementing this proposal: the worm-version of q-hylomorphismand the stage-version. The strict, non-derivative subject of a K-state is a stage. Thestrict subject of a K-path is a cross-temporal fusion of stages, a spacetime worm.According to the worm-version of q-hylomorphism, an ordinary object of kindK is the sum of a K-path and the worm that is the strict subject of that K-path.According to the stage-version, on the other hand, an ordinary object of kind K isthe sum of a K-path and a stage that is the strict subject of any K-state containedin that K-path. On both versions, an ordinary object is a compound of form andmatter, where the form in each case is a K-path. Their difference concerns anobject’s matter. While the worm-version views an ordinary object’s underlyingmatter as a temporally extended worm, the stage-version views the under-lying matter as a temporally unextended stage.The most important aspect of q-hylomorphism is hylomorphic divergence:

the qualitative profile of an ordinary object’s matter and the profile of the sameobject’s form may diverge. One type of hylomorphic divergence, which willprove highly useful in handling problems to be discussed in later chapters,concerns persistence: it should be possible for the temporal path of an ordinaryobject’s matter to diverge from the path of its K-path. Only the stage-version of

30 q-hylomorphism

q-hylomorphism can accommodate hylomorphic divergence of persistence.According to the worm-version, an ordinary object’s matter is the unique subjectof its K-path, and has the same temporal extension as the K-path itself; theirpaths cannot diverge. According to the stage-version, by contrast, an ordinaryobject’s matter is a single stage that does not persist at all, and therefore does notfollow the temporal trajectory of the object’s K-path. Assuming that hylomorphicdivergence concerning persistence is desirable, the worm-version suffers from asignificant limitation. Despite this limitation, the worm-version will stay in thepicture, because it accommodates, or could be extended to accommodate, otherrelevant types of hylomorphic divergence as successfully as the stage-version.47

In the course of this volume, q-hylomorphism will be defended on the groundsof its performance in treating a range of philosophical problems about ordinaryobjects. Many of these problems can be handled with equal success by the three-dimensionalist version and by at least one of the four-dimensionalist versions.The availability of a treatment of a problem that is neutral concerning thespatiotemporal profile of material objects would constitute an advantage overthose traditional approaches that presuppose taking a stand in the debatebetween three-dimensionalists and four-dimensionalists. Other things beingequal, the fewer metaphysical commitments required to solve a problem, thebetter. Accordingly, I shall strive for metaphysical neutrality wherever possible.Where the different versions of q-hylomorphism are on a par in handling aproblem, I shall focus on the three-dimensionalist one. Where the versions differin their performance, I shall indicate which version does the better job.48

47 See Chapter 8 in particular.48 In Chapters 3 and 6, I shall indicate advantages of the three-dimensionalist version. In

Chapter 8, I shall discuss a problem concerning relativity for which the four-dimensionalist versionsmay be most suitable.

q-hylomorphism 31

2

Perspectivalism

Having addressed the metaphysics of ordinary objects, let us turn to the linkbetween the proposed account of what ordinary objects fundamentally are andhow they are pre-philosophically represented. I shall attempt to establish such alink in the form of a metaphysical semantics of ordinary statements that expressthe propositional contents of our basic pre-philosophical beliefs and intuitionsabout ordinary objects—that is, of the statements that express our common-senseconception of objects. Assuming that such a metaphysical semantics takes theshape of a truth theory, my aim is to state truth conditions of object-discourse inthe reasonably fundamental terms of q-hylomorphism about ordinary objects.My central semantic thesis is that ordinary predication is perspectival, employingmodes of predication that correspond to different conceptual perspectives onordinary objects, and that predications in different modes are made true bydifferent metaphysical components of ordinary objects. The metaphysicalsemantics to be developed will be called perspectivalism. The philosophical theoryof ordinary objects composed of perspectivalism and q-hylomorphism is per-spectival hylomorphism.

2.1 Representing Ordinary Objects

We may conceive of the same ordinary objects differently in different contexts.These conceptions correspond to different perspectives. Three perspectives maybe distinguished: the sortal-sensitive, the sortal-abstract, and the absolute per-spective. From the sortal-sensitive perspective, we conceive of an object in waysthat are sensitive to the kinds to which the object belongs. This is the defaultperspective of unreflective common sense. From the sortal-abstract perspective,we strip away an ordinary object’s sortal covers and conceive of it in primarilyspatiotemporal terms, without representing it as belonging to any kind. Fromthis perspective we ignore which ordinary kind (if any) the object’s propertiesand relations realize, and accordingly do not trace the object by means of

kind-realizing properties, as we do from the sortal-sensitive perspective. Whilethe sortal-sensitive and the sortal-abstract perspectives are non-fundamentalperspectives, employed when describing objects in ordinary-language terms,the absolute perspective is the perspective from which we do fundamentalmetaphysics, transcending both the sortal-sensitive and the sortal-abstract per-spectives. This is the perspective of the philosopher who does not aim to describeobjects in ordinary-language terms, but rather aims to analyse their metaphysicalstructure in the fundamental, technical terms of the seminar room, analysingthem, for example, as compounds of matter and form. So much for an outline ofthe three perspectives. Let us look at some details.

2.1.1 The concept of an ordinary object

The ordinary world of objects is divided into persons, tables, trees, mountains,and so on. While these objects do not have their own ontological category—thereis nothing metaphysically special about them as a class, for, as we saw inChapter 1, ordinary and extraordinary objects are metaphysically on a par—they have their own pre-metaphysical, conceptual category; they play a specialrole in our overall conceptual scheme. I label this category as the category ofordinary object, though I will refrain from making claims about how we typicallydesignate this category on the street. We seem to be using different linguisticexpressions in different contexts. Ordinary uses of ‘thing’ and ‘object’ may bothmean ordinary object, in my sense.What makes something an ordinary object? As a rough approximation, let us

say that a distribution of properties in space and time is sortable just in case (i) itis sufficiently contrasted from the environment at any time—in terms of ‘gestaltfeatures’ such as colour, texture, edge, curvature, and shape1—and (ii) it iscontinuous, connected, causally unified, and maximal in some sufficiently intrin-sic respect or respects over time. (For the notions of continuity, connectedness,causal unification, and maximality, see the characterization of K-paths inSection 1.2.) Then we can say that something is an ordinary object—we mightalso speak of a sortable object—just in case it is an object with sortable properties.Tables are ordinary objects. The qualitative properties of a table yield a sufficientcontrast between the table and its environment at any time of its existence, andthe qualitative, kind-realizing profile of a table over time is continuous, con-nected, causally unified, and maximal. This table-realizing profile is made upfrom properties concerning, roughly, design, function, and composition over

1 For an account of these ‘gestalt properties’ in psychology, see, inter alia, Spelke, Gutheil, andVan de Walle (1995: 301).

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time—that is, from properties that are sufficiently intrinsic. I suggest that theconcept of an ordinary object plays the role of a category in our common-senseconception of the world, along with other conceptual categories, whichever theymay be.It will improve our grip on the conceptual category of ordinary object to

consider a few examples of things that fall outside of this category because eitherthe synchronic condition or the diachronic condition on sortability is notsatisfied. First, the water in the glass and the wood in the table are not ordinaryobjects. For these are quantities of stuff, or masses of matter, that can surviveradical scattering, as when the water in the glass is splashed across the floor, andhence are not sufficiently contrasted from their environment at all times of theirexistence. Note, however, that I take a piece of wood to be an ordinary object. Thesortal piece of wood, unlike the mass nouns water and wood, comes with acontrast-requirement, and thus a piece of wood is not radically scatterable.Second, galaxies are not ordinary objects because the first condition of sort-

ability, the synchronic one, is not satisfied, as in the case of quantities of matter.When viewed up close, a galaxy displays only a low degree of contrast from itsenvironment, though each of its components is individually well contrasted. Inother words, a galaxy is not sufficiently unified in the gestalt-psychological sensethat I propose as a criterion for when we recognize something as an ordinaryobject at a time. A galaxy is unified by gravitational influences, but this is not theunity that counts when it comes to the common, psychological concept of anordinary object. In line with these considerations, it has been proposed in theliterature (see, inter alia, Simons 1987: chapter 4) to treat galaxies not as objects,but as pluralities. The syntactically singular term ‘the Milky Way galaxy’, forexample, refers to some heavenly bodies, not to a single thing. Of course, friendsof this line need to elaborate on the persistence conditions of such pluralities.Third, restaurants are not ordinary objects because the diachronic condition of

sortability is not satisfied. Restaurants are sufficiently contrasted from theirenvironment—they are sufficiently unified at a time—but the properties thatindividuate them across time are massively relational. A restaurant may moveacross the street as a contract is signed.2 This spatial leap has nothing at all to dowith the intrinsic properties before the signing. So restaurants are not ordinaryobjects, in my sense. (Compare the highly extrinsic individuation of incars andoutcars (see Section 1.3.1), which are also not sortable.) Restaurants might be putin the conceptual category of social entities, along with institutions and states.

2 See Hawthorne (2006: 113).

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2.1.2 Three perspectives on ordinary objects

We may conceive of ordinary objects differently in different contexts. On thesortal-sensitive conception, we single out and represent ordinary objects in waysthat are sensitive to the kinds to which the objects belong—that is, in ways thatare sensitive to which properties of a given ordinary object realize which kinds,and of how these properties are distributed across space and time. When weconceive of an object as a musical instrument, we conceive of it as belonging tosome instrument kind or other. When we conceive of an object as a piano, weconceive of it as belonging to a particular kind, as having properties that realizethat kind, and as having certain persistence conditions associated with that kind.When we conceive of an object as a spinet, we conceive of it as a piano withcertain further distinguishing features. Any of these ways of thinking of anordinary object belong to the sortal-sensitive conception. This is the conceptiontypically presupposed by our everyday thought and talk about objects.In addition to the sortal-sensitive conception, there is another conception of

ordinary objects employed by ordinary thinkers (as well as philosophers). Myhypothesis is that there is a range of ‘platitudes of common sense’ that concernordinary objects as a class, and that constitute a primarily spatiotemporal con-ception of these objects, a conception that abstracts from considerations of whichproperties of ordinary objects realize which kinds, and of how these propertiesare distributed across space and time. This conception attributes to ordinaryobjects a common, minimal spatiotemporal profile. I take this sortal-abstractconception to be a high-level conception that takes all and only ordinary objects,as characterized earlier, as input. That is, the sortal-abstract domain of objects isidentical with the sortal-sensitive domain. This single-domain thesis will bemotivated in Section 2.1.4. If the thesis is correct, it is natural to view thissortal-abstract conception and the sortal-sensitive conception as two perspectiveson the same objects, the sortal-sensitive perspective and the sortal-abstractperspective. (Note that I do not take the primarily spatiotemporal object-conception of ordinary thinkers to be the only available sortal-abstract concep-tion of objects. There may be several distinct such conceptions—different ways ofadopting the sortal-abstract perspective. Henceforth, I shall focus on the spatio-temporal conception of common sense. I shall briefly return to the issue ofpluralism about sortal abstraction in Section 8.3.)Here are some pillars of the sortal-abstract frame-conception of the world,

some general platitudes of common sense about ordinary objects:

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(a) An object has a continuous spatiotemporal path. It cannot jump betweendistant places from one moment to the next; and it cannot have more thanone temporal beginning.

(b) An object has a continuous spatial location at any time. It cannot have anyparts at a given time that are completely unconnected.

(c) An object cannot exactly occupy distinct places at the same time. It cannotbe spatially distant from itself at any time.

(d) Distinct objects cannot exactly occupy the same place at the same time.Two objects in the same place at once would crowd each other out.

(e) An object cannot go out of existence by purely extrinsic causes. It cannotbe destroyed without contact.

These principles seem entirely independent of any kind-realizing features ofordinary objects—independent, that is, of the specific properties that makeobjects persons, tables, trees, or mountains. They are sortal-abstract principles.Moreover, they are not generalizations of actual experiences, beliefs, or intuitionsabout particular objects. They are principles of metaphysical impossibility, sup-ported by the prima facie inconceivability of an object’s jumping about discon-tinuously, of its scattering radically, of its occupying distinct places at once, andso on. They are principles of folk metaphysics.3

The sortal-abstract conception of ordinary objects is distinct from the familiarconception of quantities of stuff, or masses of matter. To abstract from the sortal-relevant properties of ordinary objects is not to think of them as quantities ofstuff.4 As pointed out in Section 2.1.1, quantities of stuff are not ordinary objects.To view an ordinary object from the sortal-abstract perspective is to abstractfrom its standard, sortal representation and to represent it primarily spatiotem-porally (admittedly, this characterization is not fully adequate, as it includescausal elements—this is why I describe the conception as primarily spatiotem-poral). To recognize quantities of stuff, on the other hand, is to recognize thingsthat are psychologically inviduated, roughly, by their parts or constituents,independently of their spatiotemporal as well as their object-sortal-relevantproperties. The water in the glass, for instance, can survive radical spatialscattering.The sortal-sensitive and the sortal-abstract conceptions of ordinary objects are

non-fundamental conceptions. I am leaving room for a third, fundamental

3 For discussions of the link between conceivability and possibility, see Szabó Gendler andHawthorne (2002).

4 This thesis will be restricted in Chapter 8.

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conception, the absolute one, that presents ordinary objects in yet a differentlight. My conception of ordinary objects as compounds of matter and form is anexample of such an absolute conception; and we shall see in a moment how itrelates to the other two. While the sortal-sensitive and the sortal-abstract con-ception are both pre-philosophically available, ordinary thinking never rises tothe absolute conception. The latter is pre-philosophically inaccessible. This is notto say that metaphysical claims about objects are only made from the absoluteperspective and only phrased in absolute terms. It is quite common for meta-physicians to make general claims about objects in natural-language terms. Thesecould be sortal-sensitive claims about all objects of a specific kind, as we findthem, for example, in the metaphysics of personal identity, or sortal-abstractclaims about ordinary objects on the whole that do not target their deep structure.Not every metaphysics of ordinary objects aims at a fundamental analysis.It should be emphasized that the sortal-abstract conception of ordinary objects

is distinct from the absolute, or metaphysical, conception of material objects asmere mereological sums, endorsed in Chapter 1. As pointed out above, thinkingof ordinary objects in a sortal-abstract way is different from thinking of them asquantities of matter. Now, this is quite compatible with thinking of complexmaterial objects, components of ordinary objects, as mereological sums, or,roughly, as quantities of matter, from the absolute perspective. The absoluteconception of ordinary objects and their components must not be understoodas a conception that we arrive at by a rigorous formulation of the sortal-abstractconception—that is, we do not get to it by formalizing folk metaphysics. Rather,we should expect the underlying metaphysics of ordinary objects to take quite adifferent shape from the sortal-abstract picture. While the question of the shapeof the sortal-abstract conception of ordinary objects is an empirical matterconcerning what we do in fact commonly think and say about these objectswhen abstracting from their kinds, the question of the shape of the absoluteconception of ordinary objects is a philosophical matter of what metaphysiciansshould say in light of theoretical considerations.The recognition of a fundamental conception of macroscopic objects in add-

ition to a non-fundamental, ordinary one is fairly common. For example, whilewe ordinarily think of chairs as having only material parts, some metaphysiciansview chairs as ‘bundles’ of properties, and hence as having non-material parts.Further, while we ordinarily think of chairs as having only spatial parts, somemetaphysicians view chairs as having temporal parts as well. Metaphysiciansare often prone to uncover deep attributes of objects to which ordinary folksare blind. The present, unorthodox refinement of this dichotomy between a

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non-fundamental and a fundamental conception is a distinction between differ-ent non-fundamental conceptions, namely, between the sortal-sensitive and thesortal-abstract ones. This refinement is substantial and, while prima facie plaus-ible, in need of further support. In the remainder of this sub-section, I shallmotivate this psychological distinction between conceptions and inquire intotheir relationship.

2.1.3 The psychology of object representation

Support for the distinction comes from influential work in psychology. Psycho-logical research on object representation suggests that young infants individuateobjects by spatiotemporal criteria prior to individuating objects as belonging toparticular kinds.5 The spatiotemporal criteria are principles of dividing surfacelayouts into objects. Among the criteria adduced by Elizabeth Spelke are thefollowing three.6 According to the principle of cohesion, ‘two surface points lie onthe same object only if the points are linked by a path of connected points’ (1990:49). Thus, when two surfaces are separated by a spatial gap, they are surfaces ofdistinct objects. As a corollary of this principle, Spelke suggests that ‘when surfacepoints appear at different places and times such that no connected path couldunite their appearances [ . . . ], the surface points do not lie on the same object’(1990: 49). According to the principle of boundedness, ‘two surface points lieon distinct objects only if no path of connected surfaces links them’ (1990: 49).Thus, distinct objects have no surface point in common. According to theprinciple of no action at a distance, ‘separated objects are interpreted as movingindependently of one another if such an interpretation exists’ (1990: 50). Thus,objects are expected to act on each other only on contact.Infants represent objects in a primarily spatiotemporal, sortal-abstract way,

whereas adults represent objects in a sortal-sensitive way. Infants parse the worldinto objects prior to representing them as falling under ordinary kinds. Adultsparse the world into objects of ordinary kinds. How does object representation ininfants develop into object representation in adults? Consider the following twohypotheses. The first hypothesis is that object representation changes radicallyover the course of development: the early spatiotemporal, sortal-abstract criteriaof object individuation are replaced by fundamentally different, sortal-sensitivecriteria. In the course of development, infants come to represent objects as

5 See Spelke (1990), Spelke, Gutheil, and Van de Walle (1995), Spelke, Kestenbaum, Simons, andWein (1995), Xu and Carey (1996), Xu (1997).

6 See Spelke (1990: 49–50).

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belonging to particular kinds and then abandon the sortal-abstract criteriacompletely. The second hypothesis is that object representation does not changeradically over the course of development: the early sortal-abstract criteria ofobject individuation are supplemented by sortal-sensitive criteria. Primarilyspatio-temporal criteria of object individuation are somehow integrated withadults’ representations of objects as belonging to particular kinds.7

If the sortal-abstract criteria continue to play a role in object representation byadults, then it is overwhelmingly plausible to view these criteria as forming atleast a partial basis of common-sense principles (a)–(e). The principle of cohe-sion, according to which spatially separated surfaces are represented as belongingto distinct objects, is a natural, at least partial, source of (b) and (c); and itscorollary, according to which an object is represented as having a connected path,is a natural source of (a). Likewise, the principle of boundedness, according towhich distinct objects are represented as having no surface point in common, is anatural source of (d). And the principle of no action at a distance, according towhich objects are expected to act on each other only on contact, is the naturalbackdrop for (e). Note that when I say that a psychological principle of individu-ation is at least a partial basis, or source, of a certain modal platitude of commonsense—for instance, that the principle of cohesion is a source of (c)—I mean toindicate that our inability to conceive of an ordinary object as behaving a certainway is linked to our possession of a certain perceptual principle. For instance, wecannot conceive of an object as exactly occupying distinct places at the same time,partly because we are wired with the principle of cohesion. I refrain fromclaiming, however, that the inconceivability is entirely based on perceptualprinciples.There seems to be a consensus in favour of the second hypothesis. The most

straightforward argument for the latter is an argument from simplicity. A basicconstraint on an explanation of the path from object representation by infants toobject representation by adults is that the explanation should be as simple aspossible. Ceteris paribus, the simplest explanation minimizes the cognitive dis-tance between infants and adults.8 The hypothesis according to which there is noradical developmental change and principles governing object representation byinfants continue to operate in the adult scheme, forming the basis of common-sense principles (a)–(e), is clearly the simpler, and hence preferable, hypothesis,provided that a plausible integrated account of adults’ object representation inconcert with the spatiotemporal criteria is available. Given that the underlyingcriteria of representation are sortal-abstract, (a)–(e) should be construed as

7 See Spelke (1990: 51–2, 54). 8 See Hirsch (1997: 411).

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sortal-abstract, as well.9,10 This is a good reason for dividing the common-sensepicture of the world of macroscopic objects into a sortal-sensitive conceptionand a sortal-abstract conception, where the latter is characterized in primarilyspatiotemporal terms.

2.1.4 The limits of sortal abstraction

While principles (a)–(e) provide a sense of the content of the sortal-abstractconception possessed by ordinary thinkers, some further remarks on the limits ofthis conception are in order.The first question to be addressed is the following: while the sortal-abstract

conception of objects describes objects without recourse to any specific sortals,does this conception itself constitute a general, purely spatiotemporal sortal? Thisis a controversial issue. One mark of a sortal, pointed out in Section 1.2.2, is that itspecifies persistence conditions, criteria for tracking its instances through time.I doubt that the sortal-abstract conception includes any sufficient persistenceconditions of objects, and therefore I doubt that this conception yields a sortal.Suppose that we start with a table, abstracting from whichever specific properties

9 Carey and Xu (2001) argue that the object representations of young infants are identical withthe object files of mid-level visual cognition, suggesting that at least two distinct representationalsystems play a role in object individuation in adults, a sortal-abstract system that privilegesspatiotemporal information and a sortal-sensitive, kind-based system. The role of sortal-abstractobject-representations in mid-level visual cognition is different from the cognitive role that I ascribeto this type of representation, which is encoded in such general beliefs as (a)–(e). But there need notbe a conflict here.

10 Michael Jubien (2009: 15ff.) also places great emphasis on two ways of thinking about ordinaryobjects. What he calls the ‘great divide’ separates our conception of objects as belonging to familiarkinds from our conception of them as ‘physical objects’. According to Jubien, ‘the different ways ofthinking about a given thing are accompanied by differing attitudes about its parts and about thearrangement of its parts. [ . . . ] When thought of just as an object, the parts of a thing seem definiteand their arrangement seems inconsequential. But when thought of as an object of a familiar kindthere is a striking reversal: we think of the arrangement as important and the parts themselves asinessential’ (2009: 15). I have doubts about Jubien’s claim that we commonly think of one and thesame object as a structured object, say as a chair, and also as an unstructured object, say as a hunk orquantity of wood. For these conceptions clearly seem to yield distinct common-sense domains ofobjects—the chairs versus the hunks of wood, where some of the latter constitute some of theformer. So Jubien’s central conceptual distinction is different from mine. On my view, we recognize,from the sortal-sensitive perspective, structured ordinary objects, such as chairs, as well as distinct,unstructured ordinary objects, such as hunks or quantities of wood. Our recognition of thesedifferent domains bears little theoretical relevance for present purposes. What matters most in thepresent context is rather, that all of these ordinary objects can also be represented in a sortal-abstract, primarily spatiotemporal way. (That the sortal-abstract conception is neutral with respectto the structured–unstructured divide is pointed out in Prasada, Ferenz, and Haskell (2002: 142).)Note also that the psychological status of the structured/unstructured divide is to be separated fromits metaphysical status. In the present discussion, it plays only a small psychological but a bigmetaphysical role (see Chapter 1 and Section 2.2.2).

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make it a table or an object of any other specific kind (leaving room for viewing atable as belonging to several kinds), and then remove particles one by one. Thereis one object at the beginning of this process of gradual decay. (Recall that byprinciple (d) of the sortal-abstract conception any spatial region is filled by atmost one object at a time.) What happens to it? Does it shrink or does it spreadout, becoming increasingly scattered? Spatiotemporal continuity may seem like agood criterion by which to approach this question. If spatiotemporal continuity isa guide, then the object shrinks. Suppose, however, that the process of shrinkingterminates in a point-sized object. We surely do not judge the macroscopic objectto shrink to a point. So we would expect the object to go out of existence at sometime during the shrinking process. But we are clearly unable to determine whenthat happens—we cannot even determine it roughly—without recognizing somediscontinuity in specific qualitative properties, the sorts of properties that realizea specific kind. Or suppose we start with a brick wall, abstracting from whicheverspecific properties make it a brick wall or an object of any other specific kind, andthen add further bricks. What happens to the object? Does it retain its originalshape and size while receiving external attachments or does it grow? Spatiotem-poral continuity is cheap, going both ways: the object to which new things areadded has a spatiotemporally continuous path, but so does the object that grows.Again, we are unable to determine what happens without tracking some specificqualitative, kind-realizing properties.These cases suggest that we do not possess a sufficient criterion of tracking

objects through time that is independent of the ways of tracking associated withspecific sortal concepts. I claim, therefore, that the thesis of the availability of apre-theoretical, sortal-abstract conception of objects is plausible only if thisconception is allowed to be fragmented and amorphous, yielding at most a partialprinciple of individuation, and hence yielding no spatiotemporal sortal.11 Ofcourse, our familiar object-sortals are subject to quite a lot of indeterminacy(as we shall see later). Specifying indeterminate persistence conditions, however,is significantly different from specifying no persistence conditions whatsoever.The second question regarding the limits of sortal abstraction is whether the

ordinary sortal-abstract and sortal-sensitive conceptions have the same or dis-tinct domains of objects. One option is that the two conceptions purport to applyto wholly different collections of objects—that their domains are disconnected.This option can be ruled out right away. For there cannot be any doubt that we

11 Note that the concept of a material object, as used here, does not function as a liberal sortalconcept. A material object is merely an object with a non-derivative spatiotemporal location; seeSection 1.2.1.

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intend the platitudes of common sense (a)–(e) to apply to all ordinary objects, toall persons, tables, trees, pieces of wood, and lumps of metal. A follow-up issue iswhether the sortal-abstract conception applies to some objects to which thesortal-sensitive conception does not apply—that is, whether the sortal-abstractdomain of objects is distinct from but includes the sortal-sensitive domain—orwhether the sortal-abstract domain is identical with the sortal-sensitive domain.A reason frequently adduced for letting the sortal-abstract conception reach

beyond familiar objects concerns our ability to handle novel objects. Imaginebeing presented with an unfamiliar kind of object, say an object of Martiandescent, and being unable to apply any specific sortal concept to it. It seemsclear that we might still be able to locate the object in space and track it throughtime. Since none of our familiar sortals applies, one might think that the only wayof locating and tracking the object is by a non-sortal method, a method thatdiffers fundamentally from the usual approach employing specific sortalconcepts.12

Perhaps this account of novel objects is correct. But I favour an alternativehypothesis. I suggest that when we are able to locate a novel object in space andtrack it through time, that is so because it is a sortable object—an object with aprofile that is sufficiently contrasted from the environment at a time, and that iscontinuous, connected, causally unified, and maximal in some not-too-relationalrespect over time (see Section 2.1.1). As no specific sortal is available to match itssortable profile, the object is registered as a novel object and the introduction of anew sortal is called for. The key point here is that novel objects do not require usto abandon our sortal-sensitive approach in favour of a sortal-abstract one.Unfamiliar objects are not individuated any differently from familiar objects.We just lack a label for them. When presented with novel objects, we look toextend the sortal-sensitive domain of ordinary objects with the very tools bymeans of which this domain was specified in the first place. This is a simpler andperhaps also more plausible account of novel objects than the view that thesortal-sensitive conception is transgressed in the face of novel objects, and thatthe latter are individuated in a fundamentally different way. On the presenthypothesis, our approach to novel objects is sortal-sensitive through andthrough.13

12 See, inter alia, Hirsch (1982, 1997) and Xu (1997). As Hirsch puts it, the view is that in additionto ordinary objects, our common-sense ontology contains objects that are individuated in ‘sortalignorance’, and that are ‘lurking in the background’; see Hirsch (1997: 408).

13 Novel objects, as encountered in science fiction, are sortable objects for which we lack a sortalconcept. By the standards of sortability operative in our community, however, extraordinary objects,such as widely scattered fusions and incars, are unsortable (see Section 1.1.4).

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If this is correct, novel objects provide no reason for viewing our pre-theoret-ical, sortal-abstract conception of macroscopic objects as determining a differentdomain than our sortal-sensitive conception. The sortal-abstract conception isnot required to reach beyond and to fill holes left by our sortal representations ofthe world. On the view I favour, the sortal-abstract conception is a high-levelconception that takes all and only the objects parsed under the sortal-sensitiveconception as input; the sortal-abstract domain of objects is identical with thesortal-sensitive domain. If so, it is plausible to view the sortal-abstract conceptionand the sortal-sensitive conception as two perspectives on the same objects.At this point, one will wonder whether these perspectives are consistent;

whether ordinary objects could fit both our sortal-sensitive and our sortal-abstract descriptions. For the conceptions’ inconsistency would provide a reasonfor reconsidering the prima facie implausible two-domain account. This is acentral question. In the next section, I will outline how to alleviate worries aboutinconsistency.It should be emphasized again that the sortal-abstract perspective is a second

non-fundamental perspective. The perspective of fundamental metaphysics is theabsolute one, different from both the sortal-sensitive and the sortal-abstractperspectives. This is the metaphysically ultimate point of view, completely undis-torted by sortal representations of the world. From this angle, many types ofunsortable entity may be recognized to which the non-fundamental perspectivesare blind. The sortal-sensitive perspective is ordinary folks’ default point of view.Sortal abstraction starts with these sortable objects and then strips them fromtheir specific sortal profile, leaving a spatiotemporal conception of sortableobjects as a class.These considerations were meant to yield an initial grip on three categorially

different ways of conceptualizing ordinary objects, three perspectives, as part of atheory of ordinary objects that integrates metaphysical, semantical, and psycho-logical aspects. The next step in the development of this framework is to look atdiscourse about ordinary objects in light of its manifesting these different per-spectives and link it to the metaphysics of objects developed in the previouschapter.

2.2 Modes of Predication and Q-Hylomorphism

My aim in this section is to outline a metaphysical semantics of ordinarystatements that express the propositional contents of our basic pre-philosophicalbeliefs and intuitions about ordinary objects—that is, of the statements thatexpress our common-sense conception of objects. Taking a metaphysical

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semantics to be a truth theory, I intend to state truth conditions of thesestatements in the reasonably fundamental terms of q-hylomorphism aboutordinary objects. Object-discourse, as I shall use the term, is discourse whosequantifiers range over ordinary objects, and whose singular terms refer toordinary objects, assuming that the concept of an ordinary, or sortable, objectis a conceptual category of ordinary thinkers.14 My focus will be on howpredication works in object-discourse. I shall put forth the semantical thesisthat predication in object-discourse is perspectival, employing modes of predi-cation that correspond to different perspectives on ordinary objects.To a type of perspective on ordinary objects corresponds amode of predication.

Such a mode is here understood as a certain way of predicating a property orrelation of an object. Different modes of predication may be employed indifferent contexts, depending on which perspective on the object or objects tobe described is adopted in the context. By adopting the sortal-sensitive perspec-tive on an ordinary object, a speaker employs the formal mode of predicationwhen describing the object. By adopting the sortal-abstract perspective on anordinary object, a speaker employs the material mode of predication whendescribing the object. By adopting the absolute perspective on an ordinary object,a speaker employs the absolute mode of predication when describing the object.While tradition recognizes only one mode of predication, the absolute one,I propose to distinguish between three modes.Consider, for example, a chair, o. In a context in which I want to speak about o

as an instance of a specific kind, focusing on the properties that make o a chair,I adopt the sortal-sensitive perspective on o. If I conceive of o in this way and saythat o has four legs, is designed in the Bauhaus style, and is comfortable, then myutterance is a formal predication. In a context in which I want to speak about o asan instance of a conception that applies to all objects, ignoring which of itsspecific properties make it a chair, focusing instead on universally shared

14 I shall adopt the common position that the reference of singular terms in object-discourse isfixed by an intention on the part of the reference-fixer to refer to a thing falling under a certainobject-sortal. Suppose that a speaker, A, points in the direction of a chair and intends to dub it ‘C’.Assuming that the dubbing is successful, ‘C’ designates the chair. What makes a dubbing successful?In the direction of the pointing lies not just the chair, but also the piece of plastic constituting thechair. How did A manage to confer the name to the chair, and not to the piece of plastic? The answeris that A intended to refer to a chair. Suppose, further, that a speaker, B, points in the direction of ahallucinated chair, and intends to dub it ‘C’. Assuming that the dubbing is unsuccessful, the namefails to refer. What makes a dubbing unsuccessful? Why did B not manage to confer the name to anempty spatial region or to a cloud of air molecules? The answer is that B intended to refer to a chair.Without recourse to specific sortals in speakers’ intentions it is hard to explain how referring termsrefer to the objects that we expect them to refer to, and how they fail to refer to the objects that we donot expect them to refer to. Cf. Thomasson (2007: section 2.3).

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spatiotemporal properties, then I adopt the sortal-abstract perspective on o. IfI conceive of o in this way, and say that o occupies a unique place at a time, thenmy utterance is a material predication. As pointed out earlier, we take the sortal-abstract perspective on sortally individuated objects, stripping them off theirsortal covers. Accordingly, we can take the sortal-abstract perspective on agiven object in a context in which we refer to that object by means of a specificsortal concept. For example, the predication ‘That chair occupies a unique placeat a time’, which has a noun phrase in subject position that is governed by thesortal chair, is to be read as a material predication, if the assertion is made on thegrounds of the belief that all objects occupy a unique place at a time. Finally, ifI conceive of o as a compound and say that o has a certain material object and acertain chair-path as parts, then my utterance is an absolute predication.In accordance with what has been said about the accessibility of the various

perspectives, predications about objects in ordinary discourse may employ theformal or the material mode, the formal mode being the default. The absolutemode, however, is not represented in ordinary discourse about objects; it isconfined to the technical language of the seminar room,15 with one importantexception. Ordinary sortal predicates, such as the predicate ‘is a chair’, apply totheir instances absolutely. The properties (and relations) that apply to objectsnon-absolutely—that is, formally or materially—are properties whose ascriptionis sensitive to which perspective is adopted. The property of being a chair, bycontrast, is insensitive to which perspective is adopted: an object is a chair fromall perspectives.The point of distinguishing between different modes of predication is that one

and the same object can have a certain property in one mode, manifesting oneperspective, and lack that property in another mode, manifesting another per-spective. That is, an ordinary object may have different qualitative profiles fromdifferent perspectives. I call this aspect perspectival divergence. In developing theproposed picture, I shall begin with the syntax of predications in different modes.Then I shall turn to the metaphysical semantics of the formal and the materialmode. Finally, I will show how this framework allows for perspectival divergence.

2.2.1 Formal predication

Consider a singular monadic predication ‘o is F’ about an ordinary object o. (Theextension to singular polyadic and temporal predications will be straightforward.)

15 Let me emphasize, though, that this thesis is restricted to object-discourse, and thereby leavesopen whether the absolute mode of predication is represented in ordinary discourse about othercategories of things.

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This predication may be read in three different ways, as an absolute predication,as a formal predication and as a material predication. In order to represent modesof predication in a formal language, an indicator of the mode of predication mustattach to the indicator of predication. The familiar parentheses will be used asindicator of predication. The subscripted tag of ‘form’ to the right-parenthesiswill indicate the formal mode of predication; and the subscripted tag of ‘mat’to the right-parenthesis will indicate the material mode of predication. Theunsubscripted right-parenthesis will indicate the absolute mode of predication.Thus, if ‘o is F’ is read as an absolute predication, then it has the familiar logicalform ‘F(o)’. If ‘o is F’ is read as a formal predication, then it has the logical form‘F(o)form’. If ‘o is F’ is read as a material predication, then it has the logicalform ‘F(o)mat’. Henceforth, I shall specify these readings semi-formally, as ‘o isabsolutely F’, ‘o is formally F’, and ‘o is materially F’, respectively. In an ordinarypredication with a copula ‘is’ the best way to indicate the formal and the materialmode of predication is to subscript a marker ‘form’ or ‘mat’ to the copula, themark of predication, as in ‘o isform F’ or ‘o ismat F’. Since we will regularlyencounter formal and material predications without a copula, such as ‘o existsat t’, I shall not follow the subscription strategy, and rather indicate the formaland the material mode of predication, in informal contexts, by means of theadverbs ‘formally’ and ‘materially’. It must be kept in mind, however, that‘formally’ and ‘materially’ are not to be understood as predicate modifiers.In order to state a metaphysical semantics of the different modes of predica-

tion, I shall, first, assume q-hylomorphism about ordinary objects, as developedin Chapter 1. That is, I shall assume that an ordinary object is a compound ofmatter and form, a mereological sum of a material object and a K-path, for somekind K, that has that material object as a subject. The upcoming metaphysicalsemantics based on q-hylomorphism is perspectivalism. The theory of ordinaryobjects consisting of q-hylomorphism and perspectivalism is perspectivalhylomorphism.Q-hylomorphism is an account of ordinary objects, crafted by taking the

absolute, metaphysically fundamental perspective on ordinary objects. Accord-ingly, this account is stated in terms of predications in the absolute mode. Thesemantics of absolute predication, whether temporal or atemporal, will be takenas understood, and no truth conditions will be specified. The focus will be onspecifying truth conditions of predications about ordinary objects in the formaland the material mode, the two modes represented in natural-language object-discourse.Very roughly, when we ask, from the sortal-sensitive perspective, what a given

object is like formally, we ask which properties are contained in the object’s

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individual form. When we ask what the object is like materially, abstracting fromthe object’s kinds, we ask which properties are instantiated by the object’sunderlying matter. In short, formal, sortal-sensitive predication concerns form,whereas material, sortal-abstract predication concerns matter. The core idea ofperspectivalism is that while our typical, sortal-sensitive talk tracks ordinaryobjects under sortal covers, sortal-abstract talk strips away all those covers.Since ordinary objects are double-layered, composed of form and matter, shiftingbetween sortal-sensitive and sortal-abstract talk—between formal and materialpredication—is shifting between different aspects of the same subject.Perspectivalism also applies to ordinary statements of identity. Such state-

ments do not ascribe identity absolutely; they only do so formally or materially.This is an instance of my thesis that the absolute mode of predication is notrepresented in everyday object-discourse. Consider a chair o and a chair o*.Adopting the sortal-sensitive perspective, we can ask whether o is formallyidentical with o*; and adopting the sortal-abstract perspective, we can askwhether o is materially identical with o*. Both of these questions are distinctfrom the fundamental question whether o and o* are absolutely identical. Whenwe ask whether o and o* are formally identical, we ask whether they have thesame individual form. When we ask whether o and o* are materially identical, weask whether they have the same underlying matter. And when the metaphysicianasks whether o and o* are absolutely identical, she asks whether they have thesame individual form and the same underlying matter. Given the close relation-ship between the concept of identity and the concept of number, if statements ofidentity can be read in these different ways, then so can statements of cardinality,statements about the number of objects.Perspectivalism will not be applied to ordinary assertions of existence, such as

‘Tables exist’ or ‘There are tables’. I shall assume that claims of existence sim-pliciter (in contrast to claims of existence at a time) have the simple form, ‘∃x�’,and that the existential quantifier has the orthodox syntax and semantics. That is,no distinction will be drawn between a formal mode and a material mode ofascribing the predicate ‘exists’ to an ordinary object. This predicate is, rather,analysed in terms of the existential quantifier, for which different modes have notbeen introduced. Nor will I appeal to a distinction between a formal and amaterial restriction of the domain of the existential quantifier, or draw a distinc-tion between different existential quantifiers. Ordinary objects do not havedifferent modes of being, of Sein, but they do have different modes of being-so,of Sosein.16

16 While perspectivalism does not apply to existence simpliciter, it does apply to existence at atime.

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The metaphysical semantics of formal and material predication will now bedeveloped in greater detail. Formal predication concerns an object’s individualform, its component K-path. Consider the statement ‘P is formally happy at t’,where P is a person.17 P has a component person-path and a component materialobject. A person-path is a particular distribution of person-realizing facts acrossspace and time. Such a distribution includes the causally connected possession ofdifferent beliefs, desires, emotions, and so on, by the same or different materialobjects at different times. For P to be formally happy at t is for P’s componentperson-path to contain happiness at t. In order for P’s person-path to containhappiness at t, it is not necessary that P’s component material object itselfinstantiate happiness at t—if P = �c(a, i), then for P to be formally happy at t,it is not necessary that a be happy at t. For a person-path to contain a property isfor some subject of the person-path, not any particular subject, to instantiate theproperty. If K-paths have many subjects, then property-containment is a divisionof labour among them.18

The metaphysical truth conditions of monadic temporal predications in theformal mode may be stated as follows:19 taking ‘F’ to stand for any monadicqualitative property, for any ordinary object o,

(T1) o exists formally at t iff there is a kind K and a K-path i, such that o has ias a part, and for some material object a, i includes the fact that a exists at t.20

(T2) o is formally F at t iff there is a kind K and a K-path i, such that o has i asa part, and for some material object a, i includes the fact that a is F at t.21

As regards the relationship between formally having a property at a time andformally existing at that time, we intuitively expect that a person, for example, isformally happy at a time only if it exists formally at that time. In the presentframework, if o is formally F at t, then o’s component K-path includes a K-state ofsome material object a that obtains at t. A K-state of a material object a thatobtains at t is required to include the fact that a exists at t (see Section 1.2). If o’s

17 Remember that ‘formally’ is not a predicate modifier, but rather, a copula modifier, indicatingthe formal mode of predication.

18 For simplicity, I am here assuming that ‘P’ refers determinately to a certain compound. In whatfollows I shall open the door for referential indeterminacy of ordinary proper names.

19 Modal predication about ordinary objects will be a subject of Chapter 5.20 Designators of the form ‘the fact that a exists at t’ and ‘the fact that a is F at t’ are to be read as

‘the fact that a exists absolutely at t’ and ‘the fact that a is absolutely F at t’.21 This schema is straightforwardly extendable to negative predicates. The truth conditions of

attributions of non-existence are the following: o does formally not exist at t iff o has a K-path i as acomponent, and for any material object a, i does not include the fact that a exists at t. Analogouslyfor the truth conditions of negative predications of the form ‘o is formally not-F at t’.

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component K-path includes a K-state that includes the fact that a exists at t, theno exists formally at t. Hence, if o is formally F at t, then o exists formally at t, justas expected.How should (T2) be extended to formal predications of relations? Let us set

aside for a moment the special relations of parthood and identity, to be con-sidered in some detail shortly, and start with the simple relational predication ‘Pis formally taller than P* at t’, where P and P* are persons. This is a predication ofan internal relation, a relation of similarity or difference in intrinsic respects.Internal relations are grounded in the intrinsic profiles of its relata, in the presentcase the heights of persons.22 For P to be formally taller than P* at t is for P’scomponent person-path to include the fact that a has height H at t, for somematerial object a, and for P*’s component person-path to include the fact that bhas height H* at t, for some material object b, such that the pair of a’s having H att and b’s having H* at t ground the fact that a is taller than b at t. The relation ofgrounding obtains in this case when the value of H is greater than the value of H*.The point can be put by saying that while P’s and P*’s person-paths both explicitlycontain a certain height, the pair of P’s and P*’s person-paths implicitly containthe taller-than relation. In general, where R is any internal relation other thanparthood and identity, for any ordinary objects o and o*,

(T3) o is formally R to o* at t iff there is a kind K, a kind K*, a K-path i, and aK*-path i*, and there are properties ç and ç*, such that (i) o has i as a part, andfor some material object a, i includes the fact that a has ç at t, (ii) o* has i* as apart, and for some material object b, i* includes the fact that b has ç* at t, and(iii) the pair of a’s having ç at t and b’s having ç* at t ground the fact that a isR to b at t.

How about external relations, relations that are not grounded in the intrinsicprofiles of their relata? The clearest cases of external relations are spatiotemporalrelations. Consider the sentence ‘B is formally north of B* at t’, where B and B*are buildings. It is common to view spatiotemporal predications that superficiallyascribe a spatial or temporal relation to objects as really ascribing such a relationto places or times occupied by these objects. The mentioned example may then beread as ‘B formally occupies a place p at t, B* formally occupies a place p* at t, andp is north of p*.’ Here the ascription of the north-of relation is not sortal-sensitive, only the ascription of occupation is. Moreover, ‘B formally occupies

22 See Lewis (1986: 62).

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place p at t’ is covered by truth conditions (T2) of monadic formal predications, if‘occupies p’ is read as a complex monadic predicate.23,24

2.2.2 Formal parthood and quasi-structure

Let us now consider formal predications of parthood, such as ‘The wheel isformally a part of the car at t.’ Chapter 1 contains a metaphysical account ofordinary objects in absolute, classical-mereological terms. Ordinary objects areunstructured compounds of material objects, themselves unstructured classical-mereological composites, and K-paths. How does this metaphysical accountrelate to everyday thought and talk about the parts of ordinary objects? Inother words, what are the q-hylomorphic metaphysical truth conditions ofmereological statements about ordinary objects?A large part of our object-discourse is sortal-sensitive. This sensitivity of our

thought and talk to which kinds an object belongs is the source of a range ofphilosophical problems about ordinary objects, which will be discussed in thisessay. One such problem has already been encountered in Chapter 1. As we sawin Section 1.1.3, we seem to possess certain sortal-sensitive intuitions of mereo-logical structure about ordinary objects. This observation is highly relevantfor the debate between classical mereologists and Aristotelian hylomorphists,since the classical-mereological account of ordinary objects seems insufficientto capture these intuitions of mereological structure, whereas the Aristotelian-hylomorphist account is partly designed to accommodate them. Let us remindourselves of the two cases of Section 1.1.3 and of the problem they raise forclassical mereology. This problem and the Aristotelian-hylomorphist solutionwill provide the background for my q-hylomorphist account of sortal-sensitiveascriptions of parthood.The first case concerns the parts of Michelangelo’s David. Intuitively, David’s

left arm, while being a part of the statue, is not a part of the coincident block ofmarble. The block has the same microparts as the statue, but the block does nothave arms. This is a sortal-sensitive intuition of mereological structure: anobject of a given kind only has parts of certain kinds. The standard classical-mereological conception of ordinary objects is incapable of capturing this

23 The property of occupying a certain place is here viewed as an intrinsic property of a materialobject. This type of relational property is thus a candidate for being explicitly contained in a K-path.

24 How about the relation of marriage? It is not an internal relation between two people. Nor is ita relation between places or times. A rough but natural suggestion is that it really is an internalrelation between two people and a social institution, in which case it could be treated by straight-forward extension of (T3). A more detailed discussion of relations such as these lies beyond thescope of this volume.

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intuition of mereological structure, since an ordinary object, according to thisconception, is but an unstructured sum of material objects. In this framework,David’s arm is as much a part of the block of marble as it is a part of the statue.The block of marble and the statue share all the same parts at the times of theircoincidence.The second case concerns the parts of my car. For the purpose of focusing the

problem arising from this case, let us assume the standard combination of theclassical-mereological account of ordinary objects with four-dimensionalism.According to standard four-dimensionalism, an ordinary object’s temporalmereological profile is derived from the atemporal mereological profile of theobject’s instantaneous temporal parts: a has b as a part at t iff a’s temporal partlocated at t has b as a part simpliciter. Now suppose that my car has a certainwheel as a part at time t, and that there is a spacetime region, R, that has a partoccupied by the car’s wheel as well as a part occupied by Socrates. By universal-ism, there is an R-object that is the mereological sum of all objects contained inR. This object has the wheel and Socrates as parts simpliciter. Since the temporalpart of the R-object at t is identical with the temporal part of the wheel at t, andsince this temporal part is an absolute part of the car’s temporal part at t, itfollows that the R-object is a part of my car at t. Surely, however, an object thatcontains Socrates as a part is not a part of my car at any time. As in the case ofDavid, this is a sortal-sensitive intuition of mereological structure: the kind towhich an object belongs can be relevant to whether it is a part of an ordinaryobject. The four-dimensionalist classical-mereological conception of ordinaryobjects is blind to such sortal-sensitive mereological structure.It is a striking advantage of Aristotelian hylomorphism, forcefully presented by

Fine, that it is capable of accommodating these intuitions. As pointed out inSection 1.1.2, Aristotelians take the forms that belong to a particular kind ofobject as determining a manner of arrangement of other objects, and as deter-mining what kinds of object can enter into that arrangement. Aristotelians canthus rule out David’s left arm as a part of the block of marble and the R-object asa part of the car, on the grounds that the form of the piece of marble lacks a slotfor arms, and that the form of the car lacks a slot for R-objects. The ability tocapture these intuitions of mereological structure constitutes a strong reason forconstruing ordinary objects as structured by a form.However, the standard Aristotelian-hylomorphist understanding of form

comes with a hefty price. For the nature of structuring composition operationsand their corresponding forms is rather mysterious. According to Aristotelianhylomorphism, presupposing Fine’s general framework for theorizing aboutparthood, there is a primitive composition operation that applies to a carwise

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arrangement of a chassis, four wheels, and so on, generating a particular carpossessing a form with slots for objects of specific kinds in a specific automotivearrangement. What makes this operation mysterious is how it can be sensitive tovery specific, high-level kinds of object and manners of arrangement. As stated inSection 1.1.3, when a mechanism is geared to such specific, rather unnaturalproperties and relations, then we expect an explanation of the mechanism inmore basic terms—we expect an explanation in terms of more natural propertiesand relations. But no such explanation is to be gained from Aristotelians. Thesensitivity of the mentioned composition operation to highly specific, unnaturalkinds and manners of arrangement is understood as primitive. Without anaccount in more fundamental terms, this composition operation and its associ-ated forms are difficult to accept.Fortunately, primitive composition operations and forms with slots for certain

kinds of object are not required for capturing the intuitions of mereologicalstructure highlighted by the two cases above. I agree with Aristotelians that inorder to capture our intuitions, a division of ordinary objects into form andmatter is called for. Forms, however, need not possess irreducible slots for certainkinds of object. Instead, I shall attempt to capture ordinary sortal-sensitiveascriptions of parthood in more fundamental and more transparent terms. Myclaim is that perspectival hylomorphism offers mereological structure of ordinaryobjects at a much lower cost. I must emphasize, as a caveat, that it is not my aimto ‘emulate’ every structural aspect of the Aristotelian-hylomorphist account ofordinary objects within my framework. I am exclusively concerned with captur-ing sortal-sensitive mereological intuitions of the type exhibited by the cases ofthe block of marble and the car in a metaphysically transparent way. It is thesestructural aspects that I see most clearly present in our common-sense concep-tion of objects, while various other structural aspects recognized by Aristotelians,such as the hierarchical layering of an ordinary object’s parts, which the accountto be proposed does not recognize, seem to be less clearly, if at all, represented inordinary thought and talk. (This claim about attributes not represented in thecommon-sense conception of objects is controversial but will not be supported indetail here.)To begin with, I shall take predications of parthood to admit of the formal and

the material mode, in addition to occurring in the absolute mode. Formalpredications of parthood have the form: o is formally a part of o* at t. Further-more, I shall understand formal parthood in terms of formal proper parthoodand formal identity:25 o is formally a part of o* at t =df o is formally a proper part

25 Cf. Simons (1987) for starting with proper parthood.

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of o* at t or o is formally identical with o*. Now I shall propose metaphysical truthconditions of formal attributions of proper parthood (followed below bytruth conditions of formal identity). Prior to stating precise conditions, I shallintroduce the basic idea by recourse to our two cases of mereological structure.Why is the arm a part of the statue but not of the spatially coextensive

block of marble? I suggest that what stands behind this mereological differenceis that while the arm’s kind-realizing profile—consisting of various facts con-taining specific arm-realizing properties—partly grounds the statue’s kind-realizing profile—consisting of various facts containing specific statue-realizingproperties—the arm’s kind-realizing profile does not partly ground the block’skind-realizing profile. Suppose, simplifying for ease of exposition, that thearm’s kind-realizing property is its specific arm-shape. Suppose, secondly, thatthe statue’s kind-realizing property is its specific statue-shape. Suppose, thirdly,that the block of marble’s kind-realizing property is its specific chemical makeup.While the arm’s having its specific shape partly grounds the statue’s having itsspecific shape, the arm’s having its specific shape does not partly ground theblock’s having its specific chemical makeup. What makes the arm belong to itskind makes no contribution at all to what makes the block of marble belong to itskind. Second, why is the wheel a part of my car but not the R-object temporarilyconstituted by the wheel? I suggest that while the wheel’s kind-realizing profilepartly grounds the car’s kind-realizing profile, the R-object’s kind-realizingprofile does not partly ground the car’s kind-realizing profile. Given that theproperty of being located in region R is among the R-object’s kind-realizingproperties, it is clear that the car-realizing profile is not partly grounded in theR-object-realizing profile. Facts concerning where an object is located make nocontribution to what makes the object a car; specifically, facts about the mon-strous spacetime region R make no contribution to what makes my car belong toits kind. It is plausible, on the other hand, to hold that the car-realizing profile ispartly grounded in the specific wheel-realizing profile, whichever properties thisprofile might contain.Calling a fact K-realizing when it contains only K-realizing properties, meta-

physical truth conditions of formal predications of parthood can be stated asfollows: for any ordinary objects o and o*,

(T4) o is formally a proper part of o* at t iff there is a kind K, a kind K*, aK-path i, and a K*-path i*, such that (i) o* has i* as a part, and for somematerial objects a and b, i* includes the fact that a has b as a proper part at t,(ii) o has i as a part, such that i includes the fact that b exists at t, and (iii) each

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K-realizing fact included in i at t partly grounds some K*-realizing factincluded in i* at t.

This account reduces formal proper parthood to absolute parthood of classicalmereology and partial grounding of K-realizing facts. The responsibility ofcapturing intuitions of mereological structure is shouldered by condition (iii),according to which o is formally a proper part of o* at t only if the K-realizingfacts in o’s form at t partly ground the K-realizing facts in o*’s form at t. By thiscondition and the assumptions made above, the arm is formally a proper part ofthe statue at t, but the arm is not formally a proper part of the block of marble at t,since the arm-realizing facts in the arm’s form at t partly ground the statue-realizing facts in the statue’s form at t, whereas these arm-realizing facts do notpartly ground the block-of-marble-realizing facts in the block of marble’s format t. Likewise, the wheel is formally a proper part of the car at t, while the R-objectis not, just as expected, since the wheel-realizing facts in the wheel’s form at tpartly ground the car-realizing facts in the car’s form at t, but the R-object-realizing facts in the R-object’s form at t, which include the fact that a is locatedsomewhere in R, for some material object a, do not partly ground the car-realizing facts in the car’s form at t.Two points of clarification. First, the temporal relativization of inclusion of

K-realizing facts in condition (iii) is needed for the following reason. A K-pathmay contain different K-realizing facts at different times—that is, different K-statesin a K-path obtaining at different times may contain different K-realizing proper-ties (though these properties are required to be K-connected; see Section 1.1.3).Now suppose that the K-realizing facts contained in o’s form at t partly ground theK*-realizing facts contained in o*’s form at t, while the K-realizing facts containedin o’s form at another time do not partly ground the K*-realizing facts contained ino*’s form at t. In this situation, unlike in the case of the R-object and the car, we stillwant to say that o is formally a part of o* at t. A fetus might be a case in point. It is apart of its mother over a certain period of time, although the specific organism-realizing facts in its form at a much later time, when the fetus has developed into anadult human organism, do not partly ground the organism-realizing facts in themother’s form at the earlier time.Second, in Section 1.1.3, K-paths were characterized as individuated by kind

K, in the sense that no K-path can also be a K*-path, for non-identical kinds Kand K*, where some facts in the K/K*-path are K-realizers while others areK*-realizers. Accordingly, no ordinary object belongs to different invariantkinds. This individuative condition has the following consequence for formalparthood. Suppose, contrary to the uniqueness assumption, that o’s form is both

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a K-path and a K*-path, containing both K-realizing facts and K*-realizing factsat time t, where K is distinct from K*, and hence that o is both a K and a K*.Suppose, further, that the K-realizing facts at t partly ground the K**-realizingfacts in a further object, o*, at t, while the K*-realizing facts do not. It follows by(T4) that o is formally a part of o* at t. What we should say in this case instead,however, is that while o is formally a part of o* at t, when o is conceived of as a K,o is not formally a part of o* at t, when o is conceived of as a K*. That is, if K-pathsare not viewed as individuated by particular kinds, then formal ascriptions ofparthood require some relativization to a kind. Since I adopt the individuativecondition on K-paths, no such relativization is required, thus allowing for a muchsimpler account of formal parthood. (Similar considerations apply to other typesof formal predication; see especially Section 5.1.)Would partial grounding of K-realizing facts alone be an acceptable basis for

formal proper parthood? That is, would clause (iii) be sufficient on its own,without the need for (i) and (ii)? No. For illustration, consider a Hirschean incar(see Section 1.3.1). The kind incar is partly realized by extrinsic properties,including, in any particular case, by the property of being located in a particulargarage. So the garage’s kind-realizing profile partly grounds the incar’s kind-realizing profile. We would not want to say, however, that the garage is a part ofthe incar. Or consider an island.26 The kind island is partly realized by theproperty of being surrounded by water. Thus, the kind-realizing facts in theform of a water molecule just off the island partly ground the kind-realizing factsin the form of the island. We would not want to say, however, that the watermolecule is a part of the island, as it lies outside of the latter. Clauses (i) and (ii) in(T4) block these consequences by basing formal proper parthood on absoluteproper parthood. The incar’s individual form does not contain the property ofhaving a as an absolute proper part (at any time), for any material object a, suchthat the garage’s individual form contains a’s existence. Hence, the garage is notformally a proper part of the incar. The case is analogous for the water moleculeand the island.The proposed perspectival-hylomorphist treatment of ordinary sortal-sensitive

predications of parthood matches the Aristotelian-hylomorphist success in cap-turing certain intuitions of mereological structure. Yet the perspectivalist affordsthis flexibility without commitment to the extravagant postulate of compositionoperations and corresponding forms of objects as irreducibly sensitive to highlyspecific and fairly unnatural properties and relations. Instead, the perspectivalistviews mereological structure as formal structure, or as quasi-structure, which

26 The following case is Hawthorne’s (2006: vii).

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resembles Aristotelian structure in its sensitivity to certain kinds, but differs fromAristotelian structure in being non-fundamental, derived from classical mere-ology and partial grounding of K-realizing facts. Without the commitment toprimitive slots for select kinds, mereological quasi-structure is available at a muchlower cost than genuine, Aristotelian structure. Sensitivity to kinds is not merelypostulated; it is explained. I consider this gain in metaphysical transparency apoint in favour of the new picture.27

While my primary aim in this and the previous chapter is to lay the founda-tions of perspectival hylomorphism, we have here a first substantial philosophicalproblem, to which the proposed framework finds fruitful application. Beforeconsidering further problems and applications in the following chapters, it isnecessary to complete the groundwork.

2.2.3 Formal identity

A further class of formal predications requiring separate treatment are formalpredications of identity. This chair and that chair are formally identical just incase they have the same component chair-path, the same individual form. Ingeneral, for any ordinary objects o and o*,

(T5) o is formally identical with o* iff there is a kind K, a kind K*, a K-path i,and a K*-path i*, such that o has i as a part, o* has i* as a part, and i is identicalwith i*.28

Given the intimate relationship between the concept of identity and the conceptof number, cardinality statements have a formal reading if identity statements do.Formally counting Ks is, roughly, determining formal distinctness of Ks. Deter-mining formal distinctness of Ks amounts to determining absolute distinctness ofK-paths. Thus, formally counting Ks is counting K-paths.Many have objected to the claim that ordinary statements apparently predi-

cating strict identity in fact predicate another relation.29 I do not endorse this

27 To emphasize, I do not mean to reject Aristotelian mereological structure across the board.I claim that in order to capture intuitions of mereological structure in the realm of ordinary objects,classical-mereological summation is the only composition operation we need. Whether we needadditional composition operations to account for the parts of entities of other categories is a furtherissue.

28 As regards the truth conditions of attributions of formal, sortal-sensitive distinctness to o ando*, notice that such attributions are true only if o is a K and o* is a K*, for some K and K*. Thus, o isformally distinct from o* iff there is a kind K, a kind K*, a K-path i, and a K*-path i*, such that o has ias a part, o* has i* as a part, and i is distinct from i*. Formal attributions of distinctness are differentfrom formal attributions of non-identity.

29 See Bishop Butler’s view, and more recently Chisholm’s, that we typically identify and countordinary objects by a ‘loose and popular sense’ of ‘identity’; see Butler (2000: Dissertation I) andChisholm (1976: chapter 3). See also Baxter (1988).

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revisionary idea. Formal predications of identity, as well as material and absoluteones, neither have unexpected subjects nor predicate unexpected relations. Theypredicate the same familiar relation, strict identity, to the same familiar objects indifferent modes. Strict identity is ascribed to the same objects from differentperspectives. Here it is important not to confuse predications in the formal or thematerial mode with their truthmakers. While the statement that o is formallyidentical with o* is made true by the fact that o and o* have the same componentK-path, the statement does not predicate the relation of having the same com-ponent K-path to o an o*. The statement rather predicates the relation of strictidentity to o and o* in the formal mode. Similarly for identity statements in thematerial mode (to be addressed below).Consider now an objection to the claim that absolute identity of objects is not

represented in ordinary language. When we assert in an everyday context that oand o* are (numerically) identical, then we expect o and o* to be indiscernible, tohave all their properties in common. If all we mean, however, is that o and o* areformally identical, then we do not have reason to expect them to be indiscernible,since o may have a property, such as having a certain material object as acomponent, that o* lacks. Thus, we do not mean formal identity, but rather arelation that preserves indiscernibility, namely absolute identity.The natural response to this objection is to point out that our ordinary

expectations of indiscernibility are restricted in accordance with the thesis thatthe absolute perspective on the world of objects is off-limits to ordinary speakers.When we assert that o and o* are formally identical, we do not expect o and o* tobe absolutely indiscernible. Our assertion of formal identity indicates that weview o and o* from the sortal-sensitive perspective, and accordingly that weexpect o and o* to be formally indiscernible. The principle of the formal indis-cernibility of formally identical objects may be stated as follows: for any ordinaryobjects o and o*,

(FI) If o is formally identical with o*, then for all properties ç and all times t,o has ç formally at t iff o* has ç formally at t.

Given that absolutely identical K-paths are absolutely indiscernible, and giventruth conditions (T1)–(T5), this principle is satisfied.It is important, furthermore, to point out that sortal-sensitive, or formal,

identity claims must not be confused with sortal-relative identity claims. Thestandard view is that an attribute is sortal-relative if it applies to one or moreobjects under one kind to which the object or objects belong, whereas it fails to

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apply to the object or objects under another kind to which it or they belong. Ifidentity is sortal-relative, then o may be the same person as o*, while o is adifferent organism than o*, where being the same person and being the sameorganism are distinct, sortal-relative identity relations.30 No form of sortalrelativity will be defended here.Notice, finally, that the present picture of ordinary identity statements raises

an issue about proper names. Consider three absolutely distinct material objectsa1, a2, and a3. Let a1 be absolutely F at t1, let a2 be absolutely F at t2 but not at t1,and let a3 be absolutely F at t3 but not at t1, for some property F-ness. Further-more, let chair-path i include the facts that a1 is F at t1, that a2 is F at t2, and thata3 is F at t3. Then there are three compounds, three chairs, o1, o2, and o3, whereo1 = �c(a1, i), o2 = �c(a2, i), and o3 = �c(a3, i). By the semantics of formalpredication, o1, o2, and o3 are formally identical and formally F at t1, because eachhas i as a component, and i includes the fact that a1 is F at t1. Notice that this isthe case, even though a2 and a3 are not F at t1. Suppose further that i is the onlychair-path that contains F-ness at t1. Now consider the definite description ‘thechair that is formally F at t1’. For an object to satisfy this definite description is forit to satisfy the formula ‘x and only x is formally F at t1, and x is a chair’. Since thisformula employs the formal mode of predication, the ‘only’ is to be unpacked interms of formal identity: ‘x is formally F at t1 and x is a chair, and for all y, if y isformally F at t1 and y is a chair, then y is formally identical with x’. Since o1, o2,and o3 are formally identical chairs, and since i, their common individual form, isthe only chair-path that contains F-ness at t1, each of o1, o2, and o3 satisfies thedescription ‘the chair that is formally F at t1’. Suppose, finally, that the propername ‘C’ is introduced by this definite description. Given that three compoundssatisfy the description, to which of these compounds does the proper name ‘C’refer? I shall not address this issue in any detail but mention a natural view to takein response. According to Hartry Field (1973), the word ‘mass’ as used in pre-relativistic physics was referentially indeterminate, in the sense that it partlydenoted proper mass and partly denoted relativistic mass. The theory of relativitythen allowed physicists to distinguish between the two types of magnitude.Analogously, the proper name ‘C’, as used by ordinary speakers, could be takento be referentially indeterminate, in the sense that it partly denotes multipleordinary objects, namely o1, o2, and o3. The absolute perspective allows meta-physicians to distinguish these ordinary objects. (Henceforth, I shall ignore thistype of referential indeterminacy.)

30 See Geach (1962, 1967).

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2.2.4 Material predication

Moving on from formal predication, material predication concerns an object’smatter. Assume that ordinary object o is the compound of material object a and acertain K-path, for some K. This compound has the parts of a as well as a itself asparts. Material object a is thus the biggest material object that is a part of o—themaximal material part of o, for short. The truth conditions of material predica-tions only concern maximal material parts of ordinary objects. Suppose, forexample, that I adopt the sortal-abstract perspective on the world of objects andassert that omaterially occupies a unique spatial region at a time. For omateriallyto occupy a unique spatial region at a time is for o’s maximal material partabsolutely to occupy a unique spatial region at a time. The metaphysical truthconditions of temporal predications and identity predications in the materialmode may be stated as follows: for any ordinary objects o and o*,

(T6) o exists materially at t iff there is a material object a, such that o has a asits maximal material part, and a exists at t.31

(T7) o is materially F at t iff there is a material object a, such that o has a as itsmaximal material part, and a is F at t.

(T8) o is materially R to o* at t iff there is a material object a and a materialobject b, such that o has a as its maximal material part, o* has b as its maximalmaterial part, and a is R to b at t.32

(T9) o is materially identical with o* iff there is a material object a and amaterial object b, such that o has a as its maximal material part, o* has b as itsmaximal material part, and a is identical with b.

Furthermore, the principle of the formal indiscernibility of formally identicalobjects, (FI), has a material analogue: for any ordinary objects o and o*,

(MI) If o is materially identical with o*, then for all properties ç and alltimes t, o has ç materially at t iff o* has ç materially at t.

31 In this and the following principles, all predications with material objects as subjects are to beunderstood as absolute predications.

32 It is not necessary, unlike in the formal case, to state separate conditions for materialpredications of parthood, since (T8) applies straightforwardly to the latter. Thus, o is materially aproper part of o* at t iff there is a material object a and a material object b, such that o has a as itsmaximal material part, o* has b as its maximal material part, and a is a proper part of b at t. Inanalogy with my strategy of defining formal parthood in terms of formal proper parthood andformal identity, I shall understand material parthood in terms of material proper parthoodand material identity: o is materially a part of o* at t =df o is materially a proper part of o* at t oro is materially identical with o*.

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Given that absolutely identical material objects are absolutely indiscernible, andgiven truth conditions (T6)–(T9), this principle is satisfied.Summing up the story so far, the core idea of perspectival hylomorphism—the

amalgam of metaphysical q-hylomorphism and semantical perspectivalism—isthat we can describe ordinary objects under specific sortal covers or we can stripaway these covers, thus employing different modes of predication in differentcontexts, which manifest different perspectives on the objects. The formal, sortal-sensitive description tracks properties that are contained in an ordinary object’scomponent K-path, whereas the material, sortal-abstract description tracks prop-erties that are instantiated by an ordinary object’s maximal component materialobject. Take the example of persistence statements. While person P’s formalpersistence through time depends on the temporal trajectory included in P’scomponent person-path—by virtue of this path’s including, for example, the factsthat a exists at t and that b exists at t*, for some material objects a and b—P’smaterial persistence depends on the temporal trajectory of P’s maximal compo-nent material object.Does perspectival hylomorphism with its different modes of predication incur

extravagant metaphysical commitments? No. The picture is metaphysically mod-est: the formal and the material mode of predication do not correspond tomultiple modes of instantiating a property or relation. A mode of predicationat the syntactic level corresponds to an operation on properties or relations inreality. Let us assume that a predicate F stands for a property ç of a sort suited tobeing instantiated by material objects. For a material object a designated by a, if⌜F(a)⌝ is true, then it is true because a instantiates ç. For an ordinary object o—letit be compound �c(a, i)—designated by o, if ⌜F(o)form⌝ is true, then it is truebecause o instantiates a property ç* determined by ç along the lines of (T2),namely the property of having a component K-path that includes the fact thatb instantiates ç, for some material object b. Similarly, for an ordinary objecto designated by o, if ⌜F(o)mat⌝ is true, then it is true because o instantiates aproperty ç0 determined by ç along the lines of (T7), namely, the property ofhaving a material object as its maximal material part that instantiates ç. Assum-ing further that the predicate I stands for the relation of identity, we can say thefollowing for ordinary objects o and o*, designated by o and o*: if ⌜I(o, o*)form⌝ istrue, then it is true because o bears a relation R to o* determined by the relation ofidentity along the lines of (T5), namely, the relation of having the same compo-nent K-path; and if ⌜I(o, o*)mat⌝ is true, then it is true because o bears a relationR* to o* determined by the relation of identity along the lines of (T9), namely, therelation of having the same material object as maximal material part.

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2.2.5 Perspectival divergence

The key feature of perspectival hylomorphism is that it allows perspectivaldivergence: incompatible properties may be ascribed consistently to the sameordinary object from different perspectives; a shift in perspective, and hence inmode of predication, may yield a shift in truth value. Perspectival divergence isbased on hylomorphic divergence: an object may have different qualitativeprofiles from different perspectives, because the profile of an ordinary object’smatter and the profile of the same object’s form may diverge. According toperspectival hylomorphism, ordinary objects lead double lives.One type of perspectival divergence concerns an ordinary object’s trajectory in

time. Consider a table, a compound of a table-path, and a material subject of thattable-path. We saw that the material subjects of table-paths need not behave in atable-ish way. Specifically, table-paths need not carve their material subjects attheir spatiotemporal boundaries: the persistence conditions of material objectsdiffer from the persistence conditions of table-paths. While a table-path encodestable-ish persistence conditions, partly in virtue of being a series of table-states,each of which contains a table-shape (though not necessarily the same one), nomaterial object has table-ish persistence conditions, in that being table-shapednever plays any role in determining the spatiotemporal boundary of a materialobject. Recall that the persistence conditions of three-dimensionalist compositematerial objects were assumed to be purely mereological (see Section 1.2). Sup-pose, then, that material object a exists at t1 but not at t2, that material object bdoes exist at t2, and that a table-path i includes the facts that a exists at t1 and thatb exists at t2. Consequently, there is a table o, the compound of a and i, such that,by truth conditions (T1), o exists formally at t2, and by truth conditions (T6), odoes not exist materially at t2. In short, the formal trajectory of o diverges fromthe material trajectory of o. Moreover, it is true that an object is a table only if it isformally table-shaped throughout its life, whereas it is false that an object is atable only if it is materially table-shaped throughout its life. The persistenceconditions we commonly ascribe to tables are formal persistence conditions,encoded by table-paths, whereas the material persistence conditions of tablesmay look quite differently.Another type of perspectival divergence concerns an ordinary object’s parts.

By truth conditions (T4), formal parthood depends on partial grounding ofK-realizing facts. As a consequence, formal parthood is sensitive to the kinds towhich parts belong. Recall that while Michelangelo’s David has arms as partsat a given time, its coincident block of marble lacks arms as parts at thattime, since the arms’ kind-realizing profiles, though partly grounding the statue’s

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kind-realizing profile, do not partly ground the block of marble’s kind-realizingprofile. Material parthood, on the other hand, is kind-insensitive. By (T8), ifan ordinary object’s material component, its underlying matter, is a part ofanother ordinary object’s material component at a given time, then the first is amaterial part of the second at that time. Thus, while David’s arms are notformally parts of the block of marble at time t, they are materially parts of theblock at t, since the arm’s material components are proper parts of the block’smaterial component at t. Thus, an ordinary object’s mereological profile can varyfrom one perspective to another. From the sortal-sensitive perspective, an ordin-ary object is mereologically structured, or, more accurately, quasi-structured,whereas from the sortal-abstract perspective, the same object is unstructured.Perspectival divergence also extends to predications of identity. By truth

conditions (T5), being formally identical comes down to having the same com-ponent K-path. By truth conditions (T9), being materially identical comes downto having the same component material object. Table o has a certain table-path asits formal part and a certain material object as its maximal material part. Table o*has the same table-path as its formal part but a distinct material object as itsmaximal material part. Then o is formally identical with o* but materially distinctfrom o*. Moreover, table o and piece of wood o** have the same material objectas their maximal material part but distinct K-paths, a table-path and a piece-of-wood-path, as their formal parts. Then o is formally distinct from o** butmaterially identical.Perspectival divergence of identity may be put to work right away in alleviating

the worry, encountered in Section 1.3, that the world may end up counterintui-tively overpopulated with ordinary objects if q-hylomorphism is correct. Con-sider a particular table-path, i. According to the basic account of K-paths, i mayhave a plurality of material objects as subjects. Suppose, then, that i has distinctmaterial objects a, b, and c as subjects. As a consequence, there are three tables,�c(a, i), �c(b, i), and �c(c, i), where we thought there was just one. I respond thatthis abundance of ordinary objects does not clash with common sense, because itis merely an absolute abundance, the result of counting in the absolute mode,which is not represented in ordinary discourse about objects. The formal numberof ordinary objects, the number we come up with when counting from the sortal-sensitive perspective, is different and accords with the expectations of commonsense. For �c(a, i), �c(b, i), and �c(c, i) are formally identical: they all share thesame table-path, the same form.Perspectival divergence comes in many flavours. In the chapters to follow, we

shall encounter perspectival divergence concerning ordinary objects’ temporalproperties (Chapters 3 and 4), their de re modal properties (Chapter 5), their

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deterministic properties (Chapter 6), their indeterminate properties (Chapter 7),their relativistic properties (Chapter 8), and their identity and number as con-strained by these various properties.

2.2.6 Formal and material predication with stages

Metaphysical truth conditions of predications in the formal and the materialmode have until now been stated on the assumption of the three-dimensionalistversion of q-hylomorphism about ordinary objects (see Section 1.2). It thusremains to complete the presentation of the basic version of perspectival hylo-morphism by reformulating these truth conditions in the context of four-dimen-sionalist versions of q-hylomorphism. Here are modified truth conditions ofmonadic temporal predications in the formal and the material mode: for anyordinary object o,

(T10) o exists formally at t iff there is a kind K and a K-path i, such that o hasi as a part, and for some stage s located at t, i includes the fact that s exists.

(T11) o is formally F at t iff there is a kind K and a K-path i, such that o has ias a part, and for some stage s located at t, i includes the fact that s is F.

(T12) o exists materially at t iff there is a material object a, such that o has aas its maximal material part, and a has a stage located at t.

(T13) o is materially F at t iff there is a material object a, such that o has a asits maximal material part, and a has a stage located at t that is F.

These truth conditions are neutral between the worm-version and the stage-version of q-hylomorphism. On the worm-version, a in (T12) and (T13) is aspacetime worm that is required to have a stage at t that is F, whereas on the stage-version, a is a stage that is required to be located at t and to be F. The extension ofthese truth conditions to polyadic predications, including mereological predica-tions, along the lines of Sections 2.2.1 and 2.2.2 is straightforward. Finally, thetruth conditions of formal and material predications of identity stated earlierapply here without modification. So much for a bare-bones statement of perspec-tivalism with a four-dimensionalist basis.We saw in Section 1.3.2 that the worm-version of q-hylomorphism does not

allow for hylomorphic divergence in temporal trajectory. By the truth conditionsabove, it follows that on the worm-version an ordinary object’s formal trajectorycannot diverge from its material trajectory. Thus, if the possibility of divergencein trajectory is desirable, then the stage-version is in a better shape. In Chapter 3,I shall illustrate the relevance of this difference in application to a particular typeof problem. For now, I shall rest content having shown that perspectivalism is not

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committed to three-dimensionalism about material objects, which I take to be awelcome feature of the framework (see Section 1.3.2). In following chapters,I shall focus on the three-dimensionalist version where the different versionshandle a problem equally well. Where differences between the versions becomerelevant, I shall indicate which version is best suited for the task at hand.

2.2.7 Perspectivalism without hylomorphism?

Is a double-layered q-hylomorphic ontology a compulsory metaphysical founda-tion for perspectivalism? Or is full-scale perspectival divergence available on thebasis of an ontology with a simpler architecture? I doubt it. I will take a brief lookat three schemes of temporal predication that rest on simpler analyses of ordinaryobjects, and that resemble the proposed semantical framework at least in theiraccount of sortal-sensitive predication. My intention here is not to criticize theseviews. My intention is merely to highlight that important features of the presentframework are hard to get for cheap. More detailed comparison with differentvariants of these approaches, in application to philosophical problems, will followin ensuing chapters.First, friends of temporal counterpart-theory construe an ordinary object as

an instantaneous material object, a stage, and understand temporal predicationin terms of temporal counterpart-relations, or R-relations, between stages: anordinary object o is F at t iff o has a temporal counterpart at t that is F.33 On thispicture, sortal sensitivity is built into the semantics of predications in the scope oftemporal operators. Temporal predication of a property is a matter of locatingthe instantiation of that property along a diachronic chain of R-related stages,along a series of temporal counterparts. R-relations correspond to persistenceconditions of objects encoded in sortal concepts. Since stages typically stand indifferent R-relations—a given stage may have both temporal person-counterpartsand temporal body-counterparts—a speaker must determine a particular R-rela-tion by representing the subject of the predication as possessing the persistenceconditions corresponding to this R-relation. In other words, the speaker mustthink of the object under a specific sortal concept.The defining feature of temporal counterpart-theory is that the temporal

attribution of a property to an object may be true in virtue of a distinct, R-relatedobject’s having that property. It should be obvious that perspectival hylomorphism’s

33 See Sider (1996, 2001a: section 5.8), and Hawley (2001: section 5.7). Sider and Hawley offertemporal analogues of Lewis’s modal counterpart-theory; see Lewis (1983a: chapters 3 and 4). Seealso Gibbard (1975) and Gupta (1980) for sortal-sensitive modal predication. I shall turn to modalpredication in Chapter 5.

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formal temporal predication shares exactly this feature. The present accountof formal temporal predication may thus be characterized as a version of temporalcounterpart-theory. This is especially clear in the case of the stage-version of formaltemporal predication (see (T10) and (T11)).Does standard temporal counterpart-theory allow for sortal abstraction? From

the sortal-abstract perspective, we parse objects by spatiotemporal properties,independently of specific kind-realizing properties. In Section 2.1, I pointed outan important limitation of our ordinary sortal-abstract conception of objects:sortal abstraction does not yield full-blown, purely spatiotemporal persistenceconditions of objects. We lack a sufficient criterion of tracking objects throughtime that is independent of the ways of tracking associated with ordinary sortalconcepts. The thesis of the pre-philosophical availability of a sortal-abstractconception of objects is sensible only if this conception is allowed to yield atmost a partial principle of individuation. Now, we saw that temporal counter-part-theory requires speakers to think of the subject of predication in a way that isrich enough to determine a particular R-relation. Given that sortal abstractiondoes not yield sufficient persistence conditions, conceiving of an object ina purely spatiotemporal way does not determine any particular R-relation.Sortal-abstract temporal predication is therefore unavailable in standard tem-poral counterpart-theory. In short, the latter semantics is non-perspectival.34

With the purpose of obtaining a perspectivalist semantics, one might considerextending standard temporal-counterpart theory in the following way: assumingthat ordinary objects are stages, an ordinary object o is formally F at t iff o has atemporal counterpart at t that is F, and o is materially F at t iff o itself is located att and is F. This is a variant of perspectivalism: if o is conceived of as an instance ofa given kind K, temporal predications about o are made true by properties ofK-counterparts of o; and if o is conceived of in a kind-independent way, thentemporal predications about o are made true by properties of o itself. Toemphasize, the reason why it is worth considering this variant is that it rests ona single-layered ontology of ordinary objects—according to which these objectsare just stages—and is thus a non-hylomorphic version of perspectivalism, whichis simpler than the hylomorphic versions I developed earlier.On the downside, this perspectival extension of standard temporal counter-

part-theory is a lot less powerful than perspectival hylomorphism. Most import-antly, it is unclear how the single-layered view could accommodate perspectivaldivergence concerning predications of identity, since ordinary objects lack the

34 This difference is even clearer when perspectival modal predication is compared to modalcounterpart-theory; see Section 5.1.

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disparate components that could serve as truthmakers for identity statements indifferent modes of predication. It is thus natural to understand the view asfollowing standard, non-perspectival counterpart theory in remaining orthodoxabout predications of identity, by virtue of taking all identity predications aboutordinary objects qua stages to be absolute ones. Perspectival hylomorphism, bycontrast, is able to recognize different modes of predicating strict identity, whichwill prove to be a significant advantage.35

Furthermore, perspectival hylomorphism permits three-dimensionalist as wellas four-dimensionalist versions, whereas standard temporal counterpart-theoryand its perspectival extension seem to be committed to four-dimensionalism. Thereason is that a three-dimensionalist object cannot be a temporal counterpart ofanother three-dimensionalist object, since three-dimensionalist objects change intheir qualitative profiles over time. The best thing to say is that a-at-t1 is acounterpart of b-at-t2, where a and b are three-dimensionalist material objects.The expressions ‘a-at-t1’ and ‘b-at-t2’, however, do not designate objects,but rather states of objects. The metaphysical neutrality concerning three-dimensionalism and four-dimensionalism is another significant advantage ofq-hylomorphism-based perspectivalism.A third scheme of temporal predication that deserves to be compared to the

proposed perspectivalist one is to construe an ordinary object as being simplyidentical with a K-path, for some kind K, and to say that o is F at t iff o includesthe fact that a is F at t, for some material object a (compare (T1) in Section 2.2).36

The ontology of this view differs from q-hylomorphism in that ordinary objectsare not compounds of material objects and complex facts; and it differs from theprevious two views in that ordinary objects are not material objects. Where doesthe view leave sortal abstraction? If a K-path has more than one material object asa subject, then it is hard to make sense of the idea of stripping away an ordinaryobject’s form. If the ordinary object has different material subjects at differenttimes, which material object are we stripping it down to? For example, we want tobe able to give determinate and divergent answers to the questions whether agiven table exists formally at a given time and whether it exists materially at thattime.37 If tables are just K-paths having multiple material subjects with different

35 One problem for the orthodox take on identity concerns cross-temporal counting. See Sider(1996) and Sattig (2006) for discussion. This defect of temporal counterpart-theory will surface inChapter 4, where the theory’s application to paradoxes of fission is discussed.

36 This type of view has enjoyed support from Broad (1925: 34–8), Montague (1979), and thelater Chisholm (1986: 66–7).

37 Here I am ignoring indeterminacy concerning when exactly a table comes into and goes out ofexistence. This type of indeterminacy will be addressed in Chapter 7.

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trajectories, it is entirely unclear how determinate material descriptions of atable’s trajectory should be possible. One might propose to relativize strippingaway an ordinary object’s sortal cover to a time t, and to understand strippingaway a sortal cover at t as passing from a K-path to its unique subject at t (if it hasone). Thus, an ordinary object exists materially at t just in case it has a materialsubject at t. This strategy delivers determinate material trajectories, but it fails toallow an ordinary object’s material trajectory to diverge from its formal trajec-tory.38 For the strategy requires ‘looking for’ a material object along a K-path,whereas sortal abstraction is meant to permit the ascription of a trajectory incomplete ignorance of K-paths. Temporal predication that requires sortal infor-mation in order to ‘locate’ a material object in time is not sortal-abstractpredication.39 Assuming q-hylomorphism, by contrast, sortal-abstract predica-tion and determinate perspectival divergence are clearly available, becauseeach ordinary object has a unique maximal material component with kind-independent persistence conditions.40

2.3 Metaphysics, Metaphysical Semantics,and Common Sense

Why believe that ordinary objects lead double lives? My short answer is thatperspectival hylomorphism does a better job in saving the appearances than itsrivals. Here ‘the appearances’ are the pre-philosophical beliefs and intuitionsconstituting our common-sense conception of objects.41 I shall take ‘saving’ thesebeliefs and intuitions as involving two tasks.

2.3.1 Equilibrium

Saving the appearances involves, firstly, the task of establishing an equilibriumbetween metaphysics and common sense. The common-sense conception ofobjects is constituted by the sortal-sensitive and the sortal-abstract beliefs andintuitions about ordinary objects that most of us take for granted. Can we trustthese beliefs and intuitions? It is clear that we have taken many things as obviousthat turned out to be false on inspection. Common sense gives us no certain

38 Reasons for appreciating such divergence will be adduced later.39 An analogous problem arises when it comes to perspectival modal predication. More in

Chapter 5.40 For a critical discussion of the perspectival prospects of the view that ordinary objects are

K-paths, which focuses on questions of identity, see Sattig (2010a: section 4).41 Among the pre-metaphysical beliefs I count not only the beliefs of people on the street, but also

beliefs by metaphysicians who are competent with the separation of intuition from theory.

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knowledge about the world. But are our common-sense beliefs and intuitionsprima facie, defeasibly justified, where defeasible justification does not guaranteecorrectness? Is it at least reasonable to believe these things? Radical sceptics denythis, holding that our common-sense conception does not give us any justifica-tion for believing that ordinary objects have one nature rather than another.Many contemporary metaphysicians resist this sceptical attack in Mooreanfashion. They hold, roughly, that our unadulterated convictions, though onlydefeasibly justified, are more certain than any of the premises in a scepticalargument to the contrary, and hence that it is more sensible to conclude thatthere is something wrong with the sceptic’s premises, even if we do not knowwhat is wrong with them. Mooreans face the question of why it is more plausibleto trust our pre-philosophical beliefs and intuitions than to follow the sceptic intodarkness. Is it just because most of us take them to be obvious? That soundstoo easy.42 Few will adopt an anti-sceptical stance on these meagre grounds. Forour common-sense conception of objects includes many beliefs that, whileentrenched, exude little prima facie credibility. I recommend a more modestapproach. We need to be more restrictive in our trust of common sense andaddress the epistemological status of the various components of the common-sense conception of objects individually.At the heart of the common-sense conception stand sortal-sensitive beliefs and

intuitions about particular ordinary objects, which arise on the basis of percep-tual experiences, such as the belief that there is a table in front of me and thebelief that the table was created last night. Given how basic a source of informa-tion perception is, it is very natural to assume that perceptual experiences andbeliefs arising from them can be taken at face value. It will thus be morereasonable to reject the premises in a sceptical argument to the contrary thanto accept the argument’s conclusion.43 This move falls short of calling thesceptic’s mistake. It is but an expression of confidence in the possibility ofestablishing, somehow or other, that we can justifiably believe such things asthat there is a table in front of me.44 How this could be established is an issue foranother day. Here is not the place to engage with the sceptic. Of course, ourperceptual justification for beliefs about ordinary objects is defeasible—we are

42 See Zimmerman (2008: 223) for this bold view.43 A familiar sceptical attack against our entitlement to our perceptual beliefs is premised on the

claim that we are justified in a given perceptual belief only if we have independent evidence thatperception is reliable. Another argument could be mounted on the claim that it is a biologicalaccident that we have the belief-forming mechanisms that we do, or more specifically, that myperceptual beliefs represent the ordinary objects that they do. For a development of the secondargument, see Korman (2014). See also Section 1.3.1.

44 See Pryor (2000: 517–18).

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often deceived by our senses. Moreover, our perceptual evidence for such beliefsmight be defeated quite easily—it might take little to attain an epistemic state inwhich the evidence no longer supports the belief. Nevertheless, we are prima facieentitled to our perceptual beliefs and intuitions about objects.45 Likewise forspecific sortal-sensitive beliefs and intuitions about ordinary objects that arisefrom memory or introspection, as these are foundational sources of information,as well.How about beliefs and intuitions that concern not how the world is, but rather,

how the world could be? Our common-sense conception of objects is suffusedwith modal beliefs and intuitions, including sortal-sensitive modal beliefs aboutparticular objects and sortal-abstract modal beliefs about all ordinary objects—the platitudes of common sense. Granted that modal reasoning often leads usastray, and that such reasoning is not grounded in sense experience, do we at leasthave defeasible justification for our pre-philosophical modal beliefs and intu-itions about ordinary objects? Many philosophers working in the epistemologyof modality today share an anti-sceptical attitude towards the evidential status ofmodal beliefs and intuitions, similar to the Moorean stance in the case ofperception. They agree that it is natural to hold that we are entitled to takemodal appearances as revealing how the world could be, just as it is natural tohold that we are entitled to take perceptual appearances as revealing how theworld is.46 As in the case of perception, our modal beliefs and intuitions aboutordinary objects are only defeasibly justified—we are often convinced by furtherconsiderations that something we took to be possible is not possible after all.Moreover, our modal beliefs about objects might be defeated quite easily. Takethe sortal-abstract platitudes of common sense. I have little hope that thesegeneral principles of folk metaphysics withstand scrutiny in their entirety.47

Nevertheless, we are prima facie entitled to our basic modal beliefs and intuitionsabout objects.A philosophical account of ordinary objects should aim to preserve the pre-

philosophical beliefs and intuitions about objects that arise from our basicsources of information about how the world is and how it could be. These beliefsand intuitions are defeasible guides to reality and possibility. In a Moorean, anti-sceptical spirit, we should resist giving them up too easily. Henceforth, I shall

45 Cf. Hofweber (ms: chapter 7).46 What is the source of our justification for our beliefs and intuitions about modality? Prominent

options include conceivability and inconceivability à la Yablo (1993) and counterfactual reasoning àla Williamson (2007).

47 See especially Section 4.2.

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address only these trustworthy convictions when I speak of the common-senseconception of ordinary objects.On the other hand, most metaphysicians today believe that metaphysical

questions concern fundamental facts about the world, which are often beyondthe reach of ordinary belief and intuition, and which cannot be settled solely byconceptual analysis. Metaphysicians studying ordinary objects typically seek touncover deep attributes of objects to which ordinary folks are often blind. Thereis the, arguably double-layered, common-sense conception and there are variousabsolute conceptions that characterize objects in reasonably fundamental terms,trying to get at what these objects really are. My theory of ordinary objects asq-hylomorphic compounds of matter and form is an example of such an absoluteconception. Foundational metaphysicians adopt a quasi-scientific methodology,according to which match with pre-metaphysical belief plays some role inassessing a metaphysical theory, but not the only one—fundamental metaphys-ical principles cannot be read off directly from our ordinary conception. Inaddition, they trust metaphysical reasoning by such methodological criteria assimplicity, explanatory strength, theoretical insight, and integration with funda-mental physics.48 Typically, an equilibrium between pre-metaphysical beliefs andfoundational metaphysical theory is sought.49

The way in which I seek to establish such an equilibrium in the domain underconsideration is by giving a metaphysical semantics of ordinary statements thatexpress the propositional contents of our basic pre-philosophical beliefs andintuitions about ordinary objects; a metaphysical semantics, that is, of thestatements expressing our common-sense conception of objects.50 Assumingthat such a metaphysical semantics takes the form of a truth theory, the aim isto state fully compositional truth conditions of object-discourse in the terms of areasonably fundamental theory of ordinary objects, which make as many aspossible of the basic beliefs and intuitions constituting our common-senseconception true. Absolutely fundamental truth conditions are as illusory as aperfect match with our entire common-sense conception. The aim can only bethe best possible match of common sense with a reasonably fundamentalmetaphysics.Metaphysical semantics and linguistic semantics differ in their explanatory

aims.51 The aim of metaphysical semantics to link ordinary linguistic behaviour

48 See Sider (2009: 385). 49 See Lewis (1983a: x).50 The label ‘metaphysical semantics’, in contrast to ‘linguistic semantics’, is due to Sider (2011:

section 7.4).51 See Sider (2011: 112–13).

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with deep metaphysics is not shared by linguistic semantics. On the other hand,the aim of a traditional, Fregean conception of semantics to explain a competentspeaker’s knowledge of meaning is not shared by metaphysical semantics. It isopen to the metaphysical semanticist to assign semantic values that are inaccess-ible to competent speakers. Specifically, the truth conditions of predications inthe formal and the material mode stated earlier are not meant to be grasped byeveryone who understands these predications.At the same time, I view metaphysical semantics and linguistic semantics as

constraining each other.52 For a relevant example, I have been assuming that thebest linguistic semantics of ordinary discourse assigns truth conditions thatquantify over ordinary objects. I therefore expect a metaphysical semantics totell us which more or less fundamental facts about these ordinary objects underliewhat we say about them on the street. This is a case of a direct influence oflinguistic semantics on metaphysical semantics. Guidance by syntactic andsemantic input from linguistics is necessary for a semantic bridge between deepmetaphysics and ordinary discourse to be sufficiently explanatory. The directionof influence could also go the other way. A metaphysical semantics that owes itsstriking explanatory power to certain metaphysical claims about ordinary objectsmight well push linguistic semantics of object-discourse in a particular direction.Furthermore, I expect metaphysical semantics of object-discourse to integratewith relevant psychology, specifically with research in the psychology of objectrepresentation, which I take to recommend a bifurcation of object-perspectives.An attempt at integration with these non-metaphysical domains is the mark of anambitious metaphysical semantics, of a serious strife for equilibrium.Adopting this methodological stance puts me in opposition to the anti-

Moorean view that an object-ontology’s match with pre-metaphysical belief hasnext to no significance as a factor in theory choice, for the reason that our basicbeliefs and intuitions about ordinary objects cannot be trusted, not even primafacie. To my mind, giving up Moorean modesty is not an option here. Thisapproach makes it implausibly hard to get things right on the street; it puts us ona path to radical scepticism. My methodological stance is also opposed to theview that an object-ontology’s match with pre-metaphysical belief has verylimited significance in a metaphysical study, for the reason that our common-sense conception’s commitments concerning macroscopic objects are metaphys-ically innocent. Few would disagree that we straightforwardly refer to andquantify over macroscopic objects in ordinary discourse. One might hold, how-ever, that while this observation is to be respected in linguistic semantics,

52 Pace Sider (2011: 122).

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metaphysical semantics is completely unconstrained by linguistic semantics.There is meant to be a neo-Carnapian dissociation between the two endeav-ours.53 The metaphysical semanticist can, on this outlook, consider our ordinarystatements about objects to be true without buying into an ontology of ordinaryobjects, because metaphysical semantics is free to assign fundamental truthconditions to our statements in independence of linguistic considerations of,inter alia, reference and quantification.54 This is a half-hearted version of meta-physical semantics, prone to shrouding the explanatory link between metaphysicsand ordinary talk in darkness. I shall set it aside. Finally, my methodologicalstance is opposed to the view that the power of abstract metaphysics is overrated.One version of such a deflationary position is to hold that the only sense onecan give to metaphysical claims about ordinary objects derives from that ofpre-metaphysical claims. And since the latter are easy to know—knowledge ofanalytic truths by mere reflection on language-use might be part of it—metaphysical results are easy to attain.55 This view makes it implausibly easy toget things right in the seminar room. Giving up robust metaphysics is not anoption here.An appropriate engagement with these methodological positions would take

its own metametaphysical study. I shall rest content with this brief, opinionateddescription of the stage on which the present inquiry unfolds.

2.3.2 Consistency

Saving the appearances involves, secondly, the task of charitable interpretation.According to the influential principle of charity in linguistic interpretation,ordinary speakers should be interpreted in a way that makes their assertionsand beliefs come out reasonable.56 It is important for present purposes that theprinciple of charity does not only concern what people actually say or believe, butalso what they would say or believe, once implicit commitments of their actualassertions and beliefs are brought out in the open. As Sider (2004: 680) puts it,charitable interpretation takes into consideration what people would say ‘withtheir eyes wide open’.57 As applied to the task of interpreting the common-senseconception of objects, the principle of charity demands an interpretation thatrenders this conception a reasonable one to hold, and hence a conception that isfree of internal inconsistency. Notice that this demand for reasonableness of the

53 Cf. Carnap (1950). 54 Sider (2011: 122–3) holds this view.55 Thomasson (2007) develops a version of ontological deflationism about ordinary objects.

I shall address this view in Chapter 3.56 See Davidson (1984) and Lewis (1983a). 57 See Hirsch (2008: 368–9).

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common-sense conception of objects is weaker than the Moorean plea to con-sider ourselves prima facie justified in taking this conception to be true in the faceof sceptical attack. While Mooreanism aims for truth or correctness of thoseordinary beliefs and intuitions about ordinary objects to which we are naturallyentitled, the principle of charity, as understood here, requires ordinary beliefsmerely to be reasonable, and hence at least to be consistent, even if false.58 Onemight, accordingly, aim for reasonableness without aiming for truth, on thegrounds that one might find it hard to accept that ordinary thinkers shouldbe deeply irrational, while downplaying the role of intuitions as a guide to truth.To put my cards on the table, I shall be aiming for the truth as well as thereasonableness of the common-sense conception of objects (under the restric-tions of the previous sub-section).Sustaining pre-philosophical convictions about ordinary objects under philo-

sophical pressure and avoiding internal tensions within the common-senseconception of objects are hard tasks. In support of perspectival hylomorphism,I shall argue that it manages these tasks better than its rivals. Roughly, as regardsequilibrium, there are many cases where an everyday belief about ordinaryobjects of specific kinds seems to stand in conflict with a general principleabout ordinary objects, which principle may be supported by a powerful meta-physical argument or may itself be endorsed by intuition. Where traditional,single-layered views of ordinary objects and of ordinary discourse about suchobjects are forced to reject either the specific belief or the general principle,perspectival hylomorphism with its double-layered view of ordinary objectsand of object discourse is able to sustain both, on the grounds that the specificbelief and the general principle are made true by different metaphysical compo-nents of the same objects. Moreover, where traditional views have no or only avery weak account of how the folk could reasonably hold certain beliefs aboutordinary objects, given the seeming incompatibility of these beliefs, perspectivalhylomorphism offers a plausible explanation, namely, that the different beliefsmanifest different perspectives on the same objects, where the plausibility of thisexplanation partly derives from the fact that perspectivalism is psychologicallysensible, in virtue of its link with widely accepted work in the psychology ofobject representation. The task of maintaining internal consistency of the com-mon-sense conception might be considered a very different beast from the task ofestablishing an equilibrium with a fundamental metaphysical theory of ordinaryobjects. The strategies I shall offer are closely related, for it is a metaphysicallysubstantive feature of ordinary objects—their q-hylomorphic constitution—that

58 Cf. Korman (2009: 245).

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ultimately affords both equilibrium and consistency. Relatedly, perspectival hylo-morphism offers a more systematic response to a range of problems with thecommon-sense conception of objects than its rivals, which tend to use disparatekeys to unlock different problems. The key that unlocks each of a large class ofproblems is perspectival divergence: we may correctly describe the same object indifferent ways from different perspectives, employing different modes of predi-cation. To summarize the main theme of this volume, many philosophical mys-teries about ordinary objects dissolve once we realize that they lead double lives.Let me emphasize, finally, that perspectival hylomorphism has its limits.

I certainly do not expect the framework to sustain all relevant pre-philosophicalconvictions under philosophical pressure and to avoid all internal conceptualinconsistencies. The framework is thus limited in its scope of application. Inparticular, since perspectivalism does not extend to existence claims, perspectivaldivergence is not available for resolving problems concerning the existence ofordinary objects. So my ambitions in this volume are modest. I do not promisea single strategy that saves the common-sense conception of objects in itsentirety.59

59 A standard existence problem for a plenitudinous ontology such as the present one is thatspeakers of our community appear to deny the existence of extraordinary objects, such as arbitraryfusions of ordinary objects, incars, and the like. If we can trust our positive beliefs about ordinaryobjects, should we not be able to trust our negative ones, as well? This type of problem aboutexistence will not be approached perspectivally. That is, it will not be argued that objects exist indifferent modes, such that in one mode they are sparse, while in another mode they are abundant.The problem requires a different sort of treatment. The standard response of plenitude lovers is thatthe quantifiers in ordinary discourse about objects are restricted in a way that excludes extraordinaryobjects. (The locus classicus is Lewis (1986: 213). See also Sosa (1999: 142), Sider (2001a: 218), andHirsch (2002: 111–12).) I am sympathetic to this type of response. As this strategy of saving ordinaryexistence claims is broadly familiar and in no need of perspectivalist resources, I shall not take up thetask of detailing and defending it here. I admit, however, that this is no small task. (See Korman(2008) for various challenges.)

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3

Coincidence

Distinct ordinary objects cannot fit into the same place at the same time; theycannot coincide. This seems to be a platitude of common sense. The paradoxesof coincidence are instances of a breakdown of this platitude in light of coun-terexamples that are licensed by innocuous assumptions about particular kindsof ordinary object. Since both the anti-coincidence principle and the assump-tions driving the counterexamples flow from the folk conception of ordinaryobjects, the paradoxes threaten this conception with inconsistency. Typicalapproaches to the paradoxes are incompatibilist, conceding that the common-sense conception of objects is genuinely unstable, and partly revising the latterby rejecting the anti-coincidence principle or some portion of the assumptionsdriving the counterexamples. The framework of perspectival hylomorphism, bycontrast, offers a compatibilist solution to the paradoxes, allowing the variouscases of distinct coincidents and the anti-coincidence principle to manifestdifferent perspectives on ordinary objects, and therefore to be compatible. InSection 3.1, a range of paradoxes of coincidence will be presented. In Section 3.2,various incompatibilist responses to the paradoxes will be discussed briefly. InSection 3.3, the compatibilist response based on perspectival hylomorphism willbe presented and motivated.

3.1 Paradoxes of Coincidence

Let us say that for any ordinary objects o and o*, and for any time t,

(CO) o coincides with o* at t =df o and o* exactly occupy the same place at t.1

How many ordinary objects can fit exactly into a given place, a given region ofspace, at a time? According to pre-philosophical opinion, the answer would seem

1 Coincidence is often understood as both sharing of location and sharing of parts (at some levelof decomposition). As I shall use the term, coincidence is merely sharing of location.

to be one. For it seems prima facie inconceivable that distinct ordinary objectsexactly occupy the same place at the same time. Coincidence of several objectswould amount to overcrowding. The following anti-coincidence principle thusappears to rank as a platitude of common sense:

(AC) Necessarily, for any ordinary objects o and o*, and for any time t, if ocoincides with o* at t, then o is identical with o*.2

This principle seems to have a number of compelling counterexamples, givingrise to various paradoxes of coincidence. What follows are five cases, (A)–(E),supporting the coincidence of distinct ordinary objects (under the actual laws ofnature). Cases (A), (B), and (E) are cases of coincidence of distinct objects fallingunder different kinds, whereas cases (C) and (D) are cases of coincidence ofdistinct objects falling under the same kind. Moreover, cases (A)–(D) establishthe distinctness of coinciding objects on the basis of differences between theseobjects at times other than the time of coincidence, whereas case (E) establishesthe distinctness of coinciding objects on the basis of differences between theobjects at the time of coincidence. While the upcoming selection of cases coversconsiderable ground, it is not exhaustive. In particular, no cases are included thatestablish the distinctness of coinciding objects on the basis of differences betweenthese objects at possible worlds other than the world of coincidence. Such modalparadoxes of coincidence will be discussed in Chapter 5.

(A)A child builds a paper aeroplane by folding a piece of paper in a certain way. Once thefolding process is completed, there is a paper plane and there is a piece of paper. While thepiece of paper existed before the child went to work, the paper plane did not. By Leibniz’sLaw, which says that identical objects must share all their attributes, it follows that thepaper plane is distinct from the piece of paper. Yet the paper plane and the piece of paperare ordinary, spatiotemporally extended artefacts that exactly occupy the same places overthe period of time during which the paper plane traverses the skies. Hence, the paperplane and the piece of paper are distinct, coinciding artefacts.3

(B)Tibbles is a cat, whereas Tib is a lump of feline tissue consisting of all of Tibbles except forher tail. By Leibniz’s Law, Tibbles and Tib are distinct objects. Now suppose that Tibblesloses her tail. Since a cat can survive the loss of certain parts, such as tails, Tibbles survives.

2 The necessity in (AC) is understood as metaphysical necessity; (AC) is a principle of folkmetaphysics (see Section 2.1.2). Since the principle is restricted to ordinary objects, it leaves room forthe coincidence of distinct fundamental particles and of distinct universals or tropes.

3 This is a variant of the prominent paradox of the statue and the lump of clay. I prefer the case ofthe paper plane and the piece of paper, because it makes no appeal to complex aesthetic properties ofthe sort needed to characterize statues.

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Moreover, since nothing happens to Tib apart from having something external detachedfrom it, Tib survives as well. Since both Tibbles and Tib survive, and since both Tibblesand Tib are ordinary spatiotemporally extended objects that exactly occupy the sameplace after the tail is detached, distinct ordinary objects coincide at that time.4

(C)Suppose with Fine (2000) that Bruce writes a letter to his wife Bertha on a piece of paper.Upon receiving the letter, Bertha writes a letter to Bruce on the other side of the samepiece of paper without affecting what Bruce had written. As a consequence, there is a letterthat Bruce wrote and a letter that Bertha wrote. Is the former identical with the latter? Itseems not. For a letter typically comes into existence when it is written. Bruce writes aletter at one time, Bertha writes a letter at another time. Since one cannot write a letterthat exists already, Bertha’s letter is distinct from Bruce’s letter. So we have two letters.Moreover, since Bruce’s letter is not destroyed when Bertha writes hers, Bertha’s letter andBruce’s letter coexist at various times. As Fine points out, these letters have all thestandard attributes of ordinary spatiotemporally extended objects: ‘they can be stacked,weighed, damaged, destroyed, and so on’. Further, it is plausible to say that at any time atwhich either letter exists, its exact location is the location of the piece of paper on which itis written. As in case (A), we have coincidence of distinct artefacts. But this time theartefacts belong to the same kind.5

(D)A human organism lives for a thousand years. During this time span it undergoesperpetual psychological change, to the effect that its early memories and character traitsfade gradually and are eventually replaced by completely different memories and char-acter traits. The organism ends up lacking any psychological connection with its earlierstages across long periods of time.6 Where there is a human organism with higher-ordermental capacities, there is a person constituted by this organism.7 Suppose that the

4 See Geach (1962) and Wiggins (1967). This is a modern version of the paradox of Dion andTheon by the Stoic philosopher Chrysippus.

5 Here is another case of coincidence of distinct artefacts of the same kind. Consider two roadswith a common stretch. They are distinct, as each has a road-segment that the other lacks.Presumably roads can change in length over time; a road will survive the loss of a short segment.Now suppose that both roads gradually lose one road-segment after another, in such a way that theyboth shrink to the size of their common segment. As a result of this process, both roads end upoccupying exactly the same place at the same time. This may be characterized as a case of fusion.(For related cases of fission, see Chapter 4.)

6 There is a standard distinction between psychological connectedness and psychological con-tinuity in the literature on personal identity. Stages of an organism are psychologically connected ifthey are psychologically similar to a certain minimal degree; they share at least some memories andcharacter traits. Stages of an organism are psychologically continuous if they are connected by achain of stages, such that adjacent stages in the chain are massively psychologically similar. Thepresent case stresses connectedness.

7 In this context, the relation of constitution is invoked without philosophical ambition, and accord-ingly its nature is left unspecified. By analogywith the treatment of the relationship of the paper plane andthe piece of paper to be proposed in the following sections, it will turn out that constitution is not identity.At any rate, as long as we are dealing with the case of the long-lived organism, issues regarding therelationship between a person and the organism it constitutes may be set aside.

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organism at time t constitutes a person P, and that the organism at a time 800 years laterthan t constitutes a person P*. Is P identical with P*? The answer seems to be no, giventhat psychological connectedness has faded away completely. So personal identity seemsto require psychological connectedness: a person P at t1 is identical with a person P* at t2only if P at t1 is psychologically connected to P* at t2. Let us follow Lewis (1983a: 66) instipulating that psychological connectedness has a maximal span of 137 years. Then noperson persists through a span of more than 137 years. Let us further assume that forevery span of 137 years or less lived by our organism, some person persists through thatspan. Given that the organism persists from 1900 to 2100, some person, P, persists from1900 to 2000, and some person, P*, persists from 2000 to 2100. Since no person persistsfrom 1900 to 2100, P and P* are distinct. On the plausible assumption that each personconstituted by the organism at time t exactly occupies the place occupied by the organismat t, it follows that P and P* are distinct persons coinciding spatially in year 2000.Moreover, since year 2000 is part of infinitely many 137-year spans, we must admitthat infinitely many persons coincide then.8

(E)A chair is built from a piece of wood. Once the building process is completed, there is achair and a coincident piece of wood. The chair has artefactual as well as physicalproperties: in addition to having a certain shape and mass, it has four legs and isfunctionally defective. The piece of wood, on the other hand, does not have any legsand is not defective. Hence, the chair and the piece of wood are distinct, coincidingobjects. In the previous cases, coincidence of distinct objects is established on the basis of adifference in temporal extension, a diachronic difference; one of the coinciding objectscomes into or goes out of existence before the other does. In the present case, coincidenceof distinct objects is established on the basis of differences obtaining at the same time—that is, on the basis of synchronic differences.9

The paradoxes are here presented as concerning distinct objects that share theirexact spatial location at a time. It is a common claim that the mentioned cases arealso intuitively puzzling because they violate the principle that distinct ordinaryobjects cannot share all of their parts (at some level of decomposition) at anytime.10 I have doubts about the claim that the sharing of parts of distinct objectsat a time is prima facie just as puzzling as the sharing of location at a time. Here is

8 This type of case is discussed in Parfit (1971: 217–19) and Lewis (1983a: 65–7). A modal caseclosely related to this one is ‘Chisholm’s Paradox’; see Chisholm (1967) and Section 5.3. I shall setaside doubts about the empirical basis of the long-lived organism case and assume that it isnomologically possible, thereby rendering it maximally disturbing. Metaphysicians worried aboutcoincidence should face this type of case head-on, in order to avoid giving hostage to empiricalfortune.

9 Compare the mereological differences between Michelangelo’s David and its coincident blockof marble discussed in Sections 1.1 and 2.2. For another synchronic case, recall the two lettersintroduced in (C). One letter is addressed to Bruce, the other to Bertha; one letter is written on thefront side of the paper, the other is written on the back. See Fine (2003: 206) for more examples ofthis synchronic type.

10 See, inter alia, Sider (2001a: 141–2) and Wasserman (2009: section 2).

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a natural way of setting up case (A). Some matter is arranged piece-of-paper-wise,and so a piece of paper comes into existence. Later, the same matter is rearrangedpaper-plane-wise, without breaking up the piece-of-paper-arrangement, and soa paper plane comes into existence, in addition to the piece of paper. Theseassumptions seem intuitively innocuous by themselves. Kind-dependent com-position, just as kind-dependent persistence, seems to be part and parcel ofthe common-sense conception of objects, and correspondingly would appearto constitute an undisputed premise on the way to paradox, as opposed to adisputed consequence. What does seem intuitively repugnant, by contrast, is thatdistinct objects can fit into the same place at the same time. Would one object notcrowd any other objects out? In other words, while the complete sharing of parts(at some level) of distinct ordinary objects is easy to accept by the lights ofcommon sense, the sharing of exact spatial location of distinct objects is hard toaccept. Since sharing all parts at a time seems to entail sharing location at thattime, we have a paradox.11 To be sure, the complete sharing of parts of distinctobjects raises hard metaphysical problems, such as the problem of how exactlycomposition works if it is not just classical-mereological fusion (see Section 1.1),and the problem of how to explain the various differences between objects madeof the same matter (see Chapter 5 for discussion). But these problems are notparadoxes; they do not mark an apparent inconsistency within the common-sense conception of objects, in the way that the problems of coincidence do.

3.2 Incompatibilism about Coincidence

Responses to these paradoxes in the literature are almost all incompatibilist,viewing the paradoxes as uncovering a genuine inconsistency in the common-sense conception of objects and rejecting one or more compelling premises.Resolving the apparent conflict between the anti-coincidence principle (AC)and the various cases of distinct, coinciding objects is usually thought to requirea choice between rejecting the principle and denying the plausibility of thecases, a choice between pluralism and monism about coincidence.12

Responses to the paradoxes differ further with respect to their scope ofapplication. An important question is whether the response is unified—that is,

11 In David Wiggins influential contemporary presentation of the paradoxes of coincidence, theyare construed as violating intuitions about overcrowding: ‘It is a truism frequently called in evidenceand confidently relied upon in philosophy that two things cannot be in the same place at the sametime’ (Wiggins 1968: 90).

12 I borrow the terms ‘pluralism’ and ‘monism’ from Fine (2003).

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whether it works both for cases of coincidence of distinct objects of differentkinds and for cases of coincidence of distinct objects of the same kind, andwhether it works for diachronic cases, for synchronic cases, and for modal casesof coincidence.13 Most published responses are disunified, using disparate keys tounlock different paradoxes.This section is a brief critical review of the main approaches to non-modal

paradoxes of coincidence to be found in the literature, all of which incompatibi-list and most of which disunified. The review will be followed by a presentation ofmy own compatibilist and unified approach, which reconciles the mentionedparadoxes’ seemingly inconsistent premises in one framework.14

3.2.1 Monism

Monists accept (AC) and reject one or more of the assumptions driving thespecific cases of distinct coincidents. A prominent monist approach is thedominant-kinds view, according to which an ordinary object may belong todifferent kinds, only one of which is dominant. The dominant kind of the objectis the one that determines the object’s persistence conditions. As applied to case(A), this account manages to reduce the number of artefacts present at eachtime to one by rejecting the seemingly innocuous assumption that the piece ofpaper making up the paper plane is identical with the original unfolded pieceof paper. According to this account, folding a piece of paper in the right waydestroys the latter. Likewise, the account rejects the assumption of case (B) thatthe lump of tissue survives the removal of Tibbles tail, a removal of a mereexternal attachment. The dominant-kinds account is, moreover, limited in scope,in virtue of applying only to cases of coincidence involving objects of differentkinds. It is also unclear how synchronic cases of coincidence are to be treatedwithin this framework.15

13 Modal cases will be covered in Chapter 5.14 Monists and pluralists about coincidence typically agree that ordinary objects, the protagonists

of the coincidence paradoxes, exist. Eliminativists deny this. One variant of eliminativism says thatalthough atoms may be arranged tablewise, no plurality of atoms ever compose anything, and hencethere are no tables. See, inter alia, Unger (1979) and van Inwagen (1990). Eliminativism issometimes portrayed as a solution to the paradoxes of coincidence: there is no problem about thecoincidence of distinct ordinary objects, because ordinary objects do not exist. In the eyes of theMoorean, who aims to save as much of the common-sense conception of objects as possible,eliminativism is prima facie the least appealing picture of all. While various attempts have beenmade to reconcile eliminativism with common sense, these have arguably been unsuccessful. SeeKorman (2009), McGrath (2005), O’Leary-Hawthorne and Michael (1996), and Uzquiano (2004),for critical discussion. As I see it, eliminativists have nothing interesting to say about coincidence assuch. I shall not discuss the picture here.

15 For the dominant-kinds view, see Burke (1994, 1997a, 1997b). For further development, seeRea (2000).

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Another monist approach is the sortal-relativity account, according to whichan object has attributes that are relativized to different sortal concepts, orkinds, under which the object falls. In case (A), one and the same object is botha piece of paper and a paper plane. This object exists at a time qua piece ofpaper, whereas it fails to exist at that time qua paper plane. Similarly for case(E). One and the same object is both a chair and a piece of wood. This objecthas legs and is defective qua chair but fails to have legs and fails to be defectivequa piece of wood. Conflict with Leibniz’s Law is avoided in both cases,because the different sortal-relative attributes are compatible. On the criticalside, this way of avoiding conflict creates some tension with unreflectivecommon sense. There is an artefact that is present at time t, and there is anartefact that is absent at t. Without a doubt, the philosophically uninitiated willinfer that we are dealing with distinct artefacts, taking for granted thatpresence at t and absence at t are incompatible properties. The friend of sortalrelativity does not permit the naive inference, as presence at t and absence at tmay turn out to be compatible properties, depending on how they are sortallyrelativized.As regards scope, the sortal-relativity account is severely limited. First, the

account does not apply to case (B). Tibbles and Tib are distinct, because onehas a tail that the other lacks. So there are two objects. Since both objectssurvive the tail-removal, and both objects end up in the same spatial region, p,at time t, there should be at least two objects in region p at t. This description ofthe case seems innocuous. Yet monists insist that region p contains a singleobject at t. It is entirely unclear how sortal-relative attributes are supposed tohelp with this seemingly inconsistent scenario. Secondly, the account does notcover all cases of same-kind coincidence. Consider case (C). A letter L exists att1 and at t2, and a coinciding letter L* exists at t2 but not at t1. If L and L* arethe same object, then this object both exists and fails to exist at t1. Throwingsortal relativity into the mix, to the effect that L/L* exists at t1 qua letter anddoes not exist at t1 qua letter, obviously fails to alleviate the threat of incon-sistency. Moreover, enriching the sortal modifiers, to the effect that L/L* existsat t1 qua letter to Bertha but fails to exist at t1 qua letter to Bruce, provides atemporary remedy at best. For suppose that Bertha returns the original letter toBruce without a response. As a result, Bruce tries again and writes anotherletter to Bertha on the back of the original. Then we have two spatiallycoinciding letters to Bertha, and hence a single material object that exists att1 qua letter to Bertha, and that also fails to exist at t1 qua letter to Bertha.Contradiction reinstated. In general, for any enriched sortal term +K, if cases of

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distinct, coincident Ks are possible, then cases of distinct, coincident +Kscannot be ruled out easily.16

3.2.2 Pluralism

Pluralists accept at least some of the cases of distinct coincidents but reject thecompelling principle (AC). Pluralists thus accept that the folk conception ofobjects is internally inconsistent. They accept what we find pre-theoreticallyvery hard to accept: that distinct macroscopic objects can fit into the sameplace at the same time. They do, however, try to sugar the pill by claiming thatwhile there is a conceptual problem about coincidence (more on the exact natureof the problem shortly), there is at least no metaphysical problem, becausecoincidence of distinct objects is metaphysically harmless. What seems mysteri-ous on the surface, turns out to be innocuous deep down.One pluralist approach is the four-dimensionalist account of coincidence as

temporal overlap, according to which distinct ordinary objects, such as the paperplane and the piece of paper of case (A) or Tibbles and Tib of case (B), coincide ata time in virtue of sharing a common temporal part, or stage, at that time.Somewhat more perspicuously, the standard four-dimensionalist claims thatthe fact that the piece of paper and the paper plane both (exactly) occupy placep at time t is grounded in, or derives from, the fact that the piece of paper and thepaper plane have a common temporal part at t that occupies p simpliciter. Giventhat occupation at a time is grounded in occupation simpliciter in this way, nospatial region is, at bottom, occupied ‘twice over’.17 This is why, according tostandard four-dimensionalists, coincidence of distinct objects is metaphysicallyharmless.18

While the temporal-overlap account handles distinct coincidents of the samekind as easily as it handles distinct coincidents of different kinds, the account is

16 Friends of sortal relativity include Gibbard (1975), Gupta (1980), and Lewis (1968 and 1971),although their focus is on modality. I shall return to their approach to the modal paradoxes inChapter 5. Lewis’s counterpart theory has been ‘temporalized’ by Sider (2001a: section 5.8), althoughhe does not employ the ‘qua K’ operator. For a recent discussion that questions the viability of sortalrelativity as a hypothesis about ordinary language, see Fine (2003). For responses, see Frances(2006), King (2006), and Sattig (2006: section 5.6).

17 The relation between four-dimensionalist objects and spacetime will be discussed in greaterdetail in Chapter 8.

18 Those who view ordinary objects as events, processes, or K-paths (see Section 2.2), and whomight combine this view with a three-dimensionalist ontology of material objects (in the technicalsense of ‘material’), are likely to adopt a pluralist approach to the paradoxes of coincidence that isanalogous to the four-dimensionalist one. They might say that the coincidence at a time of distinctevents, processes, or K-paths is metaphysically harmless, because the latter share a state, state ofaffairs, or fact at that time.

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still limited in scope, since it only applies to diachronic cases of coincidence,leaving synchronic cases in the dark. The problem for the temporal-overlapstrategy of accepting but deflating distinct coincidents is that the account failsto capture the qualitative differences between the chair and the piece of wood incase (E), given that sharing a temporal part at a time results in sharing allattributes at that time.19 A different type of resolution is needed in this case.(Likewise for the modal paradoxes, as we shall see in Chapter 5.)20

Many pluralists who reject four-dimensionalism about objects in favour ofthree-dimensionalism adopt some version of the view that distinct, coincidingobjects are intimately related by an asymmetrical dependence relation of consti-tution. In order to present the basic idea, let us focus on case (A) again.Intuitively, an object is constituted by the thing or things from which it ismade. The paper plane is made from the piece of paper by shaping the latterpaper-plane-wise, but not vice versa. Hence, the paper plane is constituted by thepiece of paper, whereas the piece of paper is not constituted by the paper plane.The constitutionalist’s opening claim, as I understand it,21 is that this intuitiverelation between the piece of paper and the paper plane is to be taken as ametaphysically deep relation. And the so-called ‘problem of constitution’ is toanalyse this deep relation in a way that explains why the piece of paper and thepaper plane can differ qualitatively—for example, in their temporal and modalprofiles—despite being similar in parts, location, shape, weight, colour, and soon.22 Notice that constitutionalism stands in sharp contrast to the classical-mereological, four-dimensionalist account of the relation between the piece ofpaper and the paper plane mentioned above, according to which their metaphys-ical relation is just the relation of sharing some temporal parts, and according towhich the piece of paper is becoming paper-plane-shaped carries no metaphys-ical weight, no object-generating power, whatsoever.23

19 Standard four-dimensionalism’s inability to capture intuitive differences in mereologicalstructure were discussed in Section 1.1.

20 Four-dimensionalist pluralists follow the lead of Lewis (1983a). While not fully unified, thefour-dimensionalist account presented in Sider (2001a: chapter 5) is a pluralist account of all thediachronic paradoxes.

21 Especially in reference to one of the leading constitutionalists, namely, Wiggins (1968, 1980,2001).

22 The ‘grounding problem’, to be discussed in Chapter 5, is one such problem of constitution.23 Constitutionalism is naturally associated with Aristotelian hylomorphism, broadly construed

(see Chapter 1), in virtue of assigning the act of shaping a piece of paper in a certain way ametaphysicalobject-generating power. In this connection, see Koslicki’s (2008: 184–6) neo-Aristotelian, mereo-logical analysis of constitution. For two further well-known explications of the constitution relation,see Baker (2000, 2007) and Thomson (1998).

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According to constitutionalists, then, distinct, coinciding objects are related byconstitution. How exactly does constitution help with the paradoxes of coinci-dence? The general strategy is meant to be same as the four-dimensionalists’:while it is conceded that there remains a conceptual problem—namely, that thecommon-sense conception of objects threatens to be internally inconsistent—there is at least no metaphysical problem, because coincidence of distinct objectsis metaphysically harmless. The constitutionalists’ standard account of why thisis so goes roughly as follows: the fact that the paper plane (exactly) occupies aplace p at a time t is explained by the fact that the paper plane is constituted by apiece of paper which occupies p at t. I can see two ways of making sense of thisexplanation, neither of which seems to work in favour of constitutionalism.First proposal: the relation of (exact) occupation at a time is to be analysed in

terms of a more fundamental relation of occupation. This is what happens in thefour-dimensionalist case: occupation at a time is analysed in terms of occupationsimpliciter, in such a way that multiple occupancy at a time is grounded in uniqueoccupancy simpliciter.24 This strategy, however, does not work for the three-dimensionalist who standardly construes occupation at a time as a non-derivativerelation. And it is unclear, within this framework, what other, more fundamentalrelation could ground the occupation relation in which the piece of paper and thepaper plane stand to the same place, such that the mystery of multiple occupancydisappears.Second proposal: a constituted object does not really bear the relation of

occupation at a time to a place; this is just a ‘way of speaking’. Only its constituteris, strictly speaking, located at a time. This is how the singleton set of a lump ofmatter could be said to occupy a place at a time; it does so only superficially, invirtue of having a unique member that properly occupies that place at that time.Again, this is not what standard constitutionalists have in mind. According tothem, the paper plane is just as genuinely located as its constituting piece ofpaper.Now, an Aristotelian hylomorphist might consider the view that matter-form

compounds do not really occupy a place. While they are non-spatial, due tohaving a non-spatial form as a constituent, we ordinarily say that the compoundsdo occupy a place if they have material constituents that jointly occupy that place.

24 The crux of the four-dimensionalist strategy of explaining away overcrowding may have beenslightly misrepresented by some four-dimensionalists. Sider (2001a: 155–6) says that coincidence isgrounded in overlap of spacetime worms. What would have been more accurate to say is thatcoincidence at a time is grounded in coincidence simpliciter, on the assumption of overlappingspacetime worms.

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This way lies trouble, too. If all composition in the realm of material objects ishylomorphic composition (see Section 1.1), this hylomorphist has reason toworry about the possibility that the compositional hierarchy does not bottomout—that there are no mereologically simple objects. For in this case, no materialobject at all would really have a spatial location. Moreover, if the mode oflocation-inheritance under consideration requires the existence of ultimateentities with a proper spatial location, as it may well do, then no object haseven a derivative spatial location.At this point, the constitutionalist might declare that we have overlooked an

easy, or perhaps even the obvious, response to the worry about coincidence: thepiece of paper and the paper plane share their location because they have thesame parts (at some low level of decomposition); the joint location of the partsjust is their location.25 This third response will not do, either. First of all, if thesolution to the paradox were that easy, one wonders how the paradox could havearisen in the first place. This concern is a symptom of the main problem with theresponse, namely, that it does not address the key issue. Compare the followingtwo questions:

(Q1) What explains the fact that a given mereologically complex objectoccupies this place (rather than another place) at a given time?

(Q2) What explains the fact that a given mereologically complex objectoccupies (rather than fails to occupy) a given place at a given time?

Question (Q1) concerns the grounds for the identity of the place occupied,whereas question (Q2) concerns the grounds for the obtaining of the relationof (exact) occupation. (Q2) is the key question in the present context. For it is thequestion what occupation consists in that requires an answer if we are tounderstand how distinct objects can fit into the same place at the same timewithout crowding each other out. Without such an account, the mysteryremains. To say that a complex object’s location is just the joint location of itsparts is an acceptable answer to (Q1). It is, however, not an acceptable answer to(Q2) that the relation of occupation holding between a complex object and aplace is grounded in the same relation holding between the object’s parts andthe place’s parts. For this answer does not offer an account of what occupationconsists in.26 In light of the foregoing considerations, it is unclear how consti-tutionalists intend to answer this question, and hence their attempt to render

25 See, inter alia, Wasserman (2009: section 2).26 For a notion of grounding that is suited to back contrastive explanations, see Schaffer (2012).

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coincidence metaphysically harmless threatens to fail.27 It is noteworthy thatthis simple response to paradoxes of coincidence has been sufficiently influen-tial to earn the label ‘the standard account’. I dare say that the standard accountrests on a confusion. If there was a mystery to begin with, it is still there.28

As regards the issue of scope, typical proponents of the constitution accounthold that it only applies to cases of coincidence involving objects of differentkinds, and hence that cases involving a single kind require a different approach.The reason is, roughly, that constitution is typically viewed as kind-based. Thepaper plane emerges as a new object that is constituted by the piece of paper,because the piece of paper receives the form of a paper plane. More generally, aconstituted object appears only in the company of a form associated with a kindthat is different from the kind(s) of the constituter(s). In the case of the two letters,(C), no new form comes into play, and hence no new object appears. While this isthe standard constitutionalist stance, it is not out of the question to construeconstitution as based on property differences that are more fine-grained thankind differences.29 With such a relation at her disposal, the constitutionalistmight interpret (C) as a case in which the later letter, L2, is constituted by theearlier letter, L1, or just as a case in which L1 and L2 are co-constituted by the samepiece of paper. Hence, a unified approach to the paradoxes of coincidencemay wellbe within reach of the constitution lover.

3.2.3 Deflationism

According to standard constitutionalism, the constitution relation is a metaphys-ically deep relation. Amie Thomasson (2007) has recently given constitution adeflationary spin. Her picture is, very roughly, that the dependence of a consti-tuted object on its constituter(s) has a mere conceptual nature, and hence is, in asense, metaphysically shallow. For example, that the piece of paper in case (A) isfolded to attain a paper-plane-shape analytically entails that a paper plane

27 Thomson (1983, 1998) goes further than is now standard for constitutionalists by claiming thatthe paper plane and its constituent piece of paper are parts of each other. Pace Sider (2001a: 155–6),this version seems to do no better in explaining away overcrowding than the standard version. Forthe obtaining of the relation of exact occupation at a time still does not seem to be grounded in factsabout parthood. The hard question, (Q2), remains unanswered.

28 The problem of overweighing seems easier to handle. For it seems fine to say that the piece ofpaper with its mass of 100g and the coinciding paper plane with its mass of 100g do not put 200g onthe scales, because they share the same parts, and because their mass is grounded in the masses oftheir parts. What is doing the work here is an analysis of masses along the lines of Zimmerman’s(1995): x has mass n iff there is a complete decomposition S of x, such that the sum of the masses ofthe members of S is n. By contrast, no additive analysis of the relation of exact occupation (asopposed to the place occupied) seems plausible.

29 Fine (1999) has such a view. Though see Koslicki (2008) for criticism.

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distinct from the piece of paper exists. The existence of the paper plane is thusconceptually grounded in, or derived from, the piece of paper and its attributes. AsThomasson also puts this view, whatevermakes it true that the piece of paper existsalso makes it true that the paper plane exists.30 The deflationary suggestion thatexistence claims about ordinary objects can be analytic has been greeted with awave of resistance. Many find the claim plainly unintelligible. Others argue againstit.31 I cannot address these issues here. My focus will be on the question what thispicture tells us about the paradoxes of coincidence. My answer will be: very little.In the face of the paradoxes of coincidence, the deflationary constitutionalist

will want to deflate the coincidence of distinct objects. How? From the point ofview of the deflationist, coincidence is metaphysically harmless only if it can beconceptually derived from a basis without coincidence. But to tell a story abouthow the existence of the paper plane is conceptually grounded is not automatic-ally to tell a story about how the spatial occupation of the paper plane isconceptually grounded. In the previous sub-section, I considered three waysof grounding spatial occupation and found none of them workable in a consti-tutionalist framework. First, a three-dimensionalist constitutionalist cannotground occupation at a time in occupation simpliciter. Second, a constitutionalistwill not want to deflate the instantiation of the relation of occupation byconstituted objects to the effect that the latter do not really stand in this relationat all. Third, a constitutionalist who claims that coincidence is harmless becausethe place occupied by these objects is just the sum of the places occupied by theircommon parts confuses the grounding of occupation with the grounding of whatis occupied. These considerations apply equally to the deflationary variant ofconstitutionalism and to the non-deflationary variant.We saw that in addition to a metaphysical worry about explaining away

coincidence there is the non-metaphysical worry that the common-sense con-ception of objects threatens to be internally inconsistent: pluralism about coin-cidence captures our intuitions about pieces of paper and paper planes but seemsto render the compelling anti-coincidence principle, (AC), false. Constitutional-ists standardly view their position as incompatibilist. Thomasson, however,claims to have found a way of avoiding incompatibilism. First, she points outthat while principle (AC) is false, the following restricted version of (AC) is true:

(AC*) Necessarily, for any ordinary objects o and o*, and for any time t, if ocoincides with o* at t, and if o is constitutionally unrelated to, or analyticallyindependent from, o*, then o is identical with o*.

30 See Thomasson (2007: 78–80). 31 See, inter alia, Bennett (2009) and Sider (2009).

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Thomasson claims further that ‘the plausibility of this restricted version of the nocoincidence principle can explain our initial conviction that the principle is true,but the restricted principle clearly does not interfere with accepting the existenceof constituted objects as well as their constituting bases’ (2007: 80). If this is toalleviate the worry that the folk conception of objects is internally inconsistent,then ‘our conviction’must be a pre-metaphysical conviction of ordinary thinkers.Here the key background claim seems to be that ordinary thinkers find it soobviously harmless that constitutionally related, or analytically dependent,objects can coincide that these thinkers can only be sensibly interpreted asadopting the restricted version of (AC). Without this background claim thesuggested restriction is ad hoc.Compatibilism about coincidence is not to be had so cheaply. I have two

objections. First, the paradoxes of coincidence have been around for the longesttime. If Thomasson is right, and all that is required to remove conceptual tensionis to point out that the piece of paper constitutes the paper plane, then theappearance and persistence of paradox become a mystery. Thomasson mightrespond that the cases seem paradoxical on the false presupposition that they arecases of constitutionally unrelated, coinciding objects, analogous to the case of aperson walking through a wall.32 But this move seems unmotivated, given howobvious it is that we are dealing with cases of constitutionally related objects—recall that the paper plane’s being made from, and hence its being constituted by,the piece of paper is a premise of puzzle case (A).33 The second, and moreimportant, objection is that coincidence of constitutionally related objects isnot obviously harmless, as I argued above. Constitutionalists who are makingthis claim are either confused about the grounds of exact occupation or arechanging the subject.

3.3 Compatibilism about Coincidence

My aim in the remainder of this chapter is to offer a plausible compatibilist wayout of the apparent conflict between the various cases of coincidence and theplatitude of common sense that no distinct ordinary objects can ever coincide:properly understood, there is no conflict; the cases and the platitude are com-patible. My compatibilism about coincidence is based on the theory of

32 Cf. Thomasson (2007: 78).33 It is also hard to believe that ordinary thinkers should find coincidence of distinct objects

obviously harmless on the grounds that these objects are analytically related. For the folk presum-ably lack a grasp of complicated analytical dependence relations among ordinary existence facts.After all, most philosophers claim to lack a grasp of such relations.

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perspectival hylomorphism, as developed in Chapters 1 and 2. The theory’sperformance in handling the paradoxes of coincidence provides a good reason,one of many, for taking the theory seriously. Let me begin with two methodo-logical considerations concerning why compatibilism about coincidence isdesirable.First, the debate over the paradoxes of coincidence has traditionally been a

debate between monists and pluralists. Monists resolve the paradoxes by addu-cing metaphysical reasons for rejecting various compelling assumptions drivingsuch cases as (A)–(E). Pluralists resolve the paradoxes by adducing metaphysicalreasons for rejecting the compelling anti-coincidence principle (AC). Howeverplausible their various metaphysical commitments may be when compared toeach other, all of these approaches face a simple Moorean worry. Many of usdoubt that philosophy is able to come up with arguments that genuinely threatenwhat we ordinarily believe. As Mooreans, we hold that our basic ordinary beliefsand intuitions, though only defeasibly justified, possess a plausibility that shouldmake us sceptical of any philosopher’s argument to the contrary. This attitudeyields a certain reluctance to let either the various cases of coinciding objects orthe anti-coincidence principle go for the philosophical reasons adduced bymonists and pluralists. If a way of preserving both the cases and the principle isavailable, Moorean modesty commands that we look into, and perhaps fight for,this alternative.Second, the debate between monists and pluralists is framed by the concession

that the folk conception of ordinary objects is unstable. If cases (A)–(E) contra-dict the anti-coincidence principle, then the folk conception is inconsistent, sincethe assumptions driving the counterexamples themselves flow from this concep-tion. The principle of charity in interpretation commands us to interpret ordin-ary thought and talk in a way that renders it reasonable for non-philosophers tothink and say these things.34 Prima facie, it is hard to represent the folk asreasonable when they hold straightforwardly inconsistent beliefs, such as thatno distinct objects can fit into the same place at the same time, while pieces ofpaper and paper planes obviously can. From the compatibilist’s point of view, bycontrast, explaining reasonableness is easy. Notice that this demand for reason-ableness of the common-sense conception of objects is weaker than the Mooreandemand for the stability of this conception with respect to philosophical inquiry.

34 This is a comparatively weak construal of the principle of charity. See Hirsch (2002, 2005) for astronger construal, according to which a charitable interpretation aims to preserve truth as well asexplaining reasonableness. See Lewis (1974: 336–7), Korman (2010), Varzi (2002: 61–5), andWiggins (1980: 198–200) for criticism.

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While Mooreanism aims for truth or correctness of ordinary beliefs that arisefrom our basic sources of information about how the world is and could be, theprinciple of charity, as understood here, requires ordinary beliefs to be reason-able, even if false.35

In Section 3.3.1, I shall present the compatibilist dissolution of the paradoxesof coincidence offered by perspectival hylomorphism, which immediately allevi-ates Moorean worries. In Section 3.3.2, I will show that this dissolution is neutralwith respect to whether material objects are understood according to three-dimensionalism or four-dimensionalism. In Section 3.3.3, I shall argue that theapproach also provides the best explanation of reasonableness.

3.3.1 Perspectival hylomorphism and coincidence

In outline, the proposed way out of the paradoxes looks as follows. Ordinaryobjects are double-layered compounds of form and matter. The different layerspermit different perspectives on the objects, a sortal-sensitive one and a sortal-abstract one. Ordinary discourse about objects employs different modes ofpredication that correspond to these perspectives, where predications in theformal mode are made true by facts about an ordinary object’s form, whereaspredications in the material mode are made true by facts about an ordinaryobject’s matter. Applying this framework, our descriptions of specific distinctordinary objects as coinciding manifest the sortal-sensitive perspective, andaccordingly are descriptions in the formal mode. Our sweeping rejection of thepossibility of distinct, coinciding objects manifests the sortal-abstract perspective,and accordingly employs the material mode of predication. In short, from thesortal-sensitive perspective, the world is crowded with distinct coincidents,whereas from the sortal-abstract perspective, no distinct coincidents are to befound anywhere. Given the q-hylomorphic basis of perspectivalism, whichpermits hylomorphic divergence, these different descriptions are compatible.Furthermore, this solution to the paradoxes of coincidence is unified; all of thementioned cases will be shown to be compatible with the anti-coincidenceprinciple on the same grounds. The mystery of coincidence disappears com-pletely once we realize that ordinary objects lead double lives.Now to the details. My view is that the cases of coinciding ordinary objects

(A)–(E) and the anti-coincidence principle, (AC), are compatible because theyemploy different modes of predication: the cases describe objects formally,whereas the principle describes them materially. I shall begin by showing that if(A)–(E) and (AC) are read in this way, then they are compatible, assuming the

35 Cf. Korman (2009: 245).

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perspectival semantics of object-discourse and its underlying metaphysicssketched in Chapters 1 and 2. Subsequently, I shall reflect on the motivationfor these perspectival readings.The crux of cases (A)–(E) may be compressed into the following claims.

(A) A piece of paper P exists at t1 and t2, and a paper aeroplane P* exists at t2 butnot at t1. Hence, P is distinct from P*. Moreover, P coincides with P* at t2.

(B) A cat Tibbles exists at t1. A lump of tissue Tib also exists at t1. Since tail T isa part of Tibbles at t1 but not a part of Tib at t1, Tibbles is distinct fromTib. Since Tibbles still exists at t2 after T is destroyed, and Tib still exists att2 as well, Tibbles and Tib coincide at t2.

(C) A letter L exists at t1 and t2, and a letter L* exists at t2 but not at t1. Hence,L is distinct from L*. Moreover, L coincides with L* at t2.

(D) A person P exists at t1 and at t2 but not at t3, and a person P* exists at t2and at t3 but not at t1. Hence, P is distinct from P*. Moreover, P coincideswith P* at t2.

(E) Chair C is defective at t, but piece of woodW is not; and leg G is a part ofC at t, but G is not a part ofW at t. Hence, C is distinct fromW. Moreover,C coincides with W at t.

These claims appear to clash with the anti-coincidence principle:

(AC) Necessarily, for any ordinary objects o and o*, and for any time t, if ocoincides with o* at t, then o is identical with o*.

I propose to read (A)–(E) as sortal-sensitive claims, and hence as employingthe formal mode of predication; and I propose to read (AC) as a sortal-abstractclaim, and hence as employing the material mode of predication. (My reasons forthese readings will be adduced shortly.)

(Aform) A piece of paper P exists formally at t1 and t2, and a paper aeroplaneP* exists formally at t2 but not at t1. Hence, P is formally distinct from P*.Moreover, P coincides formally with P* at t2.

36

(Bform) A cat Tibbles exists formally at t1. A lump of tissue Tib also existsformally at t1. Since tail T is formally a part of Tibbles at t1 but not formally apart of Tib at t1, Tibbles is formally distinct from Tib. Since Tibbles still exists

36 This inference employs principle (FI) from Section 2.2: If o is formally identical with o*, thenfor all properties ç and all times t, o has ç formally at t iff o* has ç formally at t. Likewise for theinferences to formal distinctness in (Bform)–(Eform).

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formally at t2 after T is formally destroyed, and Tib still exists formally at t2 aswell, Tibbles and Tib coincide formally at t2.

(Cform) A letter L exists formally at t1 and t2, and a letter L* exists formally att2 but not at t1. Hence, L is formally distinct from L*. Moreover, L coincidesformally with L* at t2.

(Dform) A person P exists formally at t1 and at t2 but not at t3, and a person P*exists formally at t2 and at t3 but not at t1. Hence, P is formally distinct from P*.Moreover, P coincides formally with P* at t2.

(Eform) Chair C is formally defective at t, but piece of woodW is not; and legG is formally a part of C at t, but G is not formally a part ofW at t. Hence, C isformally distinct from W. Moreover, C coincides formally with W at t.

(ACmat) Necessarily, for any ordinary objects o and o*, and for any time t, if ocoincides materially with o* at t, then o is materially identical with o*.

If (A)–(E) are understood as (Aform)–(Eform), and (AC) is understood as(ACmat), then paradox vanishes, since (Aform)–(Eform) are compatible with(ACmat). This may be shown by specifying the metaphysical basis of each of(Aform)–(Eform) in a way that preserves (ACmat). The metaphysical basis of(Aform)–(Eform) will be specified in terms of the three-dimensionalist, classical-mereological account of material objects and the q-hylomorphic account ofordinary objects presented in Chapter 1: material objects (in my technicalsense) are characterized in terms of three-dimensionalism, mereological univer-salism, and mereological extensionality; ordinary objects are compounds ofmaterial objects and K-paths. In light of the present discussion of coincidence,let us make the further metaphysical assumption that if a material object acoincides absolutely at any time with a material object b, then a is absolutelyidentical with b—that is, absolutely distinct material objects cannot coincideabsolutely at any time. (As in this case, all ascriptions of properties in theupcoming metaphysical specifications will be understood as absolute ascrip-tions.) I shall, furthermore, assume truth conditions (T1)–(T5) of formal predi-cation and truth conditions (T6)–(T9) of material predication, and refer to themas the (metaphysical) semantics of formal predication and the (metaphysical)semantics of material predication, respectively. In (Aform)–(Eform) perspectivalismwas naturally extended to predications of coincidence. Accordingly, the defin-ition of coincidence stated in Section 3.1 has different readings. For any ordinaryobjects o and o*, and for any time t,

(COform) o formally coincides with o* at t =df o and o* formally occupy thesame place at t.

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(COmat) omaterially coincides with o* at t =df o and o* materially occupy thesame place at t.

On the assumption just made that distinct material objects cannot coincide at anytime, (ACmat) follows from q-hylomorphism about ordinary objects and thesemantics of material predication, including (COmat).

37 Let us now specify ametaphysical basis for each of (Aform)–(Eform) that preserves (ACmat).First, a material object a exists at times t1 and t2. Moreover, a is piece-of-paper-

shaped at t1 and t2, whereas a is paper-plane-shaped at t2 but not at t1. (Hence-forth, I shall use ‘K-shaped’ to indicate the possession of K-realizing properties,whatever these properties may be.) Given that material objects have purely mereo-logical persistence conditions, a material object’s becoming paper-plane-shaped isnot sufficient to bring a new, coincident material object into existence. So we mayassume that this case involves no distinct, coinciding material objects. Further,piece-of-paper-path i includes the fact that a exists at t1, that a exists at t2, andthat a exactly occupies place p at t2. Paper-plane-path i*, on the other hand,includes the fact that a exists at t2, that a exactly occupies place p at t2, but doesnot contain existence at t1. Thus, i and i* are distinct but include the instantiationof the same locational properties at t2. Finally, piece of paper P is the compound�c(a, i), whereas paper plane P* is the compound �c(a, i*). By the semantics offormal predication, these specifications make (Aform) true. (What we get here is asimple version of case (A) in which no formal mereological variation occurs inthe transition from piece of paper to paper plane.) By the semantics of materialpredication, these specifications are consistent with (ACmat), since P is materiallyidentical with P*. This analysis of case (Aform) may be illustrated by Figure 3.1.Second, a material object a1 is cat-shaped and exists at t1. Since a tail-shaped

part of a1 is destroyed after t1, and since a1 is mereologically individuated, a1 doesnot exist at t2. In general, it will be assumed in conjunction with mereologicalextensionality that removing a part from a complex material object will neverresult in distinct, coinciding material objects. Further, material object a2 is aproper part of a1 in the shape of a cat without a tail, that exists at t1 and at t2. Cat-path i includes the fact that a1 exists at t1 and that a2 exists at t2, but not thata2 exists at t1. Lump-of-tissue-path i*, on the other hand, includes the fact that a2exists at t1 and that a2 exists at t2. Moreover, distinct paths i and i* include the

37 Formal predications of the form ‘o formally occupies p at t’, as they occur on the right-handside of (COform), are covered by truth conditions (T2) of monadic formal predications, if ‘occupies pat t’ is read as a complex monadic predicate. Similarly, material predications of the form ‘omateriallyoccupies p at t’ are covered by truth conditions (T7).

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instantiation of the same locational properties at t2 (a condition spelled out indetail for case (Aform) above). Finally, Tibbles the cat is the compound �c(a1, i)and Tib the lump of tissue is the compound �c(a2, i*).

38 By the semantics offormal predication, these specifications make (Bform) true. And by the semanticsof material predication, the specifications are consistent with (ACmat); since Tibbut not Tibbles persists materially from t1 to t2, Tibbles and Tib do not coincidematerially at t2.

39 This analysis of case (Bform) may be illustrated by Figure 3.2.Third, a material object a1 is letter-shaped and exists at time t1. A material

object a2 is also letter-shaped and exists at time t2. Objects a1 and a2 are distinctin virtue of minor differences in their mereological composition, because of theink particles present in a2 but not in a1 (still assuming that material objects areindividuated by their parts). Letter-path i includes the fact that a1 exists at t1 andthat a2 exists at t2, whereas letter-path i* includes the fact that a2 exists at t2 butdoes not contain existence at t1. Moreover, distinct paths i and i* include theinstantiation of the same locational properties at t2. Finally, letter L is thecompound �c(a1, i) and letter L* is the compound �c(a2, i*). By the semantics

a

i*

i

t

x

t2

t1

Figure 3.1 The piece of paper and the paper plane

38 The assignment of the compound �c(a1, i) to the name ‘Tibbles’ is arbitrary, given that ourspecifications present us with another cat, namely �c(a2, i), that is an equally good candidate to bethe referent of ‘Tibbles’. I shall set issues of reference aside (see Section 2.2 regarding proper names),and merely note that since �c(a1, i) is formally identical with �c(a2, i), the intuition that case (Bform)involves a single cat is preserved. As pointed out in Section 2.2, formal identity is weaker thanabsolute identity. It is plausible, however, to interpret the default mode of counting cats on the streetas sortal-sensitive. Analogous considerations apply to the treatment of cases (Cform) and (Dform)below.

39 I assumed that a1 does not exist at t2, after its tail-shaped part is destroyed. Suppose, instead,that the atoms composing the tail-shaped part at t1 are scattered rather than destroyed at t2, andhence that a1 still exists at t2. These specifications are still consistent with (ACmat). Both Tibbles andTib exist materially at t2. However, Tibbles’ component material object, a1, and Tib’s componentmaterial object, a2, differ in parts and location at t2, as they did at t1. Since material coincidence ofTibbles and Tib at t2 requires the sharing of location by a1 and a2 at t2, Tibbles does not coincidematerially with Tib at t2.

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of formal predication, these specifications make (Cform) true. (Note that we arehere construing case (C) as involving minor formal mereological variation in theoriginal letter L between times t1 and t2.) By the semantics of material predica-tion, the specifications are consistent with (ACmat); L and L* do not coincidematerially at t2, since their component material objects, a1 and a2, differ in partsand location at t2. (The analyses of this and the following two cases will not beillustrated by separate figures.)Fourth, a person-shaped material object a1 exists at time t1, a person-shaped

material object a2 exists at t2, and a person-shaped material object a3 exists at t3,where t1 and t2 as well as t2 and t3 are a hundred years apart. Objects a1, a2, and a3are distinct in virtue of major differences in their mereological composition.Person-path i includes the fact that a1 exists at t1 and that a2 exists at t2, butdoes not contain existence at t3. Person-path i*, on the other hand, includes thefact that a2 exists at t2 and that a3 exists at t3, but does not contain existence at t1.Moreover, distinct paths i and i* include the instantiation of the same locationalproperties at t2. Finally, person P is the compound �c(a1, i) and person P* is thecompound �c(a2, i*). By the semantics of formal predication, these specificationsmake (Dform) true. (Note that we are here construing case (D) as involving majorformal mereological variations in person P between t1 and t2 and in person P*between t2 and t3.) By the semantics of material predication, the specifications areconsistent with (ACmat); P and P* do not coincide materially at t2, since theircomponent material objects, a1 and a2, differ in parts and location at t2.Fifth, a material object a is both piece-of-wood-shaped and chair-shaped at

time t, and hence a is a subject of a chair-path i and of a piece-of-wood-path i*.Moreover, a material object b is leg-shaped at t, and hence b is a subject of a leg-path i**. Let chair C be the compound �c(a, i), let piece of wood W be �c(a, i*),and let leg G be �c(b, i**). Since chair-path i includes the fact that a is

a2

i*

i

t

x

t2

t1

a1

Figure 3.2 Tibbles and Tib

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(functionally) defective at t, whereas piece-of-wood-path i* does not include thefact that a is defective at t, it follows by the semantics of formal predication that Cis formally defective at t, whereasW is not. (Recall from Section 1.2 that K-pathsare sensitive to the spheres of discourse of sortal nouns.) As regards the mereo-logical portion of (Eform), assume that C’s chair-path i includes the fact that a hasb as a proper part at t. Assume also that i**’s leg-realizing profile partly groundsi’s chair-realizing profile. By the semantics of formal predication—specifically, bythe truth conditions of formal parthood, (T5)—it follows that G is formally a partof C at t. Since, on the other hand, i**’s leg-realizing profile does not partlyground i*’s piece-of-wood-realizing profile, G is not formally a part ofW at t. (SeeSection 2.2.2 for further details on formal parthood.) Adding that distinct paths iand i* include the instantiation of the same locational properties at t, it followsthat C and W are formally distinct and coincide formally at t. Taken together,these specifications make (Eform) true. By the semantics of material predication,the specifications are consistent with (ACmat), since C is materially identicalwith W.40

Having demonstrated the compatibility of cases (Aform)–(Eform) with principle(ACmat), it must be emphasized that this compatibility rests on the possibility ofperspectival divergence (see Section 2.2). In essence, cases (Aform)–(Dform) arecompatible with (ACmat), because an ordinary object’s individual form maycontain properties that the object’s underlying matter fails to possess. And case(Eform) is compatible with (ACmat), because an ordinary object’s underlyingmatter may possess properties that the object’s individual form fails to contain.41

The formal coincidence of formally distinct ordinary objects is metaphysicallyshallow, in the sense that it is ‘built on’ coincidence-free facts about materialobjects. Coincidence does not run deep; at the level of material objects, places donot get crowded. Owing to this metaphysical modesty, the perspectival-hylo-morphist picture of coincidence has a very easy time responding to the challengeof showing why coincidence of distinct objects is metaphysically harmless, whichproved a tough challenge for constitutionalists of all stripes. Furthermore, thepresent compatibilist approach to coincidence looks highly attractive from aMoorean standpoint. Given that our common-sense conception of objects

40 Corresponding to their material identity, C andW are materially indiscernible in mereologicalrespects at t. Since b is a proper part of a, and since a is the maximal material component of both CandW, G is materially a part of C andW at t. That is, from the sortal-sensitive perspective, C andWhave different parts, whereas from the sortal-abstract perspective, they have the same parts.

41 This holds in simple cases, such as the piece of wood’s failing to be formally defective. Thesituation in mereological cases, such as the leg’s failing to be formally a part of the piece of wood, isless straightforward, as these involve grounding of kind-realizing profiles.

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possesses a plausibility that should make us sceptical of any philosophical threatsagainst it, it is hard to let go of either the various cases of coinciding objects or theanti-coincidence principle, as they both are deeply embedded in pre-philosophicalthought. The perspectivalist compatibilist, unlike the monist and the pluralist,offers a way of preserving both the cases and the principle.

3.3.2 Compatibilism with stages

The foregoing compatibilist dissolution of the paradoxes of coincidence isformulated on the assumption of three-dimensionalism about material objects.This assumption is not necessary. A four-dimensionalist version of perspectivalhylomorphism is available that gets the job done, as well. In order to show this,I shall, first, assume the four-dimensionalist ontology of stages and the stage-version of q-hylomorphism presented in Section 1.3: an ordinary object is acompound of a stage and a K-path, for some kind K, where the stage is thesubject of some K-state in the K-path. I shall, secondly, make the standardassumption that distinct stages and distinct sums of stages cannot coincideabsolutely. That is, there is no non-derivative coincidence of distinct materialobjects. I shall, as a final preliminary, assume stage-theoretic analogues of truthconditions (T1)–(T5) of formal predication and truth conditions (T6)–(T9) ofmaterial predication; covering the basics, (T10)–(T13) in Section 2.2.6 arestage-theoretic truth conditions of monadic temporal predication in the formaland the material mode.A four-dimensionalist metaphysical basis for each of (Aform)–(Eform) may now

be specified in a way that preserves (ACmat). For reasons of length, I shall only dothis for (Aform). A stage s1 is located at time t1 and a stage s2 is located at time t2.Stage s2 is piece-of-paper-shaped and paper-plane-shaped, whereas s1 is onlypiece-of-paper-shaped. Further, piece-of-paper-path i includes the fact that s1exists, that s2 exists, and that s2 exactly occupy place p. Paper-plane-path i*, onthe other hand, includes the fact that s2 exists, and that s2 exactly occupies place p,but does not contain existence at t1. Thus, i and i* are distinct but include theinstantiation of the same locational properties at t2. Finally, let piece of paper P bethe compound �c(s1, i), and let paper plane P* be the compound �c(s2, i*). (Notethat ‘P’ and ‘P*’ have many different candidate referents besides these.) By thesemantics of formal predication, these specifications make (Aform) true. By thesemantics of material predication, these specifications are consistent with(ACmat): while P and P* are materially distinct, they do not coincide materiallyat any time, since P exists materially only at t1 and P* exists materially only at t2.Alternatively, we could have construed P as the compound �c(s2, i) and P* as thecompound �c(s2, i*). These specifications still make (Aform) compatible with

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(ACmat): while P and P* now coincide materially at t2, they are materiallyidentical, and so we still do not face materially distinct yet coincident objects.42

The key to this dissolution is perspectival divergence. From the sortal-sensitiveperspective, distinct ordinary objects can coincide; from the sortal-abstract per-spective, they cannot. Sortal-sensitive claims are made true by facts about K-paths; sortal-abstract claims are made true by facts about stages; and an ordinaryobject’s K-path may contain properties that its underlying stage fails to possess.Notice that the availability of this dissolution privileges the stage-version of

perspectival hylomorphism over the worm-version, because the approach isunavailable to the latter. The reason is that the worm-version does not permitperspectival variation with respect to temporal trajectory (see Sections 1.3.2 and2.2.3). Piece-of-paper-path i and paper-plane-path i* have different temporalextensions, and accordingly have different spacetime worms, w1 and w2, as theirrespective unique strict subjects. Since the worm-version construes ordinaryobjects as compounds of K-paths and their unique strict subjects, P is thecompound �c(w1, i1) and P* is the compound �c(w2, i2). (There are no othercandidates.) By the worm-version’s semantics of material predication, it followsthat P and P* are materially distinct and coincide materially at t2, violating(ACmat). The case and the principle are thus incompatible.While the four-dimensionalist stage-version and the three-dimensionalist

version of perspectival hylomorphism both offer a perspectival dissolution ofthe paradoxes of coincidence, there is a striking difference between them.According to the first, predications in the material mode are made true by factsabout temporally unextended material objects, whereas according to the second,predications in the material mode are made true by temporally extended materialobjects. Thus, according to the first, ordinary objects never persist materially,whereas according to the second, they usually do. This aspect gives the three-dimensionalist version an intuitive advantage, for the sortal-abstract folk con-ception of ordinary objects certainly seems to include the expectation that theseobjects persist. Yet a failure to render correct a certain aspect of the sortal-abstract conception should not be viewed as decisive, for the three-dimensional-ist, classical-mereological account of material objects, underlying the alternativevariant of perspectival hylomorphism, does not achieve a perfect fit with thesortal-abstract conception, either (see Section 4.2). I expect that either way some

42 Notice also that while this case involves an abundance of absolutely distinct pieces of paper andpaper planes—corresponding to an abundance of stages—all the pieces of paper are formallyidentical and all the paper planes are formally identical, as only one piece-of-paper-path is involvedand only one paper-plane path is involved. Our pre-philosophical intuitions concerning identity arethus preserved.

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parts of this conception will have to be given up in the end. Issues concerningdegree of fit aside, the most important conclusion to be drawn from the foregoingconsiderations is that the proposed perspectival-hylomorphist dissolution of theparadoxes of coincidence has a three-dimensionalist and a four-dimensionalistimplementation, and therefore does not require a substantial metaphysical com-mitment in this area. This is a welcome feature of the proposed framework.

3.3.3 Perspectivalism, charitable interpretation, and object representation

A serious worry remains. While the perspectival-hylomorphist picture is meta-physically modest and saves common-sense beliefs about coincidence in theirentirety, it is linguistically unorthodox, in virtue of recognizing different modesof predication. Can semantic perspectivalism be motivated independently ofmetaphysical andMoorean considerations? Is there any linguistic or psychologicalevidence for the proposed semantics? It is to this issue that I shall now turn.Ordinary speakers accept that the piece of paper and the paper plane of case

(A) are distinct and located in the same place at the same time. Yet they are alsowilling to accept that, in general, no distinct ordinary objects can be located in thesame place at the same time. The principle of charity in interpretation demandsan explanation of this seemingly inconsistent behaviour. What could possiblyexplain why non-philosophers find it at all reasonable to accept both of thesepropositions? (Recall the difference between this challenge and the Moorean one:the latter concerns correctness, whereas the former concerns reasonableness.)I shall argue that perspectivalism provides the best answer to this question.To begin with, an incompatibilist about coincidence might propose the fol-

lowing response to the problem of reasonableness.43 The explanation rests on theclaim that we do not come across distinct, coinciding objects in everyday life—that all cases of distinct coincidents are recherché cases. Given that virtually anyspecific pair of distinct objects encountered in everyday life is non-coincident, itis quite reasonable for the folk to expect all distinct ordinary objects to conformto this rule. The friend of this explanation might see an analogy with Russell’sParadox. The comprehension axiom of naive set theory is a generalization withmany obvious instances and no obvious exceptions. The generalization thusseems plausible only as long as we do not realize that there is no set of all setsthat are not members of themselves.44

43 See, inter alia, Hirsch (2002: 116) and Korman (2009: 245–6).44 See Korman (2009: 245–6). It is clear that this explanation is only an option for pluralist

incompatibilists. It will not be endorsed by monists, who hold on to the anti-coincidence principlewhile being well aware of the various counterexamples.

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An immediate worry about this explanation is that many cases of distinct,coinciding ordinary objects are far from recherché. There is nothing unusualabout creating a new object by modifying a single, pre-existing object, as ithappens in case (A). This case is not a merely counterfactual case, and it isquite unlike the case of the barber who shaves all and only those who do notshave themselves, which is surprising due to its self-referentiality.Setting this worry aside, however, the main problem with the proposed

explanation is that the anti-coincidence principle, (AC), is not a generalizationfrom specific cases, as the explanation assumes, but rather a generalization that isarrived at independently from specific cases. In Section 2.1, I motivated this claimby recourse to an influential tradition in the psychology of object representation.I shall review these considerations, as they pertain to coincidence, briefly.Psychological research on object representation undertaken by Spelke and

colleagues suggests that young infants represent objects by spatiotemporal cri-teria prior to representing objects as belonging to particular kinds.45 The spatio-temporal criteria are principles of dividing surface layouts into objects. Amongthe criteria adduced by Spelke is the principle of boundedness, according towhich ‘two surface points lie on distinct objects only if no path of connectedsurfaces links them’ (Spelke 1990: 49). Thus, distinct objects have no surfacepoint in common. While infants represent objects in a primarily spatiotemporal,sortal-abstract way, adults represent objects in a sortal-sensitive way. How doesobject representation in infants develop into object representation in adults? Thehypothesis ranking as orthodoxy in psychology is that the early sortal-abstractcriteria of object representation are supplemented by sortal-sensitive criteria, andhence that object representation does not change radically over the course ofdevelopment. Primarily spatiotemporal criteria of object representation aresomehow integrated with adults’ representations of objects as belonging toparticular kinds.46 This hypothesis is supported by an argument from simplicity.A basic constraint on an explanation of the path from object representation byinfants to object representation by adults is that the explanation should be assimple as possible. Other things being equal, the simplest explanation minimizesthe cognitive distance between infants and adults.47 The hypothesis, according towhich there is no radical developmental change and principles governing objectindividuation by infants continue to operate in the adult scheme, is clearlysimpler and preferable to the rival hypothesis that the early sortal-abstract criteriaof object representation are abandoned completely in the course of development,

45 See Spelke (1990), Spelke et al. (1995), Xu and Carey (1996), Xu (1997).46 See Spelke (1990: 51–2, 54). 47 See Hirsch (1997: 411).

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provided that a plausible integrated account of adults’ object representation inconcert with the spatiotemporal criteria is available. Now, if the sortal-abstractprinciple of boundedness, according to which distinct objects are represented ashaving no surface point in common, continues to play a role in object represen-tation by adults, then it is highly plausible to view this principle as forming thebasis of the common-sense principle that distinct objects cannot fit into the sameplace at the same time. Given that the principle of boundedness is sortal-abstract,the anti-coincidence principle should be construed as sortal-abstract, as well.This connection is just crying out to be made.These sorts of psychological considerations strongly suggest a division within

the common-sense conception of objects. On the one hand, common sensecarves the world into persons, tables, trees, and mountains. We locate thesemacroscopic objects in space and track them through time by means of thequalitative criteria associated with their sortal concepts. This way of determiningwhere and when an object begins and ends constitutes the sortal-sensitiveconception of objects. Our everyday thought and talk about particular physicalobjects typically presupposes this sortal-sensitive conception. On the other hand,ordinary thinkers possess a range of ‘platitudes of common sense’ that concernmacroscopic objects on the whole, and that constitute a primarily spatiotemporalconception of these objects, a conception that abstracts from considerations ofwhich properties of a given object realize which ordinary kinds, and of how theseproperties are distributed across space and time. This sortal-abstract conceptionattributes to macroscopic objects a common, minimal spatiotemporal profile.Among these platitudes is the anti-coincidence principle, (AC).48 This principleis entirely independent of any kind-realizing features of macroscopic objects—independent of the specific properties that make objects persons, tables, trees, ormountains.Let us now return to the task of explaining why it is reasonable for non-

philosophers to accept (AC) as well as the various apparent counterexamples(A)–(E). In light of the foregoing considerations, the explanation cannot be thatthe folk accept (AC) only as long as they are unaware of such cases as (A)–(E),because the belief that distinct objects cannot coincide is not a sortal-sensitivegeneralization, but rather a sortal-abstract one; it is independent of any sortal-sensitive beliefs about specific cases. This is why (AC) remains plausible evenwhen the apparent counterexamples are in full view. The rejection of the possi-bility of a place’s being overcrowded with objects in no way depends on theawareness of any specific instances or exceptions. The anti-coincidence principle

48 For further sortal-abstract principles, see (a)–(e) in Section 2.1.

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is a pillar of our pre-philosophical, spatiotemporal conception of the world ofobjects.49

How, then, is the problem of reasonableness to be solved? Distinguishingbetween a sortal-sensitive and a sortal-abstract conception still leaves the prob-lem of explaining how these conceptions could both be adopted, if they areinconsistent—that is, if ordinary objects cannot fit both our sortal-sensitive andour sortal-abstract descriptions of them.50 The most natural answer to thisproblem, I suggest, is that the sortal-sensitive and the sortal-abstract conceptionsconstitute different perspectives on the same objects, and that ordinary descrip-tions of these objects are sensitive to these perspectives, in virtue of employingdifferent modes of predication in different contexts, which manifest the differentperspectives. Thus, principle (AC) is to be understood as the sortal-abstract(ACmat), given the link with Spelke’s principle of boundedness. Moreover,descriptions (A)–(E) are plausibly construed as manifesting the sortal-sensitiveperspective on the world, and hence are to be understood as (Aform)–(Eform). Incases (Aform)–(Dform), distinctness of coinciding objects is established on the basisof diachronic differences specific to pieces of paper, paper planes, cats, lumps oftissue, letters, and persons. In case (Eform), distinctness of coinciding objects isestablished on the basis of synchronic differences specific to chairs and pieces ofwood. Since the principle and the cases thus construed are compatible, asI showed earlier, it is quite reasonable to accept both.51

This perspectival account of the shift between the sortal-sensitive and thesortal-abstract conceptions of objects, and specifically of the relationship betweenthe anti-coincidence principle and the various cases of distinct coincidents,allows us to avoid the far more radical view that this is a shift in subject-matter,to the effect that either sortal-abstract principle (AC) and sortal-sensitive cases(A)–(E) have different domains of quantification and reference—(A)–(E) mightbe viewed as concerning objects of familiar kinds, while viewing (AC) as con-cerning different objects falling under a purely spatiotemporal kind52—or thatthey predicate different properties and relations, such as different properties ofexisting at a time and different relations of exact spatial occupation and

49 Notice the disanalogy with Russell’s Paradox: once we realize that there can be no set of all setsthat are not members of themselves, naive comprehension loses its plausibility and any air ofparadox disappears.

50 This problem of inconsistency seems to have been ignored or at least down-played massively inpsychology. See Xu (1997) for some hand-waving.

51 This way of motivating an ambiguity between different modes of predication broadly con-forms to the standard test for ambiguity by investigating contradiction. See Zwicky and Sadock(1975: 7–8).

52 I criticize this view in Section 2.1.

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numerical identity.53 I suspect that few would be willing to endorse such extremeand counterintuitive conclusions. I do not endorse them, either. According to myperspectival picture, the shift is not in what we quantify over or refer to, nor inwhat we predicate, but rather in how we predicate the same, familiar property orrelation of the same, familiar object or objects. These points are not meant toprovide conclusive reasons for the perspectival approach to coincidence para-doxes. What they do achieve, though, is to open up an avenue of support for theproposed approach that is independent from Moorean considerations of correct-ness, by appealing to considerations of interpretive charity, or reasonableness,and psychological research on object representation.I conclude that perspectival hylomorphism offers a unified, compatibilist

solution to a wide range of paradoxes of coincidence. Our pluralist intuitionssupporting the cases of distinct coincidents and our monist intuitions supportingthe anti-coincidence principle manifest different perspectives on the world; ourordinary conception of the world is spliced together from sortal-sensitive andsortal-abstract beliefs. The cases of coincidence are cases of formal coincidence,manifesting the sortal-sensitive perspective on the world. In each of the cases,distinctness of coinciding objects is established on the basis of features specific towhich kind or kinds of object are involved. The anti-coincidence principle, on theother hand, is a principle of material anti-coincidence, manifesting the sortal-abstract perspective on the world. The principle abstracts from sortal input,registering only a minimal spatiotemporal profile common to all objects. Thiscompatibilist solution has the significant advantages over its incompatibilistrivals of, firstly, satisfying the Moorean desire to save the appearances, to allowcommon-sense beliefs about coincidence to be correct, and, secondly, of offeringa plausible, psychologically sensible explanation of why ordinary thinkers’ beliefsabout coinciding objects are reasonable.

53 I noted the resistance to the view that we ordinarily ascribe identity only in a ‘loose andpopular’ sense in Section 2.2, where also Geach’s relative-identity view received a critical mention.

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4

Discontinuity

We typically track ordinary objects through time along lines of qualitative andcausal continuity, associated with the kinds to which the objects belong. It seemspossible for such lines to branch out, and hence to form a path with spatiallydiscontinuous segments. These are cases of fission. It also seems possible for suchlines to be gappy, to form a path with temporally discontinuous segments. Theseare cases of intermittent existence. Both types of case are paradoxical. Given ourfamiliar ways of tracking objects of particular kinds, the objects involved inthe specific cases of fission and of intermittent existence end up with a qualitativeprofile that clashes with one or more platitudes of common sense about thespatiotemporal profile of ordinary objects in general. The cases thereby threatenthe common-sense conception of objects with inconsistency. Standard responsesto paradoxes of fission and of intermittent existence are incompatibilist, viewingthe paradoxes as locating genuine instabilities in the common-sense conceptionof objects, and differing over which part of the conception requires revision. Inthis chapter, I will show that this entrenched view is not compulsory. I willpresent a compatibilist solution to the paradoxes on the basis of perspectivalhylomorphism, maintaining the consistency of our pre-philosophical conceptionof objects. The strategy is the same as the one adopted in dissolving coincidenceparadoxes: the various specific cases of fission and of intermittent existenceare compatible with any common-sense principles about the spatiotemporalprofile of objects on the whole, because the cases and the principles manifestdifferent perspectives on the same objects.In Section 4.1, various fission paradoxes will be presented and standard, in-

compatibilist responses discussed briefly. In Section 4.2, a compatibilist responsebased on perspectival hylomorphism will be presented and motivated. InSection 4.3, some paradoxes of intermittent existence will be sketched and dis-solved in an analogous fashion.

4.1 Paradoxes of Fission

In this section, I shall first present the paradox of personal fission in detail andthen briefly characterize some further fission paradoxes involving other kinds ofobject. Second, I shall review two common incompatibilist responses to theseparadoxes. And third, I shall consider and reject an allegedly compatibilistresponse based on the stage view of ordinary objects.

4.1.1 Dividing persons, organisms, and artefacts

Suppose that a person P’s cerebrum, the organ chiefly responsible for theperson’s higher-order mental capacities is implanted into a new head andfully connected, with the result that there is a post-operation person who isin every way psychologically continuous with P; the post-operation personremembers the pre-operation person’s past experiences, shares her personalitytraits, and so on.1 Is the post-operation person identical with the pre-operationperson? The standard intuition is that the answer is yes; psychological continu-ity yields personal identity. So let us assume that a psychological criterion ofpersonal identity over time is associated with our ordinary concept of a person.Next, consider a modification of this case. This time P’s cerebrum is separated

into its two hemispheres by cutting the nerves that connect them. One of thehemispheres is then implanted into a new head and fully connected, with thesame result as in the first case: there is a post-operation person who is in everyway psychologically continuous with P. Let us again follow common judgementin holding that P survives in this simple transplant case, in which only the lefthemisphere or only the right hemisphere is transplanted, for the same reason thatit survives the full-cerebrum transplant: psychological continuity is preserved.For a final case, suppose again that a person P’s cerebrum is separated into its

two hemispheres. But now each hemisphere is removed and implanted into ahead distinct from the one where it came from. Each hemisphere is fullyconnected and comes to function in its respective new skull just as it used tofunction in the old one. As a result of this operation, so I shall assume, there arepersons Lefty and Righty, who are in every way psychologically continuous withP, the person before the operation; Lefty and Righty share memories, personality,and other psychological features with P. This is a case of personal fission.2

1 This case can be traced back to Locke’s example of the prince and the cobbler, in Locke (1690/1975). For a prominent contemporary presentation, see Shoemaker (1963).

2 For standard contemporary sources, see Parfit (1984), Wiggins (1967), and Williams (1956).For the history of personal fission cases, see Martin, Barresi, and Giovanelli (1998).

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What happens to P, the pre-operation person, in this case, given that the pre-operation person survives in the non-branching case, and hence given thatpersonal identity is grounded in psychological continuity? The fission caseunder consideration is symmetrical; Lefty and Righty are psychologically con-tinuous with P to the same degree. The response that either Lefty or Righty isidentical with P is therefore not available, since there is, ex hypothesi, no fact ofthe matter that could select one candidate. This leaves us with four relevantdescriptions of what happens to P.The first description of the outcome of fission is to say that P survives ‘twice

over’ and wakes up in distinct rooms after the operation. The seemingly distinctpost-operation persons are really one and the same person exactly located inwholly distinct places at the same time. As a consequence of the operation, P isspatially separated from herself and able to differ from herself in virtue of beingable to have incompatible weights, shapes, and moods at the same time. All of thissounds unacceptable. Ordinary objects in general, and hence persons, are non-repeatable entities, confined to a single place at a time. In short, the bilocationdescription of fission clashes with the following platitude of common sense, theanti-bilocation principle:

(AB) Necessarily, for any ordinary objects o and o* and any time t, if o and o*occupy distinct places at t, then o is distinct from o*.

I have already addressed this and following principles in previous chapters, andwill say more about them later on. For now, I rest content voicing them.The second description of fission is to say that P was not alone before the

operation. Fission does not divide one person, but rather, separates distinctpersons; distinct persons part ways.3 At pre-operation times, these persons arequalitatively indistinguishable and exactly occupy the same places; they coincideat these times.4 Just as the previous attempt of understanding fission, this oneis incompatible with the folk conception of ordinary objects in general. Aspersons and other ordinary objects are conceived of on the street, two of themcannot fit into the same place at the same time. The coincidence description offission thus clashes with the following platitude of common sense, the anti-coincidence principle, familiar from Chapter 3:

(AC) Necessarily, for any ordinary objects o and o* and any time t, if o and o*coincide at t, then o is identical with o*.

3 See Lewis (1983a), Perry (1972), and Robinson (1985).4 See Section 3.1 for the definition of coincidence in play here.

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According to the third description, P dies in the operation. But how can Psurvive a successful transplant of one hemisphere, yet die when both hemispheresare successfully transplanted? In Derek Parfit’s words, ‘How can a double successbe a failure?’ (1984: 256). The answer urged by best-candidate theories ofpersonal identity is that the persistence of persons is non-local.5 The persistenceof persons is non-local if a person-state x-at-t1 and a person-state y-at-t2 belongto some one person just in case y-at-t2 is the ‘closest continuer’ of x-at-t1, in virtueof exhibiting a higher degree of psychological continuity with x-at-t1 than anyother state at t2.

6 In the simple transplant case, a pre-operation state of P, P-at-t1,has a closest continuer, P*-at-t2. Hence P-at-t1 and P*-at-t2 are states of oneperson; P survives. In the fission case, however, a pre-operation state of P, P-at-t1,has two equally close continuers at the same time, Lefty-at-t2 and Righty-at-t2.Hence P-at-t1 has no closest continuer, and accordingly neither P-at-t1 and Lefty-at-t2 are states of one person, nor P-at-t1 and Righty-at-t2 are states of one person;P dies. This is how a double success can be a failure.The non-locality description of what happens in the fission case has wild

consequences. Suppose that P’s hemispheres are separated and transplanted asbefore. While t1 is a time before the operation, t2 is the time at which the lefthemisphere is fired up in person Lefty in operation room L. Suppose further thattwo minutes later, at t3, the right hemisphere is fired up in person Righty inoperation room R, while in room L at t3 there is a person Lefty*. By the closest-continuer view, Lefty-at-t2 is the closest continuer of P-at-t1, and hence there is aperson with both P-at-t1 and Lefty-at-t2 as states. However, Righty-at-t3 andLefty*-at-t3 are equally close continuers of P-at-t1, and hence there is neither aperson with P-at-t1 and Righty-at-t3 as states, nor is there a person with P-at-t1and Lefty*-at-t3 as states.

7 What this implies in more accessible terms is that pre-operation person P survives and wakes up in room L at t2 but dies two minuteslater as a consequence of the events occurring at t3 in room R. Thus, P goes outof existence by a cause that does not involve P at all; P dies by a purelyextrinsic cause. Immaculate destruction—a strange way of killing a person!

5 See Nozick (1981). I adopt the term ‘locality’ from Eklund (2002: 469).6 A person-state is an instantaneous qualitative cross-section of a person. The notion invoked

here is meant to be less metaphysically loaded than the notion of a K-state introduced in Section 1.2.7 The fact that Lefty*-at-t3 has a psychologically continuous preceding state at t2 but Righty-at-t3

does not, surely bestows no higher degree of psychological continuity with P-at-t1 on Lefty*-at-t3,since t2 and t3 are only two minutes apart. In other words, a short temporal delay in transplantingthe right hemisphere does not break the symmetry and yield a decision concerning whether Psurvives or not. If in doubt, let the degree of psychological continuity between P-at-t1 and Righty-at-t3 be slightly higher than between P-at-t1 and Lefty*-at-t3, in order to compensate for the temporaldelay. Cf. Johnston’s case of the brain-state transfer machine in his work (1987).

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This consequence of the closest-continuer view is unpalatable. The situation, inshort, is that the non-local-persistence description of fission, predicting the deathof pre-fission person P, clashes with the following platitude of common sense, theanti-extrinsicness principle holding for all ordinary objects:

(AE) Necessarily, for any ordinary object o, o does not go out of existence bypurely extrinsic causes.8

The fourth and final description of fission is to say that the outcome is indeter-minate. There is no fact of the matter as to whether there is a single pre-fissionperson who is identical with both fission-products or with none, or whether thereare distinct, coinciding pre-fission persons. In short, it is indeterminate which ofthe reviewed descriptions of the case applies.9 It is thus indeterminate whether aperson can occupy distinct places at the same time. The problem with this claimis that prima facie it still clashes with principle (AB). For if this principle istaken seriously, then it should be read as saying that it is determinately true thata person cannot occupy distinct places at the same time. For analogous reasons, theindeterminacy description seems to conflict with principles (AC) and (AE). All ofthese platitudes of common sense should be understood as assertions of determin-ate impossibilities. Hence, the present move faces more resistance than its com-petitors; it seems to conflict with all featured common-sense principles. Theindeterminacy move fails to escape the threat of conceptual inconsistency, sincewe do not refrain from making a decision in favour of one of these descriptions.Instead, we decide against each of them by holding (AB), (AC), and (AE).Let me add that, on the assumption of a celebrated linguistic theory of

vagueness, the idea that person is vague, which is naturally seen as driving theindeterminacy description of fission, really leads to a very different description offission than the one mentioned above. If vagueness and indeterminacy arelinguistic phenomena, then vagueness may be viewed as a matter of ‘semanticindecision’.10 A vague expression has an imprecise meaning. There are different

8 As my aim in this chapter is largely constructive, I shall refrain from attacking cycles ofmodifications of the best-candidate outlook in response to this type of problem. I am concerned toargue that even if immaculate destruction is an unavoidable consequence of the non-local-persist-ence description of fission, there is a way of saving the latter from clashing with (AE). I shall adopt ananalogous stance on the other proposals reviewed here.

9 See Johnston (1989, 1997). In stating this description, I am not presupposing any particularview of indeterminacy. A linguistic view will be invoked below. Metaphysical views will be addressedin Chapter 7.

10 See Lewis (1986: 212). This linguistic view of vagueness is known as supervaluationism. Fordiscussion and references, see Williamson (1994: chapter 5). More on supervaluationism inChapter 7.

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admissible ways of making this meaning precise, where a precisification isadmissible if it coheres with our ordinary use of the expression, but no factsabout our use of the expression nor any facts about the world pick out a uniqueprecisification in any context. Moreover, a statement containing a vague expres-sion is determinately true if the statement is true on all admissible precisifica-tions of the expression’s meaning, determinately false if it is false on all, andindeterminate if it is true on some but false on other admissible precisifications.In accordance with this characterization, the sortal term person may be con-strued as vague in virtue of having an imprecise meaning with different admis-sible ways of making this meaning precise. This imprecise meaning encapsulatesa criterion of personal identity that has actual non-branching cases as clearcases and counterfactual branching cases as borderline cases. Any precisificationis admissible if and only if it coheres with our ordinary use of person. Sinceprinciples (AB), (AC), and (AE) prima facie are part of our ordinary use ofperson, a precisification of person is admissible only if it coheres with theseprinciples. Now, each precisification of person must make true one or the otherof the reviewed descriptions of the fission case; each precisification must extendour intuitive description of non-branching cases to branching cases. Since eachof these descriptions clashes with (AB), (AC), or (AE), none of these precisifica-tions is admissible. The complete lack of admissible precisifications for person,however, makes the noun semantically defective, yielding the darkest vision ofall, namely, that there are no persons whatsoever.These four attempts of describing what happens to a person undergoing fission

are problematic because they clash with the highly compelling principles (AB),(AC), or (AE). Given that the four descriptions exhaust the logical space ofoptions, assuming a psychological criterion of personal identity over time, itfollows that there is a rift in our conception of persons.11 This is the paradox ofpersonal fission.This type of paradox does not exclusively threaten our conception of persons.

By whichever lines of qualitative continuity and connectedness we typically trackan object of an ordinary kind K through time, if it is nomologically possible forsuch a line to branch out, then there is a paradox of fission for Ks. For in each ofthese cases, we are stuck with descriptions of the outcome of fission that seem toclash with principles (AB), (AC), or (AE).

11 A conception of Ks, as I shall use the term, is, roughly, a set of deeply entrenched and widelyshared beliefs about Ks. I wish to distinguish a conception of Ks from the concept of a K. As willbecome clear in later sections, our conception of Ks may include beliefs about Ks that are in no wayencoded in our concept of a K.

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There is a broad consensus that organisms follow lines of biological continuity.If it is nomologically possible for causal lines of biological continuity to branchout, then a paradox of dividing organisms is waiting in the wings. One often hearsthat the division of amoebae constitutes an actual case of this type of fission.12

Probing into the realm of the counterfactual, one might even construct cases ofbiological fission involving human organisms, cases in which a human bodysplits down the middle, while each resulting half bears to the original body thetype of biological continuity by which we track human organisms in actual, non-branching cases.There is, further, an abundance of cases of dividing artefacts. The ship of

Theseus, as first presented by Hobbes (1839/2004), is a glamorous representative.The ship is made of wooden planks. Suppose that the ship is restored by graduallyreplacing its planks one after the other by new ones until all the original planksare gone; call the result of this process ‘the restored ship’. Suppose further thateach plank that is removed in the process of restoration is collected by anantiquarian. Once sufficiently many planks are accumulated, the antiquarianassembles them into a ship, with the result of a ship that is composed of exactlythe planks Theseus’ ship was composed of; call this result ‘the reassembled ship’.What happens to the ship of Theseus in this case? It seems clear that a ship cansurvive the replacement of a single plank. It seems also clear that a ship can betransported over land by disassembly and subsequent reassembly. Thus, both therestored ship and the reassembled ship have what it takes to be the ship ofTheseus; the line of qualitative continuity by which we typically track a shipthrough time branches out, and paradox ensues. In this case, branching lines ofpersistence threaten our conception of ships. Notice, though, that the case ofships leaves more room to manoeuvre than the case of persons, since the formerinvolves a combination of different persistence conditions of ships, persistence bypart-replacement and persistence by disassembly–reassembly, whereas the caseof persons rests on a single, psychological persistence condition. If there is a wayof discrediting one mode of persistence of ships in favour of the other, then theparadox goes away. One might hold, for example, that the restored ship has abetter claim to be the original ship, since it exhibits a greater degree of spatio-temporal continuity with the ship of Theseus.13 While the case may indeed beasymmetrical, I shall allow it to be symmetrical, and hence to assume its mostdangerous shape, raising a paradox that is analogous to the paradox of personalfission described earlier. This type of metaphysical paradox of symmetrical

12 See Robinson (1985) for a discussion of fission in terms of amoeba division.13 See Wiggins (1967). For another plea for asymmetry, see Lowe (1983).

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fission, in whichever form it may arise, will be discussed in what follows. For easeof exposition, I shall focus on personal fission.14

4.1.2 Incompatibilism about fission

Fission cases are commonly viewed as philosophically significant thought experi-ments, as raising paradoxes with an important lesson. Adopting this stance oftaking fission seriously, I shall allow purely imaginary cases to elucidate ourconcepts, and shall ignore any attempt to weaken the force of fission by ques-tioning the cases’ empirical basis. In the case of personal fission, I shall thusassume that cases of branching lines of psychological continuity are nomologic-ally possible (even if certain ways of telling the story are not), rendering themmaximally disturbing.The apparent conflict in the face of fission between psychological persistence

conditions of persons and principles (AB), (AC), and (AE) is typically thought torequire a choice between rejecting such persistence conditions and rejecting oneor more of the principles. Among those who take the first route, most deny thatpsychological continuity is sufficient for personal identity, pleading for physicalor biological persistence conditions of persons instead. They consequently denythat a person can survive hemisphere-transplant even in the non-branching case,rejecting a description of this case that most of us find unexceptionable. Giventhis initial, costly step, describing the pre-operation person as dying in thebranching case does not render a person’s persistence non-local, and hencedoes not clash with principle (AE).15 Notice that this move may well prove atemporary remedy at best. While those philosophers who bite the bullet andadopt a physical or biological approach to personal identity in place of apsychological one buy themselves out of the predicament created by personalfission, they may well face the paradox in other variants. Can we be sure thatbranching lines of biological continuity are impossible?16

14 Fission cases also raise a range of puzzles about the psychological and moral profile of persons.For Parfit-style issues of what matters, see Parfit (1971, 1984); see also Rovane (1990). I shall setissues of value theory aside, partly for reasons of space and partly for reasons of generality. My aim isto advance a unified solution to metaphysical paradoxes of fission that works for non-personswithout any psychological or moral profile as much as for persons.

15 See, inter alia, Williams (1970), Thomson (1997), and Olson (1997).16 Another way of denying that psychological continuity is sufficient for personal identity is to

take facts of personal persistence as metaphysically primitive. Having thus abandoned all reasonablestandards of explanation, our platitudes of common sense may be respected on the whole bybreaking the fission case’s symmetry and allowing the pre-fission person to go one way ratherthan the other. See Swinburne and Shoemaker (1984).

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It is worth pointing out that some authors hold that person is indeterminatebetween psychological persistence conditions and physical or biological ones, orthat the noun may shift between these conditions depending on the context ofuse.17 This view, to which I am sympathetic, is of little significance for the presentproblem, since the paradox of personal fission arises as soon as psychologicalpersistence conditions are in the picture, and they usually enter the picture inresponse to non-branching cases of cerebrum transplant. That different condi-tions are triggered by other scenarios is irrelevant. Moreover, as noted above, afission paradox probably arises for biological persistence conditions, as well.The second route is to reject (AB), (AC), or (AE) or a combination of these

principles. From this point of view, fission reveals that persons really can bebilocated or really can coincide or really can go out of existence by purelyextrinsic causes or really can perform a combination or even all of these feats.18

This type of approach may be accompanied by a recipe for living with deviancefrom common sense, by a framework within which the intuitively problematicdescription of fission can be shown to be metaphysically harmless. Lewis’s four-dimensionalism is a prominent example of such a framework. As pointed out inSection 3.2, coincidence of distinct ordinary objects at a time is metaphysicallyharmless, because sharing a place at a time is grounded in sharing a commontemporal part at that time, which occupies that place simpliciter. Similarly, beingin two places at a given time may be grounded in having distinct temporal partsthat occupy distinct places at the same time. Finally, going out of existence bypurely extrinsic causes is metaphysically harmless, because nothing really goesout of existence, anyway. Ordinary talk of objects coming into and going out ofexistence is made true by facts concerning which collections of distinct, instant-aneous stages are qualitatively related in which kind-realizing ways.19

Both of these approaches accept that the paradox of fission uncovers an incon-sistency in the common-sense conception of persons—that is, both approachesare incompatibilist. They concede that fission cuts deep, that one or the otherbelief partly constitutive of our conception of persons is defective and requires

17 See, inter alia, Johnston (1989), Rovane (1998), and Sider (2001b).18 For versions of this approach, see Nozick (1981) and Lewis (1983a).19 On this approach of questioning the principles, their denial is viewed as repugnant on the

surface but harmless deep down. One might even question the surface appeal of (AB) by pointing totime-travel cases in which a person, say, travels back in time to meet her younger self, and henceends up bilocated then. This attack on (AB) is weak, however, since it is highly controversial whetherthe mentioned time-travel scenarios involving ordinary objects are correctly described as yieldingbilocation. Indeed, part of the puzzlement about time travel may be attributed to the prima facieappeal of (AB). Some authors even hold that given the ordinary notion of location, multilocation,and hence bilocation, is conceptually incoherent; see Hofweber and Velleman (2010).

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revision. Incompatibilists aboutfission face a simpleMooreanworry, familiar fromthe discussion of coincidence paradoxes in Chapter 3. The Mooreans among usshare the conviction that our basic ordinary beliefs and intuitions, though onlydefeasibly justified, possess a plausibility that motivates a sceptical attitude towardsany philosophical considerations to the contrary (cf. Section 2.3). This attitudetowards the common-sense conception of persons should make us reluctant toreject either psychological persistence conditions of persons or to reject any of thevarious platitudes concerning ordinary objects in general. Any plausible way ofpreserving both psychological persistence conditions and the principles is thus tobe taken very seriously.20 In what follows, I shall discuss two compatibilistapproaches to fission.21

4.1.3 The stage view and fission

Friends of the stage view of ordinary objects and of the associated temporalversion of counterpart theory have attempted a compatibilist dissolution offission paradoxes.22 The stage view construes ordinary objects as instantaneousstages. Stages stand in temporal counterpart-relations to other stages (and tothemselves). For example, two stages stand in the temporal counterpart-relationfor persons just in case the stages are psychologically similar and their psycho-logical profiles are linked by lawful causal dependence. Given stages and temporalcounterpart-relations between them, metaphysical truth conditions of monadictemporal predications may be specified as follows: for any ordinary object o, andany time t, o exists at t iff o has a temporal counterpart at t; and o is F at t iff o hasa temporal counterpart at t that is F.23 Moreover, all ordinary predications ofidentity and distinctness are predications of absolute identity and distinctness.

20 For a view, according to which we should learn to live with conceptual inconsistency, seeEklund (2002).

21 Incompatibilists also face a problem of reasonableness, distinct from the Moorean problem ofsaving the truth of the common-sense conception (see Section 2.3). I shall address this secondproblem in Section 4.2.

22 See Hawley (2001) and Sider (2001a).23 Note that stages typically stand in different temporal counterpart-relations to other stages,

such as the temporal counterpart-relation for persons, which is a complex relation of psychologicalsimilarity and causal dependence, and the temporal counterpart relation for organisms, which is acomplex relation of biological similarity and causal dependence. Accordingly, whether o exists at tand whether o is F at t depends on how o is conceived of. It may be the case that when o is conceivedof as a person, then o exists at a time t, but when o is conceived of as an organism, then o does notexist at t. In this sense, temporal predication is sortal-relative. Cf. Lewis (1986: section 4.5); see alsoSection 2.2. As the paradox of fission arises for objects of a single kind, this sortal relativity need notconcern us here.

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Correspondingly, counting persons is counting stages by absolute identity anddistinctness.24

How does the stage view handle fission? The metaphysical basis of fission,according to the stage view, includes stage a uniquely located in place p1 at pre-fission time t1, stage b uniquely located in place p2 at post-fission time t2, andstage c uniquely located in a third place p3 at t2, such that a and b as well as a andc, but not b and c are related by the temporal counterpart-relation for persons.The stage view offers the following description of this case at the level of persons.Assuming that a, b, and c are persons, at t1 there is exactly one, uniquely locatedperson, a. This person persists along local lines of psychological continuity andconnectedness in virtue of having both b and c as temporal counterparts. And yetat t2 there are exactly two, uniquely located persons, b and c.

25 This description offission is compatible with the platitudes of common sense, (AB), (AC), and (AE):since there are two persons after fission, bilocation is avoided; since there is oneperson before fission, coincidence of distinct objects is avoided; and since personsfollow local lines of psychological continuity and connectedness, non-local per-sistence is avoided.There are two significant problems with this proposal. First, the stage view’s

compatibilist attempt remains silent on the genuinely cross-temporal paradox offission. Consider the natural and familiar question of how many persons areinvolved in the process of double-hemisphere transplant. When we ask thisquestion, we adopt a cross-temporal attitude towards the case; we request acount of persons across time, not merely a count of persons at a particulartime. In response to the cross-temporal question, only four sensible answerspresent themselves: one person is involved; two persons are involved; threepersons are involved; or it is indeterminate whether one, two, or three personsare involved. If one person is involved, then there is bilocation after fission, whichcontradicts (AB); if two persons are involved, then there is coincidence beforefission, which contradicts (AC); and if three persons are involved, then persist-ence is non-local (assuming a psychological view of personal persistence), whichcontradicts (AE). Since the stage view’s description of fission given above merelyoffers counts of persons at particular times, the stage view has still to address thegenuinely cross-temporal paradox of fission.Second, once the stage view does address this version of the paradox, it clashes

violently with common sense. Start with a simple case. We want to be able to say

24 The stage view as stated here is Sider’s; see his (1996, 2001a: section 5.8). Hawley’s version(2001: section 5.7) is similar.

25 See Sider (1996, 2001a: 201).

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that there is a single cup on the table over a period of time T. Notice that theintended meaning of this assertion is not that at each instant in T, there is asingle cup on the table, but rather that there is a single cup, such that it is on thetable throughout T. Assuming that cups are instantaneous stages and that we areforced to count by absolute identity and distinctness, there are indefinitely manycups on the table over the course of T, as opposed to one. Likewise, there areindefinitely many persons involved throughout the process of hemisphere trans-plant, while the only sensible counts are one, two, or three persons. This result is afar cry from saving the appearances.A word on two possible replies. First, counting persons across time by psy-

chological continuity plus connectedness instead of strict identity, as suggestedby Hawley (2001: Section 5.7), is out of the question. For counting across timerequires an equivalence relation, as all counting does, whereas psychologicalcontinuity plus connectedness is not an equivalence relation, since it is intransi-tive. Second, Sider’s ambiguity-strategy of allowing sortals, such as person, incross-temporal contexts to apply to spacetime worms as opposed to stages (seeSider 1996), leaves the genuinely cross-temporal paradox of fission without acompatibilist solution. For then either (AB), (AC), or (AE) must be rejected.26

Combining the two objections, the problem with the stage view’s allegedcompatibilism is that it only succeeds as long as the natural cross-temporalangle on fission is ignored. Compatibilism is not to be had for cheap. Fortunately,we can do better.27

4.2 Compatibilism about Fission

In this section, I shall propose a solution to the paradox, which avoids thebreakdown of our conception of persons in the face of fission. What I shall offeris a dissolution of the apparent conflict between our four alternative descriptions ofthe outcome of fission and principles (AB), (AC), and (AE): properly understood,there is no conflict; the descriptions and the principles are compatible. What holdsfor our conception of persons holds for our conceptions of organisms and of

26 For more discussion of cross-temporal counting, see Sider (1996) and Sattig (2006).27 Another compatibilist approach to fission is premised on admitting identity to be temporary;

see Gallois (2003). The idea is to reconcile the intuition that there is one pre-fission person, at t1,with the intuition that there are two post-fission persons, at t2, by saying that Lefty is distinct fromRighty at t2 and that Lefty is identical with Righty at t1. This view of identity and the associatedposition that in fission one person becomes two persons are highly counterintuitive, and to beconsidered a last-ditch attempt. In the following section, I will show that no such radical measuresare required.

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artefacts. The strategy I shall propose for dissolving one fission paradox willdissolve them all.The perspectival-hylomorphist picture to be defended looks roughly as

follows. Metaphysically, persons, as well as other ordinary objects, are double-layered compounds. The different layers permit different perspectives on per-sons, from which we are able to describe them in different ways. The variousdescriptions of the outcome of personal fission manifest the sortal-sensitiveperspective, privileging psychological properties that realize the kind person.The principles, by contrast, manifest the sortal-abstract perspective, privilegingspatiotemporal properties shared by all ordinary objects. The descriptions andthe principles, manifesting different perspectives, are compatible because they aremade true or false by different metaphysical components of persons. The mysteryof personal fission dissolves once we realize that persons lead double lives.What holds for the fission of persons, holds for the fission of other kinds of

object. By whichever lines of qualitative continuity we typically track an object ofkind K through time, if it is possible for such a line to branch out, then there is aparadox of fission for Ks. To those who attempt settlement of a fission paradoxfor Ks by rejecting a particular criterion of identity of Ks, the prospects of aunified treatment of all fission cases look poor. Different remedies are likely to berequired for different cases. The proposed solution of the paradox of personalfission is more powerful in this respect: it straightforwardly extends to allpotential cases of fission. Any expected clash of the space of possible accountsof K-fission with various platitudes of common sense about Ks is merely appar-ent, since the accounts as plausibly interpreted in a K-sensitive way are compat-ible with the platitudes as plausibly interpreted in a K-abstract way.

4.2.1 Fission from different perspectives

On to the details. We encountered four alternative descriptions of symmetricpersonal fission: bilocation (B), coincidence (C), non-local, or extrinsic, persist-ence (E), and indeterminate persistence (I). These descriptions of fission seem tostand in conflict with principles (AB), (AC), and (AE), which conflict wouldrequire a choice between rejecting one or more of the descriptions or rejectingone or more of the principles. This paradox of personal fission will be dissolved intwo steps. First, I will interpret the various descriptions of personal fission as wellas the various principles within the framework of perspectival hylomorphism.Second, I will show that the descriptions and the principles thus construed arecompatible.To begin with, descriptions (B), (C), (E), and (I) are plausibly construed as

manifesting the sortal-sensitive perspective on the world. Each description is

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specifically about the behaviour of persons undergoing fission, presupposing thatour ordinary concept of a person encodes psychological persistence conditions ofsome form or other. Assuming that ordinary thought and talk may be sortal-sensitive in the way characterized in Chapter 2, (B), (C), (E), and (I) should beread as employing the formal mode of predication:

(Bform) P is formally identical with both Lefty and Righty. Hence, P formallyoccupies distinct places after fission.

(Cform) There are pre-fission persons P and P*, such that P is formallydistinct from P*, P is formally identical with Lefty, P* is formally identicalwith Righty, and P formally coincides with P* before fission.

(Eform) P formally goes out of existence in the operation, since Lefty andRighty are equally good candidates for being formally identical with P. Theformal persistence of P is non-local.

(Iform) It is indeterminate whether (Bform), (Cform), or (Eform) applies to thefission case.

Our acceptance of principles (AB), (AC), and (AE) is the reason why we findcases of fission so puzzling. No description of fission seems compatible with allof them. What is the status of these principles? My hypothesis is that they aresortal-abstract principles. They are about ordinary objects, including persons.What they say about ordinary objects, however, abstracts from specific K-realizing attributes, for any K. In particular, the principles do not seem toderive from any of the psychological, biological, or social ways in which wethink about persons. The impressions that ordinary objects cannot bilocate,that distinct ordinary objects cannot coincide, and that one cannot destroy anordinary object without exerting any causal influence on it, seem entirelyindependent of the specific qualitative features that make an object a person.We have a minimal conception of the behaviour of an object in space and time,which is independent of representing the object as belonging to a particularkind. This conception embraces and unifies the rich and varied realm ofordinary objects. The principles partly constitute this conception. WhileI find the construal of the principles as sortal-abstract intuitively compelling,further support is available.As pointed out in Section 2.1, psychological research on object representation

suggests that young infants represent objects by spatiotemporal criteria prior torepresenting objects as belonging to particular kinds. Among Spelke’s spatiotem-poral criteria of dividing surface layouts into objects are the principle of cohesion,according to which two surfaces belong to distinct objects when they are

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separated by a spatial gap; the principle of boundedness, according to whichdistinct objects have no surface point in common; and the principle of no actionat a distance, according to which objects are expected to act on each other only oncontact. Given the view—which is orthodoxy in psychology—that these prin-ciples are not abandoned in the development of object representation, and hencecontinue to operate in some way or other in the adult scheme, it is overwhelm-ingly plausible that the common-sense principles (AB), (AC), and (AE) havetheir source in the principles of cohesion, boundedness, and no action at adistance, respectively. (See Section 2.1 for a more detailed account of this link.)Given that the underlying criteria of object representation are sortal-abstract,(AB), (AC), and (AE) should be construed as sortal-abstract, as well. Their statusas sortal-abstract principles is captured in the framework of perspectival hylo-morphism by reading them as employing the material mode of predication:

(ABmat) Necessarily, for any ordinary objects o and o* and any time t, if o ando* materially occupy distinct places at t, then o is materially distinct from o*.

(ACmat) Necessarily, for any ordinary objects o and o* and any time t, if o ando* materially coincide at t, then o is materially identical with o*.

(AEmat) Necessarily, for any ordinary object o, o does not materially go out ofexistence by purely extrinsic causes.

I will now show that perspectival hylomorphism is able to save the common-sense conception of persons in the face of fission. First, I will specify a consistentmaterial basis of fission that makes true principles (ABmat), (ACmat), and (AEmat).Then, on the assumption of this material basis, I will specify alternative concep-tual bases of fission that make true descriptions (Bform), (Cform), (Eform), and(Iform), respectively.

4.2.2 The material basis of fission

According to the metaphysical account of material objects specified inSection 1.2, material objects are mereologically individuated: a material objectgoes where its parts go, and its parts go where it goes. Mereological extensionalityentails that the persistence conditions of material objects are local and non-psychological. In addition, let us make the metaphysical assumptions, consistentwith extensionality and universalism, that a material object cannot absolutelyoccupy distinct places at any time, and that absolutely distinct material objectscannot absolutely occupy the same place at the same time. (Henceforth, allproperty ascriptions to material objects are to be understood as absolute ascrip-tions.) In the framework of perspectival hylomorphism, as developed in Chapters

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1 and 2, these assumptions about material objects entail principles (ABmat),(ACmat), and (AEmat).Suppose now that in a case of personal fission there is a material object a that

exists at a time t1, before fission, that a uniquely and exclusively occupies a placep1 at t1, that a is in person-state s1 at t1, and that this person-state includes the factthat a occupies p1 at t1. Suppose further that there is a material object b that existsat time t2, after fission, that b uniquely and exclusively occupies place p2 at t2, thatb is in person-state s2 at t2, and that this person-state includes the fact that boccupies p2 at t2. Suppose, finally, that there is a material object c that also existsat t2, that c uniquely and exclusively occupies place p3, distinct from p2, at t2, thatc is in person-state s3 at t2, and that this person-state includes the fact that coccupies p3 at t2. Both b and c are related by psychological continuity, psycho-logical connectedness, and causal dependence—in short, by the psychologicalR-relation—to a. But this R-relation is neither necessary nor sufficient fordiachronic identity; no material object persists by following causal lines ofpsychological continuity and connectedness. Material objects a, b, and c, soI shall assume, are absolutely distinct. I shall refer to this specification as thematerial basis of fission, which may be illustrated by Figure 4.1, where the linesconnecting a, b, and c represent the psychological R-relation.

4.2.3 Bilocation

Let us next specify a conceptual basis of fission. The material basis of fissiondelivers a range of candidates for personhood. Each candidate is a compound ofa person-path and a material subject of this person-path. The availability of acandidate is a metaphysical matter. The choice of candidate for personhood is aconceptual matter. This choice depends on which class of person-paths the sortalperson selects. The meaning of person determines a unity criterion of person-paths in terms of the psychological R-relation: roughly, a person-path is amaximal series of R-interrelated person-states. For the purpose of describing

t

x

t1

b

a

ct2

Figure 4.1 The material basis of fission

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what happens to a person when causal lines of psychological continuity andconnectedness branch out, this proto-criterion may be clarified in at least threedifferent ways. Each of these clarifications yields a different outcome of fissionfrom the sortal-sensitive perspective, since formal truths about persons aredependent on the meaning of the sortal person. The first clarification is (P1):

(P1) A person-path is a maximal series of person-states, such that each statein the series is R-related with some other state in the series.

Different unity criteria of person-paths correspond to different ways of concep-tually carving up the Y-shaped material basis of fission. Assuming (P1), we maysuppose that person-path i includes the person-states s1, s2, and s3. Thus, a, b, andc are subjects of the same person-path, as illustrated by Figure 4.2.Given q-hylomorphism about ordinary objects, there is a person P1, a person

P2, and a person P3, such that P1 is �c(a, i), P2 is �c(b, i), and P3 is �c(c, i). By thesemantics of formal predication, these specifications make (Bform) true. While P1,P2, and P3 are absolutely distinct, they are formally identical. Moreover, P1 existsformally at t1, before fission, formally survives fission, and formally occupiesplaces p2 and p3 at t2, after fission. Likewise for P2 and P3, since they are formallyidentical with P1. Hence, both the sortal-sensitive (Bform) and the sortal-abstractanti-bilocation principle (ABmat) are true, since the truth of (Bform) rests on amaterial basis of fission that was designed to preserve (ABmat).The way for bilocation by fission is almost clear. If a person formally survives

twice over, then the same person may have incompatible properties, such ashappiness and sadness, at the same time, which should not be possible if the taskis to sustain the common-sense conception of persons. In order to remove theappearance of contradiction, our ordinary tools of temporal predication may befurther extended. Very roughly, the first step might be to require ordinarytemporal predications to be relativized not only to times, but to pairs of places

t

x

i

b

a

ct2

t1

Figure 4.2 Bilocation

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and times—place-times—yielding predications of the form ‘o is formally F at<p, t>’. The second step would then be to specify truth conditions of formalpredications modified by place-times: o is formally F at <p, t> iff there is a kindK and a K-path i, such that o has i as a part, and i includes the fact that a is F at tand that a occupies place p at t, for some material object a. The threat ofinconsistency is banned, if after fission our person is formally happy in oneplace-time and formally sad in another. In short, if there is no material bilocation,then there is no serious obstacle to extending our linguistic practices of formaltemporal predication to formal spatiotemporal predication in light of extraord-inary cases of fission.The anti-bilocation principle is one intuitively compelling principle against

spatially discontinuous paths of objects that is preserved in the present frame-work. The latter is also able to capture another intuition concerning spatialdiscontinuity, namely, that an ordinary object cannot materially ‘jump’ betweenspatially distant places in very short temporal intervals. That is, q-hylomorphismabout ordinary objects, which rests on an ontology of material objects as mer-eologically individuated, does not make this platitude false. It must be admitted,however, that the fit between intuitions about spatial discontinuity and theproposed account of ordinary objects is not perfect. For it also seems compellingthat no ordinary object is composed of spatially unconnected parts at any time ofits life. If this is read as a principle in the material mode, as it should be, then it isfalse, because material objects, according to the classical-mereological account,may survive radical scattering.I submit that this is a small price to pay. In Section 2.3, I emphasized that while

we are prima facie entitled to our basic modal beliefs and intuitions, the latter areonly defeasibly justified. Owing to their generality, it is no surprise that thesortal-abstract principles of folk metaphysics cannot be captured in their entir-ety. On the other hand, it is not to be expected that our sortal-sensitive beliefsand intuitions about particular objects, which arise from our basic sources ofinformation, are to be defeated so easily. So, the fact that the present frameworkfails to honour one or the other belief in the sortal-abstract camp is not the endof the world, considering that a complete match with the highly general sortal-abstract conception is a tall order, anyway, and considering the framework’sperformance in capturing our specific sortal-sensitive beliefs about objects, andin ensuring the consistency between our sortal-sensitive and our sortal-abstractbeliefs—that is, in ensuring the internal consistency of the common-senseconception of objects. Saving the appearances is not an all-or-nothing affair.It is a matter of degree.

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4.2.4 Coincidence

We saw that the outcome of fission at the level of persons depends on which unitycriterion of person-paths is in play. Consider the following alternative to (P1):

(P2) A person-path is a maximal series of person-states, such that each statein the series is R-related with every other state in the series.

This unity criterion, just as (P1), corresponds to a certain way of conceptuallycarving up the Y-shaped material basis of fission. Since the R-relation is intransi-tive, failing to hold between the post-fission states s2 and s3, there is, by (P2), noperson-path i that includes both states s2 and s3. We may suppose, however, thatthere are two person-paths, i1 and i2, such that i1 includes s1 and s2, while i1 doesnot contain the property of occupying p3 at t2, and i2 includes s1 and s3, while i2does not contain the property of occupying p2 at t2. Thus, a and b are subjects ofperson-path i1, and a and c are subjects of person-path i2, as illustrated byFigure 4.3.Then there is a person P, a person Lefty, a person P*, and a person Righty, such

that P is �c(a, i1), Lefty is �c(b, i1), P* is �c(a, i2), and Righty is �c(c, i2). By thesemantics of formal predication, these specifications make (Cform) true. P isformally identical with Lefty; and P* is formally identical with Righty, whileP/Lefty and P*/Righty are formally distinct. P/Lefty exists formally at t1, beforefission, at which time it formally occupies place p1, formally survives fission, andformally occupies place p2 at t2, after fission. P*/Righty exists formally at t1, atwhich time it also formally occupies place p1, formally survives fission, andformally occupies place p3 at t2. This model of sortal-sensitive (Cform) establishesthe compatibility of (Cform) with the sortal-abstract anti-coincidence principle(ACmat), since the model is built on a material basis of fission that was designedto preserve (ACmat).

t

x

i2

b

a

c

t1

t2

i1

Figure 4.3 Coincidence

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4.2.5 Non-local persistence

In order to defend a third description of personal fission, consider the followingunity criterion of person-paths:

(P3) A person-path is a maximal series of person-states, such that each statein the series is R-related to a sufficient degree with every other state in the series,and no state s in the series has a simultaneous competitor state that is R-relatedwith any other state in the series to the same or a higher degree than s.28

This unity criterion of person-paths, just as (P1) and (P2), corresponds to acertain way of conceptually carving up the Y-shaped material basis of fission.Since by (P3) no person-path includes person-states with strong simultaneouscompetitors, there is no person-path with both a and b as subjects, nor is thereone with both a and c as subjects. We may suppose, however, that there areperson-paths i1, i2, and i3, such that i1 includes s1, i2 includes s2, and i3 includes s3.Thus, a is a subject of i1, b is a subject of i2, and c is a subject of i3, as illustrated byFigure 4.4.Then there is a person P, a person Lefty, and a person Righty, such that P is

�c(a, i1), Lefty is �c(b, i2), and Righty is �c(c, i3). By the semantics of formalpredication, these specifications make (Eform) true. P is formally distinct fromboth Lefty and Righty. Thus, P formally goes out of existence in the operation.That is so because Lefty and Righty are equally good candidates for the formalcontinuation of P. The formal persistence of P is non-local. This model of sortal-sensitive (Eform) establishes the compatibility of (Eform) with the sortal-abstract

t

x

i3b

a

ct2

t1i1

i2

Figure 4.4 Non-local persistence

28 Degrees of R-relatedness are degrees of psychological continuity and connectedness.

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anti-extrinsicness principle (AEmat), since the model rests on a material basis offission that was designed to preserve (AEmat).Owing to the non-locality of the formal persistence of persons, the present

description of the branching case is consistent with the following description ofthe non-branching case. Consider distinct material objects a and b, such that aexists at pre-operation time t1, b exists at post-operation time t2, and a-at-t1 isR-related to b-at-t2, while there is no competitor state of b-at-t2 that is alsoR-related with a-at-t1. (P3) now allows there to be a person-path i, such that iincludes a-at-t1 and b-at-t2. There are further a person P, the compound �c(a, i)and a person P*, the compound �c(b, i), which are formally identical. Allowingthe original person formally to die in the double-hemisphere transplant is thuscompatible with allowing the original person formally to survive in the single-hemisphere transplant, although the mental life flows on in both cases.

4.2.6 Indeterminate persistence

Where are we now? If predication is perspectival, then several descriptions ofpersonal fission are consistent. The consistency of each of the alternatives isgrounded in the account of persons as double-layered compounds of materialobjects and person-paths—of matter and form. The key is the relationshipbetween the components: the qualitative profiles of person-paths may divergefrom the profiles of their material subjects. This is why our judgements aboutpersons may vary depending on perspective. Choosing among the consistentalternatives, on the other hand, is a matter of semantics. Given that the ontologyof ordinary objects permits an abundance of compounds, different classes ofcompounds are available as candidate extensions of the sortal person. No singlecriterion of personal identity carves nature at the joints. The question then iswhether our ordinary concept of a person is rich enough to select one specificunity-criterion of person-paths from the list of (P1), (P2), and (P3) as criterion ofpersonal identity, and hence to trigger one particular description of fission.Perhaps further conceptual considerations may be adduced to single out one ofthe alternatives as the best (more on this issue below).29 In the absence of suchconsiderations, on pain of arbitrariness, a fourth option may prove most suitable:the outcome of fission is indeterminate; as (Iform) states, there is no fact of thematter concerning whether (Bform), (Cform), or (Eform) applies.Prima facie, the indeterminacy picture is hopeless, since it seems to conflict

with the anti-bilocation, the anti-coincidence, and the anti-extrinsicness

29 In the case of personal fission, psychological and moral considerations may come into play atthis point; see n.14.

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principles, all of which are to be understood as determinately true: it is notindeterminate which description applies; it is determinate that none does (seeSection 4.1.1). As we saw, however, the sortal-sensitive principles (Bform), (Cform),and (Eform) are compatible with the sortal-abstract principles (ABmat), (ACmat),and (AEmat). Accordingly, the prospects for the indeterminacy description aregood, if it is interpreted as sortal-sensitive indeterminacy, as indeterminacyregarding what formally happens to a person when causal lines of psychologicalcontinuity and connectedness branch out.Such conceptual indeterminacy may be sustained by supervaluationism. The

sortal noun person is vague in virtue of having an imprecise meaning withdifferent admissible ways of making this meaning precise. This imprecise mean-ing encodes a criterion of personal identity that has actual non-branching cases asclear cases and counterfactual branching cases as borderline cases. The differentprecisifications of the meaning of the sortal person correspond to unity criteria(P1), (P2), and (P3), respectively. These different criteria put different persons,different compounds of material objects and person-paths, into the extension ofthe sortal. Taking the sortal-sensitive perspective on fission, the number of personsinvolved in fission and the outcome of fission vary relative to which criterion is inplay. As I showed in detail, on (P1), there is a single person involved, and thisperson is bilocated after fission; on (P2), there are two persons involved, andthese persons coincide before fission; and on (P3), there are three personsinvolved, where the pre-fission person dies in the operation and is succeededby distinct persons. What makes each of (P1), (P2), and (P3) constitute admis-sible precisifications of person is that each criterion yields the intuitively correctaccount of what happens to persons in non-branching cases.30 If the sortal personis vague in the way specified, then the outcome of fission is indeterminatebetween (Bform), (Cform), and (Eform).

4.2.7 Summing up

Having demonstrated the compatibility of descriptions (Bform), (Cform), (Eform),and (Iform) of fission with principles (ABmat), (ACmat), and (AEmat), it must beemphasized that this compatibility rests on the possibility of perspectival diver-gence. The descriptions are compatible with the principles because a person’sform may contain properties that a person’s matter may fail to instantiate. Eachformal description of fission is metaphysically shallow, in virtue of being built on

30 Notice that since principles (ABmat), (ACmat), and (AEmat) are sortal-abstract principles, in noway do they shape our ordinary concept of a person, and hence do not qualify as constraints onwhich precisifications of person are admissible.

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facts that neither involve bilocation, distinct coincidents or non-local persistence.The different descriptions are made true by facts about person-paths withdifferent unity criteria. Different unity criteria select paths with different spatio-temporal profiles. But these profiles may fail to be isomorphic to the spatiotem-poral profiles of material objects, the subjects of person-paths. For a K-path neednot mirror the path of a material object. The exotic behaviour of dividingpersons, then, does not run deep; in a sense, the different descriptions of theoutcome of personal fission are mere ‘conceptual projections’.In addition to alleviating worries about metaphysically radical commitments,

this compatibilist approach to fission paradoxes succeeds where traditionalapproaches fail, namely, in alleviating Moorean worries about saving the appear-ances. Given that our common-sense conception of persons is prima facie moreplausible than any philosophical reasons to the contrary, it is hard to let go eitherpsychological persistence conditions of persons (at least in some contexts), whichdrive the various descriptions of the outcome of fission, or the various platitud-inous principles, because both psychological persistence conditions and theprinciples are part and parcel of the common-sense conception of persons.The perspectivalist compatibilist offers a way of preserving both the persistenceconditions and the principles. This is a massive advantage of the proposed viewover its rivals.Finally, the perspectival-hylomorphist approach to fission paradoxes is motiv-

ated by considerations of reasonableness, which are independent of Mooreanconsiderations of correctness. Recall that the problem of reasonableness aboutcoincidence was to explain why non-philosophers find it reasonable to acceptboth that objects of specific kinds may be distinct and located in the same place atthe same time, while also holding that in general no distinct ordinary objects canbe located in the same place at the same time. This is a hard problem, andI argued in Chapter 3 that perspectivalism provides the best explanation. In thecase of fission, one might find it less clear that a serious problem of reasonable-ness arises. For one might point out that ordinary thinkers are perfectly reason-able in accepting psychological persistence conditions of persons, while at thesame time accepting the various spatiotemporal platitudes of common sense, onthe grounds that the sortal concept at their disposal, namely, the concept of aperson, actually only applies to non-branching cases.While branching cases may well fall outside ordinary sortal concepts’ original

sphere of application, it follows by no means that any attempt of extending theseconcepts to such cases is a purely philosophical exercise. As noted in Section 2.3,the principle of charity applies as much to what ordinary speakers would say,‘with their eyes wide open’, as to what they actually say. And it seems clear that

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once branching cases are in plain view, ordinary speakers will adopt one of thementioned descriptions of them—witness the massive occurrence of branchingscenarios in science fiction—while continuing to be drawn towards the variousplatitudes of common sense, given that the latter are sortal-abstract principles,belief in which is formed independently of considering any specific instances. Inlight of all this, there is a problem of reasonabless about fission after all. Andanalogously to the case of coincidence, perspectivalism offers the most plausibleexplanation of reasonabless in the face of apparent conceptual tension, namely,that different perspectives on the same objects are involved (see Section 3.3 fordetails on this type of explanation).

4.3 Paradoxes of Intermittent Existence

Locke famously stated that no object can have more than one temporal begin-ning, that an object cannot cease to exist and later come back into existence.31

This rejection of intermittent existence of objects, of objects with temporallydiscontinuous, or gappy, paths is another platitude of common sense. Let usformulate it as the following anti-intermittence principle:

(AI) Necessarily, for any ordinary object o, o cannot go out of existence atone time and come back into existence at a different time.

This principle seems to have a number of compelling counterexamples, givingrise to various paradoxes of intermittent existence. I shall mention three cases.Notice, preliminarily, that intermittent existence and fission are not cases of thesame type of discontinuity. Fission concerns spatial discontinuity, whereas inter-mittent existence concerns temporal discontinuity. Suppose, first, that a watch isdisassembled at time t1 and then reassembled at a later time t2. The intuitivelycorrect description of this case is that the reassembled watch is numericallyidentical with the watch before disassembly. Among the considerations drivingthis identity claim are that the reassembled watch is nearly qualitatively indis-cernible from the original watch, and that the watch-parts of the reassembledwatch are the very same parts arranged in the very same way as the parts of theoriginal watch. What happens to the watch between times t1 and t2? Does itsurvive the process of disassembly and subsequent reassembly or does it go out ofexistence for a period of time, before coming back into existence?In order to answer this question from the point of view of common sense, let

me draw attention to two pillars of the common-sense conception of objects (see

31 See Locke (1690/1975).

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Section 1.2.2). While ordinary objects can vary in many of their properties overtime and across possible worlds, there are ordinary kinds with respect to whichthey cannot vary in any way. These kinds are strictly invariant. As it is often put,the ordinary world is partly individuated by these kinds; with their help the worldis parsed into objects. The doctrine that certain ordinary kinds are invariant tothe objects falling under them is part and parcel of the common-sense conceptionof objects. Being a watch, for example, is commonly regarded as an invariantproperty of its instances. It seems obvious that whatever properties make an objecta watch, we bring a watch into existence by causing these properties to beinstantiated, and a watch cannot lose these properties without going out ofexistence. Another pillar of the common-sense conception of objects is the doctrinethat there is an informative answer to the question what it is to be a watch, to thequestion what determines membership in the class of watches. It seems, in otherwords, to be constitutive of the folk conception of Ks, where K is some ordinarykind, that an object is a K at a time in virtue of instantiating a range ofK-determining attributes at that time. Let us say, for simplicity, that being a K ispartly determined by being K-shaped, whatever exactly being K-shaped involves:for any object o, any ordinary kind K, and any time t, if o is a K at t, then o isK-shaped at t. As an instance of this sortal-determination principle, something is awatch only if it is watch-shaped at all times at which it exists. Beingmade ofmetal isnot what makes an object a watch, but being watch-shaped partly is. Returningnow to the case of the disassembled and subsequently reassembled watch, thesetwo doctrines have the consequence that the watch must be described as going outof existence between t1 and t2. For if the watch survived, it would be either not awatch after t1, before becoming a watch again at t2, or it would be a watch that failsto be watch-shaped between t1 and t2. The first option is ruled out by the doctrineof sortal invariance; the second option is ruled out by the doctrine of sortaldetermination. The result is a counterexample to (AI).32

Another case involves more than a single kind of object. Suppose that aboatshed made of wooden planks is dismantled. The planks are then used tomake a boat. The boat is later dismantled, and the wooden planks are reassem-bled in the same order to form a shed again. The official description of this real-life case is that the original shed is numerically identical with the reassembledshed.33 Moreover, by recourse to the common-sense doctrines of sortal

32 Compare the ship of Theseus and the hemisphere transplants of Section 4.1. These cases turnout to involve intermittent existence, as well. I ignored this aspect earlier when the focus was onbranching.

33 This is a rough description of Simon Starling’s conceptual installation ‘Shedboatshed (MobileArchitecture No 2)’. This sort of case is also described in Burke (1980: 391).

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invariance and sortal determination, this shed goes out of existence upon dis-assembly, is replaced by an object of a different kind, namely, a boat, and latercomes back into existence upon reassembly. The shed thus possesses a gappytemporal trajectory.Cases of objects seemingly undergoing intermittent existence are not confined

to artefacts. Scientists at the Safar Centre for Resuscitation Research at theUniversity of Pittsburgh announced recently that they had managed to bringclinically dead dogs back to life using a suspended animation technique. The deaddogs’ veins were emptied of all blood and then refilled with ice-cold salinesolution to preserve the tissues and organs. The saline solution was subsequentlyreplaced with fresh blood, and the dogs’ hearts were restarted by means of electricshocks. As the heart pumped the blood around the frozen body, the dogs cameback to life. According to the scientists involved, the dogs appeared to be unharmedby their suspension and had suffered no brain damage.34 On the compellingassumptions that no dog can cease to be a dog without going out of existence,and that part of what constitutes being a dog (as the sortal is used in certaincontexts) is being clinically alive, this is another case of intermittent existence.Published responses to these paradoxes are incompatibilist, viewing the clash

between the various cases and the anti-intermittence principle as uncovering agenuine tension in the common-sense conception of objects. Accordingly, resolv-ing the tension is thought to require a choice between denying the plausibility ofthe cases and rejecting the principle. Among those who take the first route, thereseems to be a tendency to accept that an ordinary object may exist whiledisassembled.35 Some authors are driven to this conclusion purely by their desireto honour the anti-intermittence principle. Others are moved by the acceptabilityof saying that the watch is on the table, although the table presents only ascattered collection of watch parts.36 Speaking this way is acceptable, I reply,because speaking this way is speaking non-literally. Suppose someone points tothe collection of disassembled parts of the watch on the table and asks, ‘Is thisreally a watch, given that it is not even shaped like a watch?’ Someone who waspreviously willing to describe the collection of watch-parts as a watch is likely toretract her description under this sort of pressure, which indicates that she wasspeaking loosely.37 Such non-literal talk is particularly suited when the parts areintended to be reassembled, as in the case of the watch, or when the parts are even

34 This description appeared in <www.news-medical.net>. For background, see Safar et al.(1996).

35 See Burke (1980: 392–3) for references.36 Cf. Hawthorne (2006: 53). 37 Cf. Korman (2010: 137).

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www.news-medical.net

designed to be disassembled and reassembled regularly for reasons of storage ortransport, as in the case of musical instruments such as flutes or trombones.Speaking strictly, then, the watch is to be described as going out of existence upondisassembly.38

Followers of the second incompatibilist route, of rejecting the anti-intermit-tence principle, must concede that the folk conception of objects is prima facieinternally inconsistent. They may, however, argue that while there is a conceptualproblem about intermittent existence, there is at least no metaphysical problem,because temporally gappy objects are metaphysically harmless (cf. Section 3.2).What seems mysterious on the surface is quite innocuous at the bottom. Thenow-standard strategy of explaining away intermittent existence is premised onfour-dimensionalism, according to which ordinary objects have temporal partsthat are not recognized by the common-sense conception. The explanation is thatan object’s existing at disconnected times is grounded in that object’s havingdistinct stages separated by a temporal gap. At bottom, the object at the time ofdisassembly is distinct from the object at the time of reassembly.39

Incompatibilists about intermittent existence face two worries that are familiarfrom previous discussions. There is, first, the Moorean worry that parts of thecommon-sense conception of objects turn out to be incorrect on philosophicalgrounds. Mooreans should find both the assumptions driving the mentionedcases and the anti-intermittence principle prima facie more compelling than anyphilosophical considerations to the contrary. That a watch cannot survive losingits watch-shape, for example, is prima facie more plausible than any philosoph-ical argument that the watch can survive this alteration in shape. And thatordinary objects cannot perform strange disappearance acts is prima facie moreplausible than any metaphysical framework in which they can. There is, secondly,the worry that ordinary speakers are unreasonable if the common-sense concep-tion is internally inconsistent. For they would be forced to the acceptance ofinconsistent propositions.

38 One might contemplate the response that it is indeterminate whether the watch ceases to existor whether it survives in a disassembled state, on the grounds that the sortal watch has differentpermissible interpretations, similarly to the case of the indeterminacy description of fission dis-cussed in Section 4.1. I am opposed to this move. While it is plausible that our linguistic communitynever fixed how to track a person or a ship in branching cases, it is implausible that our communitynever fixed whether a watch is required to be watch-shaped. Furthermore, if it is claimed that watchhas different meanings in different contexts, only one of which includes the requirement of beingwatch-shaped, then let us focus on contexts in which that meaning is in play—contexts, that is, inwhich the intermittence description is the correct one.

39 See Burke (1980: 404) and Simons (1987: 198) for an alternative response that is not meant torequire temporal parts.

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Two responses to these worries come to mind immediately. The first responseis to suggest that while (AI) applies in many cases, it is not meant to apply acrossthe board. If (AI) is restricted in the right way, inconsistency is avoided. Thesecond response is to read (AI) unrestrictively, and hence to concede inconsist-ency, but to avoid the problem of reasonableness by viewing ordinary speakersas accepting (AI) only in ignorance of cases of intermittent existence, and henceas behaving consistently (see Burke 1980: 404). I discuss analogous suggestionsconcerning coincidence in Sections 3.2.3 and 3.3.3. Since my reply in the case ofintermittent existence is analogous to my reply in the case of coincidence, I shallbe brief here. Apart from lacking independent motivation, the main problemwith these moves is that (AI) is not a sortal-sensitive generalization from specificcases, as both replies assume, but rather a generalization that is arrived atindependently from any belief about specific kinds of object in specific situations(cf. the discussion of (AC) in Section 3.3)—that is, (AI) is a sortal-abstractprinciple.Fortunately, a plausible compatibilist approach to intermittent existence is

available, which alleviates these worries. As I will show now, there is no reasonto be afraid of temporally gappy ordinary objects. My compatibilism aboutintermittent existence is based on the framework of perspectival hylomorphism,as developed in Chapters 1 and 2. My view is that the various cases of intermittentexistence and the anti-intermittence principle, (AI), are compatible because theyemploy different modes of predication, manifesting different perspectives on theobjects involved. The cases describe objects formally, manifesting the sortal-sensitive perspective, whereas the principle describes them materially, manifest-ing the sortal-abstract perspective.Let us focus on the case of the watch. (The extension of the ensuing treatment

to the other cases will be straightforward.) The description of the case given aboveis plausibly construed as manifesting the sortal-sensitive perspective on objects.For this description is clearly based on consideration of the specific persistenceconditions of watches. Assuming that ordinary thought and talk may be sortal-sensitive in the way characterized in Chapter 2, the description should be read asemploying the formal mode of predication:

(Wform) A watch, W, is formally disassembled at time t1 and then formallyreassembled at a later time t2. As a consequence, W formally goes out ofexistence at t1 and formally comes back into existence at t2.

The anti-intermittence principle, (AI), by contrast, is plausibly construed as asortal-abstract principle. What it says about objects abstracts from any specifickind-realizing attributes, and thus seems to be part of our minimal conception of

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the behaviour of an object in space and time, which is independent of represent-ing the object as belonging to a particular kind. While intuitively acceptable, thisconstrual of (AI) may be further supported by recourse to research in thepsychology of object representation, as I have done in Section 2.1 (where (AI)is tagged as principle (a)). Its status as a sortal-abstract principle is captured in theframework of perspectival hylomorphism by reading it as employing the materialmode of predication:

(AImat) Necessarily, for any ordinary object o, o cannot materially go out ofexistence at one time and materially come back into existence at a differenttime.

I will now specify a consistent metaphysical basis of intermittent existence thatmakes both (Wform) and (AImat) true, thereby pointing the way to a dissolution ofall paradoxes of intermittent existence. I shall assume the three-dimensionalist,classical-mereological account of material objects as well as q-hylomorphismabout ordinary objects specified in Sections 1.2 and 1.3, respectively, and addthe assumption that no material object can (absolutely) go out of existence at onetime and come back into existence at a different time. By the metaphysicalsemantics of material predication about ordinary objects, principle (AImat) istrue. Suppose, next, that there is a material object, a, that exists at time t1, that iswatch-shaped at t1, that ceases to be watch-shaped shortly after t1, as its parts (atsome level of decomposition) are spatially separated from each other, and thatlater becomes watch-shaped again at time t2, as its parts are brought back into thesame arrangement they exhibited at t1. Suppose, finally, that a is the subject of awatch-path i that includes watch-states of a before t1 and after t2 but nonebetween t1 and t2. This watch-path is temporally gappy. (Note that the possibilityfor a K-path to be gappy was explicitly factored in when K-paths were introducedin Section 1.2. I shall skip the relevant details here.) Given q-hylomorphism aboutordinary objects, there is a watch W, such that W is the compound �c(a, i). Bythe semantics of formal predication, these specifications make (Wform) true.While W formally goes out of existence at t1 and comes back into existence att2, W materially persists throughout the temporal interval between t1 and t2,undergoing a radical material change in its shape. This perspectival-hylomorph-ist account of the watch case may be illustrated by Figure 4.5.It remains to highlight the most significant features of this compatibilist

approach. First, the reconciliation rests on perspectival divergence. (Wform) iscompatible with (AImat), because a watch’s form may contain properties that thesame watch’s matter may fail to possess. As a corollary, the approach is meta-physically conservative. Formal descriptions of objects as existing intermittently

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are metaphysically shallow, in virtue of resting on intermittence-free facts aboutmaterial objects. In general, all temporally discontinuous K-paths have materialsubjects with temporally continuous trajectories. Loosely speaking, intermittentexistence of ordinary objects is a conceptual projection. Second, Moorean worriesare alleviated. Considerations of intermittent existence do not require the rejec-tion of any deeply entrenched pre-philosophical convictions on philosophicalgrounds. Finally, perspectivalism provides a psychologically sensible explanationof why ordinary thinkers are not unreasonable in their verdicts about intermit-tent existence. The explanation is that they describe the same objects fromdifferent perspectives.

a

t

x

t1

it2

Figure 4.5 Intermittent existence

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5

Modality

Perspectival hylomorphism was introduced as an account of the spatial andtemporal profile of ordinary objects. It is now time to extend this basic frameworktowards an account of themodal profile of ordinary objects. A de remodal propertyof an object is a way this particular object could have been or must have been.Traditional accounts of de re modal properties of ordinary objects are single-layered. They either see all de re modal properties as having a qualitative basis orthey see them all as having a non-qualitative basis. Friends of qualitative de remodality typically invoke facts about qualitative counterparts, who represent this-worldly objects in other worlds, as the grounds of de remodal attributions, whereasfriends of non-qualitative de re modality typically invoke facts about what a this-worldly object itself is like in other worlds as the grounds of de re modal attribu-tions.1 The account of de re modal properties of ordinary objects to be presentedhere is double-layered. The heart of the proposal is the claim that ordinary objectshave two de remodal profiles, one with a qualitative basis and another one with anon-qualitative basis, which may diverge.This account will be motivated in application to various problems concerning

de re modal properties of ordinary objects. In Section 5.1, I shall review a modalcounterexample to the compelling principle that distinct ordinary objects cannotfit into the same place at all times at which they exist, giving rise to a modalparadox of coincidence. In response, perspectival hylomorphism will be extendedand shown to offer a compatibilist dissolution of the paradox, in analogy with thetreatment of non-modal paradoxes of coincidence presented in Chapter 3, thusmaking good on the earlier claim that the proposed picture of coincidence is trulyunified. In Section 5.2, I shall review the recent debate over the groundingproblem, concerning whether and how modal differences between distinct

1 The single-layered, non-qualitative approach deserves to be called the standard approach. Themost prominent single-layered, qualitative approach is Lewis’s (1968, 1986). For alternative ways ofdeveloping the qualitative approach, see Gibbard (1975), Gupta (1980), and Noonan (1991).

coincidents are grounded in non-modal properties, and show that the problemmay be tackled satisfactorily in the framework of perspectival hylomorphism.Finally, in Section 5.3, a double-layered approach to de remodal attributions willbe shown to improve the prospects of a transworld identity-based understandingof modality de re in light of the problem of specifying sufficient conditions oftransworld identity.

5.1 A Modal Paradox of Coincidence

Let us call the coincidence of objects at all times of their existence—that is, theirexactly occupying the same places throughout their lives—coincidence in aworld, to be contrasted with coincidence at a time.2 Now suppose that a lumpof clay, Lumpl, and a statue, Goliath, are created and destroyed at the same time,so that they coincide in a world.3 Are Lumpl and Goliath numerically identical ordistinct? There are compelling reasons for believing that Lumpl and Goliath aredistinct. For they differ in their modal profile. Lumpl could survive beingsquashed into a ball, whereas Goliath could not. But there are also compellingreasons for believing that Lumpl and Goliath are identical. For it seems to bedeeply anchored in the common-sense conception of ordinary objects thatdistinct objects cannot fit into the same places throughout their lives. So themodal difference between Lumpl and Goliath seems in tension with the followingprinciple against coincidence in a world:

(ACW) Necessarily, for any ordinary objects o and o*, if o coincides with o*at all times at which o and o* exist, then o is identical with o*.4

We thus face a paradox of coincidence in a world. It may be characterized as amodal paradox, because the mentioned counterexample to (ACW) rests on a dere modal difference between Lumpl and Goliath—it is true of Lumpl that it ispossibly spherical in shape, but false of Goliath.5

2 See Fine (2008).3 The case is from Gibbard (1975).4 As in the case of (AC) in Chapter 3, the necessity in (ACW) is understood as metaphysical

necessity.5 Notice that (ACW) has non-modal counterexamples, as well. Suppose that a piece of wood and

a chair come into existence simultaneously—let the chair be cut right out of a tree—and that they aredestroyed simultaneously. Since the chair is defective, while the piece of wood is not, the twocoincide throughout their lives. Cf. Section 3.1. Moreover, as Fine (2000) has pointed out, the case ofthe two letters may be extended to become a case of worldly coincidence of objects belonging to thesame kind. Perspectival hylomorphism in its basic version applies to these cases as much as tothe simpler case (E) discussed in Chapter 3. Therefore, I shall set them aside here.

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I take it that, from the point of view of common sense, the appeal of (AC) (seeSection 3.1) and of (ACW), and hence the urgency of the non-modal and modalparadoxes of coincidence, are on a par. The intuitive worry behind (AC) concernsovercrowding: distinct objects cannot fit into the same place at the same time.And overcrowding does not get any worse in virtue of happening throughoutdistinct objects’ lives. There is, however, a metaphysical problem that is com-monly viewed as concerning primarily the rejection of (ACW). This is thegrounding problem, to be discussed in Section 5.2.

5.1.1 Incompatibilism about coincidence in a world

Incompatibilists about coincidence in a world hold that (ACW) is incompatiblewith the common-sense assumptions and presuppositions that drive Lumpl-and-Goliath-style cases. The standard responses to our modal paradox of coincidenceare all incompatibilist. A pluralist response is to accept that the modal differencesbetween Lumpl and Goliath establish their distinctness, and to reject the com-pelling principle (ACW) on these grounds. This is the way of constitutionalism,according to which Lumpl constitutes Goliath exclusively (cf. Section 3.2).6

Constitutionalists are typically unified in their acceptance of distinct coincidents;distinct coincidents in a world are just as welcome as distinct coincidents at atime. (AC) and (ACW) fall together.The standard monist response to the modal paradox is to accept (ACW), and

to deny that the modal differences between Lumpl and Goliath establish theirdistinctness. The signature move here is to claim that the modal differencesbetween Lumpl and Goliath are compatible with their being one and the sameobject. And the most critical consequence of this move is that Lumpl and Goliathare only contingently identical. There is the following possibility for Lumpl andGoliath: as Lumpl is reshaped into a ball, Goliath goes out of existence. In such apossible situation, Lumpl and Goliath are distinct (at least by the lights ofcommon sense). So Lumpl and Goliath are actually identical but could bedistinct. It is important to distinguish this de re claim of contingent identity—that Lumpl and Goliath are such that they are identical but could be distinct—from the claim that the descriptions ‘the lump of clay’ and ‘the statue’, usedexactly as we use them, could have failed to designate the same object.Among different ways of making sense of contingent identity (de re), Lewis’s

counterpart-theoretic version is the most prominent one.7 According to Lewis,

6 Those who construe ordinary objects as events, processes, or K-paths (see Section 1.2) mightalso reject (ACW), though on different metaphysical grounds.

7 See Lewis (1983a; 1986: section 4.5).

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ascriptions of de re modal properties to objects are sensitive to how the object isdescribed or conceived of in a context—in short, modality de re is inconstant.Different descriptions determine different classes of counterparts of the object indifferent possible worlds. Let us assume, for simplicity, that these different waysof conceiving of an object are conceptions of the object as falling under differentkinds. (That Lewis’s theory allows more than sortal representations to determineclasses of counterparts is irrelevant for present purposes.) Then an object o,conceived of as falling under kind K, is possibly F iff there is some object thatis similar to o in respects determined by K—a K-counterpart of o in anotherpossible world—that is F. Moreover, an object o, conceived of as falling underkind K, is necessarily F iff every K-counterpart of o is F. Since o may havedifferent K-counterparts for different kinds K, o may have different de remodal profiles relative to different sortal representations of o.Let us return to Lumpl and Goliath. According to Lewis, the de re modal

statement that it is possible for Lumpl, thought of as a lump of clay, and Goliath,thought of as a statue, to be such that the former survives being squashed into aball while the latter does not, is true because the pair <o, o>, where o is thereferent of both ‘Lumpl’ and ‘Goliath’, has a pair <oL, oS> as a counterpart, whereoL is a lump-of clay-counterpart of o and oS is a statue-counterpart of o, such thatoL survives being squashed into a ball and oS does not. He claims, moreover, thatthe statement that it is possible for Lumpl, thought of as a lump of clay, andGoliath, thought of as a statue, to be distinct, is true because the identity-pair<o, o>, where o is the referent of both ‘Lumpl’ and ‘Goliath’, has a non-identitypair <oL, oS> as a counterpart, where oL is a lump-of-clay-counterpart of o and oS

is a statue-counterpart of o. Notice, moreover, that it does not follow that Lumpl,thought of as a lump of clay, could fail to be self-identical because no lump-of-clay-counterpart of Lumpl fails to be self-identical. Thus, the contingent identityunder discussion must be distinguished from the idea that one object could fail tobe self-identical.8

Everyone should agree that the notion of contingent identity (de re) initiallyseems outrageous, even if care is taken not to confuse it with the notion ofcontingent self-identity. Lacking independent plausibility, contingent identityrequires philosophical motivation. And this motivation standardly comes fromthe notion’s role in solving the paradox of Lumpl and Goliath. The reasoning isthat we can learn to live with this counterintuitive notion because it buys us thecompelling anti-coincidence principle (ACW) (and, some will add, because it

8 For a Carnapian alternative to Lewis’s account of contingent identity, which invokes individualconcepts, see Gibbard (1975).

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dodges the grounding problem; see Section 5.2). This makes the monist who optsfor contingent identity an incompatibilist about coincidence in a world. Thismonist agrees with the pluralist that some part of the common-sense conceptionof objects has got to give.Notice, furthermore, that many monists about coincidence in a world are

pluralists about coincidence at a time, though a unified monist approach is notout of the question. This is the mixed approach of standard four-dimensionalists,such as Lewis, who accept coincidence at a time in virtue of overlap of temporalparts, but reject coincidence in a world, because completely overlapping space-time worms are identical. Here it is worth pointing out that since (ACW) and(AC) are on a par, from the point of view of common sense, this mixed positionwill gain no Moorean credit by preserving (ACW), while rejecting (AC). Forsaving intuitions contra overcrowding requires saving (AC) as well as (ACW).The standard debate about our modal paradox of coincidence thus presents us

with a choice of evils: coincidence without identity or modal differences withoutdistinctness. Pluralists argue that we should learn to live with the breakdown of(ACW). Monists typically argue that we should learn to live with contingentidentity. In what follows, I shall argue that these conclusions are overreactions.No adjustment is required of common sense. For there is no conflict between theprinciple that distinct objects cannot coincide in a world, (ACW), and theintuitive description of the case of Lumpl and Goliath as involving objects thatare distinct, on the grounds of modal differences between them. I shall, first,extend the basic framework of perspectival hylomorphism, as presented inChapters 1 and 2, to give an ontologico-semantical account of the de re modalprofiles of ordinary objects. Then I shall apply the upgraded theory to our modalparadox of coincidence. My view, in a nutshell, is that from the sortal-sensitiveperspective, Lumpl and Goliath have different de remodal profiles, and hence aredistinct worldly coincidents. Yet it is also true that distinct objects cannotcoincide in a world, as this principle manifests the sortal-abstract perspectiveon ordinary objects.

5.1.2 Worldbound K-paths and their counterparts

The following metaphysical specifications will presuppose the metaphysicalaccount of ordinary objects presented in Sections 1.2 and 1.3. Three additionsto this account will be made. First, I shall extend the account of material objectssketched earlier by the assumption that a material object exists in differentmetaphysically possible worlds, in a sense that does not rely on qualitativecounterparts of the object in those worlds, representing it in absentia as beingthere. I shall assume that a material object has properties and relations in the

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different worlds in which it exists, while remaining silent on the question whatpossible worlds are made of, and on the question whether the instantiation ofproperties in the actual world is more fundamental than the instantiationof properties in other worlds.Material objects were characterized as having purely mereological persistence

conditions. By the temporally sensitive principle of the uniqueness of compos-ition, or extensionality, the parts of a material object follow it through time and itfollows its parts through time. That is, if a material object a is composed of the xsat any time, then a is composed of the xs at all times of its existence; and if the xscompose a at any time, then the xs compose a at any time at which they exist.I shall now add the assumption that what holds for material objects across times,holds for them across worlds. The parts of a material object follow it acrossworlds, and it follows its parts across worlds. That is, if a material object a iscomposed of the xs in any world, then a is composed of the xs in all worlds inwhich it exists,9 and if the xs compose a in any world, then the xs compose a inany world in which they exist. I shall say more about the metaphysical status ofthis principle later on.Second, the basic notion of a K-state, for some kind K, will be extended in a

straightforward way. A K-state of a material object is a complex, conjunctive fact,or state of affairs, about the object at a time and in a world. A K-state, for somekind K, of a material object a at a time t, in a world w contains two types ofqualitative profile: a’s K-meaningful intrinsic profile at t, in w and a’s K-realiza-tion profile at t, in w. The K-meaningful intrinsic profile of a at t, in w contains:

the maximal conjunction of the facts that a exists at t, in w, that a has ç1 at t, in w, that ahas ç2 at t, in w, . . . , that a has çn at t, in w, such that (i) each çi is an intrinsic qualitativeproperty of a, and (ii) each çi falls in the sphere of discourse of K.

The K-realization profile of a at t, in w is constituted by two types of fact. Tobegin with, the K-realization profile contains:

the maximal conjunction of the facts that a has ł1 at t, that a has ł2 at t, . . . , that a has łnat t, such that ł1, ł2, . . . , łn together completely realize K.

Furthermore, the K-realization profile contains:

the maximal conjunction of the facts that ł1 partly realizes K, that ł2 partly realizes K, . . . ,that łn partly realizes K.

Recall that the requirement that K-states contain facts concerning which prop-erties realize which kinds rules out that a qualitative profile of a material object at

9 See n.5 in Chapter 1 on mereological essentialism.

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a time and in world, which contains both K-realizers and K*-realizers, for differentkinds K and K*, is both a K-state and a K*-state. If a material object has propertiesat t, in w, some of which realize K, while others realize K*, then the object is in aK-state and also in a distinct K*-state at t, in w.Third, a K-path, as the notion was introduced in Section 1.2, is a series of

K-states that is unified by K-continuity, K-connectedness, and lawful causaldependence, and that is maximal. These assumptions cover the spatiotemporalprofile of K-paths. As regards their modal profile, I shall assume that each K-pathis worldbound:

All of the K-states in a K-path obtain in the same world: if K-states s and s* areincluded in a K-path,ws is the world of s, andws* is the world of s*, thenws =ws*.

It is important to keep in mind that while K-paths are confined to a single world,material objects, the non-derivative subjects of K-states and the derivative sub-jects of K-paths, exist in different worlds.While K-paths are worldbound, they have counterparts in other possible

worlds. For any worldbound K-path iK and K*-path iK*, where iK and iK* obtainin the same or different worlds,

(CP) iK is a counterpart of iK* iff K is the same kind as K* and iK is K/K*-connected with iK*.10

Elaborating on the familiar notion of K-connectedness between K-states intro-duced in Section 1.2, two K-paths are K-connected just in case their K-realizationprofiles are similar to some minimal degree, where the amount of similarityrequired is a vague matter. The notion of similarity-based counterparthoodcomes, of course, from Lewis. But there are important differences. For Lewismaterial objects are worldbound and have counterparts in other worlds. On thepresent picture, K-paths are worldbound and have counterparts in other worlds,while material objects exist in multiple worlds. Furthermore, Lewis’s counterpartrelation is highly flexible, permitting counterparts in other than sortal respects,whereas the present counterpart relation is characterized exclusively in terms ofrealizers of sortal concepts. Finally, according to Lewis, a material object hasdifferent classes of counterparts depending on how the object is conceived of. Forexample, if a given material object is both a statue and a lump of clay, then it hasstatue-counterparts as well as lump-of-clay-counterparts. The present counter-part relation, by contrast, is not relativized to a description or conception of its

10 Since no complete account of the nature of kinds has been offered, no account of their identityconditions will be given, either.

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relata. Since K-paths contain facts concerning which properties realize whichkind, as part of their realization profile, no K-path is also a K*-path, where K andK* are different kinds; a K-path is individuated by kind K. Accordingly, noK-path has varying sets of counterparts depending on how it is described.A K-path has its counterparts simpliciter. To foreshadow somewhat, while theshiftiness of Lewis’s counterpart relation is responsible for a certain inconstancyin de re modal attributions of properties, no such inconstancy will be admittedhere, given a rather inflexible counterpart relation.So much for the location of material objects and K-paths in modal space. It

remains to extend q-hylomorphism about ordinary objects along the modaldimension: ordinary objects are compounds of transworld material objects andworldbound K-paths. Ordinary objects thus have a component individual formthat is tied to a particular world, that is individuated by the qualitative content ofa unique kind, and that has counterparts in other worlds, which are associatedwith the same kind. Moreover, ordinary objects have an underlying matter thatexists in different worlds. Given that a mereological sum does not go anywherewithout all of its parts, and given that an ordinary object has a worldboundK-path as a part, an ordinary object is worldbound, as well—that is, an ordinaryobject exists only in a single world.Given the profile of material objects, K-paths, and ordinary objects in modal

space, we are in a position to turn to de re modal attributions of properties toordinary objects.

5.1.3 Material and formal modality de re

Traditional, single-layered approaches to de remodal attributions construe all dere modal truths as having a qualitative basis or as having a non-qualitative basis.Qualitative de re modality is typically analysed in terms of qualitative counter-parts that represent this-worldly objects in other worlds, whereas non-qualitativede re modality typically concerns what a this-worldly object itself is like in otherworlds. My approach to modality de re is double-layered. There are ordinary de remodal attributions of properties to objects with a qualitative basis and there areordinary de re modal attributions of properties to objects with a non-qualitativebasis; ordinary objects have two de re modal profiles. Whether an object isascribed a qualitatively based de re modal profile or a non-qualitatively basedone depends on perspective. Ordinary de re modal truths manifesting the sortal-sensitive perspective on objects have a qualitative basis, whereas ordinary de remodal truths manifesting the sortal-abstract perspective have a non-qualitativebasis.

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According to perspectivalism, ordinary discourse about objects may employdifferent modes of predication, the material mode and the formal mode, mani-festing the sortal-abstract perspective and the sortal-sensitive perspective onobjects, respectively. Corresponding to the distinction between these two modesof predication, I shall distinguish between two types of modality de re, materialand formal. Corresponding to the material mode of predication there are senten-tial operators of material possibility and material necessity, yielding sentencessuch as, ‘It is materially possible that o is materially F’—◊mat(F(o)mat)—and ‘It ismaterially necessary that o is materially F’—□mat(F(o)mat). Corresponding to theformal mode of predication there are sentential operators of formal possibilityand necessity, yielding sentences such as, ‘It is formally possible that o isformally F’—◊form(F(o)form)—and ‘It is formally necessary that o is formallyF’—□form(F(o)form). Just as the different modes of predication are associatedwith different perspectives on the world of objects, so are the different types ofpossibility and necessity de re. We can represent an object as belonging to aparticular kind K and ask whether it is formally possible for it to be formally F. Orwe can abstract from any sortal representation of an object and ask whether it ismaterially possible for it to be materially F.11

How do material and formal de re modal attributions work semantically? Letus start with the material modalities. We ask the question whether a givenordinary object could lack a given property that it actually has as a question ofmaterial possibility de re if we think of the object in abstraction from any kinds towhich it may belong. Sortal abstraction clears the view for the material modalprofile of an ordinary object. This material modal profile is constituted byproperties (and relations) that an ordinary object’s maximal material subjecthas itself in different possible worlds in which it exists, independently of anyqualitative relations between that material object and others in its world and inother worlds. This is a natural extension of the account of material temporalpredication of Chapter 2, according to which an ordinary object’s materialtemporal profile is constituted by properties that the object’s maximal materialsubject has itself at different times at which it exists, independently of anyqualitative relations between that material object and others. Both temporaland modal predication in the material mode thus have a non-qualitative basis.Truth conditions of ordinary statements of material possibility and necessity dere may be stated as follows: for any ordinary object o,

11 There is no need to introduce additional modal operators corresponding to the absolute modeof predication employed only in the language of foundational metaphysics. This technical languagewill get by with absolute predications relativized to possible worlds.

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(T14) It is materially possible that o is materially F iff there is a materialobject a, such that o has a as its maximal material part, and a is F in somepossible world.

(T15) It is materially necessary that o is materially F iff there is a materialobject a, such that o has a as its maximal material part, and a is F in all possibleworlds.

On to the formal modalities. We ask the question whether a given ordinaryobject could lack a given property that it actually has as a question of formalpossibility de re if we think of the object in any way that is sensitive to itsbelonging to an ordinary kind. Formal de re modalities are sortal-sensitive.Given that ordinary objects have worldbound K-paths as components, andgiven that these have counterparts in other worlds, formal de re possibilitieswill be understood in terms of properties contained in counterparts of thesubjects’ component K-paths. The present account of formal modality de re isthus a version of modal counterpart-theory. However, standard counterparttheory, temporal and modal, is single-layered, in virtue of viewing all temporaland modal predication as dependent on qualitative representation of the subject(s).(I shall return to this contrast below.) The properties that an ordinary objectcould have formally are the properties contained in some counterpart, in somepossible world, of its K-path; and the properties that an object must have formallyare the properties contained in each of the counterparts, in any possible world, ofits K-path. This is a natural extension of the account of formal temporal predi-cation of Chapter 2, according to which an ordinary object’s formal properties ata time are the ones contained in the object’s K-path at that time, where a K-pathis partially unified by K-connectedness, which relation also plays a central role indetermining a K-path’s counterparts in other worlds. Both temporal and modalpredication in the formal mode thus have a qualitative basis. Truth conditions ofordinary statements of formal possibility and necessity de remay thus be stated asfollows: for any ordinary object o,

(T16) It is formally possible that o is formally F iff there is a kind K and aK-path i, such that o has i as a part, and for some material object a, somecounterpart of i includes the fact that a is F.

(T17) It is formally necessary that o is formally F iff there is a kind K and aK-path i, such that o has i as a part, and for each counterpart of i, there is amaterial object a, such that the counterpart includes the fact that a is F.

A point of clarification. It would be implausible to claim that a chair, say, couldhave a certain property merely on the grounds that there is a possible chair that

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has that property. Chairs come in massively different designs. And it seems that ifa given Bauhaus chair did not have its specific design, then it would not be thatchair. Product designers certainly think so. In the present framework, thisintuition is captured by letting an ordinary object’s specific kind-realizing prop-erties, as opposed to merely its kind, constrain its formally possible properties viathe requirement of a minimal degree of similarity between the specific kind-realizing properties contained in the object’s component K-path and the specifickind-realizing properties contained in the counterparts of this K-path—in short,via the requirement of K-connectedness between counterparts. (Similarly, globaltemporal property-variation is limited by specific K-realizers; see Section 1.2.)Note, further, that the combination of material modal operators with formal

predications and the combination of formal modal operators with materialpredications yield falsehoods. A material predication is ultimately about anordinary object’s matter, a material object, whereas a formal predication isultimately about an ordinary object’s form, a K-path. Correspondingly, theoperator of material possibility is defined in terms of transworld identity ofmaterial objects, whereas the operator of formal possibility is defined in termsof counterparts of K-paths. It thus cannot be materially possible for an ordinaryobject’s individual form to contain F-ness, since material possibility does notapply to worldbound K-paths. Likewise, it cannot be formally possible for anordinary object’s underlying matter to be F, since formal possibility does notapply to material objects who lack K-paths as counterparts. Analogously formaterial and formal necessity.The most important feature of this double-layered account of modality de re is

that it permits perspectival divergence in de re modal attributions: such anattribution may have different truth values depending on whether it is a materialor a formal attribution. Suppose that object o is a chair, and so formally chair-shaped. It is then formally impossible for o to fail to be chair-shaped, becauseeach of the counterparts of o’s chair-path contains the property of being chair-shaped (or rather, a specific chair-realizing shape). It is, however, materiallypossible for o to fail to be chair-shaped. Given the account sketched earlier, amaterial object does not vary in its parts across worlds, which leaves open for it tovary in its shapes, corresponding to different arrangements of its parts indifferent worlds. In this case, sortal dependence restricts material de re possibil-ities. The availability of this first type of perspectival divergence will be motivatedby application to modal paradoxes of coincidence below. Conversely, while it isnot materially possible for o to have different parts from its actual parts, giventhat material objects are individuated mereologically, it is formally possible for oto do so, if o’s chair-path has counterparts that include different mereological

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properties from the ones included in that chair-path. In this case, sortal depend-ence extends material de re possibilities. The availability of this second type ofperspectival divergence will be motivated by application to considerations ofmodal sufficiency in Section 5.3. Perspectival modal divergence rests on theneutrality of an ordinary object’s formal modal profile with respect to its materialmodal profile. While material de re possibilities have a non-qualitative basis,formal de re possibilities are mere shadows of which properties realize whichkinds.Perspectival divergence in de re modal attributions is a type of inconstancy.

But it is not Lewisian inconstancy.12 Most saliently, Lewis only recognizesmodality de re with a qualitative basis, whereas perspectival hylomorphismrecognizes a type of modality de re with a qualitative and another type with anon-qualitative basis. Moreover, Lewis allows different conceptions of the sameobject to trigger different modal profiles of that object. In the present framework,each K-path has a fixed set of counterparts (vagueness aside), and hence eachordinary object has a fixed formal modal profile.Finally, Lewis invokes inconstancy in a manner that renders certain de re

predications of identity contingently true. While Lewis recommends contingentidentity by its role in solving modal paradoxes of coincidence, perspectivalhylomorphism solves these paradoxes in a way that does not require contingentidentity. As contingent identity is seriously counterintuitive, it will be banned.I shall assume that any counterpart of an identity-pair of K-paths, <i1, i1>, is itselfan identity-pair of K-paths <i2, i2>, such that i2 is a counterpart of i1; and I shallassume that any counterpart of a distinctness-pair of K/K*-paths, <i1, i2>, is itselfa distinctness-pair of K/K*-paths, <i3, i4>, such that i3 is a counterpart of i1 and i4is a counterpart of i2. The truth conditions of de re claims of formally necessaryidentity and of materially necessary identity may then be stated as follows: for anyordinary objects o and o*,

(T18) It is formally necessary that o is formally identical with o* iff there is akind K and a kind K*, a K-path i1, and a K*-path i2, such that o has i1 as a part,o* has i2 as a part, and each counterpart of the pair <i1, i2> is an identity-pair.13

(T19) It is materially necessary that o is materially identical with o* iff there isa material object a, such that o has a as its maximal material part, and there is a

12 See Lewis (1986: section 4.5).13 Analogously, it is formally necessary that o is formally distinct from o* iff there is a kind K and

a kind K*, a K-path i1, and a K*-path i2, such that o has i1 as a part, o* has i2 as a part, and eachcounterpart of the pair <i1, i2> is a distinctness-pair.

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material object b, such that o* as b as its maximal material part, and a isidentical with b in all possible worlds.

It is obvious that, by (T18) and the above assumption on counterparts of pairs, ifo and o* are formally identical, then it is formally necessary that o and o* areformally identical. It is also obvious that, by (T19), if o and o* are materiallyidentical, then it is materially necessary that o and o* are materially identical.14,15

Having sketched a double-layered, perspectival-hylomorphist account ofmodality de re, I will now apply this account to the modal paradox of coincidencefeaturing Lumpl and Goliath.

5.1.4 Compatibilism about coincidence in a world

Perspectival hylomorphism allows a compatibilist treatment of our modal para-dox of coincidence, which saves the monist intuition that distinct objects cannotcoincide throughout their lives, and which also saves the pluralist intuition thatLumpl and Goliath are distinct, worldly coincidents. The key to this reconcili-ation is perspectival divergence: from the sortal-sensitive perspective, Lumpl andGoliath are distinct, coinciding objects with different de re modal profiles, yetfrom the sortal-abstract perspective, Lumpl and Goliath are identical and havethe same de re modal profile. As this dissolution of the modal paradox is

14 Contingent identity is not the only standard problem for counterpart theory. For reasons ofspace, I will ignore the problem counterpart theorists have with talk about actuality; see Fara andWilliamson (2005).

15 Michael Jubien (1993, 2009) also adopts what I call a perspectival picture of modal attributionsabout ordinary objects. He holds that ordinary objects can be conceived in a kind-dependent and ina kind-independent way, and that the attribution of modal properties to objects is sensitive to thisdifference in conception, which he calls the ‘great divide’ (Jubien 2009: 15ff.). Jubien’s picture,however, differs significantly from mine in detail and application. Here it will have to suffice tohighlight some key differences very briefly. First, I reject Jubien’s characterization of the great divide(see n.10 in Section 2.1). He characterizes the kind-independent, or sortal-abstract, perspectiveprimarily in mereological terms, whereas I characterize it primarily in spatiotemporal terms. Second,according to Jubien, ordinary, kind-dependent modal claims about objects that seem to be de re arereally de dicto claims about ‘K-essences’ (see Jubien 2009: 103). To think otherwise is to commit the‘fallacy of reference’—that is, to assume that ‘ordinary proper names and at least some definitedescriptions actually refer to (or denote, or designate) specific entities’ (Jubien 1993: 22). I find thisaccount implausible, and accordingly do not believe that we are in the grip of a fallacy of reference.On my view, the same object may be attributed genuinely de re modal properties under differentconceptions. (See Sider 1999 for more detailed criticism of Jubien’s semantic approach.) Third,Jubien adopts a single-layered account of ordinary objects: these objects are just mereological sums(Jubien 2009: chapter 1). By contrast, I adopt a double-layered account, namely, q-hylomorphism.One important benefit of the latter is that it allows perspectivalism to be extended to simplepredications of identity. That this is an advantage was shown with respect to various temporalparadoxes about ordinary objects in the preceding two chapters. Perspectivalism about identity willbe further supported in application to the modal paradox of coincidence below.

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analogous to the dissolution of the non-modal paradoxes in Section 3.3, I shallconfine myself to the essentials.As the first step in the reconciliation, the description of Lumpl and Goliath as

having different possible shapes, and hence as being distinct objects that coincidein a world, is plausibly construed as a description that is sensitive to the respectivekinds to which Lumpl and Goliath belong. I therefore propose to read thisdescription as employing the formal mode of predication and the formal notionof possibility de re:

(LGform) Lumpl formally coincides with Goliath at all times at which Lumpland Goliath formally exist. It is formally possible that Lumpl is formallyspherical, whereas it is not formally possible that Goliath is formally spherical.So Lumpl is formally distinct from Goliath.

Moreover, the anti-coincidence principle (ACW) is plausibly construed as asortal-abstract principle, and will therefore be read as employing the materialmode of predication.16

(ACWmat) Necessarily, for any ordinary objects o and o*, if o coincidesmaterially with o* at all times at which o and o* exist materially, then o ismaterially identical with o*.17

Next, a metaphysical basis will be specified that makes both (LGform) and(ACWmat) true. To begin with, it will be assumed, in consistency with the accountof material objects sketched earlier, that in no possible world do absolutelydistinct material objects coincide absolutely at any time, and, a fortiori, thatthey do not coincide absolutely throughout their lives. By q-hylomorphismabout ordinary objects and the metaphysical semantics of material predication,(ACWmat) is true.In order to show that the truth of (ACWmat) is consistent with the truth of

(LGform), suppose that a material object a persists through the temporal intervalfrom t1 to t2, in the actual world, @, that a is statue-shaped exactly from t1 to t2, in@, and that a is also lump-of-clay-shaped exactly from t1 to t2, in @. Moreover, ais the only subject of an @-bound statue-path i1

S that stretches from t1 to t2, andof an @-bound lump-of-clay-path i1

L, that also stretches from t1 to t2. Paths i1S

and i1L are distinct, in virtue of containing different realization profiles, but

16 The motivation for the analogous readings having been adduced in Section 3.3 is here assumedto apply as well, mutatis mutandis. For reasons of length, I shall skip these now-familiar details.

17 Notice that the necessity invoked by (ACW) is metaphysical necessity de dicto, which is heregiven the standard account as truth in all metaphysically possible worlds.

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include the same intrinsic and locational properties from t1 to t2. Let us say,simplifying a bit, that the realization profile of i1

L consists in the fact that a islump-shaped from t1 to t2, and the fact that being lump-shaped realizes the kindlump of clay; and let us say that the realization profile of i1

S consists in the factsthat a is statue-of-a-person-shaped from t1 to t2, and the fact that being statue-of-a-person-shaped realizes the kind statue. These specifications are obviouslyconsistent with the assumption that no distinct material objects can coincide ina world, and hence with (ACWmat).In this scenario, there is a statue, Goliath, where Goliath = �c(a, i1

S), and thereis a lump of clay, Lumpl, where Lumpl = �c(a, i1

L), such that Lumpl and Goliathformally coincide throughout their lives, stretching from t1 to t2, and are formallydistinct. Furthermore, as the notion of counterparthood was introduced earlier, agiven K-path’s counterparts are those K-paths, in any possible world, with moreor less the same realization profile—recall the requirement of K-connectedness.Thus, all counterparts of i1

S are such that each of their constituent statue-statescontains the property of being statue-of-a-person-shaped, at some time, in someworld. Assuming that being statue-of-a-person-shaped at any time, in any world,implies not being spherical at that time, in that world, no counterpart of i1

S

contains the property of being spherical at any time. Moreover, some counter-parts of i1

L are such that some of their constituent lump-of-clay-states contain theproperty of being spherical at some time, in some world. These counterparts maybe assumed to have the same realization profile as i1

L, since being lump-shaped atany time, in any world, does not imply the failure of being spherical at that time,in that world. Finally, given the metaphysical semantics of formal possibility dere, it follows that it is formally possible that Lumpl is formally spherical at sometime, whereas it is not formally possible that Goliath is formally spherical at anytime. Hence, (LGform) is true.The formal de re possibilities analysed here are individual de re possibilities for

Lumpl and Goliath, respectively. In order to illustrate the apparatus in action, it isalso worth analysing the joint de re possibility for Lumpl and Goliath that Lumplcould survive being squashed into a ball while Goliath does not. (Lewis’s analysisof this case was sketched in Section 5.1.1.) Consider a possible world w, in whichour familiar material object a also persists through the temporal interval from t1to t2. Suppose, moreover, that a is statue-shaped from t1 until a time earlier thant2, in w, whereas a is lump-of-clay-shaped from t1 until t2, in w. Correspondingly,a is the unique subject of a w-bound statue-path i2

S that stretches from t1 to atime earlier than t2, whereas a is the subject of a distinct w-bound lump-of-clay-path i2

L that stretches from t1 all the way to t2. Suppose, specifically, that i2L

contains the property of being spherical at t2, in w. By q-hylomorphism, w

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contains a statue, Goliath*, where Goliath* = �c(a, i2S), and a lump of clay,

Lumpl*, where Lumpl* = �c(a, i2L). Lumpl* and Goliath* are distinct from Lumpl

and Goliath, though this is of little significance for present purposes. What doesbear significance is this: given that i2

L is a counterpart of i1L and that i2

S is acounterpart of i1

S, it follows by the semantics of formal predication and thesemantics of formal modality de re, that it is formally possible that Lumpl andGoliath formally come into existence at the same time, while Lumpl formallysurvives becoming spherical, and Goliath does not.The conclusion we have reached is that from the sortal-sensitive perspective

Lumpl and Goliath are distinct and possess different de re modal profiles,whereas from the sortal-abstract perspective Lumpl and Goliath are identicaland possess exactly the same de re modal profile. We have here a case where thesortal representation of an ordinary object yields a restriction on the object’smaterial de re possibilities. Owing to the availability of this type of perspectivaldivergence, the modal paradox of Lumpl and Goliath disappears. Combiningthese considerations about coincidence in a world with the considerations ofChapter 3 about coincidence at a time, we end up with a unified account of theparadoxes of coincidence in the framework of perspectival hylomorphism, whichmanages to reconcile various portions of the common-sense conception ofobjects that have traditionally been viewed as irreconcilable.

5.2 The Grounding Problem

Everyone who believes that Lumpl and Goliath, who coincide throughout theirlives, are distinct objects with different modal profiles faces the groundingproblem, concerning how differences in Lumpl’s and Goliath’s de re modalproperties are to be explained on the basis of their non-modal properties. Thisis a problem for those who accept distinct, worldly coincidents with differentmodal profiles, irrespective of their stance towards (ACW)—that is, irrespectiveof whether they are traditional pluralists or compatibilists about worldly coinci-dence. In this section, I shall first state what is at stake in answering thegrounding problem, and then show how perspectival hylomorphism answers it.

5.2.1 What makes the difference?

Here is a standard formulation of the grounding problem.18 Lumpl and Goliathare empirically indiscernible: they share their spatiotemporal properties as well as

18 This problem has been widely discussed. See, inter alia, Bennett (2004), deRosset (2011), Fine(2008), Olson (2001), Paul (2006), Sider (2008), and Zimmerman (1995). The label ‘groundingproblem’ is Bennett’s (2004).

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their weight, shape, colour, and so on, throughout their lives. Yet Lumpl andGoliath have different modal properties. For example, Lumpl could survive beingshaped into a ball, while Goliath could not. This modal difference stands in needof explanation. Simply accepting the difference as a brute fact is out of thequestion. Yet there can be no modal difference without an underlying non-modal difference. What could this non-modal difference be? Lewisian monistshave a straightforward answer. The modal difference between Lumpl and Goliathderives from a non-modal difference in how the same object is described. As alump of clay it is possibly spherical, but as a statue it is not. Pluralists whorecognize distinct, worldly coinciding objects, on the other hand, face a seriousproblem. For they must find a non-modal difference in how the two objects are,as opposed to a mere difference in how one object is described. Yet Lumpl andGoliath do not seem to differ non-modally in a way that explains their modaldifferences, given that they coincide throughout their lives.As many commentators have pointed out, this problem should not be char-

acterized as the problem that the modal facts in the case of Lumpl and Goliath donot seem to supervene on non-modal facts. Supervenience by itself does notpresent a problem, because a supervenience claim does not come pre-packagedwith an explanatory requirement. This is why there are very weak types ofsupervenience that a friend of distinct, worldly coincidents can appeal to, suchas weak, global supervenience or ‘coincidents-friendly’ supervenience.19 Suchcheap supervenience relations fail to meet the grounding challenge. For thegrounding problem concerns the explanatory link between modal propertiesand non-modal properties, on which supervenience claims by themselves aresilent.20

This is a modal problem. Does it have a temporal analogue? The case of Lumpland Goliath is a case of distinct objects that coincide in the actual world. Thedifferences in what Lumpl and Goliath are like in other worlds requires anexplanation in terms of differences in what Lumpl and Goliath are like in theactual world. Recall the case of the piece of paper and the paper plane(Section 3.1). They have different temporal trajectories and coincide at sometimes in their lives. If differences between objects across times were required to begrounded in differences at a time, then there would be a temporal groundingproblem for those who accept that the piece of paper and the paper plane areempirically indiscernible at the present time, but differ in various ways at futuretimes. Supposing that the paper plane vanishes shortly after time t while the

19 See Bennett (2004), Olson (2001), Rea (1997), and Zimmerman (1995).20 See deRosset (2011) for elaboration.

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coinciding piece of paper remains, the problem would be to explain thesedifferent trajectories in terms of facts intrinsic to t. The now-standard view isthat there is no such temporal grounding problem. As Fine (2008: 104–5)motivates the disanalogy, the cross-temporal profile of an object is a contingentmatter, and may thus plausibly be taken to lack a ground in the object’s profile ata time. An object’s modal profile, by contrast, is a necessary matter, and may thusnot plausibly be taken to lack a ground in the object’s actual profile. While thisclaim of asymmetry is controversial, I shall not spend any more time with it andsimply assume its correctness. I shall thus assume that the grounding problemarises only for cases of distinct, worldly coincidents, whereas the problem thatdistinct coincidents would crowd each other out, which was discussed inChapter 3 and in the previous section, arises for cases of distinct, temporarycoincidents as well as for cases of distinct, worldly coincidents.21

In response to the grounding problem, it is quite natural to point to sortaldifferences, or kind differences, between the distinct coincidents. The idea is toconstrue sortal differences between coinciding objects as non-modal differences,and to let such differences explain a wide variety of modal differences betweenthe objects. Thus, the non-modal explanation of why Lumpl is possibly sphericaland Goliath is not, is that Lumpl is a lump of clay but not a statue, while Goliathis a statue but not a lump of clay.22 This explanation is plausible. It is certainly farmore natural than the view that kind-membership is explained by having acertain modal profile. But the explanation is incomplete as an answer to thegrounding problem, because sortal differences between distinct coincidents arethemselves in need of explanation. While it should be acknowledged that theremay well be fundamental facts of kind-membership concerning, for example,kinds of fundamental particle, it would be implausible to view facts concerningmembership of the macroscopic kinds lump of clay and statue as fundamental.Surely, something’s belonging to these kinds is explicable in other terms.A complete answer to the grounding problem thus requires an explanation ofboth modal and sortal differences between distinct, worldly coincidents.23

21 Note, however, that if it should turn out that there is a temporal grounding problem, as well,then it may be solved analogously to the way the modal problem is solved below.

22 See Wiggins (1980).23 Those who appeal to sortal differences in explaining modal differences as a general strategy

also face the problem that there may be distinct, worldly coincidents of the same kind and withdifferent modal profiles. Fine’s case of the coinciding letters discussed in Section 3.1 may beextended to yield a case of two letters that coincide in a world, while one letter could exist withoutthe other. This modal difference clearly does not rest on a sortal difference. It rather seems to rest ondifferences in the content, author, and addressee of the letters. See Fine (2000, 2008). This case ishere only mentioned on the side, as most constitutionalist pluralists reject distinct coincidents of thesame kind (see Section 3.2).

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This is a problem for traditional pluralists, who recognize distinct, worldlycoincidents, and who reject the anti-coincidence principle (ACW). It is also aproblem for perspectival compatibilists, who recognize distinct, worldly coinci-dents, yet still accept (ACW). While Lumpl and Goliath are materially identicaland share their material modal profile, they are formally distinct and possessdifferent formal modal profiles. This formal modal difference is to be explainedby a non-modal difference. Lumpl and Goliath, however, may be actually for-mally indiscernible. Moreover, their difference in kind is itself in need of explan-ation. What explains the formal modal and sortal differences then? This is thegrounding problem for perspectival compatibilism about coincidence in a world.My aim in the remainder of this section is to show how this problem may besolved in the framework of perspectival hylomorphism.

5.2.2 The form makes the difference

Hylomorphic approaches to the grounding problem are characterized by theclaim that modal and sortal differences between distinct, worldly coincidents areexplained not by a difference in their empirical attributes—their location, shape,weight, microphysical composition, and so on—but rather by a difference in theircomponent forms. Schematically, Lumpl has a component form that explainswhy Lumpl is a lump of clay as opposed to a statue, and why it is possiblyspherical, whereas Goliath has a different component form that explains whyGoliath is a statue as opposed to a lump of clay, and why it is not possiblyspherical. The hylomorphic approach to the grounding problem is more power-ful than any pluralism that takes de re modal differences or sortal differencesbetween distinct, worldly coincidents as fundamental, though it may not be theonly non-primitivist strategy. The approach has been implemented by Aristotel-ian hylomorphism, but it also works with q-hylomorphism.24 The key move insolving the problem is the same. I will add, however, that (neo-)Aristotelianforms qua non-material parts of ordinary objects are metaphysically far moremysterious than q-hylomorphism’s forms and their relation to ordinary objects,which earlier received an explication in transparent metaphysical terms. Theq-hylomorphic approach to the grounding problem may thus be foundmore palatable. It matches the Aristotelian-hylomorphist success in handlingthe issue without incurring commitment to metaphysically extravagant forms.25

24 See Fine (2008) and Koslicki (2008) for the neo-Aristotelian approach. See also Sosa (1987) fora related response. For other types of pluralist response, see Bennett (2004), deRosset (2011), Paul(2006), and Sider (2008). For a sketch of Aristotelian hylomorphism, see Section 1.1.

25 For criticism of Aristotelian hylomorphism, see Section 1.1.3. For a similar case of matchingthe Aristotelian’s success with lighter metaphysical commitments, see the application of perspectivalhylomorphism to intuitions of mereological structure in Section 2.2.2.

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First, sortal differences between distinct, worldly coincidents have a non-modal basis. Let us assume that a material object a persists through a temporalinterval T, in the actual world. Throughout T, a instantiates properties thatrealize the kind lump of clay, and a also instantiates different propertiesthat realize the kind statue. If instantiating K-realizing properties, for somekind K, were sufficient to make a material object belong to K, then a would beboth a lump of clay and a statue. But it is not sufficient. More is required for beinga statue or a lump of clay. Given that a has properties, some of which realize thiskind, while others realize that kind, there are distinct K-paths with a as theirunique subject: a lump-of-clay path, iL, and a statue-path, iS.26 These K-pathsmay differ concerning which qualitative facts about a they include. But even if iL

and iS include exactly the same qualitative facts about a, they still differ in that iL

includes facts concerning the realization of the kind lump of clay by certainproperties of a, whereas iS includes facts concerning the realization of the kindstatue by certain other properties of a—in short, iL and iS differ in their realiza-tion profiles. Given the operation of compounding (defined in terms of standardsummation), there are the compounds �c(a, i

L) and �c(a, iS). Since iL and iS are

distinct, the compounds are distinct. Lumpl is the first compound, Goliath is thesecond one. These compounds are materially indiscernible, and they may beformally indiscernible, as well, assuming the semantics of material and formalpredication—that is, they may have all the same properties formally as well asmaterially (at any time). Yet they belong to different (invariant) kinds. Lumpl is alump of clay but not a statue, because Lumpl has a lump-of-clay-path but not astatue-path as a part; and Goliath is a statue but not a lump of clay, becauseGoliath has a statue-path but not a lump-of-clay-path as a part. In short, Lumpland Goliath have different individual forms as components, which correspondto different kinds. This is the non-modal explanation of sortal differencesbetween distinct, worldly coincidents, within the framework of perspectivalhylomorphism.Second, de re modal differences between distinct, worldly coincidents have a

non-modal basis. Lumpl’s component lump-of-clay-path and Goliath’s compon-ent statue-path include different realization profiles. This is a non-modal differ-ence. As a consequence of this difference, Lumpl’s and Goliath’s individualforms have different sets of counterparts, which in turn explains why Lumpl andGoliath have different formal modal properties. (Recall the detailed explanationgiven above for why it is formally possible that Lumpl is formally spherical at sometime, while it is not formally possible that Goliath is formally spherical at any time.)

26 The assumption that a is the unique subject of iL and iS is made only for convenience.

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Since both sortal differences and modal differences of distinct, worldly coincidentscan thus be explained in non-modal terms, we have a complete answer to thegrounding problem. I conclude that this problem poses no threat to the perspec-tival-hylomorphist view of coincidence in a world.Moving on from the application of the perspectival-hylomorphist account of

modality de re to problems concerning coinciding ordinary objects, I shall nextapply this account to a problem concerning transworld identity. (I shall return tothe grounding problem in Chapter 7, when discussing its relation to a problemconcerning determinism.)

5.3 Transworld Identity and Sufficiency

Many philosophers take modality de remetaphysically seriously, ascribing ordin-ary objects a robust modal profile that is more than a shadow of these objects’actual qualitative profile—a modal profile that carves the objects at their joints.These philosophers reject qualitative grounds of de remodal truths. In specifyingnon-qualitative grounds instead, they often invoke facts about what a this-worldly object itself is like in other worlds (provided they believe in possibleworlds). They invoke, as it is often put, transworld identity.27 In this section,I shall discuss a problem that troubles these friends of transworld identity-basedmodality de re, and show that perspectival hylomorphism offers a novel andplausible solution to this problem.

5.3.1 The sufficiency problem

A principle that enjoys widespread acceptance among friends of transworldidentity is that, for any macroscopic objects o and o*, there must be some non-trivial sufficient condition of transworld identity between o and o*. In otherwords, there must be a metaphysical way of tracking a macroscopic object acrossmodal space.28 What stands behind this expectation is the intuition that if thereare no non-trivial sufficient conditions of transworld identity, then macroscopicobjects o and o* in different possible worlds may be numerically distinct,although there is no respect in which these worlds differ over and above oneworld’s containing o and the other world’s containing o*. Such a bare distinctness

27 For a careful distinction between different transworld-identity theses, see Divers (2002:258–61). The transworld identity addressed here is of a type rejected by friends of modal realismwithout overlap. I will not be concerned with robust accounts of modality de re that refrain frominvoking transworld identity.

28 Prominent proponents of this requirement include Forbes (1994: 416), Noonan (1983),Salmon (1981), and Williamson (1990).

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would be deeply mysterious. Let us call the requirement that transworld identitybetween macroscopic objects has a sufficient condition, the modal-sufficiencyrequirement, and formulate it as follows:

(MSR) For any macroscopic object o, there are some non-trivial, intrinsic orrelational properties of o, such that if a possible object o* has these properties,then o is identical with o*.

Three points of clarification about (MSR). First, non-trivial sufficient condi-tions of the transworld identity of o and o* are conditions that do not involveidentity properties of o and o*—that is, only properties that do not mention o oro* by name or by any other device of direct reference are admitted. Non-trivialsufficient conditions may thus comprise qualitative properties of o and o* thatmention no entity by name and non-qualitative properties of o and o* that do notmention o or o*, while mentioning other objects or entities.Second, while it is standard to formulate the requirement as a mere sufficiency

requirement, it is usually understood as having explanatory import, as well. Thetask, intuitively speaking, is to specify what fixes, or grounds, the identity of anobject that is at home in different worlds—that is, to specify in virtue of what it isthis object. The obtaining of these grounding facts in any world explains why theworld contains this object. Note that the question as to what fixes the identity ofan object may be viewed as a good question independently of one’s attitudetowards issues of transworld identity and modality de re.Third, the requirement is focused on macroscopic objects, as these are consti-

tuted by other things. The air of mystery arises when a complex object in oneworld is distinct from a complex object in another world, while the two worldsdiffer in no other facts, not even in which microphysical entities, such as particlesor fields, these objects are composed of. Such a distinctness without a non-trivialdifference is puzzling, because de re facts about complex objects are expected tobe grounded in more fundamental facts. Macrophysical de re facts do not floatfree of microphysical facts.What I shall call the sufficiency problem is that there seem to be counterexam-

ples to (MSR). For a start, it is easy to see that qualitative properties alone will notbe sufficient for the transworld identity of macroscopic objects. It seems to bepossible for the universe to exhibit eternal recurrence, such that each of infinitelymany epochs is qualitatively indiscernible from each other epoch.29 In eachepoch, a trumpet is created and destroyed under the same qualitative circum-stances, with the consequence that distinct epochs contain distinct, qualitatively

29 See Lewis (1986: 227).

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indiscernible trumpets. These distinct trumpets are made of the same kind ofstuff, are constructed according to the same plan and under the same circum-stances, bear the same spatiotemporal relations to other things, have infinitelymany preceding trumpets, and so on. Letting a qualitative object-role be acomplete qualitative description of an ordinary object, it thus seems to bepossible for distinct objects to share their qualitative object-role. Qualitativeproperties do not fix the identity of macroscopic objects.Another strategy is to try specifying sufficient conditions of transworld identity

of macroscopic objects in terms of qualitative properties of these objects togetherwith non-qualitative properties that do not mention these objects, such as theproperty of being created at t and the property of being composed of the ps at t,for some time t and some plurality of microphysical particles, the ps. But eventhis strategy will not lead to success.30 Suppose that we live in a world of eternalrecurrence, w, where the same plenum of microphysical particles becomearranged in the same total qualitative way at regular intervals, for all eternity.Some of these particles regularly become arranged trumpetwise for a short periodof time before they get rearranged again. So a trumpet is created and destroyed ineach epoch, and distinct epochs contain distinct trumpets made of the samematter. Consider times t1, t2, and t3, such that the world qualitatively duplicatesitself at these times. Suppose that Louis is a trumpet made at t2 and that Miles is aqualitatively indiscernible trumpet made from the same particles at t3. Given thatLouis and Miles differ (non-trivially) only in the particular times at which theyhave their properties and relations, and given that a trumpet could vary in itstime of creation—or, as it is often put, that time of creation is inessential to atrumpet—it seems evident that Louis could have been created at t1, while Miles iscreated at t2, at which time Louis is actually created (see Figure 5.1).

w w*

t1

t2

t3

Louis

Miles

Louis

Miles

Figure 5.1 Louis, Miles, and eternal recurrence

30 For discussion of the following type of case, see Forbes (1994), Hawthorne (2006: 239–44),Hawthorne and Gendler (2000), McKay (1986), Robertson (1998), and Salmon (1981, 1989).

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More specifically, there is a world, w*, such that at t2, Miles is composed of thesame particles, and hence is made from the same quantity of matter, is con-structed according to the same plan, by the same artisan, with the same inten-tions, and is related in the same way to any other microphysical particles, as Louisis in w. Moreover, owing to eternal recurrence, there is no non-trivial differencebetween Louis in w and Miles in w* concerning their history. In particular, sinceeach trumpet is preceded by infinitely many trumpets made from the samematter, according to the same plan, by the same artisan, with the same intentions,and so on, they cannot be distinguished by the order in which they are made. Forexample, it is not the case that in w, Louis is the first trumpet made from a certainquantity of matter in a certain way, while in w*, Miles is the second trumpet madefrom that matter in that way.31

Let a total object-role be a nearly complete, non-modal description of anordinary object, which contains no de re information about any ordinary objects,while containing de re information about times, places, microphysical make-up,and so on, along with a complete qualitative description of the object. In light ofthe case of Louis and Miles, it seems to be possible for distinct objects to sharetheir total object-role. There is an ordinary object, Louis, and an ordinary object,Miles, such that Louis and Miles are numerically distinct, although Miles couldhave all non-trivial properties and relations, qualitative and non-qualitative, thatLouis actually has. This seems to leave no hope for the modal-sufficiencyrequirement, (MSR), to be satisfied.32

The sketched counterexample to (MSR) relies on the existence of worlds witheternal recurrence, which contain an infinite sequence of trumpets. One mightwonder how (MSR) fares without this assumption. As Hawthorne (2006: 241–2)shows, there is little hope of finding a sufficient condition of the transworld identityof artefacts, such as trumpets, even if we only consider worlds with finite sequencesof trumpets. For finite cases, the following might be considered a promisingsufficient condition of the transworld identity of artefacts: if an artefact o is createdat t, from a certain quantity of matterm, according to plan p, by artisan s, and therewere exactly n artefacts preceding it, made from m, according to p, by s, then apossible artefact o* that is created at t, made fromm, according to p, by s, such that

31 Order plays a key role in Forbes (1994).32 Weak haecceitism could be defined as the doctrine that it is possible for distinct objects to share

their qualitative object-role, while strong anti-haecceitism is the denial of this doctrine. Moreover,strong haecceitism could be defined as the doctrine that it is possible for distinct objects to share theirtotal object-role, while weak anti-haecceitism is the denial of this doctrine. As the issue of how todefine these notions is controversial, I shall not employ these definitions in the present discussion.See Skow (2008) for differences among definitions of haecceitism and anti-haecceitism.

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there were also exactly n artefacts before o* made fromm, according to p, by s, theno is identical with o*.33 To illustrate the point of this order-sensitive condition,suppose that in w, Louis is created at t2, and is the first trumpet made from m,according to p, by s, whereas Miles is created at t3, and is the second trumpet madefromm, according to p, by s. Since they both could have been created earlier, thereis a world, w*, in which Louis is created at t1, and is the first trumpet made fromm,according to p, by s, whereas Miles is created at t2, and is the second trumpet madefrom m, according to p, by s. This case poses no threat to the order-sensitivecondition stated above, since Louis in w and Miles in w* differ by their position inthe order of trumpets made from m, according to p, by s: in w, Louis is the first,whereas in w*, Miles is the second.However, the stated condition is still open to counterexamples. To begin

with, it seems plausible that a trumpet could have been made from a quantity ofmatter that is only slightly different from the one that the trumpet is actuallymade of. Now suppose with Hawthorne (2006: 241–2) that Louis is created att2, and is the first trumpet made from quantity of matter m, according to p, bys. Let m* be a quantity of matter that is only slightly different from m. Clearly,Louis could have been created at the earlier time t1, from m*, according to p, bys, while Miles is created at t2, from m, according to p, by s. Notice that in thisworld, w*, Miles is created at the same time, from the same matter, according tothe same plan, and by the same artisan, as Louis is in w. Furthermore, and thatis where the case differs from the previous one, in w*, Miles is also the firsttrumpet made from m, according to p, by s. The sufficient condition above thushas the counterintuitive consequence that Miles is identical with Louis. Thisexample raises serious doubts about the availability of a plausible condition oftransworld identity for certain ordinary objects, namely artefacts, even when werestrict our attention to finite cases.34

To recapitulate, the sufficiency problem is the following. Many philosopherstake modality de re metaphysically seriously, ascribing ordinary objects a robustmodal profile that is not merely a shadow of how these objects are conceived of.These philosophers typically invoke facts about what a this-worldly object itselfis like in other worlds, as the grounds of de re modal attributions. While it isplausible to expect transworld identity of macroscopic objects to have sufficientconditions, no such conditions seem to be available in light of Louis–Miles-stylecases.

33 See Hawthorne (2006: 241).34 See Hawthorne (2006: 241–2) for a revised condition and further counterexamples.

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5.3.2 A perspectival reconciliation

Some friends of robust modality de re drop the modal-sufficiency requirement inthe face of counterexamples of the mentioned sorts.35 Others cling to modalsufficiency and find fault with the alleged counterexamples.36 To those friends ofrobust modality de re who find plausibility in both the sufficiency requirementconcerning transworld identity and in Louis–Miles-style cases I shall offer aconciliatory approach, in the framework of perspectival hylomorphism.As we have seen, perspectival hylomorphism makes room for a notion of

modality de re that is independent of qualitative representations of objects. This isthe notion of material modality de re. It is materially possible that a givenordinary object materially has a certain property just in case the ordinary object’smaximal material component has that property in some possible world(Section 5.1). Thus, material modality de re is analysed in terms of transworldidentity of material objects (in my technical sense of ‘material’). Consequently, asufficient condition of transworld identity of macroscopic material objects isneeded. This requirement may be stated as follows:

(MSRmat) For any macroscopic material object a, there are some non-trivial,intrinsic or relational properties of a, such that if a possible material object a*has these properties, then a is identical with a*.37

A condition satisfying (MSRmat) was stated at the beginning of this chapter (seeSection 5.1): For any material object a, if a is composed of a plurality of materialobjects, the xs, then any possible material object that is composed of the xs isidentical with a. (Temporal modifiers may be dropped on the assumption that ifthe xs compose a at any time, then the xs compose a at all times at which theyexist.) This is just the classical-mereological principle that the identity of acomposite object depends only on which things are its parts (extensionality), asapplied to material objects. So I propose to make sense of the transworld identitythat underlies the robust de re modal profile of an ordinary object as follows: anordinary object’s material de re modal properties are the properties that its

35 See, inter alia, Hawthorne (2006: 239–44).36 See, inter alia, Forbes (1994). Note, however, that Forbes explicitly ascribes cases of distinct

objects with the same total object-role initial plausibility, and accordingly characterizes their clashwith (MSR) as a puzzle.

37 (MSR), stated earlier, is neutral on what category of object is involved. As material objects arethe only transworld objects recognized in the framework of perspectival hylomorphism, we nowfocus on the restricted sufficiency requirement (MSRmat).

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maximal material part has in different worlds; and facts of composition aresufficient for the transworld identity of complex material objects.38

Where does this leave Louis and Miles? (To keep things simple, I shallhenceforth focus on the Louis–Miles case involving eternal recurrence. Theextension of the proposed treatment to finite cases is straightforward.) My answeris that the possibility for Miles to have all non-trivial properties and relations,qualitative and non-qualitative, that Louis actually has is compatible with mater-ial de remodality plus (MSRmat), on the assumption of perspectivalism. To beginwith, the case is plausibly construed as manifesting the sortal-sensitive perspec-tive on ordinary objects. The intuition that lies at the heart of the specification ofworld w is simply that it is possible to make distinct artefacts, such as thetrumpets Louis and Miles, from the same stuff, under the same circumstances,at different times. This intuition is clearly sortal-sensitive, as it appeals to theconditions under which trumpets and other artefacts come into existence andfade away. The basic intuition is then extended to the effect that this couldhappen repeatedly, and on a global scale.The next step is to point out that Miles could have the properties and relations

that it has at a certain time in w, at a different time, specifically the time at whichLouis has its properties and relations in w. This de re possibility for Miles (andLouis) is also sortal-sensitive. We may not need to conceive of Miles as fallingunder some ordinary kind, in order to be convinced that Miles could have comeinto existence at a different time. But this intuition alone will not generate thetroubling role-switching. What does generate the latter is the intuition that Milescould have the properties of being created from a certain quantity of stuff, undercertain circumstances, in the shape of a trumpet, and so on, which it has at acertain time in w, at a different time. And since the non-modal ascription of theseproperties in w is sortal-sensitive, the ascription of a de remodal profile invokingthis non-modal total object-role is sortal-sensitive, as well.Given that (MSRmat) concerns material objects, and hence material modality

de re, and given that the case of Louis and Miles is a case of formal modality de re,no tension arises. The key to the perspectival solution of the sufficiency problemis that while material de remodality is analysed in terms of transworld identity ofmaterial objects, and is therefore metaphysically robust, formal de re modality isanalysed in terms of qualitative similarity between the individual forms of

38 This is just a sufficient condition of the transworld identity of mereologically complex materialobjects. What about material simples (if there are any)? As stated at the beginning of this sub-section, the modal-sufficiency requirement is a burning issue only for macro-objects, since de re factsabout complex objects are expected to be grounded in more fundamental facts.

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ordinary objects, their component K-paths, and is therefore metaphysicallyshallow.Let us return to Louis and Miles. In world w—suppose it to be the actual

world—the same plenum of microphysical particles become arranged in the sametotal qualitative way at regular intervals, for all eternity. Times t1, t2, and t3 areamong the times at which w qualitatively duplicates itself. Suppose that materialobject a exists at t1, t2, and t3, and that a is trumpet-shaped at each of these times.Suppose, accordingly, that a is the unique subject of three distinct trumpet-paths,i1, i2, and i3, where i1 begins at t1 and ends before t2, i2 begins at t2 and ends beforet3, and i3 begins at t3. These trumpet-paths include the instantiation of the sameproperties and relations by a at different times, as well as the same factsconcerning which properties realize the kind trumpet. Assuming q-hylomorph-ism about ordinary objects, there are three trumpets: the compound of a and i1,the compound of a and i2, and the compound of a and i3. Let Louis be thecompound of a and i2, and let Miles be the compound of a and i3. Thus, Louis isformally created at t2, and Miles is formally created at t3, in w. This scenario maybe illustrated by Figure 5.2.We now want to capture the sortal-sensitive intuition that Louis could have

been created at t1 and that Miles could have been created at t2, while remainingthe same in all other respects. Since the individual form of Louis, i2, has i1 as a

w

t1

t2

t3

trumpet-path i1

a

Miles = æc(a, i3)

Louis = æc(a, i2)trumpet-path i2

trumpet-path i3

counterpart of

counterpart of

Figure 5.2 Formal role-switching

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counterpart, and the individual form of Miles, i3, has i2 as a counterpart, it followsby the metaphysical semantics of de remodal predication in the formal mode thatit is formally possible that Louis is formally created at t1 while Miles is formallycreated at t2, at which time Louis is actually formally created, and that Miles is, att2, formally made from the same quantity of matter, and formally created underthe same circumstances, as Louis actually is. This is a way of accounting for theexpected modal profiles of Louis and Miles without recognizing distinct worldsthat contain the same total object-roles but differ concerning which object playswhich role. In fact, one and the same world, w, in virtue of containing threedistinct and highly similar trumpet-paths, is able to yield the expected formalmodal profiles of Louis and Miles.This strategy of putting counterparts to work in capturing de re possibilities of

role-switching is Lewis’s (1986: 230–2). While Lewis buys these possibilities at thecost of a deflationary, qualitative account of de re modal attributions on thewhole, I have shown that it is possible to account for the role-switching possi-bilities invoking the qualitative, formal notion of modality de re, on top ofrecognizing a non-qualitative, material notion of modality de re, which is ana-lysed in terms of transworld identity of material objects. While it is formallypossible that an ordinary object formally has all the properties that a formallydistinct object actually has, it is not materially possible for any ordinary objectthat it materially has all the properties that a materially distinct object actuallyhas. In Section 5.1, I distinguished between two types of perspectival divergencein de re modal attributions: sortal dependence may restrict or extend material dere possibilities. In dealing with formal de re possibilities of role-switching, wehave encountered a case where sortal dependence extends material de re possi-bilities. When a given ordinary object is viewed from the sortal-sensitive per-spective, it possesses some modal properties that it lacks when viewed from thesortal-abstract perspective. The threat that Louis–Miles-style intuitions initiallyseemed to pose to a transworld identity-based understanding of modality de re isthus banned.

5.3.3 Chisholm’s Paradox

There is a different kind of case for the possibility that distinct objects share theirtotal object-role, and hence a different kind of counterexample to the modal-sufficiency requirement, one that does not rely on intuitions of eternal recur-rence. The following argument is known as Chisholm’s Paradox.39 At our world,w1, there are distinct ships, Adam and Noah. Ships surely tolerate small modal

39 See Chisholm (1967).

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variations in any non-trivial respect, such as shape, weight, constitution, andcircumstances of construction. So there is a world, w2, where Adam and Noah area little different from the way they are in w1: Adam is a little more similar to theway Noah is in w1, and Noah is a little more similar to the way Adam is in w1.Moreover, it is true at w2 that Adam and Noah could be somewhat different innon-trivial respects from the way they are (in w2). So there is a world, w3, whereAdam is a little more similar to the way Noah is in w2, and Noah is a little moresimilar to the way Adam is in w2. Continuing in this way, we will arrive at aworld, wn, in which Adam is indiscernible in all non-trivial respects from Noah inw1, and Noah is indiscernible in all non-trivial respects from Adam in w1. Worldswn and w1 seem to share two total object-roles while differing concerning whichobject fills which role, thus violating the modal-sufficiency requirement.This is not the only problem raised by Chisholm’s argument. While ships can

be a little different from the way they actually are, they surely cannot be a wholelot different. It is, for example, plausible to hold that a ship must be madeaccording to more or less the same plan that governs its actual construction.Moreover, as Kripke (1980: 114, n.56) has suggested, a wooden ship mustoriginate from more or less the same wood, from which it actually originates.(Let us set issues of vagueness aside for now, and assume that it is clear to whatprecise extent a ship can vary in these respects. Suppose, say, that a ship can bemade according to a plan and be constructed from planks that are at most ten percent different from its actual plan and planks.40) Yet the case of Adam and Noahseems to show that a ship can be made according to a very different plan andfrom very different planks. If some modal variation in these respects is allowed,then massive modal variation must be countenanced, as well, or so it seems, aschains of small differences across worlds can add up to big differences.Perspectival hylomorphism offers the following response to both of these

problems. Material modality de re is a robust, non-qualitative notion, based ontransworld identity of material objects. It allows us to make sense of the questionas to what an ordinary object could be like independently of conceiving of it asfalling under this or that kind. When this notion is invoked, the case of Adam andNoah poses no threat to the friend of modal sufficiency. For it is not materiallypossible that an ordinary object, such as Adam or Noah, is materially a littledifferent from how it actually is, in all non-trivial respects. This is so, because anymaterial object is composed of the same parts in all worlds in which it exists.While Adam (or Noah) could be materially different in some respects, Adam

40 The case to be sketched is not meant to raise a sorites paradox. See Chapter 7 for a discussion ofsome questions of vagueness and indeterminacy pertaining to ordinary objects.

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could not materially differ at all in its actual parts. The argument from minormodal variation in the properties of ordinary objects to massive modal variation,and hence to role-switching possibilities for objects, does not get off the ground ifordinary objects are viewed from the sortal-abstract perspective.What, however, becomes of our intuition that a ship could undergo some

variation even in its mereological properties? My answer is that this is a sortal-sensitive intuition, and therefore invokes the notion of formal modality de re.Adam and Noah are ships in world w1 with distinct individual forms, distinctship-paths, iA and iN, as respective components. These ship-paths differ invarious respects. In particular, they contain different mereological properties.Ship-path iA has a counterpart in another world, which contains slightly differentmereological properties from iA; and analogously for iN. By the semantics offormal de re modal attributions, it is formally possible that Adam is formallycomposed of slightly different planks from its actual ones; and likewise for Noah.The intuitive possibility of minor mereological variation is thus preserved, whenconstrued as sortal-sensitive.Now, does the formal possibility of minor variation generate the formal

possibility of massive variation up to role-switching? And, second, does it violatepre-theoretical intuitions regarding the limits of modal variation? Consider achain of counterparts starting with ship-path iA in w1 and ending with a ship-path in wn that contains the same properties as iN, as well as a chain starting withship-path iN in w1 and ending with a ship-path in wn that contains the sameproperties as iA. The first point to be made is that w1 and wn are not worlds withthe same total object-roles but distinct role-fillers. Rather, w1 just is wn. So this isnot a counterexample to the modal-sufficiency requirement. Second, from thefact that there is a chain of counterparts leading from iA to iN, it does not followthat iN is a counterpart of iA, because the counterpart relation linking K-paths isnot transitive. Hence, it does not follow that Adam could formally be far moredifferent than we would have expected. The idea of employing counterparts insaving the intuition that ordinary objects could be a little different from the waythey actually are, without yielding role-switching possibilities and without vio-lating the intuition that the objects could not be massively different, is, again,Lewis’s (1986: 245). I adapt his idea in a manner that allows it to coexist with anon-qualitative understanding of modality de re.Let me sum up the discussion of this section. Philosophers who are attracted to

a robust, transworld identity-based notion of modality de re, and who see theneed for sufficient conditions of the transworld identity underlying this notion,have a hard time dealing with apparent possibilities of role-switching. They facethe sufficiency problem. My proposed way of dealing with this problem is to

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adopt a double-layered picture of modality de re, which synthesizes qualitativeand non-qualitative aspects of traditional approaches. There is a robust notion,namely material modality de re, which is analysed in terms of transworld identityof material objects, the sufficient condition of which is mereological. But this isnot the only notion. There is also the metaphysically shallow notion of formalmodality de re, which is analysed in terms of counterpart relations amongK-paths, the individual forms of ordinary objects. This notion accounts forcases that initially seemed to spoil all hopes of giving sufficient conditions oftransworld identity, in a manner that floats above material, transworld-identity-based possibilities for ordinary objects.To be sure, the proposed package is a compromise. It will not satisfy those who

expect their pre-philosophical conception of specific kinds of ordinary object—their sortal-sensitive de re modal intuitions—to be a reliable guide to the deepmodal profiles of these objects. It may, however, hold promise in the eyes of thosewho oppose a complete deflation of modality de re, maintaining that ordinaryobjects do have a metaphysically robust modal profile, while drawing the scep-tical conclusion from the problems discussed here that most everyday thoughtfails to reveal what the objects’ deep modal profile is.41

41 This is not to deny that any common-sense intuitions track material possibilities of ordinaryobjects. Examples of such intuitions are the sortal-abstract principles that no object could exactlyoccupy distinct places at the same time, and that no distinct objects could exactly occupy the sameplace at the same time.

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6

Determinism

The actual world is deterministic just in case there is only one way in which it canevolve that is compatible with the actual laws of nature. If determinism about theactual world fails, we expect it to fail for a reason of physics. Yet there arecommon-sense cases involving ordinary objects that seem to show that the actualworld is indeterministic on mundane, a priori grounds. It should not be that easyto establish indeterminism. This apparent tension between our common-senseconception of objects and philosophical considerations regarding determinismand indeterminism poses another threat to our familiar worldview. This problemis the subject of the present chapter.In Section 6.1, I shall set the stage for the problem by distinguishing between

weak qualitative determinism and strong qualitative determinism, and by arguingthat the strong conception is preferable to the weak one. In Section 6.2, I shallpresent the problem, which consists in a priori violations of strong qualitativedeterminism by common-sense cases of distinct, coinciding ordinary objects, andconsider various unsuccessful replies to the problem. In Section 6.3, I shall offer amore plausible, perspectival-hylomorphist solution to the problem.

6.1 Weak and Strong Qualitative Determinism

Determinism is a modal notion. It is a feature of a possible world and of the lawsof nature governing that world. Intuitively, a world is deterministic if at all timesin the world’s history there is only one way in which the world can evolve that iscompatible with its laws of nature. How should this initial characterization bemade precise?According to David Lewis, determinism is a matter of qualitative differences

between worlds. Let a qualitative description of a world be a description of theglobal pattern of qualitative properties and relations instantiated throughout thisworld. Such a description says, for example, that there is a green object north of ared object at a certain time. The description, however, does not say which object

is the green one and which the red one. That is, the description excludeshaecceitistic information about the world. What it takes for a world to bedeterministic, according to Lewis, may be stated as the following principle ofweak qualitative determinism (which is characterized as weak for reasons to bestated shortly):

Weak Qualitative Determinism (WQD)A possible world w is deterministic iff for all times t, there is no possible world with thesame laws of nature as w, which matches w in its qualitative description up to t, but whichdoes not match w in its total qualitative description.1

On this approach, qualitative differences between worlds are the only differencesrelevant to questions of determinism. Haecceitistic differences between worlds—differences that concern only which objects have which qualitative properties—are irrelevant. (I shall motivate this anti-haecceitistic attitude in the next section.)This analysis of determinism works well for many cases. A paradigm failure of

determinism is the case of radioactive decay. Up to time t, the actual world andsome possible world w governed by the same laws of nature are qualitativeduplicates. At the end of a certain period of time starting at t, half of a sampleof some radioactive isotope has decayed in the actual world, whereas three-quarters of the sample remains at the end of that period in w. By WQD, theactual world is indeterministic, as expected.Nevertheless, this conception of determinism is unsatisfactory. There are cases

in which WQD does not give the expected classification. These are examples ofpossible worlds that we intuitively classify as indeterministic but which WQDclassifies as deterministic. Suppose with Joseph Melia (1999: 650) that there is aworld, w, with four blue duplicate spheres, including a, positioned at the apexesof a perfect tetrahedron. Suppose further that it is a law at this world that, afterfive seconds have passed, one of the spheres turns pink. In w, a turns pink afterfive seconds, while the other spheres stay blue. Intuitively, w is an indeterministicworld. For the laws of nature fail to determine whether a sphere with a certain(intrinsic and relational) past turns pink. There are spheres in w with exactly thesame past, such that one turns pink and the others do not. According to WQD,however, w is deterministic. All the worlds with the same laws and the sameinitial conditions in which one of the spheres turns pink have the same totalqualitative description; exactly the same qualitative properties and relations areinstantiated in the same pattern at these worlds.

1 See Lewis (1999: 32–3).

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For another case, suppose with Gordon Belot (1995: 190) and Mark Wilson(1993: 215–16) that there is a world w that contains a single symmetrical,homogeneous, cylindrical tower standing on a single homogeneous, perfectlyspherical planet with a spherically symmetrical object centrally located on thetower’s top. According to the standard treatment of this phenomenon, the towerwill collapse by buckling in a particular direction if the object on top exceeds acertain critical weight. In w, the tower buckles and the tip of the elbow of collapsecomes to rest on a certain segment of the planet. Intuitively, w is an indetermin-istic world. For the laws of nature fail to determine whether a section of the planetwith a certain (intrinsic and relational) past gets hit by a tower. There are planet-segments in w with exactly the same past, such that one gets hit by a tower andthe other does not. According to WQD, however, w is deterministic. All theworlds with the same laws and the same initial conditions in which the towerbuckles in a certain direction have the same total qualitative description.We must be careful not to misdescribe these cases. One might say that the

world of the spheres is indeterministic, because it is not determined which sphereturns pink. In w, sphere a turns pink and sphere b stays blue, whereas in someother world b turns pink and a stays blue. Similarly, one might say that the worldof the tower is indeterministic, because it is not determined which segment of theplanet gets hit by a tower. In w, one segment gets hit, whereas in some otherworld another segment gets hit.2 I did not say these things. For this haecceitisticunderstanding of the cases renders them ineffective. As I shall argue in the nextsection, haecceitistic properties should not be granted the power to violatephysical determinism. Determinism is not a matter of which objects instantiatewhich qualitative properties in which worlds. Thus, if the cases can only beunderstood as concerning the question which sphere turns pink and the questionwhich part of the planet gets hit by the tower, then they need not worry us. Bycontrast, I understand the two cases as presenting intuitive violations of determin-ism that derive purely from qualitative properties and yet slip through the cracks ofWQD. It is undetermined whether a sphere of a certain qualitative descriptionturns pink and whether a planet-segment of a certain qualitative description getshit by a tower, as we can see by inspecting spheres and planet-segments of the givendescriptions in the same world—no need to inspect other worlds. The ensuingquestion is whether determinism could be formulated in a way that registers our

2 Melia describes the cases in this way: they are ‘examples of possible worlds which we intuitivelyclassify as indeterministic yet whose futures differ only over which objects play which role’ (1999:649).

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intuitive classification of the two cases, and that is insensitive to haecceitisticdifferences.Lewis is right that determinism is only violated by qualitative branching. But

there are different types of qualitative branching, namely, global and local.A qualitative description of a world is a description of the pattern of qualitativeproperties and relations instantiated throughout this world over time. A qualita-tive description of an object, of a part of a world, is a description of the qualitativeintrinsic and relational properties instantiated by an object over time. Schemat-ically, a qualitative description of an object has the form, ‘the x: x is F at t1, x isG at t1, x is H at t2, . . . ,’where ‘F’, ‘G’, ‘H’, and so on, denote qualitative intrinsic orrelational properties. We have global qualitative branching when qualitativedescriptions of worlds with the same laws of nature that match up to a certaintime diverge afterwards. And we have local qualitative branching when qualita-tive descriptions of objects that are parts of worlds with the same laws of naturematch up to a certain time but diverge afterwards.The case of the pink sphere is a case of local qualitative branching without

global qualitative branching. World w contains spheres with matching qualitativedescriptions up to a certain time but without matching total qualitative descrip-tions: one sphere with that description turns pink, the others stay blue. So thelaws of nature fail to determine what will happen to an object with that past.Similarly for the case of the collapsing tower: there is local without globalqualitative branching. World w contains segments of a planet with matchingqualitative descriptions up to a certain time but without matching total qualita-tive descriptions: one segment of the planet with a certain qualitative descriptionup to t gets hit by a buckling tower, whereas another segment with the samedescription up to t does not get hit by a tower. In both cases, w is indeterministic,not because it is undetermined how w will evolve at a global level, but rather,because it is undetermined how w will evolve at a local level. WQD ignores theselocal failures of determinism.3 In order to capture them, Lewis’s conception ofdeterminism must be replaced by a conception honouring local qualitativedifferences between worlds. Such a conception may be called ‘strong qualitativedeterminism’ and will be stated as follows:

Strong Qualitative Determinism (SQD)A possible world w is deterministic iff for all times t, and for all objects x in w, there is noobject in any possible world with the same laws of nature as w, which matches x in itsqualitative description up to t, but which does not match x in its total qualitativedescription.

3 Cf. Melia (1999: 652–4).

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To emphasize, this is still a qualitative approach to determinism; haecceitisticproperties do not play any role. The contrast with WQD is not that differencesconcerning which objects play which qualitative object-roles in which world aredeemed relevant to determinism. The contrast is rather that while WQD recog-nizes only global qualitative world-roles as relevant for determinism, SQDrecognizes local qualitative object-roles as relevant, as well.4

Notice, finally, that SQD is independent of how modality de re is analysed (cf.Sections 5.1 and 5.3). SQD is motivated by the observation that there are differenttypes of qualitative branching, local as well as global, and not by any consider-ations of modality de re. It is worth being clear about this relationship betweendeterminism and modality de re, because the formulation of SQD in terms ofqualitative descriptions of objects may be misunderstood as presupposing aqualitative analysis of modality de re, such as Lewisian counterpart theory.Neither this nor any other analysis of modality de re is presupposed. Thisconception of determinism is neutral on issues of modality de re, as a conceptionof determinism should be.5

6.2 The Problem of Cheap Indeterminism

Strong qualitative determinism, SQD, emerged as a plausible conception ofdeterminism. It classifies a wide range of cases in accordance with our intuitions.I now want to raise a problem about this conception, which rests on certain casesof distinct, coinciding ordinary objects first discussed in Chapter 3. It should beemphasized right away that the following problem concerns all folk-inspiredfriends of distinct coincidents. It is independent of which metaphysical accountof distinct coincidents is adopted—specifically, it is independent of whethercommon-sense cases of distinct coincidents are analysed in terms of constitutionin a three-dimensionalist framework or in terms of overlap of temporal parts in afour-dimensionalist framework.

4 One might worry that SQD is still not sufficient to capture all our intuitions of determinism andindeterminism. Consider a world with three objects, a, b, and c. There is, further, an asymmetricalrelation R, such that none of these objects bear R to each other until a time t. After t, it is either thecase that aRb, bRc, and cRa, or it is the case that cRb, bRa, and aRc, but the history of the world untilt does not determine which complex state of affairs obtains. By SQD, this world is deterministic, butone might insist on intuitive grounds that it is indeterministic. As Hawthorne points out, this sort ofcase could be treated by generalizing SQD to ordered n-tuples; see Hawthorne (2006: 243, n.13).

5 SQD has the further welcome feature of aiding substantivalists about spacetime in avoidingJohn Earman and John Norton’s hole argument; see Earman and Norton (1987), and Melia (1999:655–6).

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6.2.1 Distinct coincidents and local qualitative branching

Suppose, to take a now-familiar case, that in the actual world a piece of paper iscreated in the shape of an aeroplane—that is, a piece of paper and a coincidingpaper plane come into existence simultaneously. At time t, the piece of paper isflattened. Since the piece of paper survives the flattening, while the paper planedoes not, they are distinct. Let us assume, moreover, that the piece of paper andthe paper plane are qualitative duplicates up to time t; they share all theirqualitative properties and relations until that time; even the intentional relationsin which we stand to them are the same. (This assumption of indiscernibility upto t is controversial. In Section 6.2.4 it shall be questioned.) In the actual world,then, the piece of paper matches the paper plane in its qualitative description upto t, but does not match it in its qualitative description after t—the piece of paperexists after t, whereas the paper plane does not—and hence does not match it inits total qualitative description. It follows by SQD that the actual world isindeterministic.The problem with this case is not the fact that it violates determinism of the

actual world. Determinism may, of course, be false. Rather, the way in which itviolates determinism is problematic. As Earman and Norton say,

There are many ways in which determinism can and may in fact fail: space invaders in theNewtonian setting; the non-existence of a Cauchy surface in the general relativisticsetting; the existence of irreducibly stochastic elements in the quantum domain, etc.[ . . . ] Determinism may fail, but if it fails it should fail for a reason of physics. (Earmanand Norton 1987: 524)

It is implausible to be able to tell from the armchair and on little reflection thatour world is indeterministic. To be sure, determinism should be allowed to failon a priori grounds. To mention one example, the question whether quantumtheory rejects determinism is not settled by the empirical result of any experi-ment. The situation is rather that some interpretations of the quantum formal-ism posit deterministic laws while others posit irreducibly stochasticdynamics.6 What should not be accepted is the failure of determinism on apriori grounds that are also mundane. That would be cheap indeterminism.And indeterminism should not come for cheap. Determinism should, asEarman (1989: 180) puts it, ‘be given a fighting chance’. Yet the case of thepiece of paper and the paper plane seems to show the actual world to be

6 For a summary of issues concerning quantum theory and determinism, see Maudlin (2003:469–70).

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indeterministic on obvious, a priori grounds. Supposing that there is a piece ofpaper, that there is a paper plane made from the latter, and that they areflattened at t, the pre-theoretical, a priori assumptions that if the paper plane isflattened it goes out of existence, and that if the piece of paper is flattened itcontinues to exist, are sufficient to establish that there are objects with quali-tative descriptions that match before t and diverge after t, and hence that thereis local qualitative branching. This is an objectionably effortless, a prioriviolation of determinism of the actual world. It should not be that easy. Callthis the problem of cheap indeterminism.Cheap violations of determinism involving ordinary objects are numerous.

Consider another case. Suppose we arrange a number of bricks in the shape of ahouse. Then we have a house-shaped aggregate of bricks and we have a house.What happens when a further brick is added at time t? The house grows a bitbigger. The aggregate of bricks, however, does not grow at all, for the new brickmerely gets attached to it. So there are distinct objects, an aggregate of bricks anda house, whose qualitative descriptions match before t but diverge afterwards.The laws of nature thus fail to determine whether an object with a certain historywill or will not grow in parts. Again, determinism of the actual world seems to failon mundane, a priori grounds.7

This type of failure presupposes the strong version of qualitative determinism,SQD. On the weak version, WQD, the mentioned cases of distinct, indiscerniblecoincidents do not raise the problem. In the actual world, there is a piece ofpaper and a paper plane made from the latter. At time t, they are flattened. As aresult, the piece of paper exists after t but the paper plane does not. Any worldwith our laws of nature that matches our world in this description up to t, alsomatches it in the description after t. Hence, the actual world is deterministic, asdesired.Here is where the earlier discussion of conceptual issues regarding determin-

ism (Section 6.1) comes into play. For there are good reasons for adopting thestrong version, SQD, which triggers the problem. The weak version fails some ofour expectations concerning which worlds should count as deterministic and

7 Or suppose that an amoeba divides: one fission product goes left, the other goes right. Supposefurther that we have good philosophical reasons for describing this case of fission in the followingway: there are two amoebae right from the start, and they are separated by fission, where one goesleft and the other goes right (cf. Section 4.1). The two amoebae have the same qualitative descriptionup to the time of fission, while these descriptions diverge afterwards. Again the laws of nature fail todetermine whether an object with a certain history goes left or right. Since failure of determinism byfission is much less pre-theoretically compelling than failure by coincidence, I shall set fission casesaside.

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which as indeterministic. The world of the coloured spheres and the world of thecollapsing tower, for example, should be classified as indeterministic worlds. SQDachieves this classification, whereas WQD fails to do so. That is why the strongversion is preferable.The problem poses a threat to our common-sense conception of objects, which

licenses the troubling cases of distinct coincidents apparently rendering the actualworld indeterministic on objectionably mundane and a priori grounds. Earlier onI distinguished between different types of pressure on our familiar worldview.There are problems that pose a threat from within, concerning the internalconsistency of the common-sense conception of objects, and there are problemsthat pose a threat from without, concerning the consistency of the conceptionwith plausible philosophical principles. Intuitive cases of distinct, coincidingordinary objects have been shown to be involved in problems of both types.The paradoxes of coincidence discussed in Chapter 3 and in Section 5.1 posethreats from within, whereas the grounding problem discussed in Section 5.2poses a threat from without. The problem of cheap indeterminism poses a newthreat of the latter type. (In Section 6.2.4, I shall discuss how this difficulty relatesto the grounding problem.)Whether there is a violation of determinism of the actual world by local

qualitative branching cannot be a matter of common sense; it has to be a matterof physics. But if we can trust our common-sense verdicts about ordinary objects,then there are pre-theoretical, a priori cases of local qualitative branching. So wecannot trust our common-sense verdicts, one might conclude. An alternative tofolk-inspired pluralism about coincidence is folk-sceptical monism. Monistsabout coincidence who hold that folk intuitions are overrated do not face theproblem. According to them, the piece of paper and the paper plane as well as theaggregate of bricks and the house are numerically identical, and hence do notpresent cases of local qualitative branching. That is one way out of the problem.Betting against common sense, however, is a high price to pay. Can the problemof cheap indeterminism be avoided if we do not want to revise our familiar takeon coinciding objects?In what follows, I shall consider several replies, and show that each of them is

implausible, thereby setting the stage for my favoured solution in terms ofperspectival hylomorphism. The first type of reply I shall consider resorts totweaking SQD (Sections 6.2.2 and 6.2.3). The second type of reply accepts SQDbut denies that there is local qualitative branching in the cases under consider-ation (Section 6.2.4).

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6.2.2 De re determinism and regional determinism

The first reply is to strengthen SQD. Let us assume that objects that exist at agiven time may appear in different possible futures, and consider the following dere version of determinism:

De Re Determinism (DRD)A possible world w is deterministic iff for all times t, and for all objects x in w, there is nopossible world w* with the same laws of nature as w, such that x’s qualitative descriptionup to t in w* matches x’s qualitative description up to t in w, but x’s total qualitativedescription in w* does not match x’s total qualitative description in w.8

On this conception, the world of the coloured spheres is correctly classified asindeterministic. Focusing on the sphere that actually turns pink, this very objectdoes not turn pink in another world with the same laws and the same history.Likewise for the tower world. Turning to our cases of coinciding objects, theactual world, which is assumed to contain the paper plane and the coincidingpiece of paper, is classified as deterministic, just as we would have expected, onthe grounds that the paper plane does not survive the flattening in any world withthe actual laws and the same initial conditions, and the piece of paper doessurvive the flattening in any world with the actual laws and the same initialconditions. The crux of this reply is that according to DRD, local qualitativebranching violates determinism only if it happens to one and the same object;and the particular objects involved in our case of distinct coincidents do not havebranching futures of the troubling kind. Likewise for the case of the house and theaggregate of bricks: the house must grow and the aggregate cannot grow in thegiven circumstances.DRD relies on haecceitistic differences between worlds—differences that con-

cern which objects have which qualitative properties. While according to SQD,local qualitative branching violates determinism independently of which objector objects are involved, DRD recognizes a violation of determinism by localbranching only if the branching has a particular object as its locus—that is, DRDis sensitive to haecceitistic properties, such as being a or being this object. Thisdependence of determinism on haecceitistic properties is implausible. Let usmake explicit a natural constraint concerning which properties determinism issensitive to. Determinism concerns the qualitative evolution of objects over time;it is a matter of whether the laws of nature and the qualitative history of an objectup to a time determine the object’s qualitative profile after that time. To specify

8 The label ‘De Re Determinism’ is Hawthorne’s (2006: 239).

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the qualitative history of an object up to time t is to specify the qualitativeproperties and relations that the object has at any time of its existence until t,and to leave out any properties and relations it has after t. Determinism is thusnot sensitive to properties that characterize an object absolutely, or sub specieaeternitatis, for these properties are not suited to specify temporally intrinsicqualitative profiles, partial histories, of objects. Call this the temporal-intrinsic-ness constraint. DRD violates this constraint by rendering determinism sensitiveto haecceitistic properties of objects. Properties concerning the identity of anobject are not temporally intrinsic properties suited for the purpose of specifyinga partial history of the object. They are rather properties that an object hassimpliciter, or absolutely. Therefore, haecceitistic information about which objectplays which role in which world over and above local qualitative informationshould be irrelevant to determinism. The strong qualitative conception, SQD, isthus preferable to DRD, and the problem of cheap indeterminism remains.9

The second reply is to reformulate SQD in terms of spatial regions. Let aqualitative description of a spatial region be a description of the occupationprofile of an enduring spatial region over time. Schematically, a qualitativedescription of a spatial region has the form, ‘the R: at t1, R is occupied by amaterial object, state, or event that is F at t1, at t2, R is occupied by a materialobject, state, or event that is G at t2, . . . ’. Moreover, we have regional qualitativebranching when qualitative descriptions of spatial regions of worlds with thesame laws of nature match up to a certain time but diverge afterwards. Deter-minism may now be formulated as the absence of regional qualitative branching:

Regional Qualitative Determinism (RQD)A possible world w is deterministic iff for all times t, and for all spatial regions R in w,there is no spatial region in any possible world with the same laws of nature as w, whichmatches R in its qualitative description up to t, but which does not match R in its totalqualitative description.

This conception correctly classifies the world of the coloured spheres as indeter-ministic, since this is a case of regional qualitative branching without globalqualitative branching. World w contains spatial regions with matching qualitativedescriptions up to a certain time but without matching total qualitative descrip-tions: one region with a given description contains a blue sphere after t, while

9 Another motivation of this negative stance towards haecceitistic properties is to say that we areinterested in determinism in the context of physics, and that haecceitistic properties are notproperties described by physical theories. See, inter alia, Brighouse (1994, 1997). I consider thispoint weaker than the one made above, since the claim that physics is not in any way concerned withhaecceitistic properties may be questioned. Here is not the place for an appropriate discussion of thisissue.

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another region with the same description up to t contains a pink sphere after-wards. So the laws of nature fail to determine what will happen in a region withthat past. Analogously for the tower world.How does RQD classify our cases of coinciding objects? In the actual world,

there is a spatial region, R, that contains a piece of paper and a paper plane madefrom the latter until time t. At t, the two objects are flattened. As a result, Rcontinues to contain a piece of paper but ceases to contain a paper plane after t.Now, any spatial region in any world with our laws of nature, which matches R inits description up to t, also matches R in its description after t. That is, under thesame laws any region that contains a piece of paper and a coinciding paper planeup to t, and that is the site of a flattening at t, also contains just a piece of paperafter t. Hence, the actual world is classified as deterministic, just as we would haveexpected.This conception of determinism goes too far. Suppose that in a world w there

are indiscernible Æ-particles that regularly coincide from the time at which theycome into existence, and that the only law governing w is that after ten minutes ofcoincidence one of any indiscernible, coinciding Æ-particles goes out of existence.Intuitively, this is an indeterministic world. For it is undetermined whether aparticle with a certain past decays. According to RQD, however, w is determin-istic. In w, spatial region R contains n coinciding Æ-particles until time t and n-1Æ-particles after t. Any spatial region in any world with the same laws as w, whichmatches R in its qualitative description up to t, also matches R in its descriptionafter t. RQD fails to give the expected classification. Here we want determinism tofail. It is not a cheap failure; it happens for the right reasons. Yet RQD is blind tothis failure, in virtue of focusing on the profiles of spatial regions. If, by contrast,determinism is understood in terms of objectual branching, as in SQD, then wcomes out as indeterministic, as expected. For w contains Æ-particles withbranching descriptions. Thus, SQD should not be abandoned. SQD, however,opens the door to coincidence-based failures of determinism for the wrongreasons, as the case of the piece of paper and the paper plane shows. The problemof cheap indeterminism demands another approach.

6.2.3 Restricting determinism

The third reply is to restrict SQD. The aim is to argue that local qualitativebranching involving distinct, coinciding objects does not violate determinism,because it belongs to a kind of branching to which SQD is not sensitive. Let usdistinguish between genuine and non-genuine local qualitative branching, and letus say that determinism is only sensitive to the genuine type:

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Genuine Strong Qualitative Determinism (GSQD)A possible world w is deterministic iff for all times t, and for all objects x in w, there is noobject in any possible world with the same laws of nature as w, which matches x in itsqualitative description up to t, but which genuinely diverges from x in its total qualitativedescription.

When is branching genuine? That is, when does local qualitative branchingpossess determinism-violating powers? A natural idea is that branching is genu-ine when it is fundamental branching or is grounded in fundamental branching,and non-genuine otherwise. Local qualitative branching concerns qualitativeproperties of material objects. Fundamental local qualitative branching concernsfundamental, or underived, qualitative properties of material objects.In order to show how GSQD thus understood might help with the problem of

cheap indeterminism, let us assume a broadly Aristotelian, three-dimensionalistconception of material objects (see Chapter 1). Within this framework, we candraw a distinction between structured material objects, including artefacts andorganisms, whose parts are held together by some ‘principle of unity’, and unstruc-tured material objects, including simple particles and masses of matter—the latterbeing mereologically unchangeable, arbitrary sums of particles. Let us assume thatstructured objects are constituted by various unstructured objects at various times.We shall also assume that unstructured objects have many properties fundamen-tally, such as the properties of having a given mass at a time and of having a givenmaterial object as a part at a time, and that structured objects havemany propertiesthat they derive from fundamental properties of unstructured objects that consti-tute them; the former inherit these properties from the latter. Perhaps a structuredobject has a givenmass at a time and a given part at a time only in virtue of being atthat time constituted by an aggregate that has that mass and that part non-derivatively at that time.Now recall the following alleged violation of determinism. Suppose we arrange

an aggregate of particles in the shape of a house. Then we have the aggregate andwe have a house. When a further aggregate of particles, say in the shape of a brick,is added at time t, the house acquires new parts, whereas the original aggregate ofparticles does not, since the new particles merely get attached to it. So there aredistinct objects, an aggregate of particles and a house, whose qualitative descrip-tions match before t but diverge afterwards. The Aristotelian pluralist could blockthis violation of determinism by arguing that the present case does not involvegenuine branching. The house is a structured object that has its mereologicalproperties only derivatively. It is derivatively composed of certain particles at atime in virtue of being constituted by an aggregate that is non-derivativelycomposed of these particles at that time. What underlies the house’s change in

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parts over time is thus a succession of non-identical, mereologically rigid aggre-gates of particles: there is an aggregate of particles, a, and a slightly larger, non-identical aggregate, b, such that a constitutes the house before t and b constitutesthe house after t. When described at the level of non-derivative mereologicalproperties of aggregates, it is not the case anymore that there are objects whosequalitative profiles match before t but diverge mereologically afterwards. Sincemereological branching does not occur at that level, the mereological branchingis non-fundamental, and hence non-genuine with respect to the demands ofGSQD. In other words, the mereological divergence between the house and theaggregate of particles is metaphysically shallow. The divergence disappears at thelevel of non-derivative mereological properties, and therefore lacks the power ofviolating determinism. While not all Aristotelian pluralists will buy into this viewabout mereological profiles of structured objects, I think that this is their best shotat downgrading the local qualitative branching in the mereological case.10

Unfortunately, this response does not work for the case of the piece of paperand the paper plane. Here the qualitative divergence concerns persistence.While the piece of paper matches the paper plane in its qualitative descriptionup to t, the piece of paper exists after t, whereas the paper plane does not.Pluralists could avail themselves of the view that a structured object has variousproperties at a time only in virtue of being at that time constituted by an aggregatethat has those properties non-derivatively at that time. Existence at a time,however, is certainly not one of those properties. A structured object does notderivatively exist at a time in virtue of being at that time constituted by anunstructured object that non-derivatively exists at that time. If unstructuredmaterial objects persist through time non-derivatively, then so do structuredones. Moreover, it makes no difference if existence at a time is grounded inspatiotemporal occupation.11 For it is equally implausible to hold that a structuredobject derivatively occupies a spacetime region in virtue of being constituted by anunstructured object that non-derivatively occupies that region. (Three-dimension-alists might spell out the details of spatiotemporal occupation in different ways.)The familiar pluralist’s structured objects are not abstract ‘constructions’ fromunstructured aggregates, who are spatiotemporal only in a derivative sense. Rather,structured objects are spatiotemporal in the same robust sense in which unstruc-tured objects are. So the case at hand resists the proposed deflationary treatment.

10 This response is similar to Hawthorne’s (2006: 125–6) ‘inheritance-answer’ to the differentproblem of restricting the dynamical laws of our best physics, in order to avoid an apparent clashbetween these laws and the behaviour of certain ordinary objects.

11 For spatiotemporal accounts of persistence, see, inter alia, Balashov (2010) and Sattig (2006).

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The paper plane vanishes into thin air at t, whereas the piece of paper stays. Theplane’s disappearance, however, is not a metaphysical superficiality in comparisonto the coincident piece of paper’s trajectory. It is just as fundamental as the piece ofpaper’s continued persistence. This instance of local qualitative branching isgenuine, giving rise to an unwanted violation of determinism.This restriction strategy is unpromising in the framework of Aristotelian three-

dimensionalist pluralism about material objects. Standard four-dimensionalismis no better off. Focus on our case of coincidents with diverging lifelines. Thepiece of paper matches the paper plane in its qualitative description up to t, yetthe piece of paper persists beyond t, whereas the paper plane does not. Can thefour-dimensionalist discredit this instance of persistence-branching as non-genuine? I doubt it. According to four-dimensionalists, existence at a time isgrounded in having a temporal part at the time. So branching with respect topersistence is non-fundamental. The derivative nature of persistence, though, isinsufficient to deflate persistence-branching, since the qualitative divergenceamong coincidents recurs at the level of temporal parts: the piece of paper hastemporal parts beyond t, whereas the paper plane does not. It is hard to see whatcould downgrade this qualitative divergence as a mere metaphysical superficialityto which determinism should be insensitive. For the coincidents of the presentcase are, unlike the Aristotelian’s structured and unstructured objects, not hier-archically organized by the relation of constitution, such that one coincidentderives certain properties from another. One coincident’s distribution of tem-poral parts is just as fundamental as the other’s. Therefore, it is questionablewhether a standard four-dimensionalist can avail herself of a distinction betweengenuine and non-genuine branching, which is needed to appeal to GSQD inresponse to the problem of cheap indeterminism. I conclude that pluralists needto look for another way out.

6.2.4 Discerning coincidents

Perhaps it is time to shift gear and pursue another type of response. Pluralistscould try to avoid coincidence-based indeterminism in a way that does notquestion SQD, namely, by denying that the two coinciding objects match quali-tatively before t—that is, by denying that the troubling cases involve localqualitative branching in the first place. Notice, to begin with, that this strategyis entirely unsuited for standard four-dimensionalist pluralists, according towhich coincidence is a matter of sharing temporal parts. Having a property at atime comes down to having a temporal part at that time, which has the propertysimpliciter. Since the piece of paper and the paper plane share all their temporalparts prior to t, it follows that they are qualitatively indiscernible until that time.

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There is simply no room for discerning coincidents within this framework.12 Solet us ask whether and how three-dimensionalist pluralists could differentiatebetween the troubling coincidents.It is common and natural to answer that the paper plane cannot survive

flattening, whereas the piece of paper can—in short, that the paper plane is notflattenable, whereas the piece of paper is. This is a difference in the modalproperties of the two coinciding objects. The pluralist might hold that modalpotentialities, such as being flattenable, are properties that an object has at a time,and that the application of these properties to an object at a time does not dependon facts about the object at other times—that these modal properties are intrinsicto a time.13 The construal of modal potentialities as temporally intrinsic allowsthe pluralist to invoke them in specifying the qualitative history of an object up toa certain time, independently of what happens to the object later on. This puts thepluralist in a position to deny that the piece of paper and the paper plane arequalitatively indiscernible up to t, on the grounds that the former is flattenable att, whereas the latter is not. As there is no qualitative match between the twoobjects before t, there is no local qualitative branching and no violation ofdeterminism. This is a picture that promises the pluralist a way out of theproblem of cheap indeterminism.However, the picture fails to meet a plausible explanatory requirement. The

modal difference between the piece of paper and the paper plane—namely, thatone is flattenable while the other is not—stands in need of explanation. Somepluralists, a minority, will be content with brute potentialities. I am here address-ing the more ambitious ones who will not accept the difference as a brute fact,agreeing with everyone else that there can be no modal difference without anunderlying non-modal, categorical difference. The task of specifying this under-lying difference is the grounding problem, first discussed in Section 5.2. HereI am not interested primarily in the question whether constitutionalist pluralistscan solve this problem. (Let me just state that I take the prospects to be good.Recall the discussion of Fine’s hylomorphic solution in Section 5.2.14) What I amrather getting at is that on any promising way of explaining the de re modal

12 The prospects of avoiding the problem of cheap indeterminism are bad for four-dimensionalistpluralists, given that neither the restriction strategy nor the discernibility strategy seems to work.More trouble about determinism comes from a different direction. Hawthorne (2006: 133–4) arguesthat cheap violations of determinism of the actual world may be unavoidable given the combinationof four-dimensionalism with a Humean picture of laws of nature (he has in mind Sider’s view; seeSider (2001a: 224ff.)). The reasons for these violations have nothing to do with coincidence.

13 Cf. Hawthorne (2006: 101–2).14 See, inter alia, Fine (2008). See also deRosset (2011), which contains an overview of recent

approaches.

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differences between the piece of paper and the paper plane, these differences maynot be appealed to in solving the problem of cheap indeterminism. In short, thepluralist cannot solve both problems together. Let me explain.As we saw earlier, it is plausible to respond to the grounding problem by

invoking non-modal sortal differences, or kind differences, between the distinctcoincidents. The piece of paper is flattenable and the paper plane is not, becausethey belong to different kinds. This is a sensible but incomplete explanation, sincesomething’s belonging to the macroscopic kind piece of paper requires explan-ation in more fundamental terms, as well. Likewise for the kind paper plane.Now, whatever the grounds of kind-membership are, kind-membership is notfixed by an object’s qualitative profile at a time—kind-membership is not tem-porally intrinsic. The piece of paper and the paper plane belong to different kindsand yet share a categorical, non-sortal qualitative profile at various times.15 Kind-membership is rather fixed by properties that an object has simpliciter, orabsolutely. Ordinary kinds are invariant, characterizing an object sub specieaeternitatis.16 For this reason, the pluralist is not allowed to appeal to invariantkinds and their grounds as a way of preventing local qualitative branching. Recallthe temporal-intrinsicness constraint (Section 6.2.2). Determinism concernswhether the laws of nature and the qualitative history of an object up to a timedetermine the object’s qualitative profile after that time. To specify the qualitativehistory of an object up to time t is to specify temporally intrinsic properties of theobject until t. Determinism is thus not sensitive to properties that characterize anobject absolutely, or sub specie aeternitatis, for these properties are not suited tospecify partial histories of objects. This is why the pluralist is not allowed toappeal to invariant kinds (and their grounds) as a way of preventing localqualitative branching. Invariant kinds are unsuited for the purpose of specifyingthe partial history of an object. They do not belong to the category of temporallyintrinsic qualitative properties to which determinism is sensitive.17

15 The way I understand the notion, coinciding objects can be categorically indiscernible even ifone has certain properties derivatively, such as its mass, that the other has non-derivatively. Onderivative properties, see the discussion in Section 6.2.3.

16 I am here abstracting from how exactly invariant kinds are grounded. The kind piece of papermay well be more fundamental than the kind paper plane, and hence the explanations of kind-membership may differ significantly between the two cases. Nevertheless, both kinds are groundedin absolute properties of objects. This is the only aspect of relevance for the present argument.

17 I have been discussing the strategy of avoiding coincidence-based local qualitative branchingby appeal to differences in modal potentialities of the coinciding objects. One also hears pluralistsdistinguish the coincidents in terms of their essential properties. In our main case, one object isessentially paper-plane-shaped while the other is not. As essentiality is standardly understood,something has a property essentially just in case it has the property at all times and in all worldsat which it exists. Essential properties thus understood are clearly not temporally intrinsic, and

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Summing up, the objection to the solution of the problem of cheap indeter-minism in terms of modal differences between coincidents is the following. Itseems that the only hope the constitutionalist pluralist has of grounding modaldifferences between coinciding objects is to do so in terms of temporally un-relativized, absolute properties of objects that ground sortal differences betweenthe objects as well as modal ones. (Note again that I think that this can be done.)Absolute differences between the piece of paper and the paper plane, however,are not differences to which determinism is sensitive. As a result, the pluralistfaces a dilemma: solve the grounding problem by appeal to absolute properties ofobjects and leave the problem of cheap indeterminism wide open; or solve theproblem of cheap indeterminism by appeal to temporally intrinsic modal differ-ences and leave the grounding problem in the dark. The pluralist cannot have itboth ways.18

Can we sidestep the grounding problem by invoking non-modal differencesbetween distinct coincidents? We saw in Chapter 3 that distinct coincidents candiffer in a variety of non-modal ways at the same time. For example, a paperplane might be defective at a time, while the piece of paper coinciding with it atthat time is not. They might also differ in aesthetic respects or concerning whichintentional relations we bear to them (see Fine 2003). They might differ in theseways, but they need not. Those variations among coincidents are not compulsory,and therefore cannot be relied upon by the pluralist in her treatment of thepresent problem. Modal differences, on the other hand, are likely to be found inall ordinary cases of distinct coincidents.As a further instance of the discernibility strategy, the Aristotelian pluralist

might point to the following non-modal, mereological difference: the paper planehas the piece of paper as a proper part prior to t, but the piece of paper does not

therefore cannot be invoked in specifying partial histories of objects, as determinism demands. Inthe interest of length, I shall refrain from discussing non-modally understood essential properties.Suffice it to say that they would not seem to be temporally intrinsic, either. (The inadmissibility ofessential properties is closely related to the inadmissibility of haecceitistic properties addressed inSection 6.2.2.)

18 One might have other complaints about grounding modal differences of coincidents intemporally extrinsic differences. After all, this strategy allows no causal explanation of why thepaper plane vanishes at t and the piece of paper stays, in terms of facts intrinsic to t. Whatever couldmotivate the demand for such an explanation, it is not a demand I support here. (Pluralists and non-pluralists typically take the explanation of modal differences—that is, the grounding problem, asunderstood here—far more seriously than the causal explanation of temporal differences. See Fine(2008: 104–5) and Hawthorne (2006: 102–3), for liberal views on the temporal issue; see alsoSection 5.2.) My complaint is a different one. If temporally intrinsic causal explanation fails andgives rise to local qualitative branching, it had better fail for a reason of physics. Mundane violationsof determinism are out of the question.

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have itself as a proper part then. In order to evaluate this proposal, recall thataccording to Aristotelian pluralists, pieces of paper and paper planes are wholesgenerated by application of a principle of unity, or, as Fine has it, a compositionoperation, to one or more objects (see Section 1.1). If x is generated in this wayfrom the ys, then the ys are parts of x. Suppose now that a paper plane is createdfrom a pre-existing piece of paper by folding the latter in a certain way. The planeis thus generated from the piece of paper alone. In this case, it is sensible to saythat the paper plane has the piece of paper as a proper part—in fact, it has thepiece of paper as its only ‘major’ part.19 However, the case under consideration isdifferent. Here the piece of paper does not exist before the paper plane does. Theycome into existence simultaneously. Under these circumstances, it is less plaus-ible to claim that the paper plane has the piece of paper as a proper part.Intuitively, the plane is not made from the piece of paper. I find it more sensibleto describe the scenario in the following way. The same plurality of molecules isarranged in two different ways at the same time, and thus two complex, coinci-dent objects are generated at that time, which both have those molecules as theirmajor parts. Intuitively, one is not made from the other; they are both made fromthe same molecules at the same time, and thus do not differ in parts at that time.Correspondingly, it is plausible to claim that the piece of paper constitutes thepaper plane if the piece of paper predates the paper plane that is made from it.Since in the present case the piece and the plane come into existence simultan-eously, this account may be questioned.Putting the details of this case aside, the main point to be made is that while

coincidents could differ in this non-modal, mereological way, they need not.Nothing in the Aristotelian picture rules out the generation of distinct complexobjects from exactly the same plurality of objects under different principles ofunity. Mereological differences among coincidents are not compulsory, unlikemodal ones, and hence cannot sustain a resolution of the problem of cheapindeterminism.Let us take stock. A number of replies to the problem of cheap indeterminism

on behalf of traditional pluralists were rejected as defective. I hope this discussionis sufficient to show that the problem is a serious one, that it lacks an easysolution, without assuming that there is no other way out of the problem for thesepluralists. In the remainder of the chapter, I shall offer a perspectival-hylomorphistresponse to the problem. I shall suggest a cure that, unlike the previous ones,blocks all cheap violations of determinism by ordinary coincidents and that is notworse than the disease.

19 See Koslicki (2008: 179–80) for discussion of this sort of case.

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6.3 Material Determinism and Formal Branching

My solution is an instance of the restriction strategy: local qualitative branchinginvolving coinciding ordinary objects does not violate determinism, because itbelongs to a kind of branching to which determinism is not sensitive. There isgenuine local qualitative branching, which is, in some sense, metaphysically deep,and there is non-genuine branching, which is metaphysically shallow. The cruxof the approach is to reserve determinism-violating powers to genuine branchingand to expose the objectionably mundane branching of qualitative profiles ofdistinct, coinciding ordinary objects as non-genuine. We have seen an instance ofthis strategy with limited application (Section 6.2.3). I will propose an imple-mentation without the encountered limitations.Perspectival hylomorphism allows the following analysis of cases of distinct,

coinciding ordinary objects with branching qualitative profiles, which was firstpresented in Chapter 3. I shall here invoke the version of perspectival hylo-morphism that is based on three-dimensionalism about material objects, for areason to be addressed shortly (see Section 1.3 for a sketch of different versions).In the case of the piece of paper and the paper plane, there is a (three-dimen-sionalist) material object, a, that is the unique subject of a piece-of-paper-path, i1,and of a paper-plane-path, i2, such that i1 and i2 begin at the same time, i1 and i2contain the same qualitative properties and relations up to time t, the time offlattening, i1 continues beyond t, and i2 ends at t.

20 Then there is a piece of paper,the compound of a and i1, and a paper plane, the compound of a and i2.

21 By thebasic metaphysical semantics of formal predication (see Chapter 2), it followsthat the piece of paper and the paper plane are formally distinct and qualitativelyindiscernible until t, while the paper plane formally ceases to exist at t and thepiece of paper does not. This captures our intuitions about the case, on theplausible assumption that our intuitions are sortal-sensitive, and the assumptionthat the formal mode of predication corresponds to the sortal-sensitive perspec-tive on ordinary objects. What we have here, then, is a case of formal qualitativebranching: there are objects that formally have the same intrinsic and relationalqualitative properties until a certain time and formally differ afterwards. Nowconsider just the (three-dimensionalist) material basis of this case, which is to be

20 K-paths also contain realization-facts of the form, ‘ç realizes K’, for some ç and K, with respectto which the piece-of-paper-path and the paper-plane-path differ at all times. These facts arerelevant for grounding invariant kind-membership (see Section 4.2). But they are irrelevant forquestions of determinism (see Section 6.2.4).

21 For simplicity, I shall here work with the basic version of perspectival hylomorphism intro-duced in Chapters 1 and 2, leaving aside subsequent modifications.

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described in the absolute mode of predication. The two ordinary objects have acommon underlying matter, the material object a. This material object is paper-plane-shaped as well as piece-of-paper-shaped until a certain time and solelypiece-of-paper-shaped afterwards. Moreover, there is no metaphysical reason toadmit that there are distinct material objects with the same intrinsic and rela-tional properties until a certain time but different ones afterwards, and hence noreason to admit material qualitative branching. So the local qualitative branchinginvolved in the common-sense case of the piece of paper and the paper plane isformal but not material.This analysis applies to our second case of distinct coincidents, as well. The

aggregate of bricks and the house are formally indiscernible until the time when afurther brick is added but formally discernible afterwards. So there is formalqualitative branching. But no material objects involved in this case share theirintrinsic and relational properties until a certain time but not afterwards. So thereis no material qualitative branching. (See the discussion of Tibbles and Tib inChapter 3 for a careful description of the three-dimensionalist material basis ofthis sort of case.) These two cases of purely formal qualitative branching maybe illustrated by Figure 6.1 (for ease of illustration, the coincidents are drawn sideby side).In light of this account of qualitative branching by coinciding ordinary objects,

it is easy to provide a plausible explanation of why our trouble cases do notviolate determinism. SQD is a characterization of the notion of a deterministicworld in terms of the qualitative profiles of objects in this world. It is natural tounderstand the relevant qualitative profiles as those of material objects, in my

piece of paper paper plane brick aggregate house

t

= material object = K-path

Figure 6.1 Purely formal qualitative branching

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technical sense—that is, as the qualitative profiles of objects with non-derivativespatiotemporal locations. Thus, I suggest the following restriction of SQD:

Material Strong Qualitative Determinism (MSQD)A possible world w is deterministic iff for all times t, and for all material objects x in w,there is no material object in any possible world with the same laws of nature as w, whichmatches x in its qualitative description up to t, but which does not match x in its totalqualitative description.

By MSQD, formal without material branching does not make the actual worldindeterministic. Purely formal branching is metaphysically shallow, and hencenon-genuine, in the sense that it arises from a divergence of K-paths that do nottrack paths of material objects—these distributions of properties do not carvematerial objects at their joints. That is, purely formal branching is shallow withrespect to the absolute qualitative profiles of material objects; at the level ofmaterial objects, this qualitative branching disappears. Only branching in theprofiles of material objects is of the genuine type relevant for questions ofdeterminism. This is my solution to the problem of cheap indeterminism. It isan instance of the restriction strategy that does not suffer from the limitationsafflicting the Aristotelian-pluralist restriction strategy considered earlier: branch-ing concerning the persistence of coinciding ordinary objects is deprived of itsdeterminism-violating powers as much as other instances of mundane, a prioribranching.Four points of clarification. First, by MSQD questions of determinism are only

sensitive to qualitative branching of material objects. This does not mean that thederivative properties of ordinary objects, understood as double-layered com-pounds, have no relevance at all for the question whether a world is deterministic.It rather means that only the properties ordinary objects have materially arerelevant, whereas properties ordinary objects have formally but not materiallyare irrelevant. That is, MSQD is only sensitive to material qualitative branchingof ordinary objects—the kind of branching that derives from properties of theunderlying matter of these objects.Second, the proposed version of determinism not only respects our aversion

against cheap failures, but also correctly classifies the world of the collapsingtower and the world of the coloured spheres (discussed in Section 6.1 as motiv-ators for a strong conception of qualitative determinism) as indeterministic. Takeany of the five blue spheres in the sphere world w. According to the presentaccount, it is a compound of a sphere-path and a material object, a. Suppose thatthis material object turns pink at time t in w. In the same world, there is anothersphere, a compound of a different sphere-path and a different material object, b.

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The qualitative description of bmatches the qualitative description of a until timet but does not match a’s total qualitative description, because b does not turn pinkat t. So there is material qualitative branching. The laws of nature fail todetermine whether a material object with a given qualitative description willturn pink. By MSQD, w is indeterministic. This is a proper failure of determin-ism, a failure for a reason of physics. Notice that since the sphere-paths followinga and b are also qualitative duplicates until t but not afterwards, this case involvesformal as well as material qualitative branching. The presence of formal branch-ing, however, is irrelevant to the question whether a world is deterministic. Thecase of the collapsing tower is treated analogously.Third, the present solution requires a metaphysical account of material objects

that permits violations of MSQD only for reasons of physics. Standard four-dimensionalism is not such an account. The four-dimensionalist recognizes forany filled region of spacetime a material object that exactly occupies that region.Suppose, then, that a spacetime worm persists through a temporal interval thatcontains times t1, t2, and t3, in that order. It follows from the four-dimensionalistontology that this worm has a proper part that shares all of its temporal partsfrom t1 to t2 but not after t2, either because it has no temporal parts after t2 orbecause it has other temporal parts, with other qualities, after t2. These twospacetime worms are qualitatively indiscernible until t2 but diverge afterwardseither because the first ceases to exist at t2 while the second continues on, orbecause they have different qualitative properties, instantiated by different tem-poral parts, after t2. So standard four-dimensionalism yields an abundance of apriori instances of local qualitative branching of material objects, which clearlydo not give determinism ‘a fighting chance’. It is thus important that the presentsolution to the problem of cheap indeterminism was developed on the basis of athree-dimensionalist, classical-mereological account of material objects thatavoids such objectionably easy violations of MSQD. Note that while the problemunder consideration requires a choice between a three-dimensionalist and a four-dimensionalist basis for perspectival hylomorphism, no such choice was requiredby the applications of the framework in previous chapters.22

Fourth, the crux of the proposed solution is to reject the identification ofordinary objects with material objects, and to allow ordinary objects to havequalitative profiles that do not always correspond to the profiles of materialobjects. Since the present double-layered account is not alone in construing

22 As pointed out in n.12, there are further reasons for the unavoidability of the standard four-dimensionalist commitment to cheap failures of determinism, which are independent of the presentconsiderations.

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ordinary objects this way, the proposed approach to the problem has alternative,single-layered implementations. Those who hold that ordinary objects are justK-paths (see Section 1.3)—or, similarly, that they are merely events or processesof some kind—can say that the changes in ordinary objects are completelyirrelevant to questions of determinism. On this non-perspectival view, branchingqualitative profiles of ordinary objects are really just branching distributions ofqualitative properties, which may or may not track the spatiotemporal paths ofmaterial objects. This solution and mine obviously follow the same strategy. YetI find my approach in terms of perspectival hylomorphism more appealing onintuitive grounds. The reason is that I find it at least mildly objectionable to banordinary objects completely from the domain of objects to which our favouredconception of determinism applies. Do we really want to say that the evolvingqualitative profiles of our persons, tables, trees, and planets have no effectwhatsoever on the question whether the actual world is deterministic? I thinknot. And we need not say it. For according to perspectival hylomorphism, it isonly the purely formal profile of ordinary objects that is irrelevant to questions ofdeterminism, while the material profile of the same objects—the profile theobjects have independently from which kinds they belong to—is relevant indeed.Let me summarize the discussion of the problem of cheap indeterminism. The

problem marks a tension between strong qualitative determinism, SQD, andcertain cases of local qualitative branching involving distinct, coinciding ordinaryobjects: if SQD and the cases are accepted, then the actual world is indetermin-istic on mundane, a priori grounds. Prima facie, it is difficult to resolve thistension in a satisfactory way. If we reject cases of ordinary branching by coinci-dence in the first place, preferring a monist account of coincidence to a pluralistone, we bet against common sense. Moreover, if we reject SQD altogether, it ishard to see which plausible conception of determinism could take its place. Weakqualitative determinism, WQD, de re determinism, DRD, and regional deter-minism, RQD, are all inferior to SQD. Finally, restricting SQD in the context ofan Aristotelian distinction between structured and unstructured objects fails toblock all cheap violations of determinism by coincidence. I suggest we try adifferent approach, which requires looking beyond traditional accounts of ordin-ary objects. If the familiar identification of ordinary objects with material objectsis resisted, a sensible way out presents itself. I have shown that in the frameworkof perspectival hylomorphism the critical cases of distinct, ordinary coincidentsgive rise only to purely formal qualitative branching, and that since strongqualitative determinism is naturally restricted to material objects and materialqualitative branching, yielding MSQD, the cases do not violate determinism ofthe actual world. With the help of perspectival hylomorphism we can thus isolate

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all mundane, a priori failures of determinism without dropping a plausiblecharacterization of determinism and without betting against common sense.The key is to respect common-sense profiles of ordinary objects but to stripthem of their questionable indeterminism-making influence. This solution to aserious problem about determinism constitutes a further attractive feature ofperspectival hylomorphism.23

23 It is worth pointing out that perspectival hylomorphism also helps with the related problemthat the dynamical laws of our best physics do not seem to apply to all ordinary objects, which isdiscussed at length in Hawthorne (2006: 111–44). In light of the foregoing discussion, it is clear howto tackle this problem. The dynamical laws do apply to all ordinary objects, just as we initiallyexpected, but they only concern material properties of these objects, as opposed to purely formalones. When ordinary objects are thought of as mere physical bodies (under some physics-friendlysortal-abstract conception; see Section 8.3), then the dynamical laws apply, but when they arethought of as things of familiar kinds, then the laws fail to apply, since the sortal-sensitive profileof ordinary objects is metaphysically less robust. So perspectival hylomorphism offers a unifiedsolution to the two problems.

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7

Indeterminacy

After having applied perspectival hylomorphism to problems concerning spatial,temporal, de re modal, and deterministic properties of ordinary objects, I shallnow extend the framework to give an account of certain indeterminate propertiesof ordinary objects. I shall focus on the following case. Suppose that mountainM is a massive collection of rocks deposited in layers. As a result of meltingglacial ice, M gradually sheds rock mass; some rocks in the mountain’s surfacelayer slowly become loose and slide off. In this process, several surfaces becomeequally good candidates to be the boundary of the mountain. A surface includinga particular loose rock, r, is an equally good candidate to mark the boundary ofthe mountain as a surface excluding that rock. As a consequence, the rock attainsa questionable status: it is indeterminate whether M has r as a part. M’s mereo-logical boundary is indeterminate.1

This mereological indeterminacy claim has different readings: the de dicto andthe de re reading. The two readings may be specified informally by using thecolon to indicate the scope of the operator ‘It is indeterminate whether’:

De dictoIt is indeterminate whether: M has r as a part.De reM and the property of having r as a part are such that it is indeterminate whether: thisobject instantiates this properties.

The difference is that on the de dicto reading it is indeterminate whether a certaindescription of the world is true, whereas on the de re reading it is indeterminate ofa particular object and a particular property whether the latter applies to the

1 With indeterminacy of composition comes indeterminacy of location. Since the exact locationof M is fixed by the exact location of its parts, if it is unclear which parts M is composed of, it is alsounclear exactly where it is located: it is indeterminate whether M is (exactly) located in p, for someplace p. M has an indeterminate mereological and spatial boundary. In what follows, I shall focus onmereological indeterminacy. As I shall indicate later on, my account of mereological indeterminacygeneralizes straightforwardly to spatial indeterminacy.

former.2 Adopting a popular façon de parler, I shall say that if the de re reading ofour claim of mereological indeterminacy is true, then M is a vague, or fuzzy,object. Mereological indeterminacy de re is naturally viewed as an instance ofmetaphysical indeterminacy, in the sense of being independent of conceptual,linguistic, or epistemic representation.The main question of this chapter is whether such de re indeterminacy claims

about ordinary objects might be true—whether ordinary objects might be mer-eologically vague. To emphasize, the question is not whether any object could beindeterminate in any respect. The question specifically concerns the status ofintuitive mereological indeterminacy claims about ordinary objects—that is,about objects falling under ordinary sortal concepts, such as the concept of amountain.3

When philosophers contemplate the status of ordinary mereological indeter-minacy, they typically juxtapose the following two positions:

(I) All ordinary mereological indeterminacy is merely de dicto and has itssource in how we represent the world.

(II) Some ordinary mereological indeterminacy is de re and has its source inhow the world is, independently of how we represent it.

In Sections 7.1 and 7.2, I shall sketch standard versions of (I) and (II), respectively,and subject each of them to criticism. As my aim is primarily constructive, thepurpose of these sections is not to refute these positions. The point is ratherto highlight worries that give sufficient reason to scout for alternatives. InSection 7.3, I shall develop a novel version of (II) and show that it avoids theproblems for (I) and (II) considered in the previous sections. The heart of theapproach is the perspectival-hylomorphist notion of formal indeterminacy de re.

7.1 Indeterminacy De Dicto and the Problemof the Many

Perhaps the most popular instance of position (I) is the standard supervalu-ationist treatment of ordinary mereological indeterminacy, most prominently

2 See Sainsbury (1989) andWilliamson (2003) for the characterization of claims of indeterminacyde re as having the form: for some object x and some property ç, it is indeterminate whether xinstantiates ç.

3 Some find the popular talk of vague objects dubious, on the grounds that an object is only evervague, or indeterminate, in a certain respect. See, inter alia, Hawley (2002) and Williamson (2003).I share these doubts and emphasize that talk of vague objects will here be understood merely as looseand vivid talk. The serious notion in the background is that of mereological indeterminacy de re.

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endorsed by Lewis (1993).4 Supervaluationism is the dominant brand of linguis-tic theory of indeterminacy. To the supervaluationist, indeterminacy arises as aresult of semantic imprecision, where an expression is semantically imprecisewhen its meaning can be extended, can be made precise in different ways. Somebut not all precisifications of the expression are consistent with speakers’ use ofthe expression. They are the admissible precisifications. Supervaluational truthconditions of statements containing imprecise expressions may be specified interms of the notion of truth on an admissible precisification I of all impreciseexpressions in the object-language, by means of which notion super-truth andsuper-falsity are defined. A sentence s is super-true iff s is true on all Is, s is super-false iff s is false on all Is, and s is neither super-true nor super-false iff s is true onsome but not all Is. Truth in the imprecise object-language is super-truth; andfalsity in the object-language is super-falsity. Given these meta-linguistic notionsof super-truth and super-falsity, how are claims of determinacy and indetermin-acy in the object-language to be understood? According to standard supervalu-ationism, ⌜Determinately, s⌝ is true iff s is super-true. Indeterminacy of s maythen be expressed by saying that neither determinately s nor determinately not s.This is the rough framework.How can it be true that M has an indeterminate mereological boundary? Accord-

ing to standard supervaluationism, such indeterminacy arises from imprecision inhow we refer to ordinary objects, an imprecision that depends on the nature ofordinary sortal concepts. In the case at hand, there is a cluster of massivelyoverlapping aggregates of rocks with different precise decompositions (at a giventime), such that each of these aggregates is a candidate referent for the name ‘M’.Each of these aggregates is a candidate to be designated by ‘M’ because the namepurports to designate a unique object falling under the sortal concept of a mountain,and because each of the massively overlapping candidates has what it takes to be amountain. The multitude of candidate referents thus depends on the fact that thesortal fails to select a single aggregate out of a cluster of massively overlapping ones.It is then indeterminate whether M has r as a part, since it is true of some admissibleprecisification of ‘M’ that it has r as a part, but not true of all admissible precisifica-tions of ‘M’. The standard supervaluationist thus accepts the de dicto reading of ourindeterminacy claim about M. But she rejects the de re reading because it is not thecase of M that it is indeterminate whether: it has r as a part, as each candidatereferent has a clear-cut decomposition. There are no vaguemountains in this world.5

4 For classical presentations of supervaluationism, see Fine (1975) and van Fraassen (1966).5 A standard and plausible assumption in the background is that the predicate ‘is a part of ’ is a

precise predicate. The mereological indeterminacy is meant to have its exclusive source in the

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This picture has been attacked from different angles.6 I shall focus on animportant objection that concerns the standard supervaluationist response tothe problem of the many. This problem poses the task of explaining mereologicalindeterminacy of ordinary objects in a way that sustains our familiar practice ofcounting these objects. It arises for supervaluationism in the following way. Outthere on the plain, there is exactly one mountain, M—or so we think. Yet,according to the standard supervaluationist, we are not managing to refer toa unique object. There is, rather, a multitude of candidates to be the mountain,which explains M’s mereological indeterminacy. If among many candidates asingle one is a mountain, then there must be a fact of the matter singling outone candidate. Since each candidate has everything it takes to be a mountain,each of them is an equally good candidate to be the mountain, and hence thereis no fact of the matter singling out one candidate. But if each of them is amountain, then we have many mountains on the plain. And if none of themis a mountain, then we have no mountain on the plain. Either way, it is not thecase that there is one mountain on the plain, as we expected. This problemarises for all macroscopic material objects with fuzzy boundaries.7

The standard supervaluationist offers the following reply. The sortal concept ofa mountain, or the sortal term, is imprecise. Each of the many mountain-candidates is neither clearly a mountain nor clearly not a mountain—that is, itis unclear whether the concept applies to any of them.8 And yet it is true thatthere is exactly one mountain on the plain. The trick is to say that on eachadmissible precisification of the sortal concept of a mountain, the latter applies toexactly one of the massively overlapping candidates on the plain. It is then trueacross all precisifications of the sortal that there is one mountain over there,although it is not true of any of these candidates that it is the mountain. Theexistential statement is true although none of its instances is true.9

imprecision of ‘M’, which derives from the imprecision of the sortal mountain associated with ‘M’.This treatment of ordinary mereological indeterminacy is most saliently adopted by Lewis (1993).See also McGee and McLaughlin (2000).

6 See Hudson (2001: chapter 1) and Weatherson (2003, 2009) for overviews.7 See Unger (1980). The similar ‘problem of 1,001 cats’ appears in Geach (1962).8 I shall assume that ‘the set of mountain candidates’ is precise, and thereby ignore issues of

higher-order vagueness.9 I said that the problem of the many poses the task of explaining mereological indeterminacy of

ordinary objects in a way that sustains our familiar practice of counting these objects. The solutiondiscussed here embraces this task. Various other known solutions are less ambitious. Unger (1980),for example, draws the conclusion that there are many mountains or none, thereby giving up on ourintuitive cardinality claim that there is a single mountain on the plain. Markosian (1998), bycontrast, tries to capture this uniqueness claim by arguing that among many largely overlappingpluralities of rocks on the plain only one such plurality has a fusion. This approach, however, leaves the

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This response is hard to accept. I shall focus on an objection that I findparticularly pressing.10 The crux of the supervaluationist approach to the prob-lem of the many is that each precisification of the sortal mountain singles outexactly one of the many candidates. But how does that work? Does each pre-cisification specify a complex property that tells us precisely what makes anobject a mountain, and that only one of the candidates has? In other words, iseach precisification principled? This is hard to believe, given that the overlappingcandidates may differ only minutely, by a rock or two. It seems that any suchproperty would either apply to several of the candidates, making it false that thereis one mountain on the plain, or it would fail to apply to any, or sufficiently many,aggregates of rocks elsewhere, making it false that there are a few thousandmountains in Switzerland. The point is that the differences between the variouscandidates are considerably more fine-grained than the differences between anysensible and principled precisifications of the sortal—in short, the differencesbetween the candidates are sub-sortal differences.Then maybe the various precisifications single out one candidate ‘blindly’, in

the sense that, on each precisification, the sortal applies to one arbitrary candi-date. This, however, is implausible. It is a natural view about the applicationconditions of mountain that if some objects are mountains, they must be so invirtue of other properties. This explanatory requirement is independent ofconsiderations of vagueness and indeterminacy. What stands behind it is themetaphysical thought that mountainhood is not a fundamental property—thatmountainhood is not among the properties that ground all other properties in theuniverse. If supervaluationism is to satisfy this explanatory requirement, then itmust be the case that on each precisification ofmountain, an object is a mountainin virtue of having certain more fundamental properties. Yet if precisifications ofmountain are arbitrary, then mountainhood applies primitively to differentobjects on different precisifications. (Perhaps we should rather say that distinctproperties of mountainhood corresponding to distinct precisifications of thesortal apply primitively.) Hence, facts about mountains are not grounded inmountainhood-free facts.11

mountain’s fuzzy boundary in the dark. An account of mereological indeterminacy is not part of thepackage. To mention a third approach, Lewis (1993) accepts that while each of the aggregates is amountain, the common-sense claim that there is only one mountain on the plain is preserved, asordinary speakers do not count by strict identity, but rather by the weaker relation of massive overlap.This is an attempt to get the uniqueness claim to come out true. The approach by itself, however, offersno handle on mereological indeterminacy. See Sattig (2010b) for criticism along these lines.

10 A forceful rendition of the ensuing objection is presented in McKinnon (2002).11 Weatherson (2003) has attempted a defence of supervaluationism against this objection. His

main response to the variant of the objection that involves mountains is to claim that when it comes

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Let me emphasize, however, that while this is a good reason for doubting thatthe standard supervaluationist strategy applies to all ordinary cases of mereo-logical indeterminacy, the strategy may well be satisfactory for dealing with somecases of indeterminacy involving ordinary objects, which are relevantly differentfrom the case of M. For example, it may be unclear whether a given plurality ofrocks compose a mountain. Standard supervaluationism offers a natural accountof this type of indeterminacy. Any plurality of rocks composes some object;composition is unrestricted. The impression that it is indeterminate whethersome rocks compose a mountain does not arise because it is indeterminatewhether the rocks compose some thing—existence cannot be indeterminate—but rather because it is indeterminate whether that thing they determinatelycompose is a mountain. And it is indeterminate whether it is a mountain, onthe grounds that on one precisification of mountain the sortal applies to theobject, while on another precisification it does not apply to the object.12 Corres-pondingly, it may be unclear whether a given area contains one or two moun-tains, on the grounds that on one precisification ofmountain the sortal applies toone object in the area, whereas on another precisification of the sortal it appliesto two objects in the area. While I reject the supervaluationist account of the caseof M, I am inclined to accept a supervaluationist treatment of these other cases.13

7.2 Fundamental Indeterminacy De Reand Coincidence

An alternative to the construal of ordinary mereological indeterminacy as dedicto is the view that such indeterminacy is de re—this is position (II) outlined atthe beginning. Indeterminacy de re of mereological boundaries of ordinaryobjects is naturally viewed as an instance, possibly one of many instances, of

to the sortal mountain the mentioned explanatory requirement is too strong. He considers a case inwhich it is unclear whether ‘we have one mountain with a southern and a northern peak, or twomountains, one of them a little north of the other. Whether there is one mountain here or two,clearly the two peaks exist, and their fusion exists too. The real question is which of these threethings is a mountain. However this question is resolved, [ . . . ] a relatively unprincipled precisifica-tion will be acceptable’ (Weatherson 2003: 497). This conclusion is dubious. The differenceunderlying the alternative counts—one mountain versus two mountains—concerns, roughly,whether a mountain is ‘individuated’ by a single peak or by a maximal series of proximal peaks.This difference seems to be perfectly principled.

12 That ordinary sortals have borderline cases is the basis of the sorites argument against theexistence of ordinary objects given by Unger (1979). I am here setting aside standard soritesproblems, because perspectival hylomorphism presents no alternative to the many familiarapproaches on the market.

13 See also the application of supervaluationism to the paradoxes of fission in Section 4.2.

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metaphysical indeterminacy, or of indeterminacy in the world, in the sense ofbeing independent of conceptual, linguistic, or epistemic representation. If thereare facts of indeterminacy de re about ordinary objects, then these objects reallyare indeterminate, independently of how we represent them. Of course, thischaracterization of indeterminacy de re as metaphysical only says somethingabout what the indeterminacy is not, namely, a consequence of an impreciserepresentation. A positive account of its nature is a different matter.So what is the nature of mereological indeterminacy de re?14 The standard view

is to construe this indeterminacy, along with metaphysical indeterminacy ingeneral, as fundamental, either in the sense that facts about such indeterminacyare not grounded in any more basic, indeterminacy-free facts, or in the sense thatthe operator ‘it is indeterminate whether’ is perfectly natural, that it ‘carvesnature at the joints’.15 Friends of this view emphasize that while metaphysicalindeterminacy cannot be analysed reductively, the notion can still be elucidated.It is indeterminate of mountain M whether: it has r as a part. This could be madeintelligible by saying that reality itself has different precisifications, all of whichare perfectly precise, including one in which M has r as a part and one in whichM lacks r as a part. One way of developing this idea is to view metaphysicalindeterminacy as a kind of modality, which concerns worlds that are precisifica-tionally possible—in other words, which concerns multiple actualities.16 In thisframework, mereological indeterminacy may be explicated by supervaluatingover the varying mereological profiles of a given object in different actualworlds—instead of supervaluating over the mereological profiles of different,overlapping objects, as standard supervaluationism has it (see Section 7.1). It isindeterminate of M whether: it has r as a part iff there is a precisificationallypossible world, an actuality, in which M has r as a part, and another precisifica-tionally possible world, another actuality, in which M lacks r as a part.How could the problem of the many be solved on the basis of a de re account of

mereological indeterminacy? Recall that if the indeterminate boundaries ofmountains are understood in terms of mereological differences between a plur-ality of overlapping aggregates of rocks, then it is hard to uphold our intuitiveclaim that there is exactly one mountain on the plain. If, however, mountains getto be vague objects, then we are in a position to recognize but a single mountain

14 For constructive discussion of metaphysical indeterminacy, see, inter alia, Akiba (2000, 2004),Akiba and Abasnezhad (2014), Barnes (2010), Barnes and Williams (2009, 2011), Morreau (2002),Parsons (2000), Rosen and Smith (2004), Skow (2010), Smith (2005), Williams (2008), andWilliamson (2003).

15 See, inter alia, Barnes and Williams (2011: 106).16 See, inter alia, Barnes and Williams (2011).

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on the plain, and to attribute a mereologically indeterminate boundary to it. Thisis a promising start, providing a good reason for taking the de re alternativeseriously. Further work is required, though. For now the question is, Whatgrounds the fact that there is exactly one vague mountain on the plain, as wewould expect, as opposed to many? On the original assumption that compositionis always determinate, there was the problem of explaining why among manylargely overlapping pluralities of rocks only one plurality of rocks composes aprecise mountain, such that each of these rocks is a determinate part of themountain. On the new assumption that composition can be indeterminate, thereis the problem of explaining why among many largely overlapping pluralities ofrocks only one plurality of rocks composes a vague mountain, such that each ofthese rocks is a determinate part or an indeterminate part of the mountain. This isan important challenge to the standard account of indeterminacy de re. I shall haveto leave it, though. I will not be able to discuss the account at a resolution thatallows an appropriate discussion of this issue. I shall return to the problem of themany when presenting my own construal of indeterminacy de re in Section 7.3.4.The view of ordinary objects as having metaphysically indeterminate proper-

ties has been greeted with much resistance. Many, including Michael Dummett(1975), have found it unintelligible that there should be metaphysical indeter-minacy. However, progress has been made on this front. For defenders ofmetaphysical indeterminacy have offered ways of rendering such indeterminacyintelligible, as the modal approach mentioned above illustrates. If one under-stands the idea that an object can be at home in different precisificationallypossible worlds, and that it can vary in its mereological profile across theseworlds, then one understands mereological indeterminacy de re.Even if intelligibly glossed as arising from multiple precisifications of reality,

many philosophers still refuse to admit fundamental metaphysical indetermin-acy. And they may not base their attitude on arguments, because their realground is the simple intuition that metaphysical indeterminacy, conceptualizedas involving multiple actualities, is unbearably radical—for short, that it is crazy.This is a respectable attitude, comparable to Goodman and Quine’s motive forrejecting abstract entities: ‘Fundamentally this refusal is based on a philosophicalintuition that cannot be justified by an appeal to anything more ultimate’(Goodman and Quine 1947: 174).More can be said, though. An objection to mereological indeterminacy de re

that takes the form of an argument is a recent attack by Brian Weatherson.17

17 The original argument appears in Weatherson (2003: section 4). In unpublished work, Weath-erson has presented a second version of the argument that is meant to avoid a weakness in the first

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Consider again our mountain M. To start the argument, assume for reductio thatit is indeterminate of M whether rock r is a part of it. The second premise of theargument is that there is an object, M-minus, that determinately has all and onlythe parts of M that do not overlap with r; it is determinate of M-minus that: for allx, x is a part of it iff x is a part of M and x does not overlap with r. Intuitively,there is this object, rigidly designated by the name ‘M-minus’ across differentprecisificationally possible worlds, which is the mountain, M, without thatparticular rock. Note that this remainder of the mountain may itself haveindeterminate parts.Now recall that an object o coincides with an object o* at a time t just in case o

and o* occupy the same place at t. (Henceforth, I shall focus on objects at aparticular time, and drop all temporal modifiers for presentational simplicity.) IfM lacks rock r as a part, then M and M-minus share all their parts; and if theyshare all their parts, they coincide. Moreover, I shall assume that if M coincideswith M-minus, then M lacks rock r as a part. Hence, M coincides with M-minusiff M lacks rock r as a part. Since it is indeterminate of M whether r is a part of it,it is indeterminate of M and M-minus whether they coincide. The third premiseof the argument is that coinciding objects are identical. This premise may bebacked in various ways. I shall focus on the simplest way, namely, by appeal to theintuition that distinct objects cannot fit into the same place at the same time, thatdistinctness of coinciding objects leads to overcrowding (see Section 3.1).18 Forthis reason it is plausible that if M coincides with M-minus, then M is identicalwith M-minus. Since the converse obviously holds as well, M coincides withM-minus iff M is identical with M-minus. Since it was established earlier thatit is indeterminate of M and M-minus whether they coincide, it follows that it isindeterminate of M and M-minus whether they are identical. Importantly, thisstatement of indeterminate identity is de re. The final premise of the argument isthat the well-known Evans–Salmon argument shows successfully that there can beno de re indeterminate identity, contrary to what was established by means of thefirst three premises. Roughly, M-minus has the property of being indeterminatelyidentical withM. ButM lacks that property. Hence, M andM-minus are distinct.19

version, pointed out in Barnes and Williams (2009). The argument to be presented here is more orless Weatherson’s second argument. For reasons of space, I shall be unable to address differencesamong versions and the interesting debate behind them. My aim is to sketch an account of vagueordinary objects that withstands the Weatherson attack in its most severe form—that is, even underthe assumption that the Barnes–Williams-bug is fixable.

18 A more complex reason for rejecting distinct coincidents is driven by the grounding problem(see Section 5.2).

19 See Evans (1978) and Salmon (1981). As Lewis (1988) pointed out, semantically indeterminateidentity statements are not the target of the Evans–Salmon argument, but only de re indeterminate

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The argument may be summarized as follows:

(1) It is indeterminate of M whether: it has r as a part. [P1](2) There is an object, M-minus, such that it is determinate of M-minus that:

it has all and only the parts of M that do not overlap with r. [P2](3) It is determinate of M and M-minus that: the former coincides with the

latter iff the former lacks r as a part.(4) It is indeterminate of M and M-minus whether: the former coincides with

the latter.(5) It is determinate of M and M-minus that: the former coincides with the

latter iff the former is identical with the latter. [P3](6) It is indeterminate of M and M-minus whether: the former is identical

with the latter.(7) It is not indeterminate of M and M-minus whether: the former is identical

with the latter. [P4]

This argument is an attempt at a reductio of the claim that M is a mereologicallyvague object, via the assumptions that there is an object, M-minus, that iscomposed of all of M except r (P2), that coinciding objects are identical (P3),and that Evans–Salmon-style reasoning establishes the incoherence of de reindeterminate identity (P4).20 I find each of these assumptions compelling.I will not elaborate on the motivation of P2 and P4.21 Having discussed problemsof coincidence at length in previous chapters, another word on P3 is in order.As an attempt to block the argument, consider replacing P3 by the following

weaker premise, P30: [It is determinate of M and M-minus that: the formercoincides with the latter] iff M is identical with M-minus. With P30, P1 and P2do not lead to (6) below, and hence do not clash with (7). Intuitively, P3 has itthat for any way w of making our world precise—for any precisificationallypossible world w—if M and M-minus have the same mereological boundary

identity statements. Note further that the distinctness of M and M-minus may also be supportedwithout identity-involving properties. M has the property of having r as an indeterminate part. ButM-minus lacks that property. Hence, M is distinct from M-minus.

20 The problem is reminiscent of the paradox of Tibbles and Tib, which is generated bytemporary parthood, as opposed to indeterminate parthood (see Section 3.1). Tibbles is a cat. Tibhas all and only the parts of Tibbles that do not overlap with Tibbles tail. When Tibbles loses her tail,both Tibbles and Tib survive. If Tibbles and Tib are distinct, then they are distinct coincidents afterthe accident. But distinct objects cannot coincide. One way of avoiding distinct coincidents in thiscase is to let Tibbles and Tib be distinct before and identical after the loss of the tail. But many findtemporary identity just as implausible as indeterminate identity.

21 Friends of P2 are up against van Inwagen’s (1981) argument against arbitrary undetachedparts. Friends of P4 are up against the defence of indeterminate identity by Parsons (2000) andothers.

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according to w, then M is identical with M-minus according to w. P30, in contrast,has it that if M and M-minus have the same mereological boundary according toall ways of making our world precise, then M is identical with M-minus.While weakening P3 in this fashion should be acknowledged as a way of

blocking the argument, the move will strike many as ad hoc. If worries aboutdistinct coincidents are worries about overcrowding, then it is hard to see whythese worries should be limited in the way of P30. Intuitively, distinct complexobjects cannot fit into the same place at any time in any possible world and in anyprecisificationally possible world, irrespective of their spatial relationship at othertimes and in other worlds. Overcrowding is a local concern.22

Summing up the considerations of this section, friends of fundamental inde-terminacy de re face at least two worries. Many will judge the picture of funda-mental metaphysical indeterminacy, conceptualized in terms of multipleactualities, ‘crazy metaphysics’. Furthermore, mereological indeterminacy de reraises what I shall call the problem of indeterminate coincidence. In what follows,I shall develop a picture of mereological indeterminacy de re that avoids theseworries. According to this approach, the indeterminacy is metaphysical, in virtueof being representation-independent, but not fundamental.

7.3 Derivative Indeterminacy De Re

The account of ordinary mereological indeterminacy to be proposed is based onan extended version of perspectival hylomorphism. Here is the rough picture.According to the basic version of perspectival hylomorphism, an ordinary objectis a compound of a unique material object and a unique individual form. Thisversion is now extended to the effect that an ordinary object is a compound of aunique material object and multiple individual forms, which are ‘superimposed’,containing more or less the same intrinsic and realization profiles. These assump-tions are consistent with the orthodox view that material objects are ultimatelyprecise objects—that it is not fundamentally indeterminate of any material objectand any property whether the former has the latter. Given this enriched ontology,I propose to construe ordinary mereological indeterminacy as formal indeter-minacy de re. A mountain is formally indeterminate in its composition in virtue

22 If worries about distinct coincidents are worries about grounding modal differences in non-modal differences, then it is likewise hard to see why these worries should be limited in the way ofP30. If M and M-minus coincide throughout their lives in any precisificationally possible world w,then there may be no non-modal/non-sortal facts about M and M-minus in w that explain theirdifferent modal/sortal properties in w. (I have left the question of which kind M-minus belongs toopen. This question is relevant for addressing the grounding problem.)

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of having multiple mereological candidate-boundaries, where these candidate-boundaries are the boundaries encoded in different forms of the mountain. Thisindeterminacy in the mountain’s composition is metaphysical, in that it does nothave its source in representational imprecision, and it is non-fundamental, orderivative, in that it derives from perfectly precise facts about the composition ofmaterial objects.To emphasize, this is not intended as an account of every instance of indeter-

minacy, not even of every instance of mereological indeterminacy, but merelyas an account of certain familiar instances of mereological indeterminacyabout ordinary objects. In what follows, this metaphysically harmless picture ofvague ordinary objects will be developed in some detail and shown to providesatisfactory answers to both the problem of the many and the problem ofindeterminate coincidence.

7.3.1 Ordinary objects with multiple individual forms

First of all, let us make the orthodox assumption that there is no fundamentalmetaphysical indeterminacy, and hence that material objects, composite or not,are clear-cut. So it is not fundamentally indeterminate of any material object andany property whether the former has the latter. Furthermore, composite materialobjects are mereological sums of material objects that overlap with a massivenumber of other composite material objects at any time, assuming mereologicaluniversalism. Composite material objects are subjects of K-states, which containan intrinsic profile and a realization profile of a material object at a particulartime (and in a particular possible world). Here we shall be especially interested inmountain-states—in short, m-states—of composite material objects. So far, sofamiliar.What we have not yet paid any attention to is that, on the assumption of

mereological universalism, it seems plausible that if a material object a hasK-realizing properties, for any K, then there are many distinct material objectsthat massively overlap with a and that instantiate more or less the same K-real-izing properties and more or less the same intrinsic properties. To be a bit morespecific, suppose that a has properties that jointly realize the kind mountain. It isimportant that among its mountain-realizers are not only its specific shape andits specific altitude, but also the property of having a mereological and spatialboundary that is sufficiently contrasted from its environment. I shall call aK-realizing boundary of a material object a K-boundary. Comparing a moun-tain-shaped aggregate of rocks covered in snow with a mountain-shaped aggre-gate completely enclosed in a bigger aggregate of rocks, the former has a

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mountain-boundary, while the latter does not. This idea is rough but fairlyintuitive.23 The relevant new assumption, put in these terms, is that, given amountain-shaped material object a with a certain mountain-boundary, there aremany distinct material objects that massively overlap with a and that have moreor less the same mountain-shape and mountain-boundary as a. Accordingly, anymaterial object that is a subject of an m-state massively overlaps many othermaterial objects that are also subjects of m-states with more or less the sameintrinsic and realization profiles. This holds for K-states in general. I shall say thatwhen distinct K-states, for the same K, obtaining at the same time are thatsimilar, then they are superimposed.A K-path, as the notion was introduced in Section 1.2, is a series of K-states

that is unified by K-continuity, K-connectedness, and lawful causal dependence,and that is maximal. Given that each K-state has a multitude of superimposedneighbours, the question arises whether the K-states in such a cluster belong tothe same or distinct K-paths. I shall assume that superimposed K-states belongto distinct K-paths:

A K-path includes at most one K-state from a cluster of superimposedK-states: if a K-state s is included in a K-path, and s is superimposed with aK-state s*, then that K-path does not include s*.24

So, with clusters of superimposed K-states come clusters of superimposedK-paths. Given the foregoing specifications, superimposed K-paths may differin the properties they contain at a time. (I shall set aside until Section 7.3.5 thequestion whether superimposed K-paths should also be allowed to differ in theirtemporal extent.)Next, let me introduce the notion of hosting. For any K-state s, such that a

complex material object a is either the subject of s or has a proper part that is the

23 It is likely that the sortal mountain is semantically imprecise. If so, different precisifications ofthe sortal determine different clusters of mountain-realizing properties. In particular, differentprecisifications specify different minimal degrees of boundary contrast, and hence specify differentsets of eligible mountain-boundaries. While I claim that mereological indeterminacy as it occurs inthe case of M does not have its source in the semantic imprecision ofmountain, M may, in addition,be indeterminate in a way that does have its source in this semantic imprecision. The latter type ofindeterminacy requires a separate treatment. As it will not play a role here, I shall assume that it isalways a precise matter which properties realize which sortals, or kinds.

24 This is not to say that a K-path has at most one K-state at a time. In the context of thediscussion of the bilocation account of fission in Chapter 4, I left the possibility open for a K-path tocontain multiple K-states at the same time. Here I add the restriction that these must not besuperimposed. The point of distinguishing between simultaneous, non-superimposed K-statesincluded in the same K-path and simultaneous, superimposed K-states included in distinctK-paths is ultimately to differentiate between determinately having different properties in differentplaces at the same time and indeterminately having a property at a given time.

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subject of s, a hosts s. The relation of hosting between a complex material objectand multiple K-states is less intimate than the instantiation relation. But hostingis far from arbitrary. For all the K-states hosted by a material object lie within theobject’s spatial boundary. While not strictly the subject, the material object is the‘site’ of these superimposed K-states. Moreover, if a material object hosts aK-state, then it also, though derivatively, hosts any K-path that includes thatK-state.Furthermore, for any range of massively overlapping material subjects of

superimposed K-states—call these objects K-objects—there is, by the principleof mereological universalism, the fusion of all the massively overlappingK-objects—call this maximal fusion a K-plus-object. (Note that a K-plus-objectmay or may not be a K-object itself.) A K-plus-object hosts a plurality ofsuperimposed K-states. In fact, a K-plus-object hosts a maximal cluster ofsuperimposed K-states.We are now in a position to modify q-hylomorphism as it has been devel-

oped so far. An ordinary object has previously been understood as generatedfrom the application of the operation of compounding to a material object anda single K-path. The application of compounding to a and i consists in theapplication of summation to a and i under the condition that a be a subject of i.I shall now introduce a variant of compounding, compounding*, which appliesto a material object and a plurality of K-paths. The application of compound-ing* to a material object and a plurality of K-paths consists in the application ofsummation to a material object and a plurality of K-paths, for the same K,under the conditions that the material object be a K-plus-object and that thematerial object host the plurality of K-paths. Letting �c* be the compounding*operation, the condition under which compounds* exist may be stated asfollows: for any kind K,

ExistenceIf there are a material object a and K-paths i1, i2, . . . , in, such that a is a K-plus-object anda hosts all of i1, i2, . . . , in, then there is a compound* �c*(a, i1, i2, . . . , in).

Having earlier characterized an ordinary object of kind K as the compound of amaterial object and a single K-path, I shall now characterize an ordinary object ofkind K as the compound* of a material object and a plurality of K-paths. As acomponent K-path is an individual (quasi-)form of an ordinary object, ordinaryobjects are thus construed as having multiple individual forms and a uniqueunderlying quantity of matter that hosts all of these forms. These differentindividual forms of an ordinary object do not reflect joints in nature: they arenot needed to unify the parts of objects, unification being a function that forms

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are required to perform on Aristotelian conceptions. On an Aristotelian concep-tion, an ordinary object could not have multiple forms (cf. Section 1.1). The pointof the explosion of forms in this extended q-hylomorphic picture is a verydifferent one.

7.3.2 Formal indeterminacy de re and material determinacy de re

Having paired ordinary objects with multitudes of individual forms, let us turn toordinary statements of determinacy and indeterminacy about such objects.According to perspectivalism, ordinary discourse about objects may employdifferent modes of predication, the formal mode and the material mode, mani-festing the sortal-sensitive perspective and the sortal-abstract perspective onobjects, respectively. Corresponding to this distinction, I shall distinguishbetween two notions of determinacy and indeterminacy de re employed inordinary discourse about objects, formal and material. I shall make two prelim-inary assumptions. First, to say that it is indeterminate whether o is F is to saythat it is neither determinate that o is F nor determinate that o is not F. Second, ‘itis determinate that’ functions syntactically as a sentential operator. Correspond-ing to the formal mode of predication there is an operator of formal determinacy,yielding sentences such as, ‘It is formally determinate that: o is formallyF’—Δform(F(o)form). Corresponding to the material mode of predication thereis an operator of material determinacy, yielding sentences such as, ‘It is materiallydeterminate that: o is materially F’—Δmat(F(o)mat). Just as the different modes ofpredication are associated with different perspectives on the world of objects, soare the different notions of determinacy and indeterminacy. We can represent anobject as belonging to a particular kind and ask whether it has an indeterminateformal boundary. Or we can abstract from any sortal representation of an objectand ask whether it has an indeterminate material boundary.The central notion for present purposes is that of formal indeterminacy de re.

So I shall begin my explication here. Formal determinacy and indeterminacy dere are grounded in the multitude of an ordinary object’s superimposed individualforms. Predications in the formal mode about o are made true by facts concerningwhich properties are contained in a given individual form of o. The formal moderequires the specification of an individual form for a predication to be evaluatedfor truth—that is, a formal predication is evaluated relative to a particularindividual form of its subject. Relative to an individual form i of an ordinaryobject o, o is formally F iff i contains the property of being F. Given that anordinary object, o, has multiple individual forms, the simple formal predication‘o is formally F’ is not truth-evaluable, since no particular individual form is

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specified relative to which the predication may be evaluated.25 Now, a monadicstatement of formal determinacy de re, employing the formal mode of predica-tion, ‘It is formally determinate that: o is formally F’, is true simpliciter just in case‘o is formally F’ is true relative to each individual form of o—that is, just incase each individual form of o contains the property of being F. Metaphysicaltruth conditions of monadic statements of formal determinacy and indetermin-acy de re may then be stated as follows: for any ordinary object o,

(T20)It is formally determinate of o that: it is formally F iff there is a kind K, and for any K-pathi that is a part of o, there is a material object a, such that i includes the fact that a is F.

It is formally determinate of o that: it is formally not F iff there is a kind K, and forno K-path i that is a part of o, there is a material object a, such that i includes the fact thata is F.

It is formally indeterminate of o whether: it is formally F iff there is a kind K, and for someK-path i that is a part of o, but not for all K-paths that are parts of o, there is a materialobject a, such that i includes the fact that a is F.

So statements of formal determinacy and indeterminacy de re, employing theformal mode of predication, are made true by facts concerning which propertiesare contained in which of the subject’s many superimposed individual forms. Thematching properties of an object o’s individual forms, those all individual formscontain, are o’s formally determinate properties. More importantly, the differingproperties of o’s individual forms, those some but not all individual formscontain, are o’s formally indeterminate properties.It is obvious that formal indeterminacy is structurally similar to supervalu-

ational indeterminacy. The standard supervaluationist account of ‘It is indeter-minate whether: o is F’ supervaluates over the different candidate referents of ‘o’(Section 7.1). Recall also that the modal gloss of the fundamental account of ‘It isindeterminate of o whether: it is F’ supervaluates over the different qualitativeprofiles instantiated by o in various actual worlds (Section 7.2). By contrast, thepresent account of ‘It is formally indeterminate of o whether: it is formally F’supervaluates over the different K-paths, for some kind K, that are parts of o inthe unique actual world.A well-known virtue of supervalutionism is that it preserves the logical truths

of classical logic. Even if it is supervaluationally indeterminate whether: o isF—because, say, the term ‘o’ is imprecise and has multiple candidatereferents—it is still supervaluationally determinate that: either o is F or o is notF, because no matter which candidate referent is assigned to the term ‘o’, this

25 Does this make an ordinary statement such as ‘M formally has at least massm’ non-evaluable?I shall explain below why this is not the case.

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object is either F or fails to be F. Analogously, the formal account of indetermin-acy preserves the classical tautologies. Even if it is formally indeterminate of owhether: it is formally F—because some but not all individual forms of o containthe property of being F—it is still formally determinate of o that: either it isformally F or it is formally not F, because each individual form of o eithercontains the property of being F or fails to do so.26

While this semantic picture takes care of ordinary, sortal-sensitive discoursethat explicitly concerns the determinate and indeterminate properties of objects,there is a worry that the picture leaves apparently simple ordinary predications,such as ‘M formally has at least mass m’, standing in the rain. For given thatmountain M has multiple individual forms, and given that a formal predicationcan only be evaluated for truth relative to a specific individual form, suchpredications do not seem to be truth-evaluable. My response is that ordinarypredications such as this one are truth-evaluable, on the assumption that they areimplicitly modified by the formal-determinacy operator, yielding the explicitform ‘It is formally determinate of M that: it formally has at least mass m.’Formal indeterminacy de re is both metaphysical and derivative. It is meta-

physical in the sense that it does not have its source in representational impre-cision, such as imprecision of linguistic meaning. Statements of formalindeterminacy de re are made true by facts about ordinary objects, not by factsabout representations of ordinary objects. While the standard supervaluationisttruth conditions of indeterminacy claims concern different ways of specifying thesemantic values of linguistic expressions, and hence locate the indeterminacy inlanguage, the present truth conditions of singular claims of indeterminacy locatethe indeterminacy in reality, namely, in the differences among an ordinaryobject’s multiple individual forms—just as the modal truth conditions of thefundamental account locate the indeterminacy in reality, namely, in the differ-ences among an ordinary object’s multiple qualitative profiles in different actual-ities. Furthermore, formal indeterminacy de re is non-fundamental, or derivative,in the sense that facts about such indeterminacy are grounded in more basic,indeterminacy-free facts about superimposed K-paths, and in the sense thatsuperimposed K-paths, the individual forms of ordinary objects, do not, unlikeAristotelian forms, carve nature at the joints. Formal indeterminacy de re doesnot run deep.

26 The picture sketched here is merely the beginning of a reductive account of formal indeter-minacy de re. One loose end is the problem of higher-order indeterminacy—the problem of whetherthe categorization into determinate parts, determinate non-parts, and indeterminate parts ofmountains may itself be indeterminate. An adequate discussion of this problem lies beyond thescope of this volume.

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This is the main part of the story. It remains to add a word about the semanticsof ordinary statements ofmaterial determinacy de re. With the assumption in thebackground that material objects are precise, I shall give a deflationary account ofthe pre-theoretical notion of material determinacy de re, according to which theoperator ‘It is materially determinate that’ is redundant. The truth conditions ofmonadic statements of material determinacy de re of the form ‘It is materiallydeterminate of o that: it is materially F’ are simply the truth conditions of ‘o ismaterially F’ given earlier: for any ordinary object o,

(T21)It is materially determinate of o that: it is materially F iff there is a material object a, suchthat o has a as its maximal material part, and a is F.27

It follows that it cannot be true of any ordinary object o that it is neithermaterially determinate that o is materially F nor materially determinate that ois materially not F. That is, ordinary objects cannot be materially vague. Whilethe availability of true ordinary claims of formal indeterminacy de re are ourprimary concern when analysing mereological and spatial indeterminacy ofordinary objects, the availability of true claims of material determinacy de rewill come into play in response to the problem of indeterminate coincidencebelow.

7.3.3 Vague ordinary objects

We saw that as an alternative to construing indeterminate mereological bound-aries of ordinary objects such as mountains as de dicto and as deriving fromimprecision of our representational apparatus, such indeterminacy may be con-strued as de re and as arising independently of imprecision of representations ofobjects. While ordinary mereological indeterminacy de re is usually understoodas fundamental indeterminacy, the present framework allows ordinary mereo-logical indeterminacy de re to be understood as mere derivative indeterminacy.I shall now state my proposed analysis of the claim that

(IND) It is indeterminate of M whether: it has rock r as a part (at t),

and then point out advantages of this analysis over the rivals discussed earlier.First, it is plausible that (IND) manifests the sortal-sensitive perspective on

objects. That is, in the contexts in which this claim is made M is conceived ofas a mountain. Intuitively, it is indeterminate whether M has rock r as a partbecause different surfaces, some including r, some excluding r, are equally good

27 Recall (T7) from Section 2.2.

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candidates to be the boundary of the mountain. So let us ask further why we takethe different surfaces to be equally good candidates to mark M’s boundary. Theanswer seems to be that each surface preserves what makes M a mountain. In thepresent terminology, each surface preserves M’s mountainhood-realizing prop-erties. Without sortal guidance, we would be unable to distinguish alternativeboundaries of an object. Thus, our judgement that M has an indeterminatemereological boundary is sensitive to M’s being a mountain. Given that state-ments of indeterminacy de remanifesting the sortal-sensitive perspective employthe formal mode of predication and the corresponding formal notion of indeter-minacy, our ordinary attribution of an indeterminate mereological boundaryto M may be clarified as follows:

(INDform) It is formally indeterminate of M whether: it formally has rock r asa part (at t).28

Notice that this statement is not only sensitive to M’s being a mountain, butalso to r’s being a rock. We saw in Chapter 1, independently of questions ofmereological indeterminacy, that an object of a given kind only has parts ofcertain kinds (see Section 1.1.3). This kind-dependence of parthood is a certaintype of mereological structure and was given a detailed perspectival-hylomorph-ist analysis in Section 2.2.2. What holds for determinate parts, holds for indeter-minate ones. Only objects of certain kinds, such as rocks, can be indeterminateparts of mountains. For reasons of simplicity, mereological indeterminacy ofordinary objects will here be analysed separately from the mereological structureof those objects. Accordingly, I shall treat mereological attributes, such as havingr as a part and being composed of the xs, as complex monadic properties,effectively ignoring the kinds to which an object’s parts belong. On this construal,(INDform) is a monadic predication to which truth conditions (T20) apply.29

It will now be shown that statement (INDform) may be true in the presentframework. We assumed earlier that material objects are fundamentally clear-cut,and hence that it is fundamentally determinate of material objects which thingsthey are absolutely composed of. In the case under discussion, there is a moun-tain-plus-object that massively overlaps with many mountain-objects—call oneof these aggregates of atoms ‘A’—and that, accordingly, hosts a cluster of

28 More perspicuously, it is formally indeterminate of M and the property of having r as a partwhether the former instantiates the latter (at t).

29 In order to integrate the earlier analysis of mereological structure and the present analysis ofmereological indeterminacy, (T20) would need to be supplemented by truth conditions of deter-minate and indeterminate relational predications of parthood in the formal mode, starting from(T4) of Section 2.2.2.

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superimposed mountain-paths. By the extended q-hylomorphic account ofordinary objects, there is a compound* of the mountain-plus-object and all themountain-paths hosted by it—let this compound* be M. The mountain-paths areM’s multiple individual forms. These individual forms are distributions of fun-damentally determinate facts across clear-cut material objects, namely, M andproper parts of M.Let us assume, next, that one individual form of M, i1, includes the fact that

M is composed of the xs (at t), whereas another individual form of M, i2, includesthe fact that A, a proper part of M, is composed of the ys (at t), where the xsand the ys are distinct but overlap massively, in that rock r is one of the xs but notof the ys. As a consequence of the foregoing specifications, M’s multiple individ-ual forms differ with respect to which mereological properties they contain, asillustrated in Figure 7.1.By truth conditions (T20) of monadic statements of formal determinacy and

indeterminacy de re, it is formally indeterminate of M whether: it is formallycomposed of the xs or of the ys. In particular, it is formally indeterminate ofM whether: it formally has r as a part. Hence, (INDform) is true.

30

Since M’s indeterminate formal decomposition arises merely from mereo-logical differences among its multiple individual forms, (INDform) is compatiblewith the fact that it is materially determinate of M that: it materially has rock r asa part, by truth conditions (T21). On this double-layered picture, M is a formallyvague but materially precise object. What holds for M, holds for other ordinaryobjects. Their indeterminate boundaries are derivative, the result of differences

ra

i1

i2

Figure 7.1 Indeterminate mereological boundaries

30 While it is formally indeterminate of M whether: it formally has r as a part, it is not formallyindeterminate of Tibbles the cat whether: it formally has its tail as a part. Just as we would intuitivelyexpect, the tail is a formally determinate part of Tibbles. While M has an individual form thatexcludes r, all of Tibbles individual forms include the tail. This is so, because there is a material objectwith sufficient contrast from its environment that excludes r—recall that r has been loosenedgradually from the mountain’s body by melting glacial ice. Whereas there is no material objectwith sufficient contrast from its environment that excludes the tail—the tail is firmly tied into the lifeof the organism. In short, while there is an r-excluding material object with a mountain-boundary,there is no tail-excluding material object with a cat-boundary. The present account therefore doesnot overgenerate formal indeterminacies.

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among their many superimposed forms, floating above the clear-cut boundariesof their underlying matter.31

I shall conclude the statement of my account of mereological indeterminacy ofordinary objects by indicating how it extends to locational indeterminacy. Let usassume that one individual form of M, i1, includes the fact that M is exactlylocated in place p (at t), whereas another individual form of M, i2, includes thefact that A, a proper part of M, is exactly located in place p* (at t), where p and p*are distinct but overlap massively. As a consequence, M’s multiple individualforms differ with respect to which locational properties they contain. By truthconditions (T20), it is formally indeterminate of M whether: it is formally locatedin p or in p*. M has an indeterminate spatial as well as mereological boundary.

7.3.4 The problem of the many and indeterminate coincidence

What speaks in favour of this derivative account of mereological and spatialindeterminacy de re of ordinary objects? First, the account has the advantage overthe standard de dicto account, of providing a satisfactory answer to the problemof the many. We saw that the standard supervaluationist approach to view allmereological indeterminacy of ordinary objects as indeterminacy de dicto deriv-ing from the imprecision of sortal concepts has a hard time dealing with theproblem of the many. That it is indeterminate whether mountain M has rock r asa part does not have its source in the fact that ‘M’ has different candidatereferents, which are distinguished by different precisifications of mountain,such that some include r and some exclude r. For the differences between thevarious candidates are more fine-grained than the differences between anysensible and principled precisifications of the sortal—the differences are sub-sortal. And this has the consequence that there are either many mountains ornone where we thought there was just one.If the mereological indeterminacy of mountains is based on small mereological

differences between multiple, fundamentally precise aggregates of rocks, then it isdifficult to sustain our intuitive claim that there is exactly one mountain on theplain. If, on the other hand, mountains are allowed to be vague objects, then theway is clear for cutting down the mountains on the plain to a single one andattributing a mereologically indeterminate boundary to it. On the presentaccount, this indeterminate boundary is grounded in the multiplicity of themountain’s superimposed individual forms and their varying mereological prop-erties. Supervaluation over multiple candidates is replaced by supervaluation over

31 For another derivative account of mereological indeterminacy de re, developed in the contextof a relative-identity solution to the problem of the many, see Sattig (2010b).

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multiple individual forms of a single candidate. Notice that here a mountain maybe mereologically fuzzy even if the sortal mountain is perfectly precise. For thedifferences between superimposed individual forms may be sub-sortal differ-ences; they need not correspond to differences between admissible precisifica-tions of the sortal.The job, however, is not done yet. For the question remains as to what grounds

the fact that there is exactly one vague mountain on the plain, as opposed tomany. We have an explanation of what makes M mereologically indeterminate.But what explains its uniqueness? What explains M’s uniqueness is a maximalityrequirement on mountainhood: only sums of maximal fusions of massivelyoverlapping mountain-objects and the mountain-paths hosted by them aremountains—that is, only sums of mountain-plus-objects and their hosted moun-tain-paths are mountains (see Section 7.3.1). This is an instance of the generalprinciple that an ordinary object of kind K is the sum of a K-plus-object and itshosted K-paths. On the plain we find a range of massively overlapping materialobjects, each of which is a subject of a different mountain-path—they areoverlapping mountain-objects. By the principle of mereological universalism,there is a maximal fusion of these massively overlapping mountain-objects—this is a mountain-plus-object. By the principle of extensionality, there is aunique such maximal fusion. A mountain is the sum of a mountain-plus-objectand all the mountain-paths hosted by it. By extensionality, there is a unique suchsum. Ultimately, then, there is only one mountain on the plain, because there isonly one maximal mountain-object out there. Maximality explains the moun-tain’s uniqueness. It is important that maximality constitutes a principled way ofsingling out one mountain. By contrast, the standard supervaluationist proposalis to single out a mountain arbitrarily or else to recognize many mountains. Thisis how perspectival hylomorphism takes care of the problem of the many.Let me conclude the discussion of this problem with a point of clarification.

The principle that an object of kind K has the maximal fusion of a plurality ofmassively overlapping K-objects as its material component is not to be confusedwith the principle that an object of kind K has the biggest K-object out of aplurality of massively overlapping K-objects as its material component. Supposethat a kind K is partially defined by the property of having exactly n electrons asparts. Suppose, further, that in a given location there is exactly one object of thatkind, and that while this object determinately has n electrons, it is indeterminatewhich electrons these are. There are, say, electrons e1 and e2 on the object’ssurface, such that it is indeterminate whether it has e1 as a part and indeterminatewhether it has e2 as a part, but determinate that it does not have both e1 and e2 asparts. How can this be true? Assume that there is a cluster of non-identical but

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massively overlapping composites, such that each has n electrons as well as otherproperties that jointly realize K-hood. They are all K-objects. However, themaximal fusion of these composites has more than n electrons, and hence doesnot have a profile that realizes K. Now, if an object of kind K is understood ashaving the biggest K-object from a plurality of massively overlapping K-objects asits material component, then there is no object of kind K in the given location,since there is no unique biggest K-object there. This difficulty is avoided, if anobject of kind K is understood as having the maximal fusion of a plurality ofmassively overlapping K-objects as its material component. For such a fusionneed not be a K-object itself. In the case at hand, there is a unique object of kindK in the given location, just as expected, since there is a unique maximal fusion ofthe massively overlapping composites, each of which has n electrons. That thisK-plus-object does not itself have a profile that completely realizes K-hood—itdoes not have exactly n electrons—is irrelevant.What speaks in favour of the derivative account of indeterminacy de re in

comparison with the fundamental account? Those who are drawn to indeter-minacy de re but oppose fundamental indeterminacy de re on the grounds that apicture of reality as having multiple precisifications is unacceptably radicalshould welcome an account of indeterminacy de re as derivative, as arisingfrom a perfectly precise reality, just as orthodoxy conceives of it. This is anintuitive advantage. Moreover, those who recognize a distinction between fun-damental and derivative facts should be restrictive about which facts are funda-mental. They should accept the methodological principle that fundamental factsmust not be multiplied without necessity.32 Accordingly, the proposed account ofindeterminacy de re as derivative has a methodological edge over the standardaccount of indeterminacy de re as fundamental. Of course, which account isultimately preferable depends on how they compare along other dimensions,as well.Furthermore, the framework offers a plausible response to the problem of

indeterminate coincidence, which is not available to the fundamental account ofmereological indeterminacy de re. The argument from indeterminate coincidenceagainst vague objects was earlier summarized as follows:

(1) It is indeterminate of M whether: it has r as a part. [P1](2) There is an object, M-minus, such that it is determinate of M-minus that:

it has all and only the parts of M that do not overlap with r. [P2]

32 Schaffer (2009: 361) suggests that a principle along these lines should replace Occam’s Razor,according to which entities must not be multiplied without necessity.

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(3) It is determinate of M and M-minus that: the former coincides with thelatter iff the former lacks r as a part.

(4) It is indeterminate of M and M-minus whether: the former coincides withthe latter.

(5) It is determinate of M and M-minus that: the former coincides with thelatter iff the former is identical with the latter. [P3]

(6) It is indeterminate of M and M-minus whether: the former is identicalwith the latter.

(7) It is not indeterminate of M and M-minus whether: the former is identicalwith the latter. [P4]

The proposed framework allows this argument to be blocked in the followingway. As pointed out earlier, premise P1 manifests the sortal-sensitive perspective.We judge M’s boundary to be unclear, because there are several boundaries thatpreserve what makes M a mountain. Accordingly, P1 is to be read as a formalpredication:

P1* It is formally indeterminate of M whether: it formally has r as a part.

Premise P2 also manifests the sortal-sensitive perspective, since the boundaryof M-minus is recognized relative to the boundary of M.We pick out M-minus asthe object that is just like M, except for determinately lacking r. Let us call anobject, such as M-minus, that is all of a given mountain except for one or more ofits indeterminate parts, a mountain*. In virtue of its sortal sensitivity, P2 is to beread as a formal predication:

P2* There is an object, M-minus, such that it is formally determinate ofM-minus that: it formally has all and only the parts of M that do not overlapwith r.

Premise P3 incorporates the platitude of common sense that distinct objectscannot coincide. As argued in Chapter 3, this principle manifests the sortal-abstract perspective, the perspective that cuts through sortal representations,and accordingly is to be read as a principle concerning material determinacyand material coincidence (see Section 3.3 for the distinction between formal andmaterial coincidence):

P3* It is materially determinate of M andM-minus that: the former coincidesmaterially with the latter iff the former is materially identical with the latter.

I take this compelling principle to be the main troublemaker in this argumentagainst mereological indeterminacy de re. If our common-sense conception of

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ordinary objects is to be sustained, the principle must be saved. It is in light of thistask that the perspectivalist availability of material statements of determinacy dere about ordinary objects, in addition to formal statements of indeterminacy de reabout the same objects, proves valuable, as I shall explain below.Premise P4 is driven by the Evans–Salmon argument, whose conclusion is

supposed to be a truth about the world that is independent of how the worldis represented under sortal concepts: indeterminate identity holding of o and o* isout of the question, irrespective of which kinds o and o* belong to. P4 thusmanifests the sortal-abstract perspective and is to be read as a materialpredication:

P4* It is not materially indeterminate of M and M-minus whether: theformer is materially identical with the latter.

If P1–P4 are read as P1*–P4*, then these premises are jointly consistent.According to the present account, M is the sum of a mountain-plus-object andall the mountain-paths hosted by that object. Some of these mountain-pathscontain the property of having r as a part; others do not contain that property.This makes P1* true.Let us say, furthermore, that while a mountain-plus-object is the maximal

fusion of all mountain-objects from a range of massively overlapping ones, amountain*-object is any non-maximal fusion of massively overlapping moun-tain-objects. And let a mountain* be the sum of a mountain*-object and all themountain-paths hosted by that object. Intuitively, a mountain* is all of a moun-tain except for one or more of its formally indeterminate parts. Now consider thefusion of all of the mountain-objects within M’s underlying mountain-plus-object except for those that overlap with r. Let M-minus be the sum of thatfusion and of all the mountain-paths hosted by it. Accordingly, M-minus sharesall and only those individual forms of M that fail to contain the property ofoverlapping with r. This makes P2* true.From P2* it follows that M coincides formally with M-minus iff M formally

lacks r as a part. Since, by P1*, it is formally indeterminate of M whether: itformally has r as a part, it is then also formally indeterminate of M and M-minus:whether the former coincides formally with the latter. It does not follow, how-ever, that it is materially indeterminate of M and M-minus whether: the formercoincides materially with the latter. For on the assumption made in the previoussection that material objects are metaphysically clear-cut, M and M-minus arematerially distinct objects with slightly different material mereological and spatialboundaries. The indeterminate formal coincidence of M and M-minus is com-patible with their determinate material non-coincidence. Accordingly, P1* and

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P2* do not yield materially indeterminate identity of M and M-minus via P3*.And so no clash with P4* occurs.Let me sum up the foregoing discussion. The problem of indeterminate

coincidence, directed against vague ordinary objects, rests on the intuitiveworry that it cannot be indeterminate of distinct objects whether they coincide.The combination of a derivative account of formal indeterminacy de re with thepossibility of perspectival shift between formal and material claims of determin-acy and indeterminacy de re allows us to endorse the intuitive ban on indeter-minate coincidence of distinct objects, while still leaving room for indeterminatecoincidence of another type. It is formally indeterminate of M and M-minuswhether: they coincide formally. However, when M and M-minus are describedmaterially, from the sortal-abstract perspective, then there are no indeterminateboundaries, and hence no indeterminate coincidence.

7.3.5 Indeterminate temporal boundaries

Ordinary objects may have indeterminate temporal boundaries as well as inde-terminate mereological and spatial ones. That is, it may be indeterminate when agiven object comes into being and when it fades away. Consider, for example, ahuman organism, H. H’s life is a sequence of states of multiple cells. What makesa sequence of such states a life of an organism is the sequence’s marking a path ofcontinued life-sustaining biological functions. As life-sustaining functions slowlystart up in a small collection of cells, when the organism comes into existence,and as they slowly shut down in a massive collection of cells, when the organismdies, several states of small cell-collections are equally good candidates to be thefirst state in the organism’s life and several states of massive cell-collections areequally good candidates to be the last state in the organism’s life. As a result, it isunclear exactly when H comes into existence and when it goes out of existence.H’s temporal boundary is indeterminate.Different accounts of this temporal case of indeterminacy are available. It may

be viewed as a case of indeterminacy de dicto and explained in terms of multiplecandidate referents of the name ‘H’ with different precise temporal boundaries.Or it may be viewed as a case of fundamental indeterminacy de re. Havingevaluated the mereological analogues of these approaches when discussing thecase of M in previous sections, I shall set them aside now. My aim in concludingthis chapter is merely to show that the case of H has a perspectival-hylomorphisttreatment that is analogous to the proposed treatment of the case of M, namely,as an instance of formal, and hence derivative, indeterminacy de re.A perspectival-hylomorphist account of the case of H requires a further

modification of q-hylomorphism about ordinary objects. Specifically, it requires

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a modification of the characterization of K-paths. The description of H as havingan indeterminate temporal boundary is clearly a sortal-sensitive description, forwhich the persistence conditions of organisms are central. It will thus be con-strued as a case of formal indeterminacy de re of persistence. Formal indeter-minacy de re is grounded in differences between the multiple individual forms ofan ordinary object. Formal indeterminacy de re of persistence is thus grounded indifferences in the temporal extent of an object’s multiple individual forms. It isdoubtful, however, that there are superimposed K-paths differing in temporalextent, if K-paths are characterized in terms of temporal maximality. As statedearlier, a K-path is maximal in that no segment of a larger conjunction of non-superimposed K-states interrelated by K-continuity, K-connectedness, and causaldependence is a K-path; only the largest conjunction of non-superimposedK-states interrelated in this way counts as a K-path. The problem with thistemporal maximality condition on K-paths is that formal indeterminacy ofpersistence requires an ordinary object to have superimposed K-paths as indi-vidual forms, which are less than temporally maximal. For this reason, themaximality condition must be replaced.I shall say that the temporal K-boundary of a series of K-states is constituted by

the individual K-states in the series that mark a sufficiently substantial, local orglobal, change in K-relevant respects, assuming that there is a precise minimaldegree of change fixed by K. That is, a temporal K-boundary marks a disruptionin K-continuity or K-connectedness.33 (Compare the notion of a spatialK-boundary introduced in Section 7.3.1.) Instead of requiring K-paths to betemporally maximal, they will now be required to have a temporal K-boundary:

A K-path has a temporal K-boundary: a K-path is bounded by K-states thatmark a disruption in K-continuity or K-connectedness.

A K-path is thus a series of K-states, such that no K-states are superimposed, allK-states are interrelated by K-continuity, K-connectedness, and causal depend-ence, and the series has a temporal K-boundary. This modified characterizationof K-paths allows superimposed K-paths to differ in temporal extent, in the wayrequired to account for ordinary cases of indeterminacy de re of persistence, suchas the case of H.The case of H is here understood as a case of formal indeterminacy de re: it is

formally indeterminate of H at which time it formally begins to exist and at whichtime it formally ceases to exist. In order to specify a truthmaker for this claim, let

33 See Section 1.2 for the distinction between the ‘local’ notion of K-continuity and the ‘global’notion of K-connectedness.

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us assume, firstly, that it is fundamentally determinate of material objects atwhich time they begin to exist and at which time they cease to exist. Let usassume, secondly, that there is a human-organism-plus-object, a, that hosts acluster of superimposed human-organism-paths, including i1 and i2. These aresequences of human-organism-states of aggregates of cells, each tracing a certainpath of continued life-sustaining biological functions with a slightly differenttemporal human-organism-boundary from the others. That is, the first human-organism-states of i1 and i2, respectively, obtaining at different times, are equallygood candidates to mark the start-up of certain human-organism-realizing life-sustaining functions; and the last human-organism-states of i1 and i2, respect-ively, also obtaining at different times, are equally good candidates to mark theshut-down of these life-sustaining functions.34 Let us say, for simplicity, that i1begins at t1 and ends at t4, and that i2 begins at t2 and ends at t3, as illustrated inFigure 7.2.By q-hylomorphism, this scenario contains a human organism, H, namely, the

compound* of material object a and all the human-organism-paths hosted by a,including i1 and i2.

35 These human-organism-paths are H’s multiple individualforms. Since H’s multiple individual forms differ in temporal extent, it follows bytruth conditions (T20) of statements of formal indeterminacy de re that it isformally indeterminate of H whether: it formally begins to exist at t1 or t2, and itis formally indeterminate of H whether: it formally ceases to exist at t3 or t4.

a

t

x

t2t1

i1

i2

t4t3

Figure 7.2 Indeterminate temporal boundaries

34 I take these minute differences in temporal boundary between organism-paths to be sub-sortal;they are more subtle than the differences between any reasonable precisifications of the sortalhuman organism (cf. Section 7.1).

35 Superimposed organism-paths i1 and i2 may, of course, have different organism-plus-objectsas subjects, in which case there would be several absolutely distinct organisms in this scenario.Formally, however, there would still be only one organism, as expected.

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Hence, H has a formally indeterminate temporal boundary. This indeterminacyis derivative, resting on the precise absolute temporal boundaries of materialobjects. Correspondingly, H’s material temporal boundary is determinate, bytruth conditions (T21). What holds for H holds for most, perhaps all, otherordinary objects. We thus arrive at a unified, perspectival-hylomorphisttreatment of a range of puzzling cases of mereological, spatial, and temporalindeterminacy of ordinary objects.

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8

Relativity

In this final chapter, I shall apply the framework of perspectival hylomorphism togive an account of certain puzzling relativistic properties of ordinary objects. Theproblem with which I shall be concerned is the following. According to commonsense, ordinary objects cannot undergo radical change in shape, whereas accord-ing to a compelling and widely accepted metaphysical picture of objects’ shapesin Minkowski spacetime, they do undergo such radical change. This tensionraises doubts about the compatibility of the object-conception of commonsense with the object-conception of relativistic metaphysics, and thus constitutesa further threat to our familiar worldview. In Section 8.1, I shall introduce thisproblem. In Section 8.2, I shall argue that the problem is not easy to avoid. InSection 8.3, I shall extend the framework of perspectival hylomorphism in a waythat it yields a solution to the problem: the conception of common sense and theconception of relativistic metaphysics manifest different perspectives on the sameobjects, and are therefore compatible.

8.1 The Problem of Relativistic Change

According to the special theory of relativity, macroscopic objects are subject torelativistic change in shape; a macroscopic object may have different shapes indifferent inertial frames of reference. I shall begin by sketching an elegant andwidely accepted metaphysical model of macroscopic objects’ shapes in Min-kowski spacetime. This model will later allow us to recognize extreme cases ofrelativistic shape-change with disturbing consequences for our common-senseconception of the world.

8.1.1 Shape change in the relativistic world

In special relativity there is no absolute space in which objects have a true shape.A macroscopic object may have different shapes in different inertial frames ofreference. Many find it overwhelmingly plausible that this relativistic change in

shape from one reference frame to another is a perspectival phenomenonin spacetime. Supposing that a given complex object has different three-dimensional shapes at different times in different reference frames, there is apermanent shape standing behind the different three-dimensional shapes of theobject, namely, an invariant four-dimensional shape, rendering the various three-dimensional shapes different perspectival representations of the single invariantshape. We see different three-dimensional shapes of an object when viewing theobject’s unique four-dimensional shape from various angles in spacetime. Gen-eralizing, all shapes an object has at different times in different reference framesare unified by an invariant shape from which the various shapes are derived. AsYuri Balashov (2010: 202) puts it, ‘“separate and loose” 3D shapes come togetherin a remarkable unity, by lending themselves to an arrangement in a smooth 4Dvolume’. This account of relativistic shapes is analogous to the familiar, everydayphenomenon of an ordinary object’s having varying two-dimensional shapesrelative to different points of view in space, where it is clear that these two-dimensional shapes are different perspectival representations of the objective,underlying three-dimensional shape of the object.1 I shall call this compellingaccount of macroscopic objects’ relativistically changing shapes as deriving froma single, invariant shape, the unified view.2

The unified view may be fleshed out as follows. First of all, Minkowski space-time contains a four-dimensional manifold of spacetime points. Any fusion ofspacetime points is a spacetime region. While simultaneity is an invariant notionin classical spacetime, it is not an invariant notion in Minkowski spacetime; it isnot meaningful to ask whether two spacetime points are simultaneous. Althoughabsolute simultaneity is not well-defined in Minkowski spacetime, it is possible todefine a relative notion of simultaneity. The fusion of any maximal set of pointsthat are simultaneous relative to an inertial frame of reference F is an F-relativehyperplane of simultaneity. Simultaneity relativized to an inertial frame ofreference is an equivalence relation, and hence each inertial frame defines adifferent slicing of the same spacetime into hyperplanes of simultaneous points.These frame-relative hyperplanes of simultaneity may be conceived of as frame-relative moments of time. Given an inertial frame of reference F, tF is a familiarmoment of time relative to F.3

1 See Balashov (2010: 200–2) for examples of the phenomenon of perspectival shape-variation inspace.

2 The view of relativistic shapes as perspectival projections is not to be confused with perspectiv-alism as understood in previous chapters.

3 It should be emphasized that frame-relative times are not assigned any privileged metaphysicalstatus. From the point of view of physics, the content of spacetime may be described in terms of ‘flat’

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How are macroscopic objects related to Minkowski spacetime? According tostandard four-dimensionalism, upgraded to meet the demands of special relativ-ity, each macroscopic object exactly occupies a unique region in Minkowskispacetime. This invariant trajectory is known as the object’s world volume.A complex object’s world volume overlaps with various frame-relative hyper-planes of simultaneity, or frame-relative moments of time—that is, there is aspacetime region that is both a part of the world volume and a part of thehyperplane. According to standard four-dimensionalism, for each region ofoverlap between an object’s world volume and an F-relative time, for someframe of reference F, the object has a part that exactly occupies that region.I shall say that an object that exactly occupies a sub-region of an F-relative timetF is a stage at tF, and that an object that has a part that exactly occupies a sub-region of tF has a stage at tF. A macroscopic object has a stage at each time thatoverlaps with its world volume.4

In ordinary language, we do not describe an object in terms of its world volumeand its stages. We rather describe an object as existing at times. There is astraightforward way of linking familiar facts of an object’s existing at a timewith facts about stages. Given that there are frame-relative times in Minkowskispacetime, ordinary talk of persistence may be transposed to a relativistic frame-work by straightforward frame-relativization, yielding statements of the form ‘oexists at tF’, for some macroscopic object o.5 Metaphysical truth conditions offrame-relativized statements of temporal existence may be specified as follows:for any object o, any inertial frame of reference F, and any frame-relative time tF,

(T22) o exists at tF iff o has a stage at tF.

At each frame-relative time at which an object exists it has a certain shape.Given that an object o’s existence at tF consists in o’s having a stage at tF, standardfour-dimensionalists say that o’s having a certain shape at tF consists in o’s stage

hyperplanes relative to a particular inertial frame of reference. However, as Gibson and Pooley(2006: 162) put it, ‘one can equally choose to describe the content of spacetime with respect to someframe that is not so optimally adapted to the geometric structure of spacetime, or indeed, choose todescribe it in some entirely frame-independent manner’. It should also be noted that Gibson andPooley (2006: 166–7) propose an alternative, causal and frame-independent conception of a time.For considerations of length, I shall not be able to discuss this alternative here.

4 For details on four-dimensionalism in Minkowski spacetime, see Balashov (1999, 2000, 2010),Gibson and Pooley (2006), Gilmore (2006), Sider (2001a), and Sattig (2006).

5 More precisely, an utterance of a temporal predication ‘o exists at t’ may be interpreted asreferring to a time relative to an inertial frame of reference, most naturally the frame, F, in which thespeaker is at rest in the spacetime region where the utterance is made, yielding ‘o exists at tF’.

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at tF having that shape simpliciter. For any ordinary object o, any inertial frame ofreference F, any frame-relative time tF, and any shape ç,

(T23) o has ç at tF iff o has a stage at tF that has ç.

For illustration, suppose that F is the rest frame of a macroscopic object o, andthat F* is the rest frame of an observer who is moving near the speed of lightrelative to o. Object o has a certain invariant world volume in Minkwoski space-time. This world volume overlaps with various frame-relative times. Considertime tF in o’s rest frame, F, and time tF* in the observer’s rest frame, F*, such thatboth of these times overlap with o’s world volume as specified in Figure 8.1.The region where o’s world volume overlaps with tF and the region where o’s

world volume overlaps with tF* are exactly occupied by distinct stages of o.These stages may have different three-dimensional shapes. If so, it follows byprinciple (T23) that o has one three-dimensional shape at tF and another three-dimensional shape at tF*.This four-dimensionalist picture of an object’s frame-relative shapes in Min-

kowski spacetime provides a foundation for the idea that these shapes areperspectival representations of an invariant, underlying shape. Each shape anobject has at any frame-relative time is the shape of a stage of the object. Noticethat this does not and should not only hold for objects with a four-dimensionalworld volume, but also for any object with a less-than-four-dimensional worldvolume, such as any stage at any frame-relative time, which has merely a three-dimensional world volume. Such a stage may also have different shapes relative todifferent frames, which are to be understood as shapes of its stages at various

tF*

tF

t t′

x′

x

world volume of o

Figure 8.1 A standard case of relativistic change in shape

222 relativity

times, and hence as derived from its invariant three-dimensional shape. Ingeneral, different shapes of an object at different times are just cross-sections ofa single, invariant shape of that object. This is how an object’s shapes at differentframe-relative times ‘fit into’ a single volume.The unified view of relativistic shapes is standardly fleshed out in this four-

dimensionalist way. Balashov (2010: chapter 8) even argues that four-dimension-alism offers the only sensible basis for that view. I consider the issue he raises aserious one. And since an appropriate treatment of that issue lies beyond thescope of this volume, I shall assume for the purpose of my discussion, followingBalashov’s lead, that four-dimensionalism is the most hospitable, if not the onlypossible, environment for the unified view, and shall henceforth work exclusivelywith that framework. In the remainder of this section, I will show that the unifiedview of macroscopic objects’ shapes in Minkowski spacetime, as captured byfour-dimensionalists, threatens our ordinary conception of macroscopic objects.

8.1.2 Limits of shape change in the ordinary world

While ordinary objects can vary in many of their properties over time and acrossworlds, they cannot vary in any way with respect to certain kinds to which theybelong. These ordinary kinds are strictly invariant. The ordinary world is partlyindividuated by these kinds; it is parsed into persons, chairs, trees, mountains,and so on. Assuming that for any kind K and any ordinary object o, o isinvariantly a K iff o is a K at all times at which it exists and in all worlds inwhich it exists, the doctrine of sortal invariance says that certain ordinary kindsapply to their instances invariantly. This doctrine is deeply embedded in thecommon-sense conception of macroscopic objects. Chairhood, for example, istypically regarded as an invariant property of its instances. Whatever propertiesmake an object a chair, we bring a chair into existence by causing these propertiesto be instantiated, and a chair cannot lose these properties without going out ofexistence. (Sortal invariance was first introduced in the discussion of sortals inSection 1.2.2.)6

Sortal invariance rules out variation with respect to certain ordinary kindsalong all dimensions, and hence it rules out relativistic variation as well as modaland temporal variation. Relativistically sensitive sortal invariance is thus thedoctrine that certain ordinary kinds apply invariantly to the objects fallingunder them, where for any kind K and any ordinary object o, o is invariantly aK iff o is a K at all times at which it exists, in all frames of reference, and in all

6 The doctrine of sortal invariance is also known as ‘sortal essentialism’. Since many reject theaccount of essence in terms of invariance, I prefer a label that is neutral on the status of essence.

relativity 223

worlds in which it exists. If ordinary objects, such as chairs, have a place in therelativistic world, then chairhood does not vary relativistically; being a chair doesnot shift with relativistic point of view. This is a straightforward consequenceof transposing the compelling doctrine of sortal invariance to a relativisticframework.(If sortal invariance holds—if K-hood is strictly invariant, for certain ordinary

kinds K—then it is not necessary to ascribe K-hood to an object at a world or at aframe-relative time. Modal and relativistic-temporal modification of K-hood maysimply be dropped, and K-hood may be ascribed to an object simpliciter, wherefor any ordinary object o, and any kind K, o is a K simpliciter iff o is a K at anyframe-relative time, in any possible world, at which o exists.)The doctrine of sortal invariance is one pillar of our ordinary conception of

macroscopic objects. Another pillar is the doctrine that there is an informativeanswer to the question what it is to be a chair, to the question what determinesmembership in the class of chairs. It seems, in other words, to be constitutive ofthe folk conception of Ks, where K is some ordinary, invariant kind, that anobject is a K at a time in virtue of instantiating a range of K-determiningattributes at that time. Let us say, for simplicity, that being a K is partlydetermined by being K-shaped, whatever exactly being K-shaped involves: forany object o, any ordinary, invariant kind K, and any time t, if o is a K at t, then ois K-shaped at t. Since K-hood is invariant, K-hood applies to an object simplici-ter, and hence the sortal-determination doctrine may be expressed as follows: forany object o, and any ordinary, invariant kind K, if o is a K, then o is K-shaped atall times at which o exists. (While it also follows that an object is a K only if it isK-shaped in all worlds in which it exists, I shall focus on temporal invariance.) Asan instance of this sortal-determination principle, something is a chair only if it ischair-shaped at all times at which it exists. Being made of wood is not what makesan object a chair, but being chair-shaped partly is. I am not claiming that there isa universal chair-shape; there are many such shapes. Nor am I claiming that thereare necessary and sufficient conditions for the application of the concept of achair that all competent users have on their finger-tips. But I am claiming thatthere are minimal qualitative constraints on what counts as a chair, which guideus in singling out clear non-chairs. The mentioned principle is such a constraint.(Sortal determination made its first appearance in the discussion of a kind’squalitative content in Section 1.2.3.)If Ks are to be found in a relativistic world, then the pre-relativistic sortal-

determination principle linking Ks with K-shapes must have a relativistic des-cendant. The obvious way of transposing the sortal-determination principle to arelativistic framework is to frame-relativize as follows: presupposing sortal

224 relativity

invariance—the doctrine that certain ordinary kinds are invariant—for anyobject o, and any invariant kind K,

(K) If o is a K, then o is K-shaped at all frame-relative times at which o exists.

Being chair-shaped is part of what makes an object a chair. Thus, there are strictlimits to the extent to which chairs can vary in shape, limits that obtain whetherthe variation happens within a single frame of reference or across different framesof reference. No object can be a chair unless it is chair-shaped in all circumstancesin which it finds itself.7

The doctrines of sortal invariance and sortal determination seem to be con-stitutive of the common-sense conception of macroscopic objects. There is,accordingly, a place for ordinary objects in the relativistic world—a place forobjects as the folk know them—only if these doctrines are preserved. I will shownow that they cannot be jointly sustained in the face of extreme cases ofrelativistic change in shape.

8.1.3 The point-shaped chair

Consider a macroscopic object o in its rest frame F in Minkowski spacetime.8

Suppose that o comes into existence at t1F and that o goes out of existence at t2

F.Moreover, let F* be the frame of reference of an observer who is moving near lightspeed relative to o. In F*, there is a time tF* that overlaps with o’s world volume ina single spacetime point, p (see Figure 8.2).Since o has a stage that exactly occupies p, it follows by principle (T22) that o

exists at tF*. Since o’s stage in p is point-shaped, it follows by principle (T23) thato is point-shaped at tF*. By analogous considerations regarding times that lead upto tF* in frame F* and that overlap with o’s world volume, it follows that o shrinksto a point over a certain period of time in F*.This limiting case of relativistic change in shape threatens our ordinary

conception of macroscopic objects. According to standard four-dimensionalism,

7 Sortal-determination principles specify partial persistence conditions. A chair, to take the caseat hand, cannot lose its chair-shape without going out of existence. This seems obvious. And yet wecan imagine picking up a wildly distorted piece of metal, saying, ‘Look what happened to this chair.’It would, in my view, be an overreaction to drop the compelling chairhood-determination principlein response to these sorts of puzzling cases. More conservative routes are open. One might, forinstance, consider a fictionalist interpretation, according to which the relevant assertion is madeunder some kind of pretence. We want to draw attention to a certain course of events involving aradical shape-change, which task is simplified if we pretend that a single object is subject to thechange. Cf. Section 4.3.

8 I owe the following case to Cody Gilmore, who appeals to it for different reasons than I do; seeGilmore (2006: 212–13).

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an ordinary object, such as a chair, is a material object with a unique four-dimensional world volume—it is a spacetime worm. Suppose, then, that space-time worm o in the scenario sketched above is a chair. That is, suppose that achair comes into existence at t1

F and that it goes out of existence at t2F. To

suppose that the property of being a chair applies to o simpliciter reflects thecommon-sense doctrine that this property applies to its instances invariantly, andhence that possession of the property is not sensitive to the relativistic point ofview, the inertial frame of reference, from which o is viewed. According to ourordinary conception of chairs, the property of being a chair is partly a matter ofbeing chair-shaped. This doctrine is captured by principle (K): a chair is chair-shaped at all frame-relativistic times at which it exists. Since o exists at tF*, by(T22), it follows by (K) that o is chair-shaped at tF*. By (T23), however, it followsthat o is point-shaped, and hence not chair-shaped, at tF*. Contradiction.Let me present the problem in a more intuitive, somewhat embellished fashion.

A plurality of point-particles becomes arranged chair-wise very abruptly, say by apowerful machine, at t1

F, and loses its chair-wise arrangement equally abruptly,say in an explosion, at t2

F. Accordingly, a chair comes into existence at t1F and

goes out of existence at t2F; and this chair is composed of the mentioned particles

at all times at which it exists in F.9 It must be emphasized that the particles are notassumed to pop into and out of existence at t1

F and t2F, respectively. Such a

scenario would transgress the boundaries of physical possibility, due to a

t1F

tF*

t2F

t

x

world volume of o

t′

x′

Figure 8.2 An extreme case of relativistic change in shape

9 The assumption that the chair is created and destroyed instantaneously is here made for ease ofexposition. The assumption will be lifted in Section 8.2.2.

226 relativity

violation of the conservation laws.10 Instead, the particles are merely assumed tobegin to compose the chair at t1

F and to cease to compose the chair at t2F. In the

rest frame of the chair, F, the explosion and associated mutual separation of theparticles occur instantaneously. In a reference frame, F*, associated with anobserver who is moving at a high speed relative to the chair, the explosion andassociated mutual separation of the particles occur gradually. In F* the chair losesits atomic parts one by one, as the chair-wise arrangement of particles graduallybreaks up. Given how the chair is individuated in its rest frame, and given howthe chair’s world volume is fixed in this frame, F*-relative time tF* intersects thechair’s world volume in a single point. By principles (T22) and (T23), the chairexists at tF*, and ends up being (composed of ) a single particle at this time.Hence, the chair is point-shaped at tF*. But no chair can be point-shaped!11,12

The point-shaped chair is an instance of what I shall call the problem ofrelativistic change. The problem is that given the unified view of frame-relativeshapes in Minkowski spacetime, chairs are forced to change their shape in waysincompatible with our ordinary conception of chairs. If one holds that principle(K) is constitutive of the meaning of chair, then it is a conceptual truth thatnothing that shrinks to a point is a chair. In this case, the object that we took to bea chair really is not. If (K) is not meaning-constituting, then the conclusion is notthat the object fails to be a chair, but rather that we were completely misguidedabout what chairs can do. Either way, the news is that something we took to be achair can take the shape of a point. This comes as a shock. We thought we wereexperts on chairs.

10 See Balashov (2010: section 5.5).11 Penrose (1959) and Terrell (1959) pointed out independently that the Lorentz contraction is

invisible. Owing to the time it takes for light from different parts of a mereologically complex objectto reach the eye, an object passing at a significant fraction of the speed of light appears to be rotated.This effect is known as Penrose–Terrell rotation. In view of this effect, I shall refrain from makingany assumptions about what our chair looks like in reference frame F*.

12 Note also that the chair shrinks to a point very quickly. To give a sense of the values of timedilation obtaining for ordinary objects, consider a metal disk and a pair of events, diametricallyopposed on the outer edge of the disk, separated by one meter and simultaneous in frame ofreference F. Consider, moreover, a frame of reference F*, moving very rapidly relative to F. Whatsorts of time differences obtain between the two events in F*? Given that u is the relative velocity ofthe frames and c is the speed of light, here are the time differences for various values of u: u = .9c,time difference = 6.88� 10–9 seconds; u = .95c, time difference = 1.01� 10–8 seconds; u = .99c, timedifference = 2.24� 10–8 seconds. These values are very small. (Note, however, that the time-dilationinterval tends to infinity as u approaches c.) The problem stated above is that if our chair goes out ofexistence exactly at t2

F, then it is point-shaped at tF*. If the antecedent is true, then the problem arisesirrespectively of the size of the time-dilation intervals in play. How quickly the chair shrinks in F* isirrelevant, only that it shrinks counts. The status of the antecedent is a different issue. SeeSection 8.2.2 on temporally fuzzy boundaries of ordinary objects in the relativistic context.

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8.2 No Easy Way Out

Is the problem of relativistic change easy to avoid? In this section, I shall look atthree attempts to shrug it off, and raise doubts about each of them. My aim is toprovide reasons for taking the problem seriously, before invoking perspectivalhylomorphism in order to avoid it.

8.2.1 Restriction to rest frames

In an attempt to save the ordinary conception of chairs, one might consider theview that this conception is implicitly restricted to rest frames. Ordinary thinkers,so the view might go, do not believe that chairhood applies to an object invari-antly, full stop. What they really believe is that chairhood applies to an object atall times at which that object exists in its rest frame.13 Alternatively, one mighthold that ordinary thinkers do not believe that being a chair is partly a matter ofbeing chair-shaped, full stop. What they really believe is that an object’s being achair is partly a matter of being-chair-shaped in that object’s rest frame. Bothrestriction strategies would avoid the problem. If an object’s kind-membership inits rest frame is all that counts, it is irrelevant that the object that is a chair in itsrest frame is not a chair in the frame in which it shrinks to a point. Similarly, if achair’s being chair-shaped in its rest frame is all that counts, it is irrelevant thatthe chair is point-shaped in another frame.This response will not do. It is highly implausible that the common-sense

conception of ordinary objects should be restricted in these ways. Our sortal-invariance intuition is an intuition about the individuation of ordinary objects:there are kinds whose instances could not fail to belong to these kinds, in anypossible circumstances; these kinds are essential to their instances; they individu-ate them. This conception clearly rules out sortal variation across any frames ofreference, and hence it leaves no room for a restriction to rest frames. If a chairfails to be a chair in certain reference frames, then its link to the kind chair is tooloose for it to be individuated by that kind. In this case, the kind gets downgradedto a mere variant kind. Since common sense parses the world into objects bycertain kinds, relativistic variation with respect to these kinds is deeply at oddswith common sense.Moreover, our sortal-determination intuition is that there are specific kinds K,

such that being a K partly consists in being K-shaped. The explanatory force of

13 I shall set aside worries about the notion of a rest frame of a spatially extended, mereologicallycomplex object. See Balashov (2010: 191–4) and Gibson and Pooley (2006: 194, n.29) for discussionof this issue.

228 relativity

this belief clearly rules out variation in sortal determination across any frames ofreference. If being a chair is partly grounded in being chair-shaped, then a four-dimensionalist object is invariantly a chair only if each partitioning of the objectinto stages relative to any reference frame is a partitioning into chair-shapedstages, and hence only if the object is chair-shaped at each frame-relative time atwhich it exists. No restriction to rest frames will plausibly avoid the problem ofrelativistic change.14

8.2.2 Indeterminate time of destruction

The problem might seem to depend upon the idea that an ordinary object mightbe destroyed in such a way that it neatly ceases to exist at a particular moment ina particular frame of reference. For this scenario allows us to consider anotherframe of reference, moving very rapidly relative to the first, in which the objectwould gradually wither down to a single point, rather than coming to a clear-cutend. It will be objected that there is no particular moment at which an ordinaryobject clearly goes out of existence (see Section 7.3.5). When a chair is distortedor fragmented, even when done with the most violent and speedy means, thistakes some time, and it is far from clear at which point the chair ceases to exist.Chairs have fuzzy temporal boundaries.15

I reply that the problem does not depend on the assumption that ordinaryobjects have clear-cut temporal boundaries. Consider again our original scenarioinvolving chair o, reference frames F and F*, and times t2

F and tF* (as illustratedin Figure 8.2). It is plausible that it fails to be determinate that o goes out ofexistence at t2

F, contrary to what was previously assumed. It is also plausible thatit fails to be determinate that o does not go out of existence at t2

F—that is, t2F

seems to be a perfectly good candidate to mark o’s end in reference frame F. Inshort, it is indeterminate whether o goes out of existence at t2

F (where it isindeterminate whether p iff it is neither determinate that p nor determinatethat not p). We know from previous considerations that if o goes out of existenceat t2

F, then o is point-shaped at tF*. Since it is not determinate that o does not goout of existence at t2

F, it follows by the foregoing conditional that it is not

14 The same considerations discredit the related suggestion that common sense only requires thatchairhood apply to an object at all times at which it exists in some reference frame; or that an object’sbeing a chair partly consists in being-chair-shaped in some reference frame.

15 We are led to this judgement by common-sense considerations about the temporal boundariesof ordinary objects. It should be noted that considerations from physics may also support thisjudgement. Destroying a complex material object involves breaking bonds between particles. Theseare quantum-level events. Accordingly, a complex object around the time of its annihilation is in afuzzy state: a superposition of many different states. Hence, the object lacks a determinate boundaryin spacetime.

relativity 229

determinate that o is not point-shaped at tF*. If we cannot rule out that o goes outof existence at t2

F, then we cannot rule out that o is point-shaped at tF*.Intuitively, however, it is determinate that o is not point-shaped at tF*. For o isdeterminately a chair, and it is perfectly clear that a chair cannot be point-shapedat any time in any frame. Being point-shaped is a determinate impossibility forchairs.This response may be put another way. Any candidate temporal-boundary of a

given chair must preserve what makes this object a chair. Specifically, no bound-ary that leaves an object point-shaped is a candidate boundary for a chair. If t2

F isa candidate for the time at which o goes out of existence in frame F, then tF* is acandidate for the time at which o goes out of existence in frame F*. But thistemporal boundary in F* does not preserve o’s chair-shape, and hence is not acandidate boundary for o. Then t2

F is not a candidate boundary for o either,which contradicts our initial assumption. In the face of indeterminacy, the initialproblem concerning what makes a spatiotemporal boundary a boundary of achair becomes a problem concerning what makes a spatiotemporal boundary acandidate for a boundary of a chair. This is not supposed to be the last word onthe relationship between indeterminate temporal boundaries and relativisticshape-change. My aim was merely to show that there is a prima facie plausibleway of rebooting the problem in the face of indeterminacy worries, and hencethat the problem does not go away so easily.

8.2.3 Kind-dependent persistence

A third approach to the problem is to question the account of existing at a frame-relative time that has been assumed so far. Suppose, as before, that some particlesbecome arranged chair-wise at t1

F and stay arranged in this manner exactly untilt2F, at which time the arrangement breaks up. Thus a chair comes into existence

exactly at t1F and goes out of existence exactly at t2

F, and is composed of thementioned particles at all times at which it exists.16 The problem is generated byfirst fixing the chair’s invariant world volume and corresponding four-dimen-sional shape in frame F in this way and then viewing this trajectory and shape in adifferent frame, F*. The crux is that if the chair is allowed to exist at tF*, then it ispoint-shaped at that time.Why not deny that the chair exists at tF*? One might suggest that the existence

at a frame-relative time of a macroscopic object of kind K partly consists in theobject’s constituent particles being K-shaped at that time. The familiar idea

16 In light of the considerations of Section 8.2.2, issues of indeterminacy of temporal boundarieswill henceforth be set aside.

230 relativity

behind this suggestion is that the trajectory of an ordinary object of kind K isdetermined by K-dependent persistence conditions. If existing at a frame-relativetime is constrained in this way, then our chair does not exist at tF* anymore,because its atomic parts are no longer arranged chair-wise at that time. Ingeneral, no ordinary, mereologically complex object will end up point-shapedin any reference frame, because kind-dependent metaphysical principles ofcomposition and persistence will rule out this possibility.17

We started with an account of persistence and shapes of ordinary objects thatsustains the unified view of shapes in Minkowski spacetime but loses the folkconception of these objects. Now we are looking at an account of persistence andshapes of ordinary objects that respects the folk conception but is at odds with theunified view of relativistic shapes. Here is why. A macroscopic object o’s trajec-tory in a frame of reference F is the region through which o persists in F. Moreperspicuously, o’s world volume in a reference frame F is the fusion of all regionsexactly occupied by o at any time in F. This is how we naturally determine anobject’s trajectory in a reference frame. Consider now the familiar scenario thatthe world volume of chair o in reference frame F is a four-dimensional regionbounded by times t1

F and t2F, as illustrated by Figure 8.3.

Given a kind-dependent criterion of existing at a frame-relative time, o ceasesto exist at t1

F*, prior to t2F*, in reference frame F*, with the consequence that o

does not end up being point-shaped at t2F*. Since o’s trajectory in F* is the fusion

world volume of o in F

t1F

t2F

t

x

Figure 8.3 The chair’s kind-dependent trajectory in F

17 I take Balashov (2014) to suggest this reply to the problem I raise here. See also Balashov (2010:section 5.5) on a related but relevantly different problem.

relativity 231

of all the regions that o occupies at any time in F*, o’s world volume in F* isdistinct from o’s world volume in F, as illustrated by Figure 8.4.So o persists through different four-dimensional regions relative to different

reference frames. Since an object has an invariant world volume only if the objectpersists through the same four-dimensional region no matter which relativisticangle it is viewed from, o does not have an invariant world volume; o does notexactly occupy the same four-dimensional region in each frame of reference.Now recall that according to the unified view of a macroscopic object’s shapes

in Minkowski spacetime, the object has an invariant world volume and acorresponding shape that underlies and unifies the object’s different shapes atdifferent times in different reference frames. The object’s possession of a per-manent shape with different cross-sections associated with different relativistictimes renders the object’s different shapes at these times mere perspectivalrepresentations. Compare relativistic variation in shape with modal variation inshape. The plenum of possible worlds constitutes a real dimension of change: anobject’s sequence of shapes in one possible world and its different sequence ofshapes in another possible world are not grounded in a unique, modally invariantshape or sequence of shapes. The plenum of reference frames, on the other hand,does not constitute a real dimension of change: an object’s sequence of shapes inone reference frame and its different sequence of shapes in another referenceframe are grounded in the same invariant shape. Modal shape-variation is non-perspectival, whereas relativistic shape-variation is perspectival. Since object o inthe scenario above lacks an invariant world volume, its relativistic shapes cannotbe construed as perspectival representations of a stable four-dimensional shape.Kind-dependent accounts of an ordinary object’s existing at a frame-relative time

world volume of o in F*t1

F*

t2F*

t′

x′

Figure 8.4 The chair’s kind-dependent trajectory in F*

232 relativity

are therefore incompatible with the unified view of relativistic shapes of theseobjects. These accounts implausibly assimilate relativistic shape-variation tomodal shape-variation.The kind-dependence response to the problem of relativistic change may

be developed in various ways. One strategy is to render the standard four-dimensionalist picture kind-sensitive by saying that an object of kind K existsat an F-relative time tF only if it has a K-shaped stage as a part at tF. Anotherstrategy, in the neighbourhood of the first, is to adopt a counterpart-theoreticanalysis of persistence in terms of stages related in kind-relevant ways, and to saythat an object of kind K exists at an F-relative time tF only if it has a K-counter-part at tF. A third strategy is to get kind-dependent persistence conditions on thebasis of a broadly Aristotelian picture of ordinary objects as depending in theirexistence and identity on a kind-determining ‘principle of unity’ holding amongits parts. If combined with three-dimensionalism about an object’s location inspacetime, the view could be that an object of kind K exists at an F-relative time tF

only if it exactly occupies a sub-region R of tF and is K-shaped at R. Here I am notconcerned with the details of these and related versions of the view that ordinaryobjects have kind-dependent persistence conditions. For all of these versionsshare the same defect: they are incompatible with the unified view of shapes inrelativistic spacetime. To repeat the main point, if an object’s persistence is kind-dependent, then the object has different world volumes in different referenceframes, and hence it lacks an invariant shape that underlies its different shapes atdifferent times in different frames.

8.2.4 Relativistic metaphysics versus common sense

There is no easy way to reconcile the unified view of relativistic shapes ofordinary objects with the common-sense conception of the latter. So what todo? An understandable reaction at this point is simply to live with the outcome,and to view the problem of the point-shaped chair as a counterintuitive conse-quence of relativity theory that is to be accepted with natural piety. I agree thatfaith in common sense should be limited when folk beliefs clash with physics.18

This attitude, however, is insufficient to deflate the problem of the point-shaped

18 A problematic clash between common sense and physics was mentioned in Chapter 6, n.23:the laws of dynamics of our best physics do not seem to apply to all ordinary objects. Here few wouldbe inclined to blame the physics. Perhaps most famously, Arthur Eddington (1928) saw a conflictbetween two descriptions of tables: while the table of common sense is solid, the table of science is‘mostly emptiness’ (1928: x). To Eddington it was obvious how the conflict is to be decided: ‘I neednot tell you that modern physics has by delicate test and remorseless logic assured me that mysecond scientific table is the only one which is really there’ (1928: xii). (For a critical discussion ofthis alleged conflict, see Thomasson (2007: 138–44).)

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chair. For the latter does not, strictly speaking, concern such a clash. It rathermarks a clash between common sense and relativistic metaphysics. As presentedhere, the problem rests partly on the metaphysical assumptions of four-dimen-sionalism and the unified view of shapes in relativistic spacetime. This is animportant difference. For it is primarily philosophical attacks on the folk con-ception, not scientific ones, that Mooreans are sceptical about (cf. Section 2.3).Furthermore, a Moorean philosopher intent on saving the appearances will beparticularly concerned with saving the folk principles of sortal invariance andsortal determination. For these principles are fundamental from the point of viewof common sense. If they break down, then our failure is not just one ofqualification, but one of individuation. If they break down, then we did not justdescribe the world incorrectly; we parsed the world incorrectly—we got theessence of objects wrong. These are good reasons to look for another way out.In the remainder of this chapter, I will show that reconciliation is possible.

8.3 Compatibilism about Relativistic Change

Our ordinary conception of macroscopic objects apparently clashes with theunified view of these objects’ shapes in Minkowski spacetime, because accordingto common sense, ordinary objects do not undergo radical change in shape,whereas according to the relativistic metaphysics associated with the unified viewthey do. Traditional metaphysical accounts of ordinary objects seem forced eitherto drop the compelling unified view of relativistic shapes or to revise thefoundations of the common-sense conception of objects. Fortunately, we cando better than that. I shall offer a compatibilist response to the problem, based onperspectival hylomorphism. The response goes roughly as follows.Ordinary objects are double-layered compounds of form and matter. The

different layers permit different perspectives on the objects, the sortal-sensitiveperspective focusing on form and the sortal-abstract perspective focusing onmatter. An ordinary object belongs to an invariant kind K, because its formrealizes K, whereas the object’s underlying matter is independent of any kind towhich the object belongs. Thus, from the sortal-sensitive perspective an ordinaryobject’s behaviour in different reference frames is constrained by the invariant kindto which the object belongs, whereas from the sortal-abstract perspective theobject’s behaviour in different frames is unconstrained by any kind. Correspond-ingly, from the sortal-sensitive perspective ordinary objects do not undergo radicalchange in shape across different frames, for their shape-change obeys the limits setby ordinary kinds. From the sortal-abstract perspective, on the other hand, ordin-ary objects may undergo radical change in shape across different frames. The

234 relativity

sortal-sensitive perspective is the one adopted by common sense. The sortal-abstract perspective is the one adopted by relativistic metaphysics. Owing to thecompatibility of these perspectives, the unified view of relativistic shapes of ordin-ary objects does not clash with the foundations of the folk conception.The plan of this section is the following. I shall propose to reconcile the unified

view of relativistic shapes with common sense within the framework of perspec-tival hylomorphism. The unified view is best captured by a four-dimensionalistaccount of material objects. Or so I assumed in Section 8.1. Accordingly,I shall tackle the problem of relativistic change with four-dimensionalist per-spectival hylomorphism, leaving open whether three-dimensionalist perspectivalhylomorphism can deliver the same results. We saw that the four-dimensionalism-based framework has at least two versions, the worm-version and thestage-version (see Sections 1.3 and 2.2). In Section 8.3.1, the worm-version ofperspectival hylomorphism will be given a relativistic extension. In Section 8.3.2,the extended framework will be shown to yield a compatibilist dissolution ofthe problem of relativistic change. The reason for introducing the approach to theproblem in the context of the worm-version is that the latter provides the mostintuitive understanding of the strategy. Since this version is inferior to the stage-version in an important respect that is independent of relativity (see Section 3.3),I shall close this chapter by showing that the perspectival dissolution of theproblem is also available in the context of the stage-version.

8.3.1 Relativistic perspectival hylomorphism

The starting point of my relativistic extension of perspectival hylomorphismabout ordinary objects is a fairly standard four-dimensionalist characterizationof material objects. A material object has a certain non-derivative trajectory inMinkowski spacetime, a region that it exactly occupies. This spacetime region isits world volume. For each region of overlap between a material object’s worldvolume and an F-relative time, for some frame of reference F, the object has a partthat exactly occupies that region. For a time tF, the part of an object that occupiesthe region of overlap between its world volume and tF is the object’s stage at tF.According to the familiar account sketched at the beginning of this chapter,ordinary objects are just material objects in this technical sense. According to therelativistic variant of q-hylomorphism being developed now, ordinary objects aremore than material objects.A K-state, for any kind K, is the K-meaningful, intrinsic, and K-realizing

qualitative profile of a stage. For a stage s at time tF, for some frame of referenceF, a K-state of s contains as its K-meaningful, intrinsic profile the maximalconjunction of the facts that s exists, that s has ç1, that s has ç2, . . . , that s hasçn, such that each çi is an intrinsic property of s and each çi falls in the sphere of

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discourse of K. Furthermore, the K-state of s contains as its K-realization profilethe maximal conjunction of the facts that s has ł1, that s has ł2, . . . that s has łn,such that the łs jointly realize kind K; and the maximal conjunction of the factsthat ł1 realizes K, that ł2 realizes K, . . . that łn realizes K. For example, a chair-state of a stage at a given frame-relative time is a conjunctive fact that has allchair-meaningful intrinsic properties and all chair-realizing properties of s asconstituents.A pre-relativistic K-path may be glossed as a life of a K. In the relativistic

context, I shall distinguish between the life of a K in a given reference frame, to becalled a framebound K-path, and the life of a K across different reference frames,to be called a proper K-path. A framebound K-path is a series of K-states with thefollowing properties:

• All of the K-states in a framebound K-path are K-states at times in the samereference frame: if K-states j and j* are conjuncts of a K-path, tFj is the timeof j, and tF*j* is the time of j*, then F = F*.

• A framebound K-path is interrelated by K-continuity: any two K-states in aframebound K-path that are temporally close contain massively similarintrinsic and K-realizing properties. Local property-variation encoded by aK-path is small.

• A framebound K-path is interrelated by K-connectedness: the K-realizingproperties in any two K-states in a framebound K-path, no matter howtemporally distant they are from each other, are similar to some minimaldegree. Global property-variation encoded by a K-path can be extensive buthappens within limits set by K. How much similarity is required is a vaguematter.

• A framebound K-path is interrelated by lawful causal dependence: if K-statej at a given time in F and K-state j* at an earlier time in F are K-states in thesame frame-bound K-path, j causally depends on j*.

• A framebound K-path is maximal: no segment of a larger conjunction ofK-states interrelated by similarity and causal dependence is a frame-boundK-path. Only the largest conjunction of K-states interrelated in this waycounts as a framebound K-path.19

A proper K-path is a series of framebound K-paths with the followingproperties:

19 As in the case of pre-relativistic K-paths, I shall allow framebound K-paths to include morethan one K-state at a frame-relative time, and to be temporally gappy.

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• A proper K-path is interrelated by extensive overall similarity: the four-dimensional distributions of intrinsic and K-realizing properties containedin any two framebound K-paths in a proper K-path are massively similar.

• A proper K-path is interrelated by massive spatiotemporal overlap: ifK-paths bound to distinct frames fill the same four-dimensional spacetimeregion or distinct, massively overlapping regions, then they belong to thesame proper K-path.20

• A proper K-path is maximal: no segment of a larger conjunction of frame-bound K-paths interrelated by similarity and massive spatiotemporal over-lap is a proper K-path. Only the largest conjunction of framebound K-pathsinterrelated in this way counts as a proper K-path.21

A proper K-path is a series of K-states obtaining at various times and in variousreference frames. Just as the K-states in the proper K-path may differ acrosstimes, so they may differ across frames. In other words, a proper K-path mayencode qualitative change, such as a change in shape, across times in a frame andacross frames. Conditions of persistence across times and frames standardlyassociated with an ordinary kind K are here understood as the ‘unity criteria’ ofproper K-paths—as the conditions under which a series of K-states counts asa proper K-path. Suppose, then, that a proper K-path encodes a substantivequalitative change across different reference frames, a shift in the distributionof K-realizers across frames (an example will be provided shortly). In such a case,a proper K-path may fill multiple, massively overlapping four-dimensional space-time regions, each one exactly filled by a framebound K-path in the properK-path. Given that material objects have an invariant world volume, distinctframe-bound K-paths in the same proper K-path, filling distinct four-dimen-sional regions, may have distinct material subjects. Hence, a proper K-path maylack a unique material spacetime worm as its strict subject. I shall say that eachmaterial worm that is the strict subject of a framebound K-path in a properK-path is a derivative subject—possibly one of many—of that proper K-path. Thepoint of central importance for present purposes is that while proper K-pathsalways behave in a K-ish way, material objects need not behave in such a way.Since the persistence conditions of proper K-paths are kind-dependent, and the

20 The spacetime region filled by a framebound K-path is the region exactly occupied by its strictsubject—that is, by the maximal fusion of the strict subjects of the framebound K-path’s componentK-states.

21 It may be added that a proper K-path has a unique framebound K-path in a frame of reference:if an F-bound K-path iF and an F*-bound K-path iF* are conjuncts of a proper K-path and F = F*,then iF = iF*.

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persistence conditions of material objects are not, the trajectories of properK-paths and those of their material subjects may diverge.With material objects and proper K-paths in the picture, ordinary objects may

be analysed: an ordinary object is a compound of a material object and a properK-path, for some kind K. Moreover, the application of compounding to amaterial object a and a proper K-path i consists in the application of the standardoperation of summation to a and i under the condition that a be the strict subjectof some frame-bound K-path included in the proper K-path, and hence aderivative subject—perhaps one of many—of i. This is a relativistic variant ofq-hylomorphism. For a given material object that is a derivative subject of aproper chair-path, the sum of the material object and the proper chair-path is achair. The material object is the chair’s matter, and the proper chair-path is thechair’s form. The key feature of q-hylomorphism in general is the possibility ofhylomorphic divergence. And the key feature of relativistic q-hylomorphism isthe possibility of hylomorphic divergence across reference frames, which will beillustrated shortly.22

Having sketched a relativistic variant of q-hylomorphism, let me propose arelativistic rendition of perspectivalism, as well. Perspectivalism is the thesis thatordinary predication about objects is perspectival, employing modes of predica-tion that correspond to different perspectives on ordinary objects. It must beemphasized right away that these perspectives are not the ‘relativistic perspec-tives’, the inertial frames of reference, invoked earlier. I shall henceforth becareful to distinguish the sortal-sensitive and the sortal-abstract perspective onordinary objects from reference frames.In the relativistic context, familiar temporal predications about ordinary

objects will be understood as frame-relativized (see Section 8.1). These predica-tions may employ the formal or the material mode. Formal and material predi-cation are modes of predicating a property of an object that has a proper K-pathand a material subject of that K-path as components, the former being the object’sform, the latter the object’s matter. While formal predication concerns whichproperties are contained in the object’s form, material predication concernswhich properties are instantiated by the object’s underlying matter. The

22 If this account of ordinary objects is to provide a basis for the account of formal indeterminacyde re developed in Chapter 7, then an ordinary object must be analysed as a compound* of a materialobject and multiple, superimposed proper K-paths hosted by that object. To secure this multiplicityof superimposed proper K-paths, superimposed K-paths bound to the same reference frame mustbelong to distinct proper K-paths. I shall therefore assume that a proper K-path has a uniqueframebound K-path in any frame of reference (see n.21). Given this assumption, the extension isfairly straightforward. For reasons of simplicity, I shall set it aside.

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metaphysical truth conditions of frame-relative temporal predications of exist-ence and shape in the formal and the material mode may be stated as follows:for any ordinary object o, any inertial frame of reference F, any time tF, and anyshape ç,

(T24) o exists formally at tF iff there is a kind K and a K-path i, such that ohas i as a part, and for some stage s at tF, i includes the fact that s exists.

(T25) o has ç formally at tF iff there is a kind K and a K-path i, such that ohas i as a part, and for some stage s at tF, i includes the fact that s has ç.

(T26) o exists materially at tF iff there is a material object a, such that o has aas its maximal material part, and a has a stage at tF.

(T27) o has çmaterially at tF iff there is a material object a, such that o has aas its maximal material part, and a has a stage at tF that has ç.

These truth conditions are intended as replacements of conditions (T22) and(T23) of Section 8.1. While the latter characterize single-layered discourse aboutordinary objects understood as four-dimensionalist material objects (in mytechnical sense of ‘material’), (T24)–(T27) characterize double-layered discourseabout ordinary objects understood as compounds of matter and form. Noticethat (T26) and (T27) are the perspectivalist analogues of (T22) and (T23). (Asordinary predications of identity are not temporally modified, no relativisticmodification of the truth conditions stated in Section 2.2 is required.) So muchfor a sketch of a relativistically acceptable variant of perspectival hylomorphism.The core idea of perspectival hylomorphism is that we can describe ordinary

objects under a sortal cover, as chairs or persons, or we can strip away this coverand describe them as mere physical bodies. The formal, sortal-sensitive descrip-tion tracks properties that are contained in an ordinary object’s componentproper K-path, whereas the material, sortal-abstract description tracks propertiesthat are instantiated by stages of an ordinary object’s maximal componentmaterial object. The recognition of different perspectives on ordinary objectsand of accompanying modes of predication allows judgements about theseobjects to diverge: it may be true to say one thing about a given compound inthe formal mode, while it is false to say it in the material mode. As we have seen,perspectival divergence comes in different flavours. A variety that has not beendiscussed so far arises from discrepancies between matter and form regardingtheir shapes in different frames of reference. It is of central interest when therelativistically upgraded framework of perspectival hylomorphism is applied tothe problem of relativistic change.

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8.3.2 A solution to the problem of relativistic change

According to common sense, ordinary objects do not undergo radical change inshape, whereas according to the sort of metaphysics suggested by the unified viewof shapes in Minkowski spacetime—for short, according to relativisticmetaphysics—they do. Common sense sees limits to how much objects canchange, to which relativistic metaphysics is blind. In order to focus the problem,recall principle (K): for any ordinary object o, and for any invariant kind K,

(K) If o is a K, then o is K-shaped at all frame-relative times at which o exists.

According to common sense, (K) is true. According to relativistic metaphysics,(K) is false. Yet common sense and metaphysics do not compete. For their claimsmanifest different perspectives, and are therefore compatible. In the remainder ofthis section, I shall spell out this account of the relationship between commonsense and relativistic metaphysics in detail.Common sense carves the world into chairs, persons, and trees, adopting the

sortal-sensitive perspective on objects. Relativistic metaphysics recognizes theseobjects but abstracts from what makes them chairs, persons, and trees, thinkingof Ks as mere physical bodies. The unified view of how an object’s various shapesin different reference frames are related is independent of which kinds the objectbelongs to. It is a view about how an object’s shapes are really related, castingaside our sortal representations of these objects.Note that while I view relativistic metaphysics as abstracting from the kinds of

ordinary objects, I do not view relativistic metaphysics as adopting exactly thesame sortal-abstract conception of these objects as common sense does. Whilethere is only a single material mode of predicating properties of ordinary objects,there may be several distinct sortal-abstract conceptions of ordinary objects—different ways of adopting the sortal-abstract perspective—that ‘trigger’ thematerial mode of predication in a given context. In short, I advocate a pluralismabout sortal abstraction. Psychological evidence suggests that ordinary thinkershave a sortal-abstract conception that is primarily characterized by spatiotem-poral principles and that is kind-independent through and through (seeSection 2.1). This is not the only sortal-abstract conception of ordinary objectsavailable. A physics-oriented sortal-abstract conception of macroscopic objectsmay represent objects differently. More specifically, there is room for a physics-friendly sortal-abstract conception of macroscopic objects as quantities of matter,where the characterization of matter invokes microphysical particles of certainkinds. This would be a conception that abstracts from sortal representationsof macroscopic objects without abstracting from sortal representations of

240 relativity

microscopic objects as quarks, leptons, and so on. That is, the conception wouldnot be completely kind-independent. More could be said about the contents ofalternative sortal-abstract conceptions, but I shall have to confine myself to thesesketchy remarks.To think of an object as a K is to recognize that it has K-realizing properties.

This is the sortal-sensitive perspective. If we think of the object as a K, and weview being a K as an invariant property of the object, then we expect the latter tobe K-shaped throughout its life, because being K-shaped partly realizes being aK. Thus, the adoption of the sortal-sensitive perspective on ordinary objectsnaturally leads to the acceptance of principle (K). To think of the object as amere physical body is to abstract from K-realizing properties. This is the sortal-abstract perspective. If we think of the object as a mere physical body, then we donot ascribe any specific persistence conditions to the object, and hence we haveno reason to expect it to be K-shaped throughout its life. The only constraintsconcerning which shapes an object can assume that are recognized from thesortal-abstract perspective are independent of the kinds to which the objectbelongs; the constraints apply to macroscopic objects as a class. The unifiedview of relativistic shapes is such a constraint. Thus, the sortal-abstract perspec-tive is a natural backdrop for questioning principle (K).Given that statements made from the sortal-sensitive perspective employ the

formal mode of predication, common sense claims that (Kform) is true: for anyordinary object o, and any invariant kind K,

(Kform) If o is a K, then o is formally K-shaped at all frame-relative times atwhich o formally exists.

And given that statements made from the sortal-abstract perspective employ thematerial mode of predication, relativistic metaphysics claims that (Kmat) is false:for any ordinary object o, and any invariant kind K,

(Kmat) If o is a K, then o is materially K-shaped at all frame-relative times atwhich o materially exists.

The distinction between a formal and a material reading of (K), manifesting aperspectival shift, puts an end to the apparent disagreement over (K). I will showthat in the framework of perspectival hylomorphism, the falsity of (Kmat) iscompatible with the truth of (Kform).

Let iF be an F-bound chair-path that has material object a as its unique strictsubject, where F is the rest frame of a. So iF traces a smooth distribution of chair-realizing properties across a’s world volume. Further, let iF* be an F*-boundchair-path—where F* is the frame of reference of an observer who is moving very

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rapidly relative to a—that has material object b as its unique strict subject, suchthat a and b are distinct but overlap extensively, and iF is massively similar to iF*,containing the same or very similar chair-realizing properties. While the laststage of a in F, at time t2

F, is chair-shaped, let the last stage of a in F*, at time t2F*,

be point-shaped (setting aside temporal indeterminacy). The case may be illus-trated by Figures 8.5 and 8.6.Given that there is a range of massively similar and massively spatiotemporally

overlapping chair-paths bound to different reference frames, including iF and iF*,there is a proper chair-path, i, that is the maximal union of all these frame-boundchair-paths. Since material object a is a derivative subject of i, there is a chair, o,such that o is�c(a, i). (Notice that b is also a derivative subject of i, and hence that

t1F

t2F

t

x

world volume of aworld volume of F-bound

chair-path iF

Figure 8.5 F-bound chair-path iF

world volume of aworld volume of F*-bound

chair-path iF* t1F*

t2F*

t′

x′

Figure 8.6. F*-bound chair-path iF*

242 relativity

there is an absolutely distinct chair, the compound of b and i; I shall return to thisaspect of the case below.)This case renders (Kmat) false, but does not touch (Kform). Since o’s maximal

material component, a, has a stage at t2F*, it follows by (T26) that o exists

materially at t2F*. Since a’s stage at t2

F* is point-shaped, it follows by (T27) thato is materially point-shaped at t2

F*. By analogous considerations regarding timesthat lead up to t2

F* in frame F*, at which a has various stages, it follows that omaterially shrinks to a point over a certain period of time in F*. Since o is a chair,and since a point-shaped object is not chair-shaped, (Kmat) is false, as expected.This limiting case of material relativistic variation in shape does not clash with

the folk conception of macroscopic objects, since the common-sense version ofprinciple (K) is (Kform), which says that Ks are formally K-shaped. While chair oexists materially at t2

F* and is materially point-shaped at t2F*, o does not exist

formally at t2F*. The last F*-relative moment at which o exists formally is the

earlier t1F*, and o is still formally chair-shaped at that moment. This is so, because

o’s formal behaviour in different reference frames is constrained by the invariantkind to which o belongs: o’s proper chair-path is a series of chair-states which arepartly characterized by chair-realizing properties, including chair-shapes; anychair-state that a proper chair-path has at any time includes the property of beingchair-shaped. By (T24) and (T25), it follows that for any time tF, if o is a chair andif o formally exists at tF, then o is formally chair-shaped at tF. Hence, (Kform) ispreserved.The present picture captures the unified view of ordinary objects’ shapes in

Minkowski spacetime by construing this view as manifesting the sortal-abstractperspective on these objects. In brief, an ordinary object’s various material shapesat different frame-relative times are just cross-sections of the invariant shape ofits underlying matter, and are not constrained by any kinds to which the objectbelongs. As a consequence, the object may undergo radical change in materialshape across different reference frames. The present picture also captures the folkview of an ordinary object’s shapes by construing this view as manifesting thesortal-sensitive perspective on these objects. In brief, an ordinary object’s variousformal shapes at different frame-relative times are shapes contained in theobject’s individual form, and are constrained by the invariant kind to which theobject belongs. As a consequence, ordinary objects do not undergo radical changein formal shape across different reference frames. Correspondingly, an ordinaryobject has an invariant trajectory from the sortal-abstract perspective. Its uniquematerial world volume is the four-dimensional spacetime region exactly occupiedby its matter. Yet the same object may have different trajectories in differentreference frames when viewed from the sortal-sensitive perspective. Its potential

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plurality of largely overlapping formal world volumes are the various four-dimensional spacetime regions filled by the various frame-bound K-paths mak-ing up the object’s proper K-path—its form. Owing to the compatibility of theseviews, relativistic metaphysics poses no threat to our pre-theoretical conceptionof an ordinary object’s shapes.Relativistic metaphysics also poses no threat to our pre-theoretical count of the

number of ordinary objects. Proper K-paths are allowed to have distinct materialobjects as derivative subjects. In the scenario sketched above, frame-bound chair-paths iF and iF*, as illustrated in Figures 8.5 and 8.6, have distinct material objectsas strict subjects. Accordingly, proper chair-path i, which includes iF and iF*, hasdistinct derivative subjects. These two derivative subjects are a and b. Thus, thereare at least two nearly spatiotemporally coinciding chairs that we may imagine tobe singled out by distinct observers in frames F and F*, respectively, namely o ando*, where o is �c(a, i) and o* is �c(b, i). Intuitively, however, this scenariocontains just one chair.The apparent tension may be removed by appealing again to different modes

of counting chairs. Since the common-sense intuition that o and o* are the samechair is a sortal-sensitive intuition, identity is ascribed in the formal mode, andaccordingly the intuitive count of one chair is a formal count. While o and o* areabsolutely and materially distinct, they are formally identical, by the now-familiarmetaphysical truth conditions of formal identity claims, because they have thesame component proper K-path, i. As regards the number of chairs in thescenario under consideration, there are many from the sortal-abstract perspec-tive, but there is one from the sortal-sensitive perspective. This is how common-sense expectations concerning the number of ordinary objects are preserved inrelativistic contexts.The proposed dissolution of the problem of relativistic change was achieved by

means of the worm-version of four-dimensionalist perspectival hylomorphism,according to which an ordinary object’s underlying matter is a four-dimensionalspacetime worm. I take this version to provide the most intuitive illustration ofthe present approach to the problem, given that the latter was initially formulatedon the familiar assumption that ordinary objects just are four-dimensionalspacetime worms. The worm-version of perspectival hylomorphism, however,has proven inferior to the stage-version with respect to the availability of aperspectival dissolution of the problems discussed in Chapters 3 and 4 (seeespecially Sections 3.3 and 4.2). I shall therefore close by showing briefly thatthe perspectival dissolution of the problem of relativistic change is also availableto the stage-version, thereby recommending the latter as the overall morepowerful option.

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According to the worm-version of perspectival hylomorphism, an ordinaryobject is the sum of a proper K-path and any material object that is the strictsubject of any frame-bound K-path included in the proper K-path. According tothe stage-version, by contrast, an ordinary object is the sum of a proper K-pathand any material object that is the strict subject of any K-state included in theproper K-path. The worm-version thus construes the matter of an ordinaryobject as a temporally extended material worm, whereas the stage-version con-strues the matter of an ordinary object as a temporally unextended material stage.Moreover, metaphysical truth conditions (T24)–(T27) of monadic temporalpredications in the formal and the material mode are neutral between thesetwo accounts of ordinary objects. (By (T26) and (T27), an ordinary object existsand has a shape çmaterially at a frame-relative time tF, in virtue of its underlyingmatter having a stage at tF that has ç. Since according to the stage-version, anordinary object’s underlying matter is just an instantaneous stage, (T26) and(T27) require an ordinary object’s matter itself to be located at tF and to have ç.)Let me show now how this modified framework reconciles the unified view of

an ordinary object’s shapes in Minkowski spacetime with the common-senseview of an ordinary object’s shapes. The unified view of relativistic shapes is hereunderstood as manifesting the sortal-abstract perspective on these objects.Accordingly, an ordinary object’s various material shapes at different frame-relative times are expected to be mere cross-sections of the invariant shape ofits underlying matter, and are not to be constrained by any kinds to which theobject belongs. The stage-version of perspectival hylomorphism satisfies thisexpectation. According to this version, an ordinary object’s material shapes indifferent reference frames are the shapes of its underlying stage in the variousframes. And a stage’s shapes in different reference frames are mere cross-sectionsof its unique, invariant shape. Of course, a stage has a very different invariantworld volume from a worm—the former is temporally unextended, whereas thelatter is temporally extended—and hence a stage’s range of shapes across refer-ence frames is quite different from a worm’s. But this is no obstacle to capturingthe unified view of relativistic shapes, since the latter only requires shapes indifferent frames to derive from a common underlying shape, no matter what thisinvariant shape is.For illustration, consider again proper chair-path i, which includes F-bound

chair path iF and F*-bound chair-path iF*, as illustrated in Figures 8.5 and 8.6.Consider, further, the last chair-state of iF, at time t2

F, whose strict subject is astage, s, located at t2

F. Assuming the stage-version of relativistic q-hylomorphism,there is a chair, o, such that o is �c(s, i). (This is one of many absolutely distinctbut formally identical chairs with i as their individual form. Since chairs, on the

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present version, are individuated by stages, the absolute number of chairs is vastlybigger than on the worm version.) Ordinary object o’s material shapes at differenttimes in different reference frames are cross-sections of s’s invariant shape, just asthe unified view of shapes in Minkowski spacetime demands. Since o’s maximalmaterial component, s, has a stage at t2

F*, it follows by (T26) that o existsmaterially at t2

F*. Since s’s stage at t2F* is point-shaped (or so we may assume),

it follows by (T27) that o is materially point-shaped at t2F*. Since o is a chair, and

since a point-shaped object is not chair-shaped, (Kmat) is false.The falsity of (Kmat) is compatible with the truth of the common-sense version

of (K), (Kform), which manifests the sortal-sensitive perspective on ordinaryobjects. While chair o exists materially at t2

F* and is materially point-shaped att2F*, o does not exist formally at t2

F*. The last moment at which o exists formallyin frame F* is not t2

F* but the earlier t1F*, and o is still formally chair-shaped at

that moment. In general, given the earlier characterization of proper K-paths andtruth conditions (T24) and (T25), for any time tF, if o is a chair and o formallyexists at tF, then o is formally chair-shaped at tF. (Kform) is thus preserved. This isa stage-based dissolution of the problem of relativistic change.The key feature of perspectival hylomorphism is the possibility of perspectival

divergence. In the relativistic context, we may distinguish between perspectivaldivergence concerning an ordinary object’s profile across time relative to anyframe of reference and perspectival divergence concerning an ordinary object’sprofile across different frames of reference. Both the worm-version and the stage-version of perspectival hylomorphism allow for the second type of divergence. Itis this type of divergence that the present dissolution of the problem of relativisticchange appeals to. Only the stage-version, however, allows for the first type ofdivergence. An ordinary object that has as its underlying matter the spacetimeworm that is the strict subject of an F-bound K-path cannot exhibit a divergencebetween its formal and material trajectory relative to F. As a consequence, it is notpossible for the worm-version to make it true, for example, that in F the piece ofpaper and the paper plane are formally but not materially distinct and coincident,nor that in F my watch formally but not materially enjoys intermittent existence.That is, the worm-version cannot avail itself of a perspectival-hylomorphistdissolution of the problems discussed in Chapters 3 and 4. The stage-version ofrelativistic perspectival hylomorphism is therefore the more powerful of the twooptions discussed.

246 relativity

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Index

Akiba, K. 196 n.14Aristotelian/neo-Aristotelian

hylomorphism 5–13, 28, 51–2, 55–6,84–5, 152, 177–9, 182–3, 233

Baker, L. R. 83 n.23Balashov, Y. 178 n.11, 220, 221 n.4, 223,

227 n.10, 228 n., 231 n.Barnes, E. J. 196 n.14–16, 198 n.17Barresi, J. 105 n.2Baxter, D. 56 n.29Belot, G. 168Bennett, K. 87 n.31, 149 n., 150 n.19,

152 n.24Brighouse, C. 175 n.Broad, C. D. 66 n.36Burke, M. 80 n.15, 128 n.33, 129 n.35,

130 n.39, 131Butler, J. 4 n., 56 n.29

Carey, S. 38 n.5, 40 n.9, 100 n.45Carnap, R. 72 n.53, 137 n.causal dependence 20–1, 236Chalmers, D. 25 n.43change, see relativity, problem of relativistic

changeChisholm, R. 4 n., 56 n.29, 66 n.36, 78 n.8,

162–3Chisholm’s Paradox 162–5classical mereologyand determinism 187and mereological structure 11–12, 52–6and spatial discontinuity 121and transworld identity 159–60in q-hylomorphism 13–15, 22–31introduced 1–5

coincidenceand determinism 170–89and indeterminacy 197–200compatibilism 87–103, 146–9deflationism 86–8modal case (Lumpl and Goliath) 135–6monism 79–82, 136–8, 173non-modal cases 75–9, 106, 171, 172pluralism 79, 82–6, 136, 150, 170

composition, see Aristotelian/neo-Aristotelianhylomorphism; classical mereology

compound, compoundingextended 203

introduced 22–4constitution 83–8, 136, 170, 177Correia, F. 17 n.counterpart theory

perspectivalist modal 138–46, 148–9, 161–2,164–5

standard modal 134, 136–7, 162, 164temporal 64–6, 113–15, 233

Davidson, D. 72 n.56dependence, see constitution, grounddeRosset, L. 149 n., 150 n.20, 152 n.24,

180 n.14determinacy operator, formal and

material 204–6determinism 166–89

conceptions 167–70, 174–7, 186problem of cheap indeterminism 170–89

Divers, J. 154 n.27dominant kind 80Dummett, M. 197

Earman, J. 170 n.5, 171Eddington, A. S. 233 n.Eklund, M. 107 n.5, 113 n.20eliminativism 80 n.14embodiment, rigid and variable

(Fine) 7–8, 10endurantism; see three-dimensionalismessence, essentiality

and coincidence 181 n.17essentiality of origin 163mereological essentialism 4, 139sortal essentialism, see sortal invariance

eternal recurrence 155–7Evans, G. 198–9, 214existence claim about ordinary objects 25, 47,

74 n.59, 87extraordinary object 25–6

Fara, M. 146 n.14Ferenz, K. 40 n.10Field, H. 58Fine, K. 2 n.2, 3 n., 5 n.8, 6 n.9, 7–9,

11–12, 13, 16 n., 17, 18 n.28, 23 n.36–7,27, 28, 51, 77, 78 n.9, 79 n.12,82 n.16, 86 n.29, 135 n.2, n.5,149 n., 151, 152 n.24, 180, 182,183, 192 n.4

fissioncompatibilism 113–27of organisms and artefacts (ship of

Theseus) 110of persons 105–9incompatibilism 111–13

Forbes, G. 154 n.28, 156 n.30, 157 n.31,159 n.36

formAristotelian/neo-Aristotelian conception,

see Aristotelian/neo-Aristotelianhylomorphismq-hylomorphic conception,

see q-hylomorphismfour-dimensionalism, see also counterpart

theory, temporaland classical mereology 2–3, 5and coincidence 82–4, 97–9, 138and determinism 170, 179–80, 187and intermittent existence 130and mereological structure 12, 15and perspectivalism 63–4and q-hylomorphism 29–31and relativity 221–3, 225–6, 233, 234, 235–9,

244–6Frances, B. 82 n.16Frege, G. 15 n.24, 71fundamentality 36–8, 43, 70, 155, 194, 196,

206, 212

Gallois, A. 115 n.27Geach, P. 58 n., 77 n.4, 103 n., 193 n.7gestalt property 33Gibbard, A. 64 n., 82 n.16, 134 n., 135 n.3, 137 n.Gibson, I. 221 nn.3–4, 228 n.Gilmore, C. 221 n.4, 225 n.8Giovanelli, A. 105 n.2Goodman, N. 1 n., 197ground 17, 53–5, 85–7, 155, 194, 196grounding problem 149–54, 180–2Gupta, A. 64 n., 82 n.16, 134 n.Gutheil, G. 33 n.

haecceitism 157 n.32,haecceity 167, 168–170, 174–5Harte, V. 6Haskell, T. 40 n.10Hawley, K. 2 n.3, 64 n., 113 n.22, 114 n.24, 115,

191 n.3Hawthorne, J. 25 n.41, 34 n., 36 n.3, 55 n.,

80 n.14, 129 n.36, 156 n., 157–8, 159 n.35,170 n.4, 174 n., 178 n.10, 180 nn.12–13,182 n.18, 189 n.

hierarchy, compositional 6, 8, 52, 85; see alsoconstitution, ground

Hirsch, E. 25 n.39, n.42, 39 n.8, 42 n.12, 55,72 n.57, 74 n., 89 n., 99 n.43, 100 n.47

Hobbes, T. 110Hofweber, T. 69 n.45, 112 n.19Hudson, H. 25 n.41, 193 n.6hylomorphism, see Aristotelian/

neo-Aristotelian hylomorphism;quasi-hylomorphism/q-hylomorphism

identity, see also predication, formal identity,material identity

contingent identity 136–8, 145indiscernibility of identicals (Leibniz’sLaw) 57, 59–60, 76, 81

loose and popular vs. strict 56–7necessary identity 145–6transworld identity 142, 144, 154–65

indeterminacyde dicto 190–5; see also supervaluationism,standard

in fission 108–9, 112, 124–5in intermittent existence 130 n.38linguistic, see supervaluationism, standardmetaphysical/de re 190–1, 195–218of identity 198–9, 214of mereological boundaries 190–215of spatial boundaries 210of temporal boundaries 215–18,229–30

indeterminism, see determinismintermittent existence

cases 127–9compatibilism 131–3incompatibilism 129–31

Johnson, W. E. 20 n.34Johnston, M. 8, 107 n.7, 108 n.9, 112 n.17Jubien, M. 40 n.10, 146 n.15

Kestenbaum, R. 38 n.5kind, see also sortal concept; perspectivalism;

perspectivein Aristotelian hylomorphism 6–7, 10, 12in classical mereology 4–5kind-dependence of parthood, seemereological structure

kind-realization/K-realization 17–19qualitative content 16–17sphere of discourse 17–18

King, J. C. 82 n.16Korman, D. 25 n.41, 68 n.43, 73 n., 74 n.,

80 n.14, 89 n., 90 n., 99 nn.43–4,129 n.37

Koslicki, K. 5 nn.6–7, 6, 8 n.11, 9 n.14, n.16,11 n.18, 12 n.21, 83 n.23, 86 n.29, 152 n.24,183 n.19

K-path, see q-hylomorphismKripke, S. 163K-state, see q-hylomorphism

256 index

Leibniz, G. W. 4 n., 76Lewis, D. 1, 2 n.3, 13, 18 n.30, 20 n.33, 26, 28, 49

n., 64 n., 70 n.49, 72 n.56, 74 n., 78, 82 n.16,83 n.20, 89 n., 106 n.3, 108 n.10, 112, 113n.23, 134 n., 136–8, 140–1, 145, 148, 150,155 n., 162, 164, 166–7, 169, 170, 192,193 n.5, 194 n.9, 198 n.19

Locke, J. 15 n.24, 16, 105 n.1, 127Lotze, H. 20 n.34Lowe, E. J. 110 n.13

McGee, V. 193 n.5McGrath, M. 80 n.14McKay, T. 156 n.McKinnon, N. 194 n.10McLaughlin, M. 193 n.5Markosian, N. 193 n.9Martin, R. 105 n.2mass noun vs. count noun 15mass/quantity of matter 34, 36material object, see Aristotelian/

neo-Aristotelian hylomorphism; classicalmereology

matterAristotelian/neo-Aristotelian conception,see Aristotelian/neo-Aristotelian

hylomorphismq-hylomorphic conception,see q-hylomorphism

atomistic vs. gunky 14 n.22Maudlin, T. 171 n.Melia, J. 167, 168 n., 169 n., 170 n.5mereological indeterminacy 190–215mereological monism vs. pluralism 9, 22mereological structure 2–3, 5–8, 10–12, 28,

40 n.10, 50–6, 61–2, 177mereological sum, see classical mereologymereology, see Aristotelian/neo-Aristotelian

hylomorphism; classical mereologymetaphysical semantics 43–4, 46, 70–2Michael, M. 80 n.14modality de re 134–65, 170modal operator, formal and material 142modal-sufficiency requirement 154–5, 159;see also sufficiency problem

monster objection (Fine) 12, 51Montague, R. 66 n.36Mooreanism 68, 69, 71, 73, 89–90, 113, 126,

130, 234Morreau, M. 196 n.14

Noonan, H. W. 134 n., 154 n.28novel object 42–3Nozick, R. 107 n.5, 112 n.18

Olson, E. 111 n.15, 149 n., 150 n.19ontological realism vs. anti-realism 25ordinary object

concept of 33–4in Aristotelian/neo-Aristotelianhylomorphism 6–9

in classical mereology 4–5in q-hylomorphism, see q-hylomorphism

Parfit, D. 78 n.8, 105 n.2, 107, 111 n.14Parsons, T. 196 n.14, 199 n.21part, parthood, see Aristotelian/neo-Aristotelian

hylomorphism; classical mereologyPaul, L. A. 149 n., 152 n.24Penrose, R. 227 n.11perception 68–9perdurantism, see four-dimensionalismPerry, J. 4 n., 106 n.3persistence, see four-dimensionalism;

three-dimensionalismpersonal identity 77–8, 105–9, 111–25,

215–18perspectivalism

applied to Chisholm’s Paradox 163–4applied to grounding problem 152–4applied to modal paradox ofcoincidence 146–9

applied to non-modal paradoxes ofcoincidence 88–103

applied to paradoxes of fission 115–27applied to paradoxes of intermittentexistence 131–3

applied to problem of cheapindeterminism 184–9

applied to problem of indeterminatecoincidence 212–15

applied to problem of relativisticchange 243–5, 240–6

applied to problem of the many 210–12applied to sufficiency problem 159–62applied to temporal indeterminacy 215–18extension, modality 141–6extension, indeterminacy 204–10extension, relativity 238–9introduced 43–67

perspective: sortal-sensitive, sortal-abstract,absolute; see also perspectivalism

introduced 32–3, 35–45role in Chisholm’s Paradox 164role in mereological indeterminacy 207–8role in modal paradox of coincidence 147role in non-modal paradoxes ofcoincidence 99–103

role in paradoxes of fission 116–18role in paradoxes of intermittentexistence 131–2

role in problem of cheap indeterminism 184role in problem of indeterminatecoincidence 213–14

role in problem of relativistic change 240–1role in sufficiency problem 160

index 257

platitudes of common sense, see also perspectiveand epistemology 69and psychology 38–40anti-bilocation 106, 118anti-coincidence 76, 87, 91–2, 106, 118, 135,

147, 199, 213anti-extrinsicness 108, 118anti-intermittence 127, 132introduced 35–6

plenitudinous ontology 9, 12, 24–6, 62,74 n.59

Pooley, O. 221 nn.3–4, 228 n.potentiality 180Prasada, S. 40 n.10predication, see also perspectivalismformal and material relativistic 238–9formal determinate/indeterminate 204–6formal identity 56–8, 60formal modal 143–4formal parthood 52–6formal temporal 45–58, 63material determinate/indeterminate 207material identity 59–60material modal 142–3, 144material temporal 46, 59–60mode of predication introduced 44–5

principle of charity 72–3, 89–90, 99, 126, 130principle of unity 6–7, 9, 233problem of the many 193–4, 196–7Pryor, J. 68 n.44psychology of object representation/

perception 38–40, 100–1, 117–18

quasi-hylomorphism/q-hylomorphismapplied to Chisholm’s Paradox 163–4applied to grounding problem 152–4applied to modal paradox of

coincidence 146–9applied to non-modal paradoxes of

coincidence 88–99applied to paradoxes of fission 115–27applied to paradoxes of intermittent

existence 131–3applied to problem of cheap

indeterminism 184–9applied to problem of indeterminate

coincidence 212–15applied to problem of relativistic

change 234–5, 240–6applied to problem of the many 210–12applied to sufficiency problem 159–62extension, mereological

indeterminacy 201–4extension, modality 138–41extension, relativity 235–8extension, temporal indeterminacy 215–16introduced 22–31

Quine, W. V. O. 1 n., 197

Rea, M. 80 n.15relativity

problem of relativistic change 219–46special 219–23, 225–7unified view of relativistic shapes 220–3,231–3, 243, 245

Robertson, T. 156 n.Robinson, D. 106 n.3, 110 n.12Rosen, G. 196 n.14Rovane, C. 111 n.14, 112 n.17

Sadock, J. M. 102 n.51Safar, P. 129 n.34Sainsbury, M. 191 n.2Salmon, N. 154 n.28, 156 n., 198–9, 214Schaffer, J. 17 n., 85 n.26, 212 n.Schnieder, B. 17 n.Shoemaker, S. 105 n.1, 111 n.16Sider, T. 2 n.3, 25 n.41, 27 n.45, 64 n., 66 n.35,

70 n.48, nn.50–1, 71 n., 72, 74 n., 78 n.10,82 n.16, 83 n.20, 84 n., 86 n.27, 87 n.31,112 n.17, 113 n.22, 114 nn.24–5, 115,146 n.15, 149 n., 152 n.24, 180 n.12,221 n.4

Simons, D. 38 n.5Simons, P. 1 n., 34, 52 n., 130 n.39singular reference 44 n.14, 58, 192Skow, B. 157 n.32, 196 n.14Smith, N. J. J. 196 n.14social entity 34sortal concept 15–16; see also perspective,

perspectivalismsortal invariance 15–16, 128, 181, 223–5sortal relativity 57–8, 81–2sortal-sensitive vs. sortal-abstract,

see perspectiveSosa, E. 74 n., 152 n.24spacetime, Minkowski, see relativity, specialSpelke, E. 33 n., 38–9, 100, 102, 117Strawson, P. 15 n.24structure, see mereological structuresubstantivity, metaphysical vs. conceptual 27sufficiency problem 154–62supervaluationism

and multiple actualities 196–7, 205and q-hylomorphism 205–6, 210–11standard 108–9, 125, 191–5, 202 n.23, 205–6

supervenience 150Swinburne, R. 111 n.16Swoyer, C. 20 n.34Szabó Gendler, T. 36 n.3

temporal part, see four-dimensionalismTerrell, J. 227 n.11Thomasson, A. 44 n., 72 n.55, 86–8, 233 n.Thomson, J. J. 5 n.6, 83 n.23, 86 n.27, 111 n.15three-dimensionalism

and Aristotelian hylomorphism 7

258 index

and classical mereology 2, 3–5and coincidence 82 n.18, 83–6, 92, 98–9and determinism 170, 177–9, 180,184–5, 187

and fission 118and intermittent existence 132and perspectivalism 61, 63–4, 66and q-hylomorphism 14, 21, 24 n.38,26, 31

and relativity 223, 233

Unger, P. 80 n.14, 193 n.7, n.9, 195 n.12Uzquiano, G. 80 n.14

vagueness, see indeterminacyvague object, see indeterminacy,

metaphysical/de reVan Cleve, J. 4 n.Van de Walle, G. 33 n., 38 n.5van Fraassen, B. 192 n.4van Inwagen, P. 80 n.14, 199 n.21

Varzi, A. 89 n.Velleman, J. D. 112 n.19

Wasserman, R. 78 n.10, 85 n.25Weatherson, B. 193 n.6, 194 n.11, 197–8Wein, D. 38 n.5Wiggins, D. 15 n.25, 77 n.4, 79 n.11, 83 n.21,

89 n., 105 n.2, 110 n.13, 151 n.22Williams, B. A. O. 105 n.2, 111 n.15Williams, J. R. G. 196 nn.14–16, 198 n.17Williamson, T. 69 n.46, 108 n.10, 146 n.14,

154 n.28, 191 nn.2–3, 196 n.14Wilson, M. 168

Xu, F. 38 n.5, 40 n.9, 42 n.12, 100 n.45, 102 n.50

Yablo, S. 69 n.46

Zimmerman, D. W. 20 n.34, 68 n.42, 86 n.28,149 n., 150 n.19

Zwicky, A. M. 102 n.51

index 259

the double lives of objects: an essay in the metaphysics of the ordinary world

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