This paper appeared in The Monist 88 (2005), pp. 466-92.

Qualitative Unity and the Bundle Theory
David Robb
Davidson College

Abstract: This paper is an articulation and defense of a trope-bundle theory of material objects. After some background remarks about objects and tropes, I start the main defense in Section III by answering a charge frequently made against the bundle theory, namely that it commits a conceptual error by saying that properties are parts of objects. I argue that there's a general and intuitive sense of "part" in which properties are in fact parts of objects. This leads to the question of qualitative unity: in virtue of what are certain properties unified as parts of an object? In Section IV I defend an account of unity for complex material objects. It turns on the thesis that the properties of such objects are structural properties. After addressing some objections, I turn in Section V to the question of unity for simple material objects. Here a different and more radical account is needed for simples, since they do not have structural properties, are not subsumed by the account of Section IV. I defend the view that a simple object just is a simple property, so that identity delivers the desired unity.

I. Introduction

It's hard to deny that there are natures or ways of being. They are most evident in our own conscious experiences, but the "what it's like" of consciousness is really just a special case of a way of being: it is a way an experience is. But the non-conscious parts of our world are various ways too. And how could it be otherwise? How could there be being without a way of being? To be is to be some way or other. I'll call these ways properties.

If there are properties, must there be, in addition to them, non-property bearers of those properties? A traditional line of thinking insists that yes, properties require something else, something that is not itself a property, but nevertheless must exist if properties do. Call this thing a substratum.[1] Here is Locke, expressing this tradition in a well-known passage from the Essay (II.xxiii.1):

The Mind being, as I have declared, furnished with a great number of the simple Ideas, conveyed in by the Senses, as they are found in exteriour things, or by Reflection on its own Operations, takes notice also, that a certain number of these simple Ideas go constantly together; which being presumed to belong to one thing, and Words being suited to common apprehensions, and made use of for quick dispatch, are called so united in one subject, by one name; which by inadvertency we are apt afterward to talk of and consider as one simple Idea, which indeed is a complication of many Ideas together; Because, as I have said, not imagining how these simple Ideas can subsist by themselves, we accustom our selves, to suppose some Substratum, wherein they do subsist, and from which they do result, which therefore we call Substance.

Here and elsewhere, Locke gives substrata two roles to fill: First, properties (what Locke here calls "ideas") do not float in isolation from one another. Rather, they are clustered into what we think of as objects. So a unifier of properties is required, something to hold properties together in these clusters. Second, properties cannot exist on their own: there must be something in which they "subsist". So a supporter of properties is required, something that keeps them in existence. The roles of unifier and supporter are distinct,[2] but Locke says we postulate a single thing to fill both: substratum.

As an account of where our idea of substratum comes from, Locke's line of reasoning may be right. But as an argument for the existence of substrata, it is unconvincing. Even if properties must be unified, why can't their unity be found in their relations to one another? And even if the properties we observe--those that Locke appeals to--are dependent entities requiring support, why should this be true of all properties? And when support is needed, why must such support be found outside the category of property? Why, that is, can't dependent properties be supported by other properties? Enter the bundle theory: the world does not contain substrata in addition to properties. To be sure, there are what we may neutrally call substances or objects--chairs, trees, human beings, electrons, stars--but these objects are not, nor do they contain as constituents, substrata: they are merely bundles of properties. Not only must a being be some way or other, it is exhausted by ways of being.

Such is the bundle theory in its starkest form, and its attractions are well known. It removes the need for substrata, which some philosophers have found to be problematic if not incoherent. And it is typically part of an elegant one-category ontology, one that includes only ways of being as basic constituents. However, I will not spend much time in this paper praising the virtues of the bundle theory, at least not in the sense of giving positive arguments for it over its rivals. Rather, this paper will be primarily defensive. My aim is to articulate the central features of the bundle theory and defend it against some common objections. As one can infer from Locke's remarks, two of the most pressing problems for any bundle theory are in accounting for the (alleged) dependence of and unity among properties. I've already indicated in brief how I would respond to these challenges, but more is needed than the rhetorical questions above.

The paper is structured as follows: After some preliminaries in Section II, I'll start the defense in Section III by answering a charge frequently made against the bundle theory, namely that it commits an egregious conceptual error in saying that properties are parts of objects. I'll argue that there's a general and intuitive sense of 'part' in which properties are in fact parts of objects. This will lead to the question of unity raised above: in virtue of what are certain properties unified as parts of an object? In Section IV, I'll defend a "principle of unity" for ordinary, complex objects. The principle will explain, as a corollary, the sense in which the properties of ordinary objects are dependent entities, though in a way that does not require that they depend on a substratum. After defending this principle from some objections, I will turn in Section V to the question of unity for simple objects; here a different and more radical account will be needed, for these sorts of objects are not subsumed by the principle in Section IV.

II. Objects and Properties

To bring into focus my favored version of the bundle theory, I'll start with some preliminary points about objects and properties.

1. Objects

The bundle theory offers an account of the ontological structure of objects. But it does not offer an analysis of the concept object. We have a rough understanding of what an object is: it is a unified, persisting, independent being. But I doubt one can turn these criteria into informative, conceptually necessary and sufficient conditions for something's being a object.[3] And in any case, whether or not such an analysis is possible, it is not the aim of the bundle theory to provide it. Whether something counts as an object may for the purposes of this paper be taken as a primitive fact about it. An account of its ontological structure, on the other hand, goes deeper.

The bundle theory's claim that an object is some bundled properties may be refined in a number of ways, including the following: Identity: an object is numerically identical with some bundled properties. Here identity is a one-many relation. Supervenience: an object supervenes on some bundled properties, where this is understood to be some relation that, while entailing a strong dependence of object on properties, is weaker than identity. Elimination: strictly speaking, there are no objects--suppose the (loose) requirements listed earlier are never appropriately satisfied--but the closest things in the world answering to our concept of object are property bundles. In spite of their differences, these refinements are all instances of the bundle theory, for on all of them bundled properties exhaust the being of objects. It is the bundle theory in this general sense, not any of these refinements, that I will defend in this paper.[4]

Finally, I will in this paper restrict the bundle theory to material objects; I'll have nothing to say about immaterial objects such as souls or abstract objects such as numbers.

2. Properties

I've already identified properties as ways of being. This much, I believe, should be uncontroversial. But I will assume a further and more controversial thesis about properties, namely that they are tropes, particularized ways incapable of being instantiated by (wholly) distinct objects at the same time. Tropes are not, and cannot be, a "one across many".[5] So the yellowness of a tennis ball is not the same as the yellowness of another tennis ball, even though these two properties resemble each other, perhaps exactly. On the bundle theory defended here, then, an object is some bundled tropes.

I should also note in connection with this that I'll follow Campbell (1990) and others in taking tropes to be simple in the following sense: tropes do not have as constituents, and are not reducible to, items in other ontological categories. So, for example, a trope is not an object's having a universal. Such an account of tropes would immediately lead the bundle theorist into trouble: Imagine saying that an object is some bundled tropes, each of which is an object's having a universal. If the latter object is the former, then the account is circular; if not, a vicious regress threatens. However, while tropes are simple in the above sense, this does not mean that they must lack parts altogether, for a trope can have other tropes as parts. The yellowness of a tennis ball has as parts the yellowness of the ball's left half and the yellowness of its right half. Far from making trouble for the bundle theory, this sort of complexity, as I hope to show, points the way toward an account of property-unity.

III. Qualitative Parts

1. Can Properties Be Parts?

If the bundle theory is true, then properties are parts of objects. Some philosophers will object that this commits a category mistake. Hoffman and Rosenkrantz, for example, criticize "collectionism" (their name for the bundle theory) because it fails to respect

the intuitive datum that no feature of a substance is a part of that substance. For example, intuitively, the right and left halves of a material object, o, are parts of o, but the shape and the size of o are not parts of o.... [Collectionism's] implication that the shape of o is a part of o also conflicts with another datum for a theory of substance: that the parts of a material substance are either material substances or portions of matter. That collectionism has implications which conflict with these data is an indication of a category mistake in the identification of substances with collections.[6]

Earlier I noted that a bundle theorist needn't identify an object with a bundle of properties, but Hoffman and Rosenkrantz's remarks about parthood also threaten supervenience and (perhaps) eliminativist versions of the bundle theory.

Hoffman and Rosenkrantz say it is an "intuitive datum" that properties are not parts of objects. Below I will propose an intuitive sense of 'part' according to which they are. But for now it's worth exploring why it does seem on the face of it that properties cannot be parts of objects. I suggest this appears to be so because of the following:

(1) Parts are independent, both of each other and of the whole of which they are parts. But properties are dependent, both on each other and on the objects of which they are properties. A chair's leg can exist separately from the chair and from other parts of the chair. But one cannot separate (without destroying it) the color of a table from the table or from other properties (e.g., the extension) of the table.

(2) An object typically comes into being by the arrangement of pre-existing (soon-to-be) parts. A house, for example, comes into being by taking bricks, planks, shingles, etc. and arranging them according to a blueprint. But an object never comes into existence by bringing together pre-existing properties (a size, a shape, and so on) and arranging them, for such properties do not exist before the object comes into being.

(3) Parts are additive: they permit the arbitrary addition of further parts. For example, there is no barrier to adding a fifth leg to a table, or gluing more fuzz on a tennis ball. In general, if some parts compose a whole in virtue of standing in some relation R to one another, then it should be at least logically possible to bring something new into R with these parts so that a larger whole is composed. But properties are not additive in this sense: It is generally speaking not possible to add a new property to an object without destroying some others. Our yellow tennis ball cannot take on redness or squareness, at least not while retaining its current color and shape.

I do not wholly endorse these claims; the extent to which I do will become clear in the last Section. But I do think (1)-(3) push us toward an important thesis about properties. But this thesis is not that properties cannot be parts. Rather, (1)-(3) seem to show that properties typically are not the sort of parts that are independent, arranged, and additive. These three features hold, not of parts generally, but only of substantial parts, parts that are themselves objects. The proper conclusion to draw from (1)-(3) is that properties typically are not substantial parts of objects.

However, this reply will seem ad hoc absent some independent reasons for thinking that properties can be parts. What the bundle theory calls for is some independently plausible, general conception of parthood according to which an object can have properties as parts. On the most general conception of parthood, I submit, the parts of something exhaust its being in the sense that it is nothing more than, nothing over and above, its parts related in some way or other.[7] More formally:

(P) B is a part of A iff there are Cs such that (i) A is the Cs related in certain ways, and (ii) B is one of the Cs.

Those who object to the grammatically questionable 'A is the Cs'[8] can substitute for it 'A is nothing over and above the Cs' or 'the Cs exhaust the being of A', where the original 'is' or these two substitutes may be taken in any of the senses listed earlier: identity, supervenience, or elimination. (Elimination is still an option here, for B may be a part of A only in the sense that B is a part of the closest thing answering to our concept of A.)

(P) is intended to be flexible in a number of respects. For one thing, 'related in certain ways' can be read as one likes, depending on one's preferred restrictions on composition. I'll return to this issue shortly. For immediate purposes, however, the most important respect in which (P) is flexible is that does not put restrictions on what can count as a part. It is compatible with (P) that a table, for example, has objects as parts: a table is some pieces of wood related in certain ways, and is some molecules..., and is some atoms..., etc. These objects are substantial parts of the table at different mereological levels. Yet (P) also allows something to have parts belonging to different ontological categories. For example, (P) allows for temporal parts: a performance is various shorter events related, say, spatiotemporally and causally. If an object has temporal parts, then the object is some time-slices related in certain ways as well. And most importantly for the bundle theorist, (P) allows for properties to be parts. If the bundle theory is true, the table is some properties related in certain ways. Note, too, that even if the table includes a substratum, the table still has properties as parts: the table is the substratum and some properties related in certain ways.[9]

Now there is to be sure a reductionist or "bottom-up" character to (P) that some will find objectionable, especially if the 'is' in clause (i) is read as identity. Anything that is just its parts (of any sort) related in certain ways, the objection goes, lacks the sort of autonomy and unity required of entities in their own right, i.e., of substances. This is not the place to confront this larger issue in any detail; I will mention just two points in reply: First, there is nothing in (P) requiring that the concept of an object's parts in a given case be conceptually prior to the concept of that object. The ontological priority of parts over wholes that (P) entails need not be reflected by any conceptual priority of part-concepts over whole-concepts. So, for example, even if an animal is just some organs arranged in a certain way, this is compatible with our being unable to conceptualize these as organs independently of conceptualizing them as parts of a larger animal. Second, and more importantly, the main point of (P) is just to articulate an intuitive notion of parthood according to which properties can be parts. If it turns out that (P) requires modification to handle "top-down" cases in which wholes have an ontological priority over their parts, I see no reason to think that the modified version would prohibit properties from being parts.

It will be useful before moving on to introduce some terms for the two kinds of part most relevant to this paper. Parts that are themselves objects I have already called, following a common usage, substantial parts. If an object has substantial parts, I will say it is substantially complex. Parts that are properties go under various names. Williams (1953) speaks of properties as "fine parts or abstract components" of objects; Paul (2002) calls them "logical parts". I will call them, somewhat tendentiously, qualitative parts. If an object has qualitative parts, I will say it is qualitatively complex.

2. Principles of Unity

On the bundle theory, an object is some properties related in certain ways: these are its qualitative parts. Parts of any kind, however, require a principle of unity.[10] A principle of unity is a relation among an object's parts, a relation in virtue of which they are parts of the object. As I noted earlier, I'm taking object here to be primitive, so a principle of unity will not deliver an analysis of objecthood. It will instead deliver something less ambitious: an account of that in virtue of which some Cs (objects or properties) are a given object's (substantial or qualitative) parts.

When I later propose a principle of qualitative unity, then, I will not attempt to account for the conditions under which some properties bundle into an object. The approach, that is, will not be of the form, 'Take some properties. Under what conditions are they qualitative parts of an object?'[11] Rather, it will be of the form, 'Take an object. What relation unifies certain properties so that the object has these properties as qualitative parts?' In a certain respect, then, the order of inquiry here will not mirror what is, so to speak, the metaphysical order. Metaphysically, properties are 'first'; that is, they are the primary beings; the unifying relation among them is second, and objects are third. But the order of inquiry in what follows starts with objects, taking them for granted.

Although my concern here is with the principle of qualitative unity, it will be useful to start with the principle of substantial unity. Recent metaphysics has revealed several candidate principles of substantial unity. Take a substantially complex object. How are its substantial parts--call them the Cs--related such that they are its substantial parts? Here are some possible answers[12] (in some cases, the ancestral of the given relation may be more appropriate):

The Cs co-exist.

The Cs are in contact.

The Cs are bonded.

The Cs constitute a life.

The Cs are metaphysically dependent on one another.

These options are not exhaustive. For example, one might also wish to include substantial unity as a primitive relation.

What are the candidate principles of qualitative unity? In virtue of what are certain properties qualitative parts of a given object? We find here, if not the same range of options, at least a similar range. For example, while 'the Cs are in contact' may not comfortably apply to properties, 'the Cs spatially coincide' or 'the Cs overlap' would. And for 'the Cs are bonded', one may wish to substitute 'the Cs are nomologically dependent on one another'. But the list one would initially draw up would look quite similar to the earlier list. It would even include an option for primitive unity.

Now the first point I want to make about these candidate principles of unity--one set for substantial parts, another for qualitative parts--is that we should expect there to be some systematic relation between them such that our choice of one constrains our choice of the other. First, (P) entails that substantial parts are intimately connected in some important way to qualitative parts. After all, if an object is its substantial parts appropriately related and its qualitative parts appropriately related, it would be odd in the extreme if these parts could "float free" from one another. And while I can't see that this shows that their respective principles of unity are systematically connected, it makes it reasonable to think they are. Second, certain choices of principles appear to be in tension with one another. Suppose one were to pair a modally weak principle of substantial unity--e.g., spatial contact--with a modally strong principle of qualitative unity--e.g., metaphysical dependence. The source of the latter's modal strength would seem to be a mystery: why would there be such a strong principle unifying an object's properties when its substantial parts are unified by mere contact?

In any case, my concern here in defending the bundle theory is only with the principle of qualitative unity. I bring up its relation to the principle of substantial unity only to make this point: a plausible principle of qualitative unity should account for its systematic relation to the principle of substantial unity. Any account of qualitative unity that leaves this relation unexplained to that extent falls short.

3. Desiderata for any Principle of Qualitative Unity

I will call this desired feature

Coordination: A principle of qualitative unity should explain how qualitative and substantial unity are systematically related to one another.

Coordination does not require that a principle of qualitative unity deliver a principle of substantial unity. Indeed, in proposing the former I will remain neutral on the latter. The idea, to look ahead a bit, will be to take the principle of substantial unity for granted and then honor Coordination by defining the principle of qualitative unity in terms of it.

To Coordination I add two more desiderata. Earlier I listed three reasons some may think that properties cannot be parts. I concluded that (1)-(3) at most establish that properties are typically not substantial parts. Now as I indicated there, I do not wholly endorse (1)-(3): they will need to be qualified later. But any account of the bundle theory should explain why (1)-(3) (or suitably qualified substitutions) are true. Because (1)-(3) differentiate qualitative and substantial parts, I call this principle

Differentiation: A principle of qualitative unity should explain why (and when) qualitative parts are not independent, assembled, and additive.

Finally, any philosophical account must, if pressed, eventually postulate brute properties or relations. But this is to be avoided for as long as possible. And furthermore, when a brute property or relation is required, strive to make it a familiar one, not a special one postulated ad hoc merely to do some metaphysical job. I'll call this final desideratum

No Mysteries: A principle of qualitative unity should avoid postulating ad hoc, primitive relations.

Some bundle theorists say that the unity among properties is primitive.[13] Others spell it out as a brute modal relation.[14] I do not, of course, think that No Mysteries is a principle so powerful that it can be used to dismiss these bundle theorists, whose accounts of unity deserve close study. Rather, I see No Mysteries as a methodological constraint as well as a potential tie-breaker: an account that avoids mystery is for that reason preferable to rivals, ceteris paribus.[15]

IV. Qualitative Unity for Substantial Complexes

I begin with the principle of qualitative unity for ordinary, substantially complex objects, such as chairs, human bodies, and planets. Campbell, himself a bundle theorist, counsels against starting with such objects.[16] Doing so, he says, invites one to confuse (using my terms) the principle of qualitative unity with that of substantial unity. To avoid this, Campbell advises the bundle theorist to start with a (substantially) simple object, such as a corpuscle in classical atomism. In reply, I agree with Campbell that the two sorts of principle are distinct and should not be conflated. But Coordination counsels us to investigate them jointly. Starting with substantially complex objects allows us to do this. I'll use a tennis ball--call it 'Alpha'--as my main example.

1. Structural Properties

If we consider a substantially complex object such as Alpha, a principle of unity presents itself, for all of the properties of such an object appear to be structural properties. Armstrong introduces the notion of a structural property as a kind of complex property, one composed of the properties of and, in most cases, relations among that object's parts.[17] Consider the property of being three feet long. If an object (a stick, say) has this property, it has three substantial parts, each of which is one foot long. There's nothing more to the object's being three feet long than the lengths of, and relations among, these three parts. A more complex structural property is a particular molecule's being methane.[18] For a molecule to have this property is just for it to have five substantial parts--a carbon atom and four hydrogen atoms--bonded to one another.

Many of Alpha's properties are clearly structural in this sense; indeed, perhaps all of them are structural.[19] Alpha's color, for example, is composed of the colors of its left and right halves, plus some relations between the halves (relations that must include, at a minimum, the principle of substantial unity). As I'll say for short, Alpha's color is structured on its left and right halves. In general, a property F is structured on some objects just in case F is a structural property composed of the properties of and relations among those objects. Note that Alpha's color is also structured on (some of) the smaller particles composing Alpha. In general, there's nothing wrong with one and the same property being structured on objects at different mereological levels.

Because structural properties are composed of properties of and relations among objects at a lower mereological level, structural properties are dependent properties. And this suggests that unity among structural properties is dependent as well on these lower-level objects. Taking a cue from this suggestion, and with Coordination in mind, I propose the following principle of qualitative unity for substantially complex objects (at a time; I will not address diachronic unity here):

(CU) For any substantially complex object O and properties F and G, F and G are qualitative parts of O iff F and G are both structured on the (exhaustive) substantial parts of O at some mereological level.

(To say that substantial parts at a mereological level are "exhaustive" means that they are all of O's parts at that level.[20] In the language of (P), O just is those parts related in certain ways.)

(CU) gives the right results for Alpha's yellowness, roundness, fuzziness, mass, and so on, for all of these properties are structured on the left and right halves of the ball (in addition to other substantial parts of the ball at lower mereological levels). (CU) does not, by the way, require that unified properties be structured on the same objects at every mereological level. Consider a wooden cube painted green. The cube's greenness and its being made of wood are both qualitative parts of the cube. Yet these properties are not structured on the same objects at a low mereological level, for there are particles in the interior of the cube involved in the cube's being made of wood that aren't involved in the cube's color, which is restricted to the surface. Nevertheless, these properties are structured on the same objects at higher mereological levels--for example, they are both structured on the left and right halves of the cube--so (CU) correctly counts them as unified.

2. The Three Desiderata

A virtue of (CU) is that it meets the three desiderata listed earlier. (CU) most clearly satisfies Coordination, for it explicitly defines qualitative unity in terms of substantial unity.

What about Differentiation? Earlier I said that qualitative parts seem not to be independent, arranged, or additive. These are some of the ways they differ from substantial parts. (CU) delivers an explanation of why this is so.

First, qualitative parts of substantially complex objects never occur in isolation from objects precisely because they are structural properties, and as such cannot exist independently of the substantial parts of an object. And given the presence of such substantial parts, it's also clear why more than one property--more than one qualitative part--must be present as well. Any property structured on some substantial parts will necessarily occur with other structural properties.

Second, qualitative parts aren't assembled because their presence depends on the (logically) prior assembly of substantial parts. One cannot bring a tennis ball into being by first taking a color, shape, and so on and arranging them in the right way, for these properties are themselves composed of, and so dependent on, the properties of and relations among certain objects, namely the substantial parts of the ball.

Third, while (CU) does not deliver a full explanation of why qualitative parts fail to be additive, it does point in the direction of one. Consider how such an explanation would look for Alpha's color: why can't Alpha take on a new color, say red, while keeping its current color of yellow? The first answer (CU) might deliver is this: Alpha's color is composed, in part, of the colors of Alpha's left and right halves. Since these halves can't become red without losing their yellowness, Alpha can't either. But this isn't too helpful, since it just invites our original question again, now applied to Alpha's halves. If (CU) is to explain in a satisfying way why Alpha cannot take on red while retaining its current color, one must look at a low mereological level, one in which the properties of the relevant substantial parts are not colored. And here is where (CU) points to an explanation: I submit that if we knew what sorts of properties were involved with Alpha's color at a low mereological level, we would just see that Alpha's substantial parts cannot retain these micro-properties while also taking on those required for being red.[21] The point is perhaps clearest if the example is switched to Alpha's shape: given how the substantial parts of Alpha must be related to one another for Alpha to be round, we can see how they could not, while keeping these relations to one another, also take on the relations required for the structural property of squareness.

Finally, what about No Mysteries? To be sure, the concept of object is taken as primitive here, but this does not violate No Mysteries, for the concept is introduced merely to pick out our subject-matter, not as an explanatory factor; and in any case, the notion of an object is certainly not unfamiliar. The notion of a substantial part appealed to may seem to violate No Mysteries. I do not, however, take substantial parthood and with it the principle of substantial unity to be primitive; rather, (CU) is neutral with respect to the nature of substantial parthood. (CU) invites us to fill in this nature, not to stop here and rest content with mystery.

3. Has There Been Progress?

In spite of meeting the desiderata, the principle proposed here may be accused of not making progress. Perhaps the most glaring problem of this sort for (CU) is that in appealing to the substantial parts of a complex object, the principle appeals to entities that must themselves be bundled properties. So they themselves must be subject to some principle of qualitative unity. This is an important worry, and I try to answer it in the final section. But for the moment I set it one side: the substantial parts appealed to in (CU) may for the time being be thought of as ontological "black boxes," objects that play an explanatory role but whose internal structure is left unspecified.

Another apparent lack of progress, however, can be confronted now. This problem finds inspiration in Bradley's argument against relations, here applied to any proposed principle of qualitative unity.[22] Any properties F and G unified into an object, the objection goes, must be unified by some relation R1. But R1 cannot do its unifying work unless it itself is "bound" to F and G. What's required, then, is some further relation, R2, to bind F, G, and R1. The result is a vicious regress.

The natural reply here is to insist that R1 is an internal relation between F and G, and so is "no addition of being" over them.[23] In that case, the question of what unifies F, G, and R1 does not arise--or at least, it's not distinct from the original question of what unifies F and G, the answer to which is: F and G themselves. This in fact is my position, though I consider it a virtue of (CU) that it tells us, in the spirit of No Mysteries, what this internal relation is: it is the relation of being structured on the same substantial parts. This relation will count as internal if it is fixed by the natures of F and G. Assuming as I do that F and G are essentially structured on the objects they are actually structured on, then if F and G exist at all, they must be unified. The relation of unification in this way ends up being nothing over and above the related properties themselves.

There is nevertheless a third lingering worry about progress. While the unification relation among properties may be internal, and for that reason not lead to a regress, it nevertheless does have as a component another relation that may seem just as problematic as the one we started with, namely, the principle of substantial unity, on which (CU) explicitly relies. The problem of identifying the principle of qualitative unity, the objection goes, has been reduced one just as difficult, that of finding the principle of substantial unity.

However, I think progress has been made by moving from the principle of qualitative unity to the principle of substantial unity, for three reasons: First, the very fact that (CU) systematically relates the two principles of unity is reason to think that it may be useful in pointing the way to a principle of substantial unity. Second, the principle of substantial unity is a different sort of relation than the principle of qualitative unity, one that holds among objects, not properties. Granted, since substantial parts will themselves be bundled properties, the principle of substantial unity will in that sense be a relation among properties. But we're no longer looking for a relation among Alpha's properties. That is, we're now no longer looking for a relation between, say, Alpha's yellowness and its roundness, but rather a relation among objects at a lower, more fundamental mereological level on which these properties are structured. Moving toward a new relation at a more fundamental level is progress. Third, and most importantly, by shifting the problem to that of finding the principle of substantial unity, we've moved to an issue that's not particular to the bundle theory. Everyone who believes in complex material objects such as Alpha will presumably have to worry about the unifying relation among Alpha's substantial parts. Thus the bundle theorist has made at least dialectical progress by reducing the problem of qualitative unity to a problem that everyone but the compositional nihilist has.

4. Non-Structural Properties?

Another line of objection to (CU) says that not all of the properties of a substantially complex object, not all of its qualitative parts, are structural. Since (CU) explicitly applies only to structural properties, it will not subsume these non-structural properties. I'll consider two such (alleged) non-structural properties here: higher-level properties and modal properties.

Some philosophers would say that while a complex object has structural properties, it also has "higher-level" properties that at best merely supervene on its structural properties. Consider color again, structured on the particles composing an object's surface. Since this color-structural property is composed of the many properties of and relations among these particles, it's plausible to think it could not survive the destruction or change of even one of these particles. Yet, the argument goes, the object's color surely could survive this: if Alpha's surface were to lose a particle, Alpha would still have the same color, that very same trope. The conclusion is that Alpha's color must not be a structural property after all: it only supervenes on some structural property of Alpha. But if Alpha's color is not a structural property, it is not subsumed by (CU), and we are left without an account of how the color is unified with Alpha's other properties.

This reasoning mistakes resemblance among properties for numerical identity. As Alpha's surface gains and loses particles, it has a succession of numerically distinct but closely resembling color-properties, each of which is structured on, at a low mereological level, the particles composing Alpha's surface at that time. It is only speaking loosely that we say that Alpha has literally the same color-property throughout these changes. Every color is a structural property--it's just that many of these structural properties resemble each other closely enough for us to call them "the same". But sameness here should be thought of as no more than resemblance. This is a traditional position for a trope-theorist to take regarding talk of "same property" among distinct objects; here the point is just applied to one object at different times (or in different worlds).

There is, by the way, a fallback position for the bundle theorist to move to regarding higher-level properties. If it could be shown that Alpha's color and other such properties merely supervene on structural properties, the bundle theorist could exploit this dependence relation, in an ad hoc manner, to account for the unity of Alpha's higher-level properties with each other and with Alpha's structural properties. Call the structural properties on which Alpha's higher-level properties supervene the latter's 'grounding properties'. The fallback principle of qualitative unity then reads as follows:

(CU*) For any substantially complex object O and properties F and G, F and G are qualitative parts of O iff F and G or their respective grounding properties are structured on the (exhaustive) substantial parts of O at some mereological level.

So long as the grounding relation is such that it's impossible for the properties of one object to ground the properties of another, (CU*) will suffice to accommodate higher-level properties.[24] In any case, postulating the brute modal relation of grounded is here in tension with No Mysteries, so in this respect it is better to stay with the earlier response, which keeps (CU).

Another sort of dependent property, however, is not so easily handled. Alpha seems to have certain modal properties, such as being essentially extended and accidentally yellow. Since such properties are, plausibly, grounded in Alpha's non-modal, structural properties, one may be tempted to move to (CU*) right away. But even if one moves to this fallback principle, a problem arises in the special case of coinciding objects. Here it's useful to switch examples to the case of the statue and the lump clay that composes it. The statue, it is said, could not survive being squashed, but the lump could. And this is because the statue is essentially statue-shaped, while the lump is so only accidentally. This is a reason for thinking that the statue and the lump are numerically distinct. If this is right, then the properties of being essentially statue-shaped and being accidentally statue-shaped are not unified--they are not qualitative parts of the same object--yet their non-modal grounding properties are unified. So, the objection goes, even the fallback (CU*) gives the wrong results in such cases

Any attempt at answering this objection will inherit all of the difficulties of the problem of material constitution, a problem for which there is no obvious solution.[25] Here I'll settle for sketching one line of response, one that denies modal "properties" are genuine properties at all. As I mentioned in the introduction, I do not think that every predication corresponds to a way of being. And notably, modal properties[26] such a being essentially extended fail all of the usual tests for being a way of being, a genuine property.

(T1) Modal properties do not bestow causal powers. A bowling ball that rolls over my foot causes pain in virtue of being massive, but what work does its being essentially massive do? Any powers one might think are bestowed by a modal property are already bestowed by more familiar, non-modal properties.[27]

(T2) Modal properties are not needed as the truthmakers for modal predications. As I mentioned earlier, the modal properties of an object are grounded in its non-modal properties. The non-modal properties of Alpha, for example, suffice for the truth of "Alpha is accidentally yellow." Once God has created Alpha with all of its non-modal properties, He need not create an additional property, being accidentally yellow, to make this statement true. The modal predication already holds in virtue of the relevant non-modal properties of the object.

(T3) Modal properties are not respects in which objects can resemble one another. Fix on the distinction--one than any realist about properties should grant--between genuine resemblance and mere "Cambridge" resemblance, i.e., merely falling under the same predicate. If Alpha and Beta (tennis balls) are both spherical, this seems to be a sense in which they genuinely resemble, but if they are both essentially spherical, is this also a case of genuine resemblance? This does not seem to be a further respect in which they resemble one another. (Here is another way to make the same point: Is essentially spherical a natural kind? Is it, for example, a kind which one would ever expect to find in scientific theories? The answers to these questions seems to be clearly No.)[28]

(T4) We are not acquainted with modal properties in conscious experience. Sometimes negative outcomes to tests (T1)-(T3) can be trumped by what is presented to us in experience. But experience does not reveal modal properties to us: they are, if anything, highly theoretical properties.

Each of these test deserves further discussion, but collectively, they make a strong prima facie case for denying that modal properties are ways of being. And if there are no modal properties in this sense, then no question arises as to how they are unified with the other properties of an object such as Alpha. As for the statue and the lump of clay that composes it, what emerges is a familiar, if minority, position: There is just one object there, one bundle of properties, but different ways of describing or conceiving of it. To think otherwise--to think that there are two objects with their own distinctive modal properties--is to fall into the fallacy of projecting the structure of thought and language onto the world.[29]

V. Unity for Simples

1. Expunging Objects?

It's now time to confront a problem I mentioned earlier but did not answer. (CU) explains qualitative unity by appealing to the notion of a substantial part. But if the bundle theory aspires to completeness, it must also say that these objects at lower mereological levels are themselves bundles of properties, and one now wants to know the principle of unity for them.

The easiest move to make here is to apply the same principle of unity to these substantial parts. Alpha's properties are unified by being structured on, say, the left and right halves of Alpha. Each of these halves is some bundled properties, and the properties of each half are unified in virtue of being structured on the substantial parts of that half, and so on. Might this continued ad infinitum? Armstrong discusses this possibility and thinks it creates a problem for the bundle theorist:

It is clear that many properties of particulars involve essential reference to proper parts of these particulars. If a thing is to be a chess-board, for instance, it must have spatial parts of a certain nature related in a certain way. These parts, however, are particulars. It appears, then, that many of the properties which figure in the bundle involve the notion of further particulars. Yet the notion of a particular is the one to be analysed.

Presumably the Bundle theorist will reply that these further particulars are themselves bundles of properties. But these new bundles may themselves include properties which involve reference to still further parts, which are again particulars. Now it is at least logically possible that this process should go on ad infinitum. A particular may lack any ultimate parts. But for such particulars, it is suggested, it is impossible to carry out the resolution of particulars into bundles of properties.[30]

Armstrong is not talking directly about qualitative unity here, but it's clear how the objection would apply to the present account. If objects are complex "all the way down"--if every object has substantial parts--then a principle of unity appealing to structural properties will never achieve its ontological account of objects. At every mereological level, unity will require objects at a lower level, and so on.

But if this is a problem for the bundle theorist, it seems to be merely a problem of analysis or description. At every mereological level, one's account of unity will always involve, via (CU), the concept of an object, and in this sense objects will never be "expunged." But I'm concerned, not with a reductive analysis or description of objecthood, but with giving an ontological picture in which the world of objects is a world of unified properties. And (CU) combines with a bundle theory to paint such a picture.[31]

In any case, I don't think that the bundle theorist has to confront Armstrong's objection, for I doubt that objects could be complex all the way down. There must be simple objects if there are objects at all. My reason for thinking this is a familiar one: Complex objects depend on their parts for their existence. Ontologically, a complex object "passes the buck," so to speak, to its parts--this is in fact a corollary of (P). Now if objects are complex all the way down, then this ontological buck will continue to be passed. But then it seems evident that there would be no objects at all. If the buck doesn't stop anywhere, if no objects exist in their own rights, then none will exist at all.[32]

2. Substantial and Qualitative Simplicity Coincide

If there are substantially simple objects, however, then a different principle of unity will be needed for them, since simples do not have structural properties.[33] Even if we allow simples to have structural properties in a trivial sense, (CU) cannot serve as an informative principle of qualitative unity for simples. Suppose, that is, we let the properties of a substantial simple S be "structured on" the 'parts' of S, namely on S itself, which is, after all, a (non-proper) part of S. Still, for these properties to be structured on S is for them to be properties of S, and so we are back where we started. (CU) is useless for substantial simples.

At this point the bundle theorist would seem to have no choice but to appeal to a brute, perhaps modal, relation among properties as the principle of qualitative unity for simples. No Mysteries, however, counsels us to keep looking before resorting to such a measure. To this end, I want to explore one fairly radical proposal, and that's that the principle of qualitative unity for a simple object is identity. A simple object, that is, just is a single, simple property.[34] This would provide an elegant account of unity for simple objects. The bundle theorist would not have to worry about how distinct simple properties become unified, for distinct simple properties are never unified into a (simple) object. The proposed principle of qualitative unity for substantial simples then looks like this:

(SU) For any substantially simple object O and properties F and G: F and G are qualitative parts of O iff F and G are each identical with O.

It's a corollary of (SU), of course, that the F and G in question are identical with each other.

Unlike the defense of (CU), the defense of (SU) cannot appeal to ordinary examples, for simples are not ordinary objects. My defense of (SU), rather, will consist in answering some objections.

Objection I: It's just a category mistake to say that a simple object is a property. Objects and properties belong to different ontological categories, so that saying an object is a property is like saying an event is a proposition, or that the number two is alive.

In reply, I should first say that if I'm making a category mistake here, it's one that bundle theorists have been making all along. If there are conjunctive properties, so that any two unified properties F and G result in the property F&G, then even a substantially complex object will be a property.[35] Alpha, for example, will be the conjunctive property this yellowness & this roundness & this fuzziness, etc. But while the bundle theory may have its faults, I don't think that here, at the very outset, it's committing something as egregious as a category mistake. And if it's not a category mistake to say that a macroscopic object is a (conjunctive) property, then I don't see why it's a category mistake to say that a simple object is a property.

That said, perhaps it will require some conceptual revision to think of a simple object as a property. But I think we should expect that our everyday distinctions will not apply straightforwardly to the world of simples, which is far removed from common-sense. Campbell writes of "[t]he way concrete particularity dissolves in the subatomic world",[36] suggesting that we have good empirical reasons (from modern physics) to think that our commonsense conceptions of properties and objects will not straightforwardly apply to the very small

Objection II: A simple object cannot be a single property because such a property would be "free-floating". But properties are dependent entities. It's impossible for a property to exist without being the property of some object.

Well, first of all, the "free-floating" properties I'm postulating are objects (namely, simple objects), and so cannot exist independently of objects. Nevertheless, it's true that the simples (SU) describes are free-floating in the sense that they are not properties of objects, nor are they unified with any other properties. But why can't there be free-floating properties in this sense? Perhaps the intuition against such properties comes from focusing only on examples from the macroscopic world. As I mentioned in the last section, I grant that Alpha's properties (e.g., its color) could not exist without being unified with other properties--indeed, not only do I grant this, (CU) explains it. But it doesn't follow from this that simple properties can't exist in isolation, for (CU) does not subsume such properties.

It will be clear by now, then, that I reject the features used earlier to distinguish qualitative parts from substantial parts; at least, I reject these features when they are said to apply to simples, for a simple qualitative part just is a simple substantial part. Simple properties, unlike complex properties, can be independent, arranged, and additive. It is in this respect that I cannot accept (1)-(3) without qualification.

Objection III: Suppose it turns out that (SU) is right, so that at the most fundamental level, an object is a property. One might just as easily say in that case that at the fundamental level, it turns out that a property is an object. We thus lose the bundle theorist's claim that the world of objects is a world of unified properties. If the object-property distinction dissolves at the lowest level, then so does the bundle theory.

According to the objector, if the bundle theorist asserts that, at most basic level,

(i) An object is a property,

then this is equivalent to asserting that

(ii) A property is an object.

Since (ii) gives doesn't give ontological priority to properties, neither does (i), so we've lost a handle on the sense in which this is a property bundle theory, at least at this fundamental level.

That there's something wrong with this reasoning can be seen by considering two ways one might describe Spinoza's theological views:

(i*) God is the physical universe.

(ii*) The physical universe is God.

There are contexts in which these express (or pragmatically imply: this distinction is not important here) different propositions. One might use (i*) to demote God to the status of the physical universe. God, according to (i*), isn't as interesting as we thought: he's not a mind, he's not omnipotent, etc. By contrast, one might use (ii*) to promote the physical universe to the status of God. The universe is more interesting than we thought: it is a mind, it is omnipotent, etc.

(i) and (ii) work the same way. By asserting (i), I am not asserting (ii). In (i), 'property' takes priority, so that the features traditionally associated with properties--being a nature, a way of being--are ascribed to objects. Simple objects, according to (i), are stranger than we thought: they are themselves ways of being. Contrast this with (ii), which demotes properties in way unacceptable to the bundle theorist. (ii) is something that might be asserted by a "blob" theorist, someone who reduces properties to (or eliminates them in favor of) nature-less objects. The objector is right that (ii) loses the sense in which properties have ontological priority. For this reason I reject (ii) but accept (i).[37]



[1] I use 'substratum' and its plural to refer to those things, not themselves ways of being, that are alleged to underlie and support properties. The term is thus meant to cover traditional Lockean substrata as well as the "refurbished" substrata defended in Martin (1980) and the Aristotelian substances defended in, e.g., Loux (1978). I will here use 'substance' and 'object' as terms neutral between the bundle theory and these rivals.

[2] They are distinguished in Bennett (1987, p. 212) and McCann (2001).

[3] Cf. Van Cleve (1986, p. 145).

[4] I will not, then, address the important objection of Van Cleve (1985), Hoffman and Rosenkrantz (1996, §1.4), and others that the bundle theory is incompatible with objects' changing and their having some of their properties only accidentally. Such an objection threatens at most the identity version of the bundle theory, not the supervenience or elimination versions. (Even the identity version can answer the objection if allowed the resources of four-dimensionalism and counterpart theory: see Hawthorne and Cover (1998).) In general, I will not discuss issues of diachronic unity in this paper; synchronic unity will be difficult enough.

[5] Trope-theory is on the rise, thanks in large part to the work of Keith Campbell (1981; 1990). It is now one of the primary players in the theory of properties. See, e.g., Martin (1980), Bacon (1995), Ehring (1997), Lowe (1998), Maurin (2002), and Heil (2003). Even David Armstrong, long a proponent of universals, believes that tropes are on (almost) equal footing with his own favored view: see, e.g., Armstrong (1997, 3.23). Alas, enthusiasm about tropes is not universal. Recent critics include Moreland (1985), Hochberg (1988), and Daly (1997).

[6] Hoffman and Rosenkrantz (1997, p. 30); see also Martin (1980) and Thompson (1983, p. 201). Even Denkel (1992) and Simons (1994), in the course of defending the bundle theory, deny that properties are parts of objects.

[7] Cf. Lewis (1991, esp. §3.6).

[8] They would include van Inwagen (1994), who would, I assume, also object to the alternatives I present next. He cannot understand these terms because they cannot be translated into what he takes to be a more perspicuous mereological idiom.

[9] Here one must take the table to be what Armstrong (1989a; 1997) calls a 'thick particular'.

[10] A principle of unity will explain what some bundle theorists call the 'compresence' or 'concurrence' of properties, terms I'll avoid because of the connotations they've acquired in the literature. I'll sometimes use 'principle of unity' for a relation among parts, other times for the linguistic formulation capturing this relation. No confusion should result

[11] Cf. van Inwagen's (1990, §2) "Special Composition Question".

[12] Critical surveys of the options can be found in van Inwagen (1990), Hoffman and Rosenkrantz (1997), and Markosian (1998).

[13] E.g., Goodman (1951) and Paul (2002).

[14] E.g., Simons (1994), Denkel (1997), and Maurin (2002).

[15] Cf. Horgan's (1993, p. 695) remarks on the principle of substantial unity.

[16] Campbell (1981, p. 131).

[17] See Armstrong (1978b, pp. 68-71). A structural property appears to be quite similar to what Kim (1998, p. 84) calls a micro-based property, though as the examples to follow show, there's nothing in the definition of a structural property, as I conceive of it, requiring the relevant parts to be microscopic. I will use the language of composition to describe the relation between a structural property and the relevant "smaller" properties and relations, though some may prefer to use the language of identity or supervenience. There are some philosophers who would object to properties' being composed of others. Maurin (2002, p. 71) is apparently one of them; cf. also Lowe (1995, pp. 512-3).

[18] The example is from Lewis (1986). Lewis' arguments in this paper are against structural universals and do not threaten the structural properties I'm discussing here, which are not universals but tropes--cf. Campbell (1990, §2.7).

[19] Cf. Sellars (1963, p. 17).

[20] On what it is to be all the parts, cf. Zimmerman's (2003, p. 513) "complete decomposition" and van Inwagen's (1987, pp. 22-23) "composition".

[21] Cf. Armstrong (1986, pp. 591-92; 1989b, ch. 6).

[22] See Bradley (1893); cf. Armstrong (1989a, p. 108) and LaBossiere (1994).

[23] For discussion, see Simons (1994), Denkel (1997), and Maurin (2002).

[24] (CU*) would certainly be needed to accommodate emergent properties, which, if there are such, are even more robustly autonomous than the higher-level properties discussed so far; see, e.g., O'Connor (1994) and Kim (1999). I cannot discuss emergent properties here, except to say that what independent reasons there are for favoring the bundle theory in general, and (CU) in particular, can be used to build a case against such properties.

[25] For a collection of papers on this problem, see Rea (1997), and for a discussion of the problem in the context of the bundle theory, Paul (2002).

[26] Here and below, 'modal properties' should be taken to mean alleged modal properties.

[27] Pace Yablo (1992); for further discussion, see Braun (1995).

[28] On this third test, cf. Armstrong (1978b; 1989a; 1997).

[29] These remarks should not be read as implying that all modal predications are description- or conception-dependent.

[30] Armstrong (1978a, p. 100); Armstrong attributes the objection to Geoffrey Harris.

[31] Hawthorne and Cover (1998, p. 215) appear to offer a similar reply to Armstrong.

[32] For a recent version of this argument, see Lowe (1998, pp. 158, 171).

[33] Simples, then, don't even have spatial parts, since I take it anything with spatial parts has structural properties.

[34] Armstrong (1989a, pp. 115-16) reports that David Lewis suggested a view like this to him. Cf. also Kris McDaniel's "Brutal Simples" (unpublished manuscript), in which he considers (and rejects) the view that a simple is a (natural) property.

[35] Cf. Armstrong's (1989a; 1997) view that a (thick) particular is a state of affairs.

[36] Campbell (1981, p. 479); see also Simons (1998).

[37] An early draft of this paper was completed while I was the recipient of a Summer Stipend from the National Endowment for the Humanities. Much of the subsequent work was completed while I was on sabbatical from Davidson College and a visiting scholar at the University of Colorado at Boulder. I thank all three institutions for their support. Thanks also to John Heil, David Barnett, Jonathan Lowe, Dan Korman, Matthew Stuart, Bob Pasnau, and especially an anonymous referee for helpful discussion of these issues and/or written comments on drafts.



[Thanks to for providing many of these links.]

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