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A

nalysis

57.1, January 1997, pp. 110. Samuel Levey

Coincidence and principles of composition

Samuel Levey

1.

On a widely favoured view of material objects,

1

two objects could bemade of the very same matter at the same time, and instances abound.Heres the familiar fable. A copper statue of Hermes is fashioned (say, allat once by nuclear fusion so that none of its matter or at any rate, noneof its copper precedes it), and later entirely dissolved in acid. The statue

and thepiece of copper

formed and destroyed in this process are, it is said,distinct objects, despite being wholly coincident. For the two differ in (e.g.)their dispositional or modal properties. The statue, unlike the piece ofcopper, could not survive a radical change in shape. So, the statue and thepiece of copper are discernible and therefore distinct; and they share alltheir matter they coincide

.

2

The lesson of this fable: Distinct materialobjects, such as statues and statue-shaped pieces of matter, can coincide.

Or so say the widely favoured views advocates. But there are, of course,dissenters, and, up to a point, I side with them.

3

I wish to discern twoelements within the widely favoured view, only the second of which, it

seems to me, is wrong. First, there is the doctrine that coincidence ofdistinct material objects is possible; call this the doctrine of coincidents.Second, there is the claim that coinciding objects fall under sorts whoseinstances such as the statue and the piece of copper abound in ordinaryexperience. In this paper I raise a serious puzzle facing the doctrine of coin-cidents, and construct a novel solution to it. The style of that solution turnsout to be quite uncongenial to the second element of the favoured view,

1

For a good sample of its many defenders see the lists compiled by Burke (1992, and1994). Note that I call their common account widely favoured whereas Burke (andothers) speak of the standard account. My departure here is due to the fact that Iwish to leave aside the cluster of issues that, as it happens, are of particular concernto Burke et al

., namely, the relations among sorts, sortals, objects and persistenceconditions.

2

Throughout I use coincidence and its cognates to mean what one could call

complete

orperfect

coincidence; for simplicity, merely partial coincidence (spatial ortemporal) is here set aside.

3

E.g., Burke 1994; Lewis 1986; Noonan 1988, and 1993; van Inwagen 1981.

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belong to its core structure, and those that supervene on that core. Nowheres the puzzle.

Coinciding objects objects that share all their matter should haveprecisely the same basic physical profile. They have the same materialnature, the same mass, the same net charge, the same shape, take upprecisely the same amount of space, and so forth. But, so-called mereCambridge properties aside, all other properties dispositional, counter-factual or modal properties in particular presumably supervene on a corephysical structure delimited by the profile. So, how could the statue and thepiece of copper, apparently identical in physical structure, possibly differin their supervening modal (etc.) properties?

The question is not

how two objects could differ just by having differentmodal or dispositional properties.

5

It is rather how two objects of precisely

the same physical profile could have different modal or dispositional prop-erties in the first place

. How could two material objects perfectly alike inmomentary, intrinsic, physical make-up differ in their abilities to lastthrough change? How, for example, could the piece of copper survivebeing flattened when the very same process would destroy its physicalduplicate, the statue?

The root of the trouble for the doctrine of coincidents can be summedup in a single proposition: Modal or dispositional differences amongobjects could only supervene on core differences that coinciding objectswould necessarily lack. (Call this last the difference thesis.) Given the

difference thesis, coinciding objects could not differ modally or disposi-tionally; and so it seems impossible that there should be coinciding objectsafter all.

6

This is the supervenience problem

and it casts doubt over thevery coherence of the doctrine of coincidents.

5

Some authors apparently have thought otherwise; cf. Johnston 1992, and Noonans1993 reply. My thanks to Eric Olson on this point.

6

I assume throughout that coinciding objects must be qualitatively diverse; mostwriters on the topic find the notion of coinciding indiscernible

objects repugnant, andI share this sentiment.

object counts as having certain capacities because the sortal concept under which weidentify it dictates that (e.g.) certain changes but not others count as substantial onesfor objects of its sort; its sortal concept determines the facts about its capacities tosurvive, and so inquiry into an objects capacities cannot be done apart from sortaltheory. I find their view difficult to believe, but as it is not feasible to enter into suchcontroversy here, I shall simply agree to disagree with hard-bitten conceptualists. For

the milder conceptualist realists such as Wiggins (and note his distance from thehard-bitten conceptualist 1980: 1412; 1986: 16970, 17980), there should be nodeep problem with the particular way in which we abstract from the concepts of sortsand sortals in the present discussion.

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coincidence and principles of composition 5

of the two kinds of particles, massive compounding occurs when theymingle, thus producing a chemically uniform mass of great structural

strength. But imagine further that the particles of the two lumps areendowed with peculiar magnetic properties, such that on contact all theparticles also become powerfully magnetically interlocked. Now, crucially,suppose the special magnetic properties of the particles are causally inde-pendent of the chemical properties in virtue of which the compoundingoccurs. Even if the particles were to lack the chemical properties responsi-ble for the compounding, they would magnetically lock into the shape ofa sphere. And even if they were not to possess those magnetic forces, theywould still chemically compound into a shiny black mass.

To finish the example, I shall suppose that the chemical bonds holdingthe particles together are causally sufficient to produce a chemical object

;

likewise, the magnetic forces at work produce a magnetic object

. It seemsto me that the chemical object and the magnetic object are distinct byvirtue of having distinct principles of composition.

7

(Ill discuss below howthat difference gives rise to further qualitative differences.) The particleschemically compose the one and magnetically compose the other. Thecomposite objects are distinct but yet coincide.

As promised, our story involves relinquishing the doctrine of unique-ness, and this perhaps deserves further comment. In so-called extensional

mereologies, according to which composite wholes are characteristicallyidentified (at a time and in a world, at any rate) simply by their parts,

uniqueness is a merely definitional feature; in intensionalist

accounts ofcomposition such as ours, on the other hand, uniqueness is a substantivethesis requiring substantive grounds. Two other theses are typically

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advanced as such grounds from which uniqueness follows: (1) Distinctobjects must differ in either their intrinsic or relational properties (a formof Leibnizs Law); (2) The intrinsic and relational properties of a compositeobject are completely determined by the intrinsic and relational propertiesof its parts. Properly understood, (1) is unobjectionable. The trouble lies in

7

As with all such examples, in supposing that the chemical and magnetic forces arecausally independent and sufficient for composition, we run dangerously close to

conceptual incoherence. Esotericpossibilities

ones that really are possible

are, Isuspect, far more difficult to specify than is often assumed. But at present my aim issimply to convey the idea

of separate principles of composition operating over thesame objects. We could be more cautious here and simply use a schema for such anexample, speaking only ofC

-forces and M

-forces, and resultant C

-objects and M

-objects, and leave it to an unspecified range of possibilities to locate possibly truesubstitution-instances.

8

Cf. van Inwagen (1990: 52f.) for a nice discussion here; but note that van Inwagendoes not commit himself to the soundness of the following argument.

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(2). In the sense that nothing else

but the properties of its parts determinea composites properties, what (2) says is true. But if thats all that is meant

by (2), uniqueness certainly does not

follow from (2) and (1). (In ourimagined case, for example, the chemical and magnetic objects have theirproperties determined by nothing else but the properties of their parts.) Sofar as I can see, the reading of (2) needed to secure uniqueness as a conse-quence (without making (2) itself simply equivalent to uniqueness), wouldbe this: a single sequence of parts could not compose two or more objectspossessing different

intrinsic or relational properties. But understood inthat way (2) can quite reasonably be rejected in an intensionalist mereology thus undercutting the inference to uniqueness. And as we develop ourpresent account, especially in the next six paragraphs, we shall see how itis that we actually reject it.

Consider how principles of composition are linked to the essentialnatures of the composite objects which they generate. The way

in whichparts are conjoined to produce a whole figures directly in determiningwhat, or which, physical properties that whole has essentially, and whichit has accidentally. In short, a composite objects essential properties aredetermined by those properties of its parts that are relevantly connectedwith its principle of composition.

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Only the properties that contribute tothe composition of a whole by its parts (and the properties necessarilyconnected with these compositional properties) count in determining theessential nature of the whole. Other properties of the parts can at best

determine only its accidental properties.Lets extend our example to illustrate those last claims. Suppose a certainsolvent could break the chemical bonds of the matter while leaving themagnetic forces unaffected; because the chemical bonding does not matterto the composition of the magnetic object by its parts, the property beingof such-and-such chemical composition

is inessential to the magneticobject. Similarly, a powerful magnetic field might scramble the magneticforces of the individual particles, thereby magnetically unlocking them, butleave the chemical bonds intact; and being magnetically reinforced

is ines-sential to the chemical object.

Were the chemical and magnetic objects wholly non-coincident, the

action of the solvent would destroy only the chemical object, and theaction of the magnetic field would destroy only the magnetic one. Thecausal nexus which support the existence of each of our composite objectsdetermine what changes those objects could or could not endure. The two

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This claim should perhaps be limited to intrinsic qualities, excluding historicalproperties and purely formal or high category properties (such as being self-identi-cal

, or being such that the number seven is odd

, etc.) Nothing in the present discus-sion turns on such details, however.

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nexus happen to be realized in the same matter, but I cannot see how thiscoincidence should make any difference to our objects separate capacities

to endure.The chemical and magnetic objects are coincident, and so their basicphysical properties are shared. Their capacities to serve as a materialsubstrate for changes are presumably fixed by their physical structurealone. Their capacities to survive

changes, however, are underdeterminedby their physical structure. Facts about their physical structure can tell usonly how their constituent matter could be spread around in space,combined with other matter, and so on. Inferences to facts about the gener-ation, survival or corruption ofobjects

made of that matter, on the otherhand, are to be licensed only under a substantive theory of composition.Such an account is needed to tell us when a composite object arises at all;

and on the present account facts about an objects principle of compositionwill fix the remaining facts about its essential nature and so its capacitiesto survive changes.

The point could be put this way. Suppose we distinguish a core clusterof an objects physical properties. The object has these properties simply invirtue of the nature of its matter and how that matter is (physically) organ-ized. But facts about the core properties of an objects matter do not bythemselves entail facts about the manner

in which an object has its corephysical properties whether essentially or accidentally. For, again, theselatter facts carry modal content, thus outstripping what could be inferred

from the straight physical facts. The manner of connection of the coreproperties, for properly composite objects, is a consequence of the princi-ple of composition in virtue of which the parts compose the object. If theprinciple is chemical, for instance, certain core properties and not otherswill be essential. The distribution of essentially possessed propertiesamong an objects core properties will differ with different principles, e.g.,magnetic principles, or vital principles (such as van Inwagens Life

,

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say),and so on.

The rest of the objects properties are logically constructed from its corephysical properties and its manner of possessing them. Deformability, forexample, is constructed from the capacity of the matter to hold an array of

shapes and the contingency of the possession of its actual shape by theobject. Because the manner in which an object possesses its core propertiesis fixed by its principle of composition, the supervenience of the rest of anobjects properties is determined by the objects core physical properties

plus

its principle of composition. Only in combination with a givencompositional principle can any cluster of physical features form a base orcore for a composite objects supervening properties.

10

Cf. van Inwagen 1990: 14565.

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3. Now we can deliver the punch-line. The difference thesis that generatesthe supervenience problem in fact comprises two separable claims. The

first is a supervenience thesis, reasonable in my view, that dispositional,counterfactual or modal differences between objects could only superveneon core differences. The second is that coinciding objects would necessarilylack such core differences, for their physical sameness requires that theymust share a single core structure. But this second claim is false. Theirphysical sameness does not secure a common core structure. And indeedcoinciding objects would not

share their cores. The core structures that arebases for the supervening properties differ for each coinciding object. Eachsuch structure is generated by a distinct principle of composition, and, aswe have seen, this is sufficient for the core structures to be qualitativelydiverse.

The sense in which coinciding objects are the same is that their basicphysical profiles are indistinguishable. For each basic physical property,one has it if and only if the other does, where those properties are specifiedpurely physically, or without reference to their manner of connection. But,as I have been arguing, the manner of connection makes all the differenceto the nature of the core structure that results, and so to the superveningproperties that an object possessing such a core could further exemplify.From sameness of physical profile, sameness of core structure simply doesnot follow.

In constructing an answer to the supervenience problem I am, inter alia,

urging a certain picture of the inner nature of composite objects; as a finalmeasure let me sketch it out a bit more vividly. Call an objects superveni-ence base its compositional structure. Taken in abstraction from itsmodal or dispositional properties, a composite object appears as a compo-sitional structure awaiting supervenient detail. (The structure is of coursejust the composite object considered in abstraction from such detail.)Taken in abstraction from its principle of composition, however, acomposite object does not appear as a bare physical structure awaitingdetail; it simply does not appear at all. To imagine the parts without thecompositional principle is only to imagine those parts as so many separateobjects. Distinct coinciding objects, considered in abstraction from their

supervenient properties, can only appear as distinct compositional struc-tures. At no point in abstraction is it possible to conceive a single structurewithout the compositional features that would distinguish it as the core ofthis coinciding object rather than thatone.

To suppose otherwise is the conceptual error buried in the differencethesis. Qualitative differences, it was suggested at the outset, could onlysupervene on intrinsic differences that coinciding objects would necessarilylack. But in fact for coinciding objects the qualitative differences reside

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intrinsically all the way down. Where the differences vanish, so do anycomposite objects. A unified physical core arises when and only when a

principle of composition is in place; that core is the compositional struc-ture. With different principles, there arise different compositionalstructures and hence diverse composite objects presumably there is nodifficulty about how objects diverse in their core structures could differ intheir supervening properties. In the light of our analysis the differencethesis can now reasonably be abandoned, and the conceptual problem itintroduces for the doctrine of coincidence is thus dissolved.

So the doctrine of coincidents is defensible, if at the price of accepting acertain metaphysic of compositional principles. That metaphysic of courseis sketched here only in barest outline, just enough to see how the super-venience problem may be dispatched; it awaits a full-dress defence hard

cases decided, compositional principles individuated, and so on thesubject for another paper. I wish to record here, however, my convictionthat the widely favoured view will not find shelter under my defence of thedoctrine of coincidents. According to that view, instances of coincidenceabound. Statues are supposed to differ from statue-shaped pieces of matterwith which they coincide. For this to occur, the material particles on handmust be causally interrelated in two ways, both independently sufficient forcomposition. But I dont see two causal principles forthcoming that woulddistinguish statues from statue-shaped pieces of matter. Certainly nothingweve considered would do it, though I suppose a far more promiscuous

ontology of compositional principles than I would endorse might makesuch distinctions. (Thats the virtue of promiscuous ontologies: an indefi-nitely pliable distinguo.) I enjoy the benefit of being able to contrive a caseto fit the opening in logical space where distinct material objects coincide.The favoured view, by contrast, is saddled with objects here in reality,where any effort to discover principles of composition that might distin-guish actual statues from statue-sized pieces of their constituent matterwould in all likelihood show itself to be unacceptably ad hoc. The doctrineof coincidents is defensible; the widely favoured view of material objects isnot.11

Syracuse UniversitySyracuse, NY 13244, USA

sslevey@mailbox.syr.edu

11 Thanks to Christie Thomas, Eric Olson and David Robb for excellent discussion andacute criticism of the present paper and the cluster of issues it treats. My thanks alsoto Peter Smith and to an anonymous referee.

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References

Burke, M. 1992. Copper statues and pieces of copper: a challenge to the standard

account. Analysis 52: 1217.Burke, M. 1994. Preserving the principle of one object to a place: a novel account of the

relations among objects, sorts, sortals, and persistence conditions. Philosophy andPhenomenological Research 54: 591624.

Johnston, M. 1992. Constitution is not identity. Mind101: 89105.Lewis, D. 1986. On The Plurality of Worlds. Oxford: Basil Blackwell.Noonan, H. 1988. Reply to Lowe on ships and structures. Analysis 48: 22123.Noonan, H. 1993. Constitution is identity. Mind102: 13346.Van Inwagen, P. 1981. The doctrine of arbitrary undetached parts. Pacific Philosophical

Quarterly 62: 12337.Van Inwagen, P. 1990. Material Beings. Ithaca: Cornell University Press.Wiggins, D. 1980. Sameness and Substance. Cambridge, Mass.: Harvard University

Press.Wiggins, D. 1986. On singling out an object determinately. In Subject, Thought, and

Context, ed. P. Pettit and J. McDowell, 16980. Oxford: Clarendon Press.