The Problem of Material Constitution

The last article asked that differences in truth be differences in being. Its hardest cases were truths with too little being behind them: there are no unicorns, there were dinosaurs. This article starts from a case where the being seems to be all there, and shared. A sculptor buys a lump of clay on Monday and on Tuesday models it into a statue of a seated woman. Every particle of the statue is a particle of the clay, the two sit in exactly the same place, and they weigh the same. Squash the thing on the plinth into a ball and the clay will still be there, but the statue will be gone.

That difference, between what the clay could survive and what the statue could survive, has to be a difference in something. The problem of material constitution is that there is nothing obvious for it to be a difference in, and nothing obvious to say about how many things are on the plinth.

The statue and the clay

Ordinary speech says that the statue is clay, or is made of clay, and moves between the two without strain. The relation needs a name before anyone decides what it is.

The plain case already contains differences. The lump existed on Monday and the statue did not. That historical difference is enough for an argument, but the more interesting differences are modal. The lump could survive being squashed into a ball, since a ball of clay is still that clay. The statue could not, since a ball is not a statue of a seated woman.

The argument is valid, its third premise is Leibniz's law, and its first two report what almost everyone would say. In the vocabulary of the beginner tier, they say that the statue and the lump differ in their essential properties: having roughly the statue's shape is essential to the statue and accidental to the lump. Things that differ in what they could not have lacked are not one thing. The difficulty is that the conclusion collides with a principle that seems nearly as secure. Locke wrote in the Essay that we cannot conceive of two things of the same kind existing in the same place at the same time, and most people would drop "of the same kind" without feeling the loss. Two ten-kilogram objects made of the same particles, standing in the same place on your plinth, sounds less like a discovery than like a mistake in counting.

Coincident objects are the mirror image of Black's spheres from the intermediate tier, which were two things in two places, alike in every quality. The statue and the lump are two things in one place. They do not threaten the identity of indiscernibles in its general form, since they differ in properties: in what they could survive, and in what kind of thing each is. What they share is every property that is neither modal nor a matter of kind: shape, mass, colour, location, microscopic make-up and, from Tuesday on, their history. The trouble will come from the thought that the modal differences have to rest on some of these.

Lumpl and Goliath

The historical difference is incidental, and Allan Gibbard, in "Contingent Identity" (1975), built a case without it. A sculptor makes the upper and lower halves of a statue separately, from two pieces of clay, and then joins them. At that moment a statue comes into existence, which Gibbard calls Goliath, and so does a single lump of clay, which he calls Lumpl, since before the joining there were two pieces and no one lump. Later the sculptor destroys them together. Lumpl and Goliath have the same parts and the same location at every moment either exists, and nothing ever happens to one that does not happen to the other.

The modal difference survives untouched. Lumpl could have been squashed and gone on existing; Goliath could not. The argument from squashing applies unchanged, and its conclusion is harder to live with, because nothing except modal facts and facts about kind separates the two.

The case also disarms an answer that works for the plain case. The perdurantist can treat the ordinary statue and lump as two objects extended through time which share their temporal parts from Tuesday onwards, as two roads can share a stretch of tarmac. But Lumpl and Goliath share all their temporal parts, so a perdurantist who counts things by their parts must count them as one, and then needs some further account of how one object can be both able and unable to survive squashing. Gibbard's case isolates the modal difference as the core of the problem.

Tibbles, Tib and the ship

A second family of puzzles produces coincidence by subtraction. The Stoics had a version attributed to Chrysippus. Dion is a whole man, and Theon is the part of Dion that consists of everything except one foot. Dion's foot is amputated, and now Dion and Theon are the same flesh in the same place. The modern version, which Peter Geach and David Wiggins both discussed, concerns a cat. Tibbles is a cat, and Tib is all of Tibbles except her tail. Before the tail is cut off, Tib is a proper part of Tibbles and so not identical with her. Afterwards they coincide exactly.

Both seem to survive. Cats survive losing their tails, and nothing happened to Tib at all. But then there are two things on the mat, each with a cat's organs, shape and life, and apparently two cats where anyone would count one. They cannot have become one cat, since they were two things before, and identity is not a relation that can begin to hold between two things.

This version is harder for the friend of coincident objects. Her natural explanation of how the statue and the lump share a place is that they are of different kinds, with different persistence conditions. Wiggins defended exactly that restriction of Locke's principle: things of different kinds can coincide, things of the same kind cannot. After the operation, Tibbles and Tib appear to be of one kind, so the case breaks the version of the principle that seemed safest. Chrysippus's own verdict was that Theon perishes, which saves the principle at the price of saying that something ceases to exist without anything happening to it.

The ship of Theseus fits the same pattern. At its launch, the ship and its original planks coincided, and if there are coincident objects they were two things, the planks constituting the ship. Hobbes's story separates them. The ship stays in the harbour while its planks are replaced, which a ship can survive; the original planks go to a shed, which a collection of planks can survive too. What looked like one thing dividing was two things going their separate ways, which explains why both candidates have strong claims. It does not settle the question the beginner article left over, since the reassembled planks now constitute a ship as well, and which ship is the original is still a question about two things of one kind.

Constitution without identity

The most widely held response accepts the conclusion of the argument from squashing and tries to make it comfortable.

Defenders of the view are called pluralists, since they count more than one object on the plinth. Wiggins was an early one. Mark Johnston argued for it under the slogan of his paper's title, "Constitution Is Not Identity" (1992), and Lynne Rudder Baker gave the most systematic account in Persons and Bodies (2000). On Baker's view, a lump constitutes a statue when it is in the right circumstances: shaped in a certain way, by someone with certain intentions, within a practice of making and displaying art. The statue is a new thing, of a different primary kind, which comes into existence when those circumstances obtain and depends on the lump without being it.

Baker also distinguishes having a property in one's own right from having it derivatively, in virtue of what one constitutes or is constituted by. The statue weighs ten kilograms derivatively, because the clay constituting it does. That is aimed at the objection everyone raises first: if two things on the plinth each weigh ten kilograms, the scale should read twenty. It reads ten because weights add only for things that share no matter. The counting worry has a related answer from the ontology tier: counting needs a sortal. Count statues and you get one; count lumps and you get one; count things none of which shares matter with another and you get one. "How many material objects?", with nothing further specified, has no answer until a way of counting is supplied.

The grounding problem

The objection that has done the pluralist most damage is the one this article opened with, and it has come to be called the grounding problem.

Contingent identity

The next three responses say there is only one thing on the plinth. Gibbard's was the most direct. Lumpl is Goliath, he argued, but the identity is contingent. Had the sculptor joined the same two pieces of clay into a ball, Lumpl would have existed and Goliath would not.

This runs into one of the best-known arguments in modern metaphysics, which Kripke made famous. Everything is necessarily identical with itself, so Lumpl has the property of being necessarily identical with Lumpl. If Goliath is Lumpl, then by Leibniz's law Goliath has that property too. So true identities cannot be contingent.

Gibbard's answer is that this argument goes wrong at the same step as the argument from squashing. Modal predicates applied to ordinary objects are, on his view, relative to a sortal: whether "could survive squashing" is true of something depends on whether it is considered as a lump or as a statue, and there is no fact about the thing considered under no sortal at all. Such predicates do not express properties the thing has in itself, so Leibniz's law, a principle about properties, does not apply to them, and both arguments fail.

The position revives something of Quine's view, met in the intermediate tier, that necessity attaches to things only as they are described, while confining the relativity to sortals. Its cost is the one Quine paid: essential properties become relative to a way of classifying, and anyone who thought the statue's need for its shape was a fact about the statue, not about the word "statue", will find that too much to give up.

Counterparts and inconstancy

David Lewis also accepted that such identities are contingent, but explained the contingency in a way that leaves Leibniz's law and identity itself in their ordinary forms. His counterpart theory, introduced in the intermediate tier, analyses a de re modal claim about a thing in terms of its counterparts: things in other worlds that resemble it closely enough in the relevant respects. His point in "Counterparts of Persons and Their Bodies" (1971), about a person and her body, was that there are many respects of resemblance and so many counterpart relations, and that different ways of referring to one thing can call up different ones. In On the Plurality of Worlds (1986) he generalised the point, arguing that counterpart relations are inconstant: which one is in play shifts with context, including the terms we use.

Applied to the plinth, there is one object. "The statue" calls up a counterpart relation on which only statues in other worlds count as its counterparts, so none of its counterparts has been squashed. "The lump" calls up one on which things made of the same clay count, whatever their shape. "The lump could survive squashing" and "the statue could not" are both true, and Leibniz's law is not broken, because "could survive squashing" does not express the same property on the two occasions, much as "is tall" does not when said of one man considered first as a jockey and then as a basketball player. A perdurantist who adopts this has a tidy picture: in the plain case, two objects sharing a stretch of their careers; in Gibbard's case, one object with two ways of being represented.

Dominant sortals

Michael Burke's view also keeps one object to a place, keeps modal properties as properties of things, and pays in a different currency.

Burke's paper, "Preserving the Principle of One Object to a Place" (1994), takes its title from the principle it means to save. On the plinth there is one object, which is both a statue and a lump of clay. It has the persistence conditions of a statue, because "statue" is its dominant sortal, so it could not survive squashing, and the first premise of the argument from squashing is false. What makes the view distinctive is its account of the history. On Monday there was a lump whose dominant sortal was "lump of clay", and which could survive squashing. When the sculptor finished on Tuesday, that object ceased to exist, and a new one began, made of the same clay. If the statue is squashed, that object ceases in turn, and another lump begins.

Applied to subtraction cases, the view gives Chrysippus's verdict. After the amputation there is one object and it is a man. Dion was a man before the operation and is one after it, whereas Theon, before it, was only a large part of a man. So the man who remains is Dion, and Theon has ceased to exist.

The view handles the grounding problem well, since there is one object and its modal profile follows from which sortal dominates, which follows from its shape and setting. The cost is the sculptor. An artist working a lump of clay destroys it without removing any of it. Burke can answer that this is the price of one object to a place, and that the lost lump is replaced by another made of exactly the same clay, so nothing anyone cared about has gone. Whether that is a reply or a restatement of the cost depends on how much weight you give the ordinary judgement that the sculptor reshaped the clay rather than replacing it.

Denying the statue

The last option removes one of the things. If there are no statues, or no lumps, nothing coincides with anything.

The most developed version is Peter van Inwagen's in Material Beings (1990). His answer to the special composition question is that some things compose something only when their activity constitutes a life. Particles arranged statuewise compose nothing, and neither do particles arranged lumpwise, so there are neither statues nor lumps, only simples arranged in those ways. There is a cat, because the activity of certain particles constitutes her life. Tib is not anything at all, since van Inwagen denies that things have arbitrary undetached parts, so the amputation leaves exactly one cat on the mat. The mereological nihilist goes further and denies composite objects altogether, cats included. A milder eliminativist removes only one side, holding that there is clay, as stuff, and a statue made of it, but no further countable object called the lump to be the statue's rival.

Eliminativism is less wild than it sounds, since van Inwagen does not tell you to stop saying that there is a statue in the hall; what the sentence gets right is that there are simples arranged statuewise there. The cost is that the statue's existence seemed as plain as anything in the room, and its destruction by squashing seemed a fact about it. Eliminativism disposes of the puzzle by disposing of what the puzzle was about, and whether that is acceptable depends on how its answer to the special composition question fares in general, not on clay.

Where it stands

Every response gives something up. Constitution without identity gives up one object to a place and owes an answer to the grounding problem. Gibbard's contingent identity gives up the necessity of identity and the idea that things have their modal properties in themselves. Lewis's inconstancy pays a similar price in another form: modal predicates still express properties, but which property shifts with the way the thing is picked out. The dominant sortal view gives up the judgement that sculpting reshapes clay rather than replacing it. Eliminativism gives up the statue, the lump, or both.

None of them finds, among the constituents of what is on the plinth, anything that could account for the modal difference. The next article asks whether that was the mistake all along. On the neo-Aristotelian view, the statue has a component the clay lacks, its form, understood either as a form embodied in matter or as a structural part. If form is a genuine constituent, the statue and the clay do not share all their parts after all, and the problem may be dissolved rather than answered.