Neo-Aristotelian Hylomorphism

The last article left the statue and the clay where it found them: in the same place, made of the same particles, and differing in what they could survive. Squash the clay into a ball and the clay is still there, but the statue is gone. The responses it surveyed come to three. Either there is really one object, and the appearance of two is explained away by contingent identity, counterparts or dominant sortals; or one of the two does not exist; or there are two, and the clay constitutes the statue without being identical to it. That last option keeps the modal difference and leaves a question hanging. If the statue and the clay have exactly the same parts, what is the difference between them in virtue of which one could survive squashing and the other could not?

This article takes up an answer much older than the modern puzzle. The statue is not just clay. It is clay with a form, which the statue has and the clay lacks. Aristotle said something close to this, and several contemporary metaphysicians have tried to say it precisely with the tools of modern mereology. If they are right, the two objects do not share all their parts after all, and the problem of material constitution rests on a false premise.

Matter and form in Aristotle

Aristotle introduced the distinction to explain change. In the first book of the Physics he argues that whenever something comes to be, something underlies the change and persists through it, and something is acquired that was not there before. When a bronze statue is cast, the bronze was there already, and what it acquires is a shape. In the second book he gives the bronze of the statue as his standard example of the material cause: that out of which a thing is made.

Three features of the pair matter for what follows.

First, matter is relative. The bricks are the matter of the house, but a brick is itself clay with a form. Aristotle says outright that matter is a relative term, each form having its own matter. Being matter is a role a thing plays relative to a higher level of organisation, not a special kind of stuff.

Second, form is not mere shape. For a statue shape is most of the story; for a living thing the form is the organisation that lets it live. In De Anima Aristotle calls the soul the form of a living body, and says there is no more need to ask whether soul and body are one than whether the wax and the shape stamped on it are one. An eye that cannot see, he adds, is an eye only in name, like a painted eye.

Third, the form is what the thing is. In the Metaphysics Aristotle identifies a thing's form with its essence, the thing stated in its definition. That makes the form the natural content of what the earlier article on essence called a real definition: an account not of what a word means but of what the thing is. For artefacts and natural things the definition mentions matter too. Aristotle's example is the house: stones, bricks and timbers (its matter) making a shelter for people and goods (its form).

The intermediate article on substance stripped the properties from a postbox to see what was left. Aristotle ran the same experiment in book Zeta of the Metaphysics, found that what remains is matter, and refused to count matter as substance in the primary sense, since it is not a separate, definite this. The primary substances of the Categories, this man and this horse, turn out to be compounds: matter organised by a form, which unifies it and fixes which changes the thing can survive.

How form went missing

For most of the twentieth century the analytic default ran the other way. The intermediate tier's mereology took parthood as a single relation governed by a few general axioms, and the classical theory says two things that matter here. Composition is unrestricted: any things whatever have a fusion. And it is extensional: composite objects with exactly the same proper parts are identical, and the same things cannot make up two different wholes.

On this picture a whole is nothing over and above its parts, and arrangement is a fact about how the parts are related, not a further ingredient of the whole. The fusion of the bricks of a house exists whether they are mortared into walls or scattered across a building site. A form has no work to do and nowhere to go, and the constitution problem takes its sharpest form.

Against it stands Leibniz's law: the clay can survive squashing and the statue cannot, so the statue is not the clay. The defender of identity accepts the argument and has to explain away the modal difference. The friend of constitution without identity keeps Leibniz's law and rejects the second premise, which leaves two things with the same parts and nothing in either to account for their difference. What grounds the fact that one could survive squashing and the other could not, when they share every part and every intrinsic qualitative feature? That is the grounding problem of the last article, and it pushes many philosophers back towards identity.

Hylomorphism goes after the first premise instead. The statue and the clay share their material parts: every particle of the clay is a particle of the statue and conversely. What the hylomorphist denies is that material parts are all the parts there are.

Fine's theory of embodiment

Kit Fine's theory, set out in "Things and Their Parts" (1999), responds to the poor fit between the classical sum and an ordinary thing. A sum exists whenever its parts exist, and has its parts without qualification as to time. A house exists only while its bricks are arranged as a house, and it can lose a brick and gain another. Fine's response is not to restrict the sum but to add further ways for things to make up a whole.

The first is rigid embodiment. Given some objects $a, b, c, \ldots$ and a relation $R$, there is an object Fine writes $a, b, c, \ldots/R$. It exists at a time just when $a, b, c, \ldots$ stand in $R$ at that time. It is located where they are. It is the same as another rigid embodiment only if the two have the same objects and the same relation. And the objects, together with the relation itself, are its timeless parts: its parts without temporal qualification, so that it can neither gain nor lose them.

Rigid embodiments cannot change their parts, so they cannot be the whole story about a river or a car. For these Fine adds variable embodiment. Take a principle $F$ that picks out, at each time, a thing that is its manifestation then: for a river, the water then flowing in its bed; for a car, the components it then has, arranged as a car. The variable embodiment $/F/$ exists at a time just when $F$ has a manifestation then, is located where that manifestation is, and has the manifestation as a part at that time. Since the manifestation can differ from time to time, the variable embodiment can survive a complete change of matter while the principle stays fixed.

Applied to the statue, the theory gives a clean diagnosis. Treat the statue as a rigid embodiment of the clay and the property of being statue-shaped, or, if it can survive losing a chip, as a variable embodiment whose manifestations are such things. Then the statue exists just when the clay is statue-shaped. Squash the clay and the property is no longer had, so the embodiment no longer exists, while the clay, which required nothing of the kind, carries on. The clay is a part of the statue, the statue is not a part of the clay, and the statue has a part, the property, which the clay lacks. Two objects that coincide in space have different parts and different conditions of existence, and the first difference explains the second.

In the vocabulary of real definition, it is true in virtue of the nature of the statue that it exists only while its clay is statue-shaped. Its inability to survive squashing is not a brute modal fact; it follows from what the statue is, and the clay's definition contains no such clause.

Fine draws a general moral: there is no single operation of composition, and the same things can make up different wholes in different ways.

Structure as a part

Kathrin Koslicki's The Structure of Objects (2008) develops the thought directly as a thesis about parts. A composite material object, on her view, has two kinds of parts: material components, such as the clay of a statue or the particles of the clay, and a formal component, its structure. The structure is, roughly, what the object's kind requires of its material: a specification of what components there must be and how they must be arranged. And it is a proper part of the object, as genuinely a part as the matter is.

Mark Johnston's "Hylomorphism" (2006) reaches a related picture by a different route. He asks what makes some items into a given whole, and answers, in Aristotle's spirit, that a whole is its parts together with a principle of unity proper to its kind, which plays the role the form played for Aristotle. The three differ in detail, but agree that the classical theory of parts left out what makes a heap into a thing.

Dissolving rather than answering

Return to the statue and the clay with the structural view in hand.

The clay may have a formal part of its own, a far less demanding one, but it does not have the statue's. So the first premise of the mereological argument is false. The two objects share all their matter and are not mereologically identical. Material constitution becomes an ordinary relation: the clay constitutes the statue when it is the statue's material component and satisfies the statue's structure.

This does not take sides among the responses of the last article. It removes the premise that made the case puzzling. On the hylomorphic account there never were two things with the same parts. There were two things with the same matter, which nobody thought impossible, and different forms, which is what you would expect of a statue and a lump.

The modal difference now has a source in the objects themselves. The statue cannot survive squashing because squashing takes its matter out of the configuration its structure requires. The clay survives because its own requirements are met by a ball as well as by a statue. That answers the grounding problem as well as the mereological argument: the difference in what they could survive is grounded in a difference in what they are made of, once form is counted among what things are made of.

Parts of the wrong category

The first objection is that a structure is the wrong kind of thing to be a part. The statue's material parts are clay, with location and mass; its structure is a pattern, or a set of requirements. The natural thought is that parthood relates things of one category: material things have material parts, and events have events as parts.

A subtler version of the worry uses structure in Sider's sense. Suppose classical parthood carves reality at its joints. Then the hylomorphist's "part" is either that relation, and its classical axioms apply, or a less natural one, and the claim that the statue has a part the clay lacks is true but cheap. Fine's pluralism suggests an answer: what carves at the joints is a generic notion of part, of which the classical sum is only one mode. That is a substantive claim about structure, and the dispute is partly over which notion of part, if any, is privileged.

Aristotle's regress

The second objection is one Aristotle raised against himself. In book Zeta of the Metaphysics he observes that the syllable BA is not just the letters B and A, since the letters survive when the syllable is broken up; likewise flesh is not just the fire and earth in it. So the syllable is the letters and something else. But if that something else is a further element alongside B and A, the same reasoning applies again: the three ingredients could exist without making the syllable, so something more is needed, without end. Aristotle concluded that the extra is not an element at all but the cause of the elements' being a syllable, and that this is the thing's substance, its form.

The argument looks aimed at exactly the neo-Aristotelian thesis. A form was introduced to explain why some matter makes a unified whole; if it is one more part, it needs the same explanation, and it cannot lift the whole into being by its own bootstraps.

Extensionality returns

The classical mereologist now brings the constitution problem back one level up. Take the statue's clay and its structure, and suppose the structure is a universal. Classical mereology says the two have a fusion, which exists whenever they do. Both survive squashing: the clay is still there, and the structure is still had by other statues, or exists unexemplified. So the fusion survives squashing while the statue does not. The statue and that fusion have exactly the same parts and differ in what they could survive, and extensionality fails on the very view that was meant to reconcile coincidence with it. If the structure is instead a particular that exists only while the clay is so arranged, the two no longer come apart in this way, but then the structure looks like the arrangement itself, and the first objection returns.

The hylomorphist has two ways out, and both depart from the classical theory. She can restrict composition, so that material and formal parts compose a whole only when the matter satisfies the form, and the clay and the structure compose the statue and nothing else. Or she can accept the fusion and give up extensionality: two objects made of the same parts can differ because they are made of them in different ways. Fine's pluralism takes the second route; the structural view, on which composition depends on a structure's being satisfied, fits the first. Either way the dissolution of the constitution problem is paid for in classical mereology, the theory that set the problem up.

Defenders of the classical principles hold that extensionality is close to definitive of parthood, since a whole is nothing over and above its parts. The hylomorphist replies that this is the claim in dispute, and points to a limit of the classical theory that its own defenders identified. In "Against Structural Universals" (1986), David Lewis argued that a structural universal such as being methane cannot be a mereological fusion of simpler universals: the universal of being hydrogen would have to occur four times in methane, but a fusion has each of its parts only once. Lewis took this as a reason to reject that conception of structural universals. The hylomorphist takes it as a demonstration that classical mereology cannot represent arrangement, and so cannot be the whole theory of how structured things are made.

Where it stands

Neo-Aristotelian hylomorphism buys a great deal with one posit. It explains why the statue and the clay differ, why ordinary things begin to exist when matter is arranged and cease when the arrangement is lost, and why each kind of object has the persistence conditions it has: its form, which the real definition of the kind states, sets them. William Jaworski's Structure and the Metaphysics of Mind (2016) carries the idea into the philosophy of mind, arguing that once structure is counted among the basic features of the world, hylomorphism offers a solution to the mind-body problem.

The price is paid in mereology. Parthood ceases to be a single relation with a simple, topic-neutral theory, and becomes either a family of relations or one relation with restricted and non-extensional laws. Forms need a place in the ontology, as universals shared among objects or as particulars that come and go with arrangements, and each choice reopens an objection. If the statue and the clay really are two, and their difference really needs grounding in what they are, hylomorphism offers the most direct explanation available: they differ in their parts. If you are willing to say there is only one thing there, the price buys nothing you need.

Next

Hylomorphism holds that a whole is more than its material parts: it has a further part, its form. The next article examines the opposite extreme, the thesis that a whole is not even something over and above its parts but is identical to them, taken together. Composition as identity promises to make believing in a fusion cost nothing beyond believing in its parts, and the question is whether identity can hold between one thing and many without collapsing into absurdity.