Composition

When do some things compose a further thing? Two hydrogen atoms and an oxygen atom compose a water molecule. Do the Eiffel Tower and your left shoe compose anything? Does a heap of sand? Do the atoms in your body, and if so, when did they start?

Van Inwagen's Material Beings (1990) put the question in a form that has organised the literature since. The Special Composition Question asks for the conditions under which composition occurs:

$$\text{Under what conditions is it true that }\exists y\text{the }xs\text{ compose }y?$$

What makes this the central question of contemporary ontology is that it looks like a request for a modest refinement and turns out to admit only radical answers.

The three answers

Universalism: always. Any plurality whatever composes something. There is an object composed of the Eiffel Tower and your left shoe; there is one composed of every third electron in the galaxy. This is the axiom of unrestricted composition from classical mereology, and it implies a vastly larger inventory than common sense allows — though the universalist replies that the cost is nil if composition is ontologically innocent.

Nihilism: never (except trivially, where one thing composes itself). There are no composite objects at all — no tables, no molecules, no people. There are only mereological simples, arranged in various ways. Ordinary talk is paraphrased: "there is a table here" becomes "there are simples arranged tablewise." The inventory is minimal and the paraphrase burden is enormous.

Restricted answers: sometimes. The natural view, and the hardest to defend. Candidates surveyed and rejected by van Inwagen include contact (glue two people together and you do not get a new object), fastening, cohesion, and fusion in the physical sense — each is either too permissive or too restrictive, and none marks a principled line. His own answer is that the $x$s compose something if and only if their activity constitutes a life, which yields an ontology of simples and living organisms: there are electrons and there are cats, but no tables and no rocks.

The argument from vagueness

The strongest argument against restricted answers is due to Lewis and sharpened by Sider, and it deserves care because it is the reason the moderate position is so hard to hold.

1. If composition is restricted, then there is a continuous series of cases running from ones where composition clearly occurs to ones where it clearly does not — assemble a table atom by atom, or disassemble one.
2. Any sharp cut-off in such a series would be metaphysically arbitrary: it is not credible that adding one atom at a precise point brings a new object into existence.
3. So a restricted answer implies borderline cases of composition — cases where it is indeterminate whether the $x$s compose anything.
4. If it is indeterminate whether composition occurs, it is indeterminate how many objects there are.
5. But "there are exactly $n$ objects" is expressible using only quantifiers, identity, and connectives:

$$\exists x_1\dots \exists x_n\left(\underset{i\ne j}{\bigwedge }{x}_i\ne x_j\wedge \forall y\underset{i}{\bigvee }y=x_i\right)$$

None of that vocabulary is vague. So such a sentence cannot be indeterminate in truth value.

6. Therefore composition is never indeterminate, and the only answers are the extremes: always, or never.

The argument's engine is step 5, and the responses attack it or step 4:

• Ontic vagueness. Deny that vagueness must be semantic. If the world itself can be indeterminate, the counting sentence can be indeterminate despite its precise vocabulary. Most find this hard to make sense of, and Evans' argument against vague identity is usually cited against it.
• Epistemicism. Accept a sharp cut-off but deny it must be non-arbitrary or knowable. Vagueness is ignorance; there is a precise atom at which the table comes to exist and we cannot know which. This preserves the restricted answer at the price of accepting exactly the arbitrariness step 2 called incredible.
• Deny step 4. Perhaps indeterminacy in composition need not infect the count — but it is hard to see how, since whether there is a table is precisely a question about how many things there are.

Nihilism examined

Nihilism is far more attractive than it first sounds, because it combines a minimal ontology with a systematic paraphrase, and it is not committed to denying anything about experience — only about what the correct inventory is. Three pressures on it:

Does it have any simples to work with? The paraphrase "simples arranged tablewise" requires that there be simples: partless things at the bottom. Physics does not obviously supply them. The effective-field-theory picture is a tower of theories each valid at its own scale, with no evident floor, and Schaffer has argued we have no warrant for assuming reality is well-founded. If there are no simples — if matter is gunk, every part having further proper parts — nihilism has nothing left standing at all, since it denies composites and there is nothing else. This is a case where the empirical situation bears directly on a supposedly a priori dispute, and it is taken up on the gunk page.

The Moorean objection. Korman's version: "here is a hand" is more certain than any premise in any argument for nihilism. When a valid argument concludes that there are no hands, the rational response is to reject a premise, even without knowing which. This is a legitimate methodological move — it is how we treat sceptical arguments — but it can be over-used, and the nihilist replies that the Moorean fact is preserved: there is something hand-shaped there, namely simples arranged handwise.

The paraphrase burden. "Simples arranged tablewise" must be shown to be systematic rather than a promissory note, and the plural machinery it needs is exactly the plural quantification that makes many-without-one respectable.

Universalism examined

Universalism has the opposite profile: no paraphrase burden, an outrageous inventory.

Its defenders argue the outrage is misplaced. We are not being asked to believe in strange objects, only in unfamiliar ones — the fusion of the tower and the shoe has no odd properties, it is simply scattered and uninteresting. Our ordinary vocabulary picks out a tiny, interest-relative subset of the fusions there are, which explains why the others sound absurd without making them so.

The costs are real nonetheless. Universalism entails coincident objects wherever a composite has a proper part that is not a further composite's part in the same way, and it makes almost every object a part of enormously many others. Combined with the extensionality of classical mereology it also entails that the statue and the clay are identical, which is where the constitution problem bites.

Conservatism

The remaining option is to accept the restricted answer and take the consequences. Conservatism (Korman) holds that there are all and only the ordinary objects — tables, trees, and hands, but no fusions of towers and shoes and no bare simples-arranged-tablewise revisionism. Its burden is to answer the debunking arguments: from arbitrariness (why these cut-offs?), from vagueness (above), and from causal overdetermination (if the simples arranged tablewise do all the causal work, the table is redundant).

The conservative's reply to arbitrariness is to deny that a metaphysical principle must be simple or non-arbitrary — the boundaries of the ordinary kinds may just be where they are. Whether that is a position or a refusal is the standing dispute.

Where composition sits

The Special Composition Question belongs to the inventory question and is the place where it is at its starkest: the candidate answers differ not by a few entities but by orders of magnitude, and each of the extreme answers is defended by serious philosophers on grounds of principle against a moderate view that is difficult to state.

It also connects the inventory to the status question more directly than any other dispute here. If quantifier variance is true, universalism and nihilism may be notational variants — the nihilist's "simples arranged tablewise" and the universalist's "table" describing the same reality in different languages, with no fact about which is right. That diagnosis is more plausible for this dispute than for almost any other, which is why it is the deflationist's favourite example.

The next page takes up what happens when two objects appear to have exactly the same parts: the problem of material constitution.