Composition and laws of nature

I’ve for a while wondered if mereology can’t be nomically strongly emergent, namely whether there couldn’t be laws of nature of the form:

1. If the xs satisfy F, then the xs cause there to be a y composed of the xs.

This is a species of Markosian’s brute composition theory: There is no set of finite informative conditions that are necessary and sufficient for composition.

One might think that above nomic story has an informative necessary and sufficient condition for composition:

2. The xs compose something if and only if there is only one x or there is a law of the form (1) that the xs satisfy the antecedent of.

Condition (2) wouldn’t count as an answer to van Inwagen’s Special Composition Question because it uses mereological vocabulary on its right hand side (since (1) uses the word “composed”). However, (2) would still be pretty informative. Nonetheless, (2) shouldn’t be acceptable to a theist, because the kind of thing that can happen by a law of nature could also be directly produced by God apart from any law: God can make the xs compose y.

A technical problem with brutal composition

Markosian once proposed brutal composition as an answer to the question of when a (proper) plurality of objects composes a whole: composition is a brute fact, where a brute fact is a fact F such that “it is not the case that F obtains in virtue of some other fact or facts.”

Here is a nitpicky objection. Obviously:

1. The xs compose a whole if and only if there is a y such that the xs compose y.

Moreover, this doesn’t just happen to be true. For:

2. The fact that the xs compose a whole is the fact that there is a y such that the xs compose y.

And:

3. If it is a fact that there is a y such that the xs compose y, then there is an object y₀ such that the fact that there is a y such that the x compose y obtains in virtue of the fact that the xs compose y₀.

This follows from the Weak Existential Grounding principle:

4. If it is a fact that ∃yF(y), then there is at least one y₀ such that the fact that F(y₀) grounds the fact that ∃yF(y).

(Strong Existential Grounding says that the fact that ∃yF(y) is grounded in every instance. There are apparent counterexamples, but Weak Existential Grounding is hard to deny.) Assuming that “obtains in virtue of” is the same as “is grounded by”, we conclude from (2)–(4) that:

5. If the xs compose a whole, then there is a y₀ such that the fact that the xs compose a whole obtains in virtue of the fact that the xs compose y₀.

What can a brutalist say about this argument? I think one move would be to deny (2).

Instead, perhaps, we have a grounding relation between the facts that the xs compose a whole and that there is a y such that the xs compose y. If this grounding relation runs right-to-left, we have an immediate contradiction to the brutal composition thesis from (2): that the xs compose a whole obtains in virtue of there being a y such that the xs compose y.

So the grounding relation would have to run left-to-right. Thus we would have to have it that the xs composing a whole grounds there being a y such that the xs compose y. But likewise the particular fact that the xs compose y₀ grounds there being such a y. Now consider the two facts:

1. that the xs compose y₀

2. that the xs compose a whole.

If neither grounds the other, then the fact that there is a y such that the xs compose y is grounding-overdetermined by (i) and (ii). This is implausible. If (i) grounds (ii), we have contradicted brutal composition. That leaves the option that (ii) grounds (i). I am dubious. For it seems implausible to think that in general the fact that the xs compose a whole grounds that the xs compose y₀. For, plausibly, we can have cases where in one world the xs compose y₀ and in another world the xs compose y₁, where y₁ ≠ y₀. (Imagine that in one world a chair is made of the xs and in another a statue is.) But if the fact that p grounds the fact that q, then p entails q by Grounding Entailment.

Two brutenesses

Some philosophers think identity over time is brute: diachronic identity facts are not further explained. Markosian proposed (though later rejected) a view on which composition is brute: whether a bunch of simples make up an object at a time has no further ground.

It seems to me that it would be very natural to hold the two views together in the case of objects composed of simples. Consider the thesis:

• When we have a plurality of particles at t₁ and a plurality of particles at t₂, it is brute whether there is one object which both pluralities compose.

If the pluralities are the same and t₁ = t₂, then as a special case we get the bruteness of composition. And if we presuppose that both pluralities compose, then we get the following bruteness of identity for objects composed of simples: namely, it being brute whether the object at t₁ composed of the xs is identical with the object at t₂ composed of the ys. Since bruteness of diachronic identity for simples is itself extremely plausible, and it is very plausible (pace gunkiness) that everything is either simple or composed of simples, it follows that the above thesis very plausibly yields bruteness of diachronic identity in general.

While one could hold to bruteness of diachronic identity without holding to bruteness of composition or vice versa, it does not seem very natural to me to do so.