Does it follow from van Inwagen's answer to the Special Composition Question that all complex things are alive?

The view that all objects are either living or simple appears to be a consequence of van Inwagen’s answer to the special composition question, namely that a proper plurality only composes a whole when the parts have a life together, where a proper plurality is a plurality of two or more things.

But this does not follow. Van Inwagen defines:

1. The xs compose y if and only if “the xs are all parts of y and no two of the xs overlap and every part of y overlaps at least one of the xs”.

Now the view that all non-simples are alive follows from van Inwagen’s answer to the special composition question (SCQ) provided that we have to have:

2. Anything that has proper parts is composed of some proper plurality of its proper parts.

3. Whenever something is composed of a plurality of things that have a life together, it is alive.

Indeed, if we have 2 and 3, then anything that has proper parts is composed of proper plurality by 2, which thus have a life together by van Inwagen’s answer to SCQ, and hence the thing composed of them is alive by 3. On the other hand, if there can be something that has proper parts but isn’t composed of a proper plurality of proper parts, then there is no way to use van Inwagen’s answer to SCQ to argue that it’s alive. Furthermore, if there is something that is composed of a proper plurality of proper parts that have a life together but isn’t alive, then we have another counterexample to van Inwagen.

Neither 2 nor 3 is completely obvious. You might, for instance, think that where you are, there is also a heap of atoms shaped just like you. If, further, you are a presentist and a materialist, you will think the atoms compose you and compose the heap. Moreover, the atoms have a life together. But the heap of atoms is not alive, unlike you. So (3) on that view is false.

For a view on which (2) is false, imagine a world consisting of four objects, A, B, C and D. Object A has B, C and D as proper parts. Object B has D as a proper part. Object C has D as a proper part. There are no other instances of proper parthood. This is a world where the company axiom of mereology fails (since B and C have D as a proper part and no other proper parts). It would be interesting to characterize in some non-trivial way the mereological theories where (2) is true. A sufficient condition is to assume atomism (Gemini Pro noted this). We can define this by saying every object has a simple part. For then if an object has a proper part, it is easily seen to be composed by its proper parts. But atomism is not a necessary condition. Consider a gunky mereological model whose domain is infinite sets of natural numbers and parthood is inclusion—then (2) is true.

We could also escape this worry by weakening the definition of composition by dropping the requirement that no two of the xs overlap. That makes van Inwagen’s answer to the SCQ put a more stringer requirement on reality, and it becomes trivial that everything that has proper parts is composed of them, and (2) becomes a matter of logic. We still need an argument for (3), however.

Gunk, etc.

If we think parts are explanatorily prior to wholes, then gunky objects—objects which have parts but no smallest parts—involve a vicious explanatory regress. But if one takes the Aristotelian view that wholes are prior to parts, then the regress involved in gunky objects doesn’t look vicious at all: the whole is prior to some parts, these parts are prior to others, and so on ad infinitum. It’s just like a forward causal regress: today’s state causes tomorrow, tomorrow’s causes the next day’s, and so on ad infinitum.

On the other hand, on the view that parts are explanatorily prior to wholes, upward compositional regresses are unproblematic: the head is a part of the cow, the cow is a part of the earth, the earth is a part of the solar system, the solar system is a part of the Orion arm, the Orion arm is a part of the Milky Way, the Milky Way is a part of the Local Group, and this could go on forever. The Aristotelian, on the other hand, has to halt upward regresses at substances, say, cows.

This suggests that nobody should accept an ontologically serious version of the Leibniz story on which composition goes infinitely far both downward and upward, and that it is fortunate that Leibniz doesn’t accept an ontologically serious version of that story, because only the monads and their inner states are to be taken ontologically seriously. But that's not quite right. For there is a third view, namely that parthood does not involve either direction of dependence: neither do parts depend on wholes nor do wholes depend on parts. I haven't met this view in practice, though.

Branchy gunk

An object is gunky provided that all of its parts have proper parts. Gunk is usually considered a really outré possibility. I want to offer some examples of intuitively conceivable gunky objects to broaden the philosophical imagination. The examples are all predicated on an Aristotelian ontology that allows for parts but denies other aspects of classical mereology. The thought behind the Aristotelian ontology of parts is that the parts of a thing correspond to natural functionally delineated subsystems. My heart is a part of me, as is my left arm. But there is no such part of me as "the left half of my heart" or "me minus my left arm".

Example 1: An infinite tree in 3D.

Here's a plausible Aristotelian thought about trees. Suppose that we have a branch A that splits into sub-branches B and C. Then branch A is an object that has both B and C as parts. However, there is no such part as A minus (B plus C). I.e., there is no object that consists of the part of A before the split. For the naturally delineated subsystem is the whole branch, including sub-branches, rather than the part of the branch without the sub-branches. Now imagine a fractal tree-like structure where the branches split into sub-branches, and the sub-branches into sub-sub-branches, and so on ad infinitum. Suppose, further, that there are no smaller natural functionally delineated subsystems than branches, sub-branches, sub-sub-sub-branches, etc. (This differs from real-world trees, which are made of cells.) The result is gunky: each part of the structure is a branch at some level, and each branch itself gives rise to sub-branches.

Dynamically, the structure can be thought of as built out of extended simples. We start with a trunk (a zero-level branch) that grows gradually. Then the trunk splits into branches. As a result, the trunk ceases to be simple: it has two or more proper simple parts, namely the branches, but it is not just the sum of the branches. The branches initially are simples, but eventually split themselves. If each step takes half the time of the preceding, after a finite amount of time we have the full infinite gunky tree.

Example 2: A four-dimensional example.

Suppose a spatial simple can survive becoming non-simple.(This was a governing assumption in the dynamical story in Example 1.) Suppose there are no proper temporal parts. Now, imagine we have a simple A, which survives becoming a non-simple made of two simples B and C. Then repeat the process with each simple. Continue ad infinitum, but don't require the process to speed up in any way. At any finite time, there are only finitely many objects. But the whole four-dimensional thing is gunky: A is made of B and C, B is made of D and E, and so on.

Example 3: Aristotelian temporal parts of a spatially simple thing.

On the Aristotelian ontology of parts, there won't be arbitrary temporal parts: there won't be the temporal part of me from my third to my fourth year. However, there might be naturally delineated temporal parts, like my adult part. Now imagine a person who never dies, and every five years receives a PhD in another discipline. If PhD-in-discipline-X counts as a naturally delineated temporal part, then the person will have a sequence of temporal parts like: doctor of biology, doctor of physics, doctor of chemistry, etc. Moreover, if we list these parts in the correct order, it gets gunk-like. If her first PhD is in biology and the second is in physics and the third is in chemistry, then the doctor of chemistry will be a part of the doctor of physics which will be a part of the doctor of biology. Moreover, there might be no such part as not-a-doctor-of-biology or not-a-doctor-of-physics (by the same token as on the Aristotelian story, there is no such part as me-minus-my-left-arm). Now, suppose that the person in question is an angel and hence has no spatial parts, and that the person has no significant temporal divisions besides the acquiring of PhDs. Then the individual is gunky: each part has a proper part. And this is easy to imagine, as long as we aren't worried about temporally extended simples.

Final remark: I don't know if these conceivable things are metaphysically possible.

Gunky ontology and virtual points

Gunk is subdivisible into smaller parts, and these are subdivisible into yet smaller parts, and this happens ad infinitum, with no smallest indivisible parts or atoms.

But here is an interesting fact: One can introduce ersatz atoms or virtual points into a gunky ontology, given some plausible mereological axioms. Suppose that O is a gunky object. Then the set M(O) of the parts of O has a partial order ≤ where x≤y if and only if x is a part of y. Now we can say that an ersatz atom of O is any ultrafilter on O with respect to the ordering.

Thus, ersatz atoms are subsets U of M(O) such that:

1. U is a non-empty proper subset of M(O)
2. if x is in U then everything that has x as a part is also in U
3. if x and y are in U, then there is a z in U such that z≤x and z≤y
4. U is maximal: any larger subset satisfying (1)-(3) is all of M(O).

We can then say that an ersatz atom U is an ersatz part of x∈M(O) provided that x∈U.

To get the existence of ersatz atoms, we need some axioms of mereology in addition to the Axiom of Choice. Fortunately, pretty weak mereological axioms suffice:

5. parthood is a partial ordering
6. O has two parts x and y that do not overlap

As usual, two things are said to overlap provided that there is something that is a part of both.

In general, given any two parts x and y that do not overlap, there will be an ersatz atom U that is an ersatz part of x but not of y. Let's further assume the strong supplementation axiom that if y is not a part of x, then there is a z that is a part of y such that z does not overlap with x. Then whenever x≠y, there will be an ersatz atom that's an ersatz part of one but not of the other. Hence, we can identify every part of O with a set of ersatz atoms. However, given gunkiness, not every set of ersatz atoms corresponds to a part. In particular, singleton sets of ersatz atoms do not correspond to parts.

So the gunk theorist can talk as if objects were made out of atoms. Now, if we have a gunky ontology, then I think we should take the parts to be non-fundamental, and grounded in the wholes rather than the other way around on pain of a grounding regress. But if we allow non-fundamental parts in our ontology, then one may worry that the gunkiness of the ontology is merely verbal and non-substantive, dependent on the verbal decision not to talk of the ersatz atoms as real parts.