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.

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.

Avoiding temporal parts of elementary particles

It would be appealing to be able to hold on to all of the following:

1. Four-dimensionalism.

2. Elementary particles are simples.

3. There is only kind of parthood and it is timeless parthood.

4. Uniqueness of fusions: a plurality of parts composes at most one thing.

But (1)–(4) have a problem in cases where one object is transformed into another object made of the same elementary particles. For instance, perhaps, an oak tree dies and then an angel meticulously gathers together all the elementary particles the oak ever has and makes a pine out of them, which he shortly destroys before it can gain any new particles. Then the elementary particles of the oak seem to compose the pine, contrary to (4).

One common solution for four-dimensionalists is to deny (2). Elementary particles have temporal parts, and you can’t make the old temporal parts of the oak’s particles live again in the pine. But there are problems with this solution. First, you might believe in a patchwork principle which should allow the old temporal parts to get re-used again. Second, it is intuitive to think that elementary particles are parts of the oak. But on the temporal part solution, this violates the transitivity of parthood, since the elementary particles will have temporal parts that outlive the oak. Third, the temporal parts of particles seem to be just as physical as the particles, and you might think that it’s the job of physics and not metaphysics to tell us what physical objects there are, so positing the temporal parts steps on the physicist’s toes in a problematic way. Fourth, and I am not fully confident I understand all the ramifications here, we need some kind of primitive relation joining the temporal parts of the particle into a single particle, since otherwise we cannot distinguish the case where two electrons swap properties and positions (and thereby reverse the sign of the wavefunction) from the case where they don’t.

The second common solution is to deny (3), distinguishing parthood from an irreducible parthood-at-t, and then say that trees are merely composed-at-t from elementary particles. I find an irreducible parthood-at-t kind of mysterious, but perhaps it’s not too terrible.

I want to offer a different solution, with an unorthodox four-dimensionalist Aristotelianism. Like orthodox Aristotelianism, the unorthodox version introduces a further entity, a form. And now we deny that a tree is composed of the elementary particles. Instead, we say that a tree is composed of form and elementary particles. One minor unorthodox feature here is that we don’t distinguish the parthood of a form in a substance and the parthood of a particle in a substance: there is just one kind of parthood. The more unorthodox thing will be, however, that we allow elementary particles to outlive their substances. The resulting unorthodox four-dimensionalist Aristotelianism then allows one to accept all of (1)–(4), since the pine is no longer composed of parts that compose the oak, as the oak’s form is not a part of the pine.

But we still have to account for parthood-at-t. After all, it just is true that some electron e is a part of the oak at some but not other times. And this surely matters—it is needed to account for, say, the mass and shape of the oak at different times. How do we that? Well, we might suppose that even if in our unorthodox Aristotelianism particles can outlive their substances, they get something from the substance’s form, even if it’s not identity. Perhaps, for instance, they get their causal powers from the substance’s form. (We then still need to say something about unaffiliated particles—particles not inside a larger substance. Perhaps when a particle, considered as a bit of matter, gets expelled from a larger substance and becomes unaffiliated, it gains its own substantial form. It loses that form when it joins into a larger substance again. At any given time, it gets its causal powers from the substance’s form.) So we can say that e is a part of the oak at t if and only if e gets its causal powers from the oak’s form at t.

The Reverse Special Composition Question

Van Inwagen famously raised the Special Composition Question (SCQ): What is an informative criterion for when a proper plurality of objects composes a whole.

There is, however, the Reverse Special Composition Question (RSCQ): What is an informative criterion for when an object is composed of a proper plurality?

The SCQ seems a more fruitful question when we think of parts as prior to the whole. The RSCQ seems a more fruitful question when we think of wholes as prior to the parts.

If by parts we mean something like “integral parts”, we have a pretty quick starter option for answering the RSCQ:

1. An object is composed of a proper plurality of parts just in case it takes up more than a point of space.

I am not inclined to accept (1) because I like the possibility of extended simples, but it is a pretty neat and simple answer. Suppose that (1) is correct. Then we have a kind of simplicity argument for the thesis that the whole is prior to its parts. If the parts are prior to the whole, SCQ is a reasonable question, but doesn’t have an elegant and plausible answer (let us suppose). If the whole is prior to the parts, SCQ is not a reasonable question but RSCQ instead is, and RSCQ has an elegant and plausible answer (let us suppose). So we have some reason to accept that the whole is prior to the parts.

Continuous variation

Some arguments against restricted composition—the view that some but not all pluralities compose a whole—are based on the idea that a feature that cuts reality at the joints, such as composition, cannot be vague, and that if composition is restricted, one can have a continuous series of cases from a case of composition to a case of having lack of composition.

But now suppose I owe you ten dollars. Then there is a continuous series of cases where the amount I pay you ranges from zero to $20. The properties wrong, right and supererogatory cut nature at the joints. But as my payment moves from $9.99 to $10.00, it switches from wrong to right, and as it hits $10.01, it switches from merely right to supererogatory. So, one can have a case where the presence of joint-cutting features depends on something that varies continuously. And there is no vagueness: if I pay less than $10, I definitely wrong you; if I pay $10 or more, I definitely do right.

Modal details in Unger's argument against his existence

Unger famously argues that he doesn’t exist, by claiming a contradiction between three claims (I am quoting (1) and (2) verbatim, but simplifying (3)):

1. I exist.

2. If I exist, then I consist of many cells, but a finite number.

3. If I exist and I consist of many but a finite number of cells, then removal of the least important cell does not affect whether I exist.

Unger then says:

these three propositions form an inconsistent set. They have it that I am still here with no cells at all, even while my existence depends on cells. … One cell, more or less, will not make any difference between my being there and not. So, take one away, and I am still there. Take another away: again, no problem. But after a while there are no cells at all.

But taken literally this is logically invalid. Premise (2) says that I consist of many but a finite number of cells. But to continue applying premise (3), Unger needs that premise (2) would still be true no matter how many cells were taken away. But premise (2) does not say anything about hypothetical situations. It says that either I don’t exist, or I consist of a large but finite number of cells. In particular, there are no modal operators in (2).

Now, no doubt this is an uncharitable objection. Presumably (2) is not just supposed to be true in the actual situation, but in the hypothetical situations that come from repeated cell-removals. At the same time, we don’t want (2) to be ad hoc designed for this argument. So, probably, what is going on is that there is an implied necessity operator in (2), so that we have:

4. Necessarily, if I exist, then I consist of many cells, but a finite number.

The same issue applies to (3), since (3) needs to be applied over and over in hypothetical situations. Another issue with (3) is that to apply it over and over, we need to be told that removal of the cell is possible. So now we should say:

5. Necessarily, if I exist and I consist of many but a finite number of cells, then removal of the least important cell is possible and does not affect whether I exist.

Now, I guess, we can have a valid argument in S4.

Is this a merely technical issue here? I am not sure. I think that once we’ve inserted “Necessarily” into (4) and (5), our intuitions may start to shift. While (2) is very plausible if we grant the implied materialism, (4) makes us wonder whether there couldn’t be weird situations where I exist but don’t consist of many but a finite number of cells. First, it’s not obviously metaphysically impossible for me to grow an infinitely long tail? That, however, is a red herring. The argument can be retooled only to suppose that I necessarily have many cells and I actually have a finite number. But, second, and more seriously, is it really true that there is no possible world where I exist with only a few cells? In fact, perhaps, I once did exist with only a few cells in this world!

Similarly about (5). It’s clear that right now I can survive the loss of my least important cell. But it is far from clear that this is a necessary truth. It could well be metaphysically possible that I be reduced to some state of non-redundancy where every cell is necessary for my existence, where removal of any cell severs an organic pathway essential to life. I would be in a very different state in such a case than I am right now. But it’s far from clear that this is impossible.

Perhaps, though, the modality here isn’t metaphysical modality, but something like nomic modality. Maybe it’s nomically impossible for me to be in a state where every cell is non-redundant. Maybe, but even that’s not clear. And it’s also harder to say that the removal of the least important cell has to (in the nomic necessity sense) be nomically possible. Couldn’t it be that nomically the only way the least important cell could be removed would be by cutting into me in ways that would kill me?

Furthermore, once we’ve made our modal complications to the argument, it becomes clear that of the three contradictory premises (1), (4) and (5), premise (1) is by far the most probable. Premise (1) is a claim about my own existence, which seems pretty evident to me, and is only a claim about how things actually are now. Premises (4) and (5) depend on difficult modal details, on how things are in other worlds, and on metaphysical intuitions that are surely more fraught than those in the cogito.

(One of the things I’ve discovered by teaching metaphysics to undergraduates, with a focus on formulating logically valid arguments, is that sometimes numbered arguments in published work by smart people are actually quite some distance from validity, and it’s hard to see exactly how to make them valid without modal logic.)

Tables and organisms

A common-sense response to Eddington’s two table problem is that a table just is composed of molecules. This leads to difficult questions of exactly which molecules it is composed of. I assume that at table boundaries, molecules fly off all the time (that’s why one can smell a wooden table!).

But I think we could have an ontology of tables where we deny that tables are composed of molecules. Instead, we simply say that tables are grounded in the global wavefunction of the universe. We then deny precise localization for tables, recognizing that nothing is localized in our quantum universe. There is some approximate shape of the table, but this shape should not be understood as precise—there is no such thing as “the set of spacetime points occupied by the table”, unless perhaps we mean something truly vast (since the tails of wavefunctions spread out very far very fast).

That said, I don’t believe in tables, so I don’t have skin in the game.

But I do believe in organisms. Similar issues come up for organisms as for tables, except that organisms (I think) also have forms or souls. So I wouldn’t want to even initially say that organisms are composed of molecules, but that organisms are partly composed of molecules (and partly of form). That still generates the same problem of which exact molecules they are composed of. And in a quantum universe where there are no sharp facts about particle number, there probably is no hope for a good answer to that question.

So maybe it would be better to say that organisms are not even partly composed of molecules, but are instead partly grounded in the global wavefunction of the universe, and partly in the form. The form delineates which aspects of the global wavefunction are relevant to the organism in question.

What plurals are there?

Plural quantification is meant to be a logical way of avoiding some technical and/or conceptual difficulties with sets and second-order quantification. Instead of quantifying over one thing, one quantifies over pluralities. Thus, a theist might say: For all xs, God thinks of the xs in their interrelationship.

What plurals are there? Intuitively, for any finite list of objects, there is a plurality of precisely those objects. After all, we can easily have a sentence about any finite plurality of things we have names for: Alice, Bob and Carl like each other. But what furthe pluralities are there?

An expansive proposal is plural comprehension: the axiom schema that says that for any formula F with free variables that include y, for any values of the free variables other than y, there are xs such that y is one of the xs iff F. Unlike the comprehension schema in naive set theory, there does not seem to be any direct Russell-type paradox for plural comprehension, because the xs are not in general an object, but multiple objects.

But plural comprehension on its own does not seem to quite settle what plurals there are. Suppose we have a plurality of nonempty disjoint sets. We can for instance ask: Is there a plurality of objects that includes exactly one object from each of these sets? If (a) there is a set of these disjoint sets, and (b) the Axiom of Choice holds for sets, then the answer is affirmative by plural comprehension. But of course whether the Axiom of Choice holds for sets is itself not philosophically settled, and further not every plurality of sets is such that there is a set of the sets in the plurality.

Observations of this sort show that plural quantification is not as metaphysically innocent as it may seem. You might have hoped that there is no further metaphysical commitment in allowing for plural quantification than in singular quantification. But we can now have substantive questions about what pluralities there are even after we have fixed what singular objects there are, even if we assume plural comprehension. For instance, suppose we think that the objects are the physical objects of the world plus the elements of a model of ZF set theory with ur-elements and with the negation of the Axiom of Choice. We can know what all the objects are, and it still not be decided what pluralities there are. For in the case of a set of disjoint nonempty sets that lacks a choice set, as far as I can tell, there still might be a "choice plurality" (a plurality that has exactly one object from each of the disjoint sets) or there might not be one. (And if you say, well, the Axiom of Choice is obviously true, I may try to come back with a similar issue regarding Choice for proper classes.)

Or I might make a similar point about the Continuum Hypothesis (CH). The following story seems quite coherent. Every uncountable subset of the real numbers is in a bijection with the set of reals (i.e., CH is true), but there is an uncountable plurality of real numbers not in bijection with the plurality of reals. (It's easy to define bijections of pluralities in terms of pluralities of pairs.) But it's also coherent that CH is true, but there is no such uncountable plurality of reals--i.e., that CH is true for sets but its analogue for pluralities is false.

We might try to get out of this by insisting that, necessarily, the right set theory has to have a stronger version of the Schema of Separation that allows for formulas free plural variables and for the plural-membership relation. But that's conceding that the theory of pluralities is metaphysically non-innocent, because now what pluralities there are will constrain what objects there are!

So the question of what restrictions we put on plurals is a really substantive question.

Next note that following point. There seem to be two particularly simple and non-arbitrary answers to the Special Composition Question which asks which pluralities compose a whole: nihilism (there are no non-trivial cases of composition) and universalism (every plurality composes a whole). But once we have realized that it is a substantive question what pluralities there are, it seems that what objects there are and affirming universalism, even with mereological essential thrown in, doesn't settle the question of what wholes there are. There is substantial metaphysics to be done to figure out what pluralities there are!

I say the above with a caution: there are various technicalities I am glossing over, and I wouldn't be surprised if some of them turned out to be really important.

What has form?

On the question of what has a substantial form, I have tended to think something similar to van Inwagen’s answer to the question of what wholes there are. Namely, I assign form to:

1. organisms, and

2. fundamental objects in physics that are good candidates for being substances.

Regarding 2, if the correct physics is particle-based (which I doubt, in light of the apparent possibility of the world being in a superposition of states with different numbers of particles), these will be particles, or at least those particles that aren’t part of an organism. If the correct physics is field-based, the substances in physics will be fields (or maybe just one field-like object, namely “the global wavefunction”).

A lot of Aristotelians have substances, with forms, that are intermediate between (1) and (2), such as hydrogen atoms or water molecules or chunks of iron, and maybe astronomical objects like stars or galaxies. While I don’t have a knock-down argument against such substances, I also don’t see any reason to posit them.

My reasons for positing form for organisms and fundamental physical objects are quite different. For organisms, the reasons are largely normative. Parrots and oak trees can flourish or languish; they have ends and proper functions. In the case of humans, the normativity extends much further. Furthermore, we need well-defined boundaries for organisms for ethical reasons—there is reason not to harm an organism, especially but not only a human one—and there need to be well-defined persistence conditions for humans for moral responsibility. Something needs to ground all this. And the best candidate is form.

It is a central commitment of Aristotelianism that all of physical reality is grounded in physical substances and their accidents. But it is false that all of physical reality is grounded in organisms. There was a time when the physical universe had no organisms. So we need other substances. The fundamental objects of physics are the best candidates. They are active and have very clear kind-boundaries. The electromagnetic field is a different kind of thing from the gravitational field (which is just spacetime, according to Einstein). Photons are clearly different from electrons. (Though if it turns out that particle number is indeterminate, then particles won’t be the fundamental objects of physics.)

Granted, it is not obvious (and somewhat counterintuitive) that organisms have well-defined kind-boundaries and identity conditions. And it is not obvious (and somewhat counterintuitive) that fundamental physical objects have norms. But here I just take these to be consequences of the theory. Organisms have well-defined kind-boundaries and identity conditions, but we don’t know where they lie. Fundamental physical objects have normative properties, but I suspect they are perfect instances of their kind, and always do exactly what they should (C. S. Lewis says something like that in Mere Christianity).

Neither of my two reasons applies much to objects like atoms, molecules, chunks of stuff, or astronomical objects. There is no strong independent reason to suppose that they have normative properties in their own right, and their boundaries are, if not quite as fuzzy as those of organisms, pretty fuzzy. How far apart do I get to move a hydrogen atom from two oxygen atoms before I destroy a water molecule? How many sodium and chloride ions do I add to water to change it from water with impurities to a salt solution? (I suppose the concept of impurity pulls in the direction of thinking there are normative properties. But here is a reason to think this is mistaken. If impure water is languishing, then we have reason to distill water independently of any practical benefit to any organism, just for the sake of the water itself. That seems absurd.)

That the reasons don’t apply doesn’t show that there aren’t other reasons to posit substantial forms for these other candidates. But I don’t see such reasons. And so we can apply Ockham’s razor.

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.

Top-down mereology and the special and general composition questions

Van Inwagen distinguishes the General Composition Question:

• (GCQ) What are the nonmereological necessary and sufficient conditions for the xs to compose y?

from the Special Composition Question:

• (SCQ) What are the nonmereological necessary and sufficient conditions for the xs to compose something?

He thinks that the GCQ is probably unanswerable, but attempts to give an answer to the SCQ. Note that an answer to the GCQ immediately yields an answer to the SCQ by existential quantification over y.

There are two main families of mereological theories:

• Bottom-Up: The proper parts explain the whole.

• Top-Down: The whole explains the proper parts.

Van Inwagen generally eschews talk of explanation, but the spirit of his work is in the bottom-up camp.

It’s interesting to ask how the GCQ and SCQ look to theorists in the top-down camp. On top-down theories, the xs that compose y are explained by or identical to y. It seems unlikely to suppose that in all cases there would be some relation among the xs that does not involve y which marks the xs out as all parts of one whole. That would be like thinking there is a necessary and sufficient condition for Alice, Bob and Carl to be siblings that makes no reference to a parent. Therefore, it is likely that any top-down answer to the SCQ must make reference to the whole that is composed of the xs. But if we can give such an answer, then it is very likely that we can also give an answer to the GCQ.

If my plausible reasoning is right, then on top-down theories either:

1. An answer can be given to the GCQ, or

2. No answer can be given to the SCQ.

The General Composition Question

Peter van Inwagen distinguishes the General Composition Question (GCQ), which is to give necessary and sufficient conditions for the claim that the xs compose y without mereological vocabulary, from the Special Composition Question (SCQ), which is to give non-mereological necessary and sufficient conditions for the claim that there is a y such that the xs compose y again without mereological vocabulary. He thinks that he can answer the SCQ as:

1. The xs compose something iff there is exactly one x or the activity of the xs constitutes a life.

But he doesn’t try to give an answer to the GCQ, and suspects an answer can’t be given.

It is now seeming to me that van Inwagen should give a parallel answer to GCQ as well:

2. The x compose y iff the xs compose* y.

3. The xs compose* y iff every one of the xs is a part* of y and everything that overlaps* y overlaps* at least one of the xs.

4. x overlaps* y iff x and y have a part* in common.

5. x is a part* of y iff x = y or x’s activity constitutes engagement in the life of y.

Here, (3) and (4) mirror the standard mereological definition of composition and overlap, but with asterisks added. The asterisked concepts, however, bottom out in non-mereological concepts.

One might worry that constitution is a mereological concept. But if it is, then van Inwagen’s answer to the SCQ is also unsatisfactory because it uses constitution.

I feel that (2)–(5) might have some simple counterexample, but I can’t see one (or at least not one that isn't also a counterexample to van Inwagen's answer to the SCQ).

By the way, there is a cheekier answer to the GCQ:

6. The xs compose y iff the xs and y satisfy the predicate “composes” of the actual world’s late 20th century philosophical English language.

Note that here the response does not make any use of mereological vocabulary, since “‘composes’” (unlike “composes”) is not a piece of mereological vocabulary, but a piece of metalinguistic vocabulary.

The composition of a substance

Start with this plausible observation:

1. Any part of me either is an accident of me or has an accident.

For consider this: my corporeal parts all have accidents of size, shape, color, etc. And my non-corporeal parts are my soul or form, as well as my accidents. My soul has accidents: such as the accident of thinking about this or that. And my accidents are my accidents.

Now, add this plausible thesis:

2. Any accident of a part of me is identical with an accident of me.

Thus, my arm’s being tanned is identical with my being tanned-in-the-arm. Further:

3. An accident of a thing is a part of that thing.

Given 1-3, we conclude the following:

4. Any part of me has at least one accident of me as a part.

For suppose that x is a part of me. Then by (1), x is an accident of me or has an accident. If x is an accident of me, then x has an accident of me, namely x itself, as an improper part. If x has an accident y, then y is a part of x by (3) and identical with an accident of me by (2), so once again x has an accident of me as a part.

Now the standard definition of composition is:

5. The xs compose y if and only if every part z of y has a part in common with at least one of the xs.

It follows from (4) and (5) that:

6. I am composed of my accidents.

For every part of me has one of my accidents as a part by (4), and that accident is of course an improper part of one of my accidents.

But (6) seems really wrong!

Thomas Aquinas has a nice way out of (6). One of my parts is my esse, my act of being, and my esse has no proper parts, and no parts in common with any of my accidents. If Aquinas is right, then it seems (4) needs to be modified to:

7. Any part of me is either my esse or has at least one accident of me as a part.

Replacing (4) with (7) in the argument, we get:

8. I am composed of my esse and my accidents.

But that seems wrong, too. For the omission of form is really glaring.

One could get out of (8) if one supposed that my form has its own esse as a part of it. But that doesn’t seem right.

My own view is that (8) may actually be correct if we stipulate “compose” to be defined by (5). But what that points to is the idea that “compose” is not rightly defined by (5).

A technical problem for organicism

Van Inwagen’s account of composition is that

1. the xs compose a whole if and only if their activity constitutes a life.

Here is a possible problem that just occurred to me. Let x₁ be me and let x₂ be one of my particles. Then x₁ and x₂ compose me.

Now when a plurality of things have an activity, that activity is a joint activity. However, just as it is ridiculous to say that I and my right leg have walking as a joint activity, it seems incorrect to say that I and my particle have a joint activity that constitutes a life. Thus, it seems incorrect to say that x₁ and x₂ have an activity that constitutes a life. Of course, x₁ by itself has an activity ϕ that constitutes a life, and x₂ participates in ϕ. But given that ϕ is the activity of x₁ by itself, it seems incorrect to say that ϕ is a joint activity of x₁ and x₂.

One might try to define a more technical concept of engaging in an activity that implies that whenever x₁ engages in an activity ϕ with the help of a part x₂, that always counts as x₁ and x₂ engaging in ϕ. Here is an attempt:

2. The xs engage in an activity ϕ if and only if each of the xs contributes to ϕ and together they accomplish all of ϕ.

But it seems wrong to say that I and my particle x₂ together accomplish a life. That would once again sound like we have a joint activity, which we don’t.

This is better:

3. The xs engage in an activity ϕ if and only if each of the xs contributes to ϕ and anything that is a part of something that contributes to ϕ overlaps one of the xs.

But this falls afoul of van Inwagen’s requirement that an answer to the special composition question make no reference to mereological concepts like parthood or overlap.

But perhaps I am needlessly fastidious about the use of language. Maybe I and my heart, or I and my topmost particle, do engage in life. We do sometimes use this locution about a government body: "x, with y at the helm, ϕed." Maybe if that's true, we can say that "x and y ϕed", despite y being a part of x. But it still sounds wrong.

If presentism is true, materialism is false

1. If the xs compose y, then y cannot have caused all of the xs.

2. I caused all my present cells.

3. If presentism is true, then all my cells are present cells.

4. So, if presentism is true, then I caused all my cells. (2, 3)

5. If materialism is true, then I am composed of my cells.

6. If materialism is true, then I did not cause all of my cells. (1, 5)

7. So, if presentism is true, materialism is not true. (4, 6)

Van Inwagen's ear

Van Inwagen holds that:

1. All and only things whose activity constitutes a life (properly) compose a whole.

2. Whether a plurality of things composes a whole depends only on their internal relations.

He considers a counterexample to (1) and (2) of the following sort. Let the xs be the particles in van Inwagen outside the right ear.

3. If van Inwagen were to have lost the right ear, the activity of the xs would have constituted a life (his life) and composed a whole (namely, van Inwagen).

4. But in fact, the activity of the xs does not constitute a life, but only partly does so, along with the activity of the right ear particles.

5. However, the internal relations between the xs were he to have lost his right ear would have been the same as they are now.

This is a problem: for by (4) and (1), the xs do not compose a whole, but by (3) they would have had he lost his right ear, and by (5) they would have had the same internal relations then, which contradicts (2).

Van Inwagen attempts to escape this problem by denying (5), saying that the internal relations between the particles in his body in the vicinity of the right ear would be affected by the ear not being there. For they would no longer experience forces from the ear particles.

But let d be the closest distance between a right-ear particle and a van Inwagen particle not in the right ear (i.e., one of the xs). But now if God were to suddenly annihilate the right ear, then it seems that none of the xs would be in any way affected until influences traveling at the speed of light could bridge the distance d. I.e., until d/c (where c is the speed of light) had passed, the xs would be without the ear just as they are with the ear. Hence, if we specify that the time of severance in (3) is less than d/c ago, van Inwagen’s response seems to fail.

One might try to get out of this by invoking (non-Bohmian) quantum mechanics, and saying that all particles have fuzzy positions, and the ear particles overlap positionally with the non-ear particles, so that the disappearance of the ear particles affects the non-ear particles instantly. But the instant part of the effect is slight. We can imagine that the disappearance of the ear is so orchestrated as to never split any molecules or atoms. But particles in different molecules are fairly localized to their respective molecules, and the effect of the tails of the wavefunction on what is going on in a neighboring molecule will presumably be negligible.

Of course, a negligible effect is still an effect. But we could imagine a third scenario: van Inwagen loses his ear, and God miraculously tweaks the movements of the xs in a slight and biologically negligible way during the d/c period so that they behave just as they do in the actual world where the ear is attached. In that scenario, the xs would compose van Inwagen, but they would have exactly the same internal relations as they do in the actual world.

Artifacts and non-naturalism

One of the reasons to be suspicious of artifacts is that it seems magical to think we have the power to create a new object just by thinking about things a certain way while manipulating stuff. If Bob gets some clay and exercise his fingers by randomly kneading it, he doesn’t make a sculpture or any other new object out of it. But if his identical twin Carl intends to shape the clay into a sculpture, and in doing so moves his fingers in exactly the same way that Bob did, and produces exactly the same shape, then—assuming artifacts exist—he creates a new object, a sculpture. It seems magical that our thoughts should affect what object exists in the world, even when the thoughts make no difference to our manipulation of the world.

When I discussed arguments with this in my Mid-Sized Objects graduate seminar, I found, however, that there was a lot of friendliness towards the view that, yes, we are capable of this magic, though some demurred at the word “magic”. And in particular, a student pointed out that we are in the image of a God who can create.

This has made me think that a non-naturalist can think that our thoughts have effects that are not screened by the movements of our bodies. Thus, it could well be that Carl’s thoughts causes the world to be different. For instance, on a hylomorphic view, Carl could have the power to create a scu;tural form for a piece of clay by his thoughts. Or on a variant of Markosian’s brute composition view, Carl could have the power simply to cause a new object composed of the clay.

In fact, this suggests an interesting new argument against physicalism, where physicalism is understood as the claim that all causal powers reduce to those of physics. Intuitively, the correct ontology includes more things than van Inwagen’s ontology of particles and organisms and but not all the things from the mereological universalist’s bloated ontology. In particular, intuitively, the correct ontology does include Carl’s new sculpture, but Bob hasn’t produced anything new, and hence the correct ontology seems to require a non-natural “magical” power over composition facts to be found in Carl’s (and presumably, albeit in this context unexercised, Bob’s) mind. And if our ontology is to include, as common-sense would suggest, galaxies, planets, mountains and rocks, we need powers in things to produce such objects—i.e., to ensure that their particulate parts do compose something—and these powers are not to be found in physics.

Markosian’s apparently preferred version of the brute composition view can almost accommodate this. On that version, the composition facts supervene on the arrangement of particles: there are infinitely many necessary truths that specify which arrangements of particles compose. But these necessary truths would include lots of arbitrary parameters (e.g., encoding the difference between some stones that are just lying there and a hillock). We don’t want necessary truths with arbitrary parameters. It is much better if any such arbitrary parameters are relocated to the laws of nature or, better, the causal powers of things.

Informative characterizations

It is hard to characterize an “informative characterization”. Here is an instructive illustration.

Ned Markosian in his famous brutal composition paper says that an informative, or non-trivial, characterization of when the xs compose something is one that is not synonymous with the statement that the xs compose something. But by that definition, here is a non-trivial characterization of when the xs compose something:

• water is H₂O and the xs compose something.

This statement is not synonymous with the statement that the xs compose something. Nor are the two statements provably equivalent. Nor are they a priori equivalent. But they are metaphysically necessarily equivalent.

Van Inwagen in Material Beings proceeds seemingly more restrictively. He wants a characterization of when the xs compose something that doesn’t use mereological vocabulary. But here is such a characterization:

• the xs have the property expressed by the actual world’s English phrase “compose something”.

This characterization mentions mereological vocabulary, but doesn’t use it. And if we want, we can avoid mentioning mereological vocabulary as well:

• the xs have the property referred to in the second bulleted item in this post in the actual world.

Obviously, none of these characterizations of “compose something” are informative.

Leibniz on infinite downward complexity

Leibniz famously thinks that ordinary material objects like trees and cats have parts, and these parts have parts, and so on ad infinitum. But he also thinks this is all made up of monads. Here is a tempting mental picture to have of this:

• Monads, …, submicroscopic parts, microscopic parts, macroscopic parts, ordinary objects.

with the “…” indicating infinitely many steps.

This is not Leibniz’s picture. The quickest way to see that it’s not is that organic objects at each level immediately have primary governing monads. There isn’t an infinite sequence of steps between the cat and the cat’s primary monad. The cat’s primary monad is just that, the cat’s primary monad. The cat is made up of, say, cells. Each cell has a primary monad. Again, there isn’t an infinite sequence of steps between the cat and the primary monads of the cells: there might turn out to be just two steps.

In fact, although I haven’t come across texts of Leibniz that speak to this question, I suspect that the best way to take his view is to say that for each monad and each object partly constituted by that monad, the “compositional distance” between the monad and the object is finite. And there is a good mathematical reason for this: There are no infinite chains with two ends.

If this is right, then the right way to express Leibniz’s infinite depth of complexity idea is not that there is infinite compositional distance between an ordinary object and its monads, but rather than there is no upper bound on the compositional distance between an ordinary object and its monads. For each ordinary object o and each natural number N, there is a monad m which is more than N compositional steps away from o.

Can free will be grounded in quantum mechanics?

Robert Kane famously physicalistically grounds free will in quantum events in the brain. Free choice, on Kane’s view, is constituted by rational deliberation involving conflicting motivational structures with a resolution by an indeterministic causal process—a causal process that Kane thinks is in fact physical.

Here is a problem. Suppose Kane’s view is true. But now imagine a possible world with a physics that is like our quantum physics, but where panpsychism is true. The particles are conscious, and some of them engage in libertarian free choices, with chances of choices exactly matching up with what quantum mechanics predicts. The world still has people with brains, in addition to particle-sized people. The people with brains have particles that are persons in their brains. Moreover, it turns out that those indeterministic causal processes in the brains that constitute free choice are in fact the free actions of the particle-sized people in the breains.

All of Kane’s conditions for freedom will be satisfied by the people with brains. For the only relevant difference is that the quantum-style causal processes are choice processes (of the particle people). But these processes are just as indeterministic as in our world, and it’s the indeterminism that matters.

But the actions of the brain possessors in that world wouldn’t be free, because they would be under the control of the particle people in the brains. We could even suppose, if we like, that the particle people know about brains and want to direct the big people in some particular direction.

One could add to Kane’s account the further condition that the indeterministic causal processes in the brain are not constituted by the free choices of another person. But this seems ad hoc, and it is not clear why this one particular way for the indeterministic causal processes to be constituted is forbidden while any other way for them to be constituted is acceptable. The details of how quantum indeterministic processes work, as long as they are truly indeterministic and follow the quantum statistics, should not matter for free will.

This problem applies to any physicalist account on which free choices are grounded in quantum processes.

There is a way out of the problem. One could accept a pair of Aristotelian dicta:

1. All persons are substances.

2. No substance is a part of another substance.

But it is not clear whether the acceptance of these dicta is plausible apart from the fuller Aristotelian metaphysics which holds that all substances are partially made of non-physical forms. In other words, it is not clear that acceptance of (1) and (2) can be well motivated within a physicalist metaphysics.