Supervenience and counterfactuals

On typical functionalist views of mind, what mental states a physical system has depends on counterfactual connections between physical properties in that system. But we can have two worlds that are exactly the same physically—have exactly the same tapestry of physical objects, properties and relations—but differ in what counterfactual connections hold between the physical properties. To see that, just imagine that one of the two worlds is purely physical, and in that world, w₁, striking a certain match causes a fire, and:

1. Were that match not struck, there would have been no fire.

But now imagine another world, w₂, which is physically exactly the same, but there is a nonphysical spirit who wants the fire to happen, and who will miraculously cause the fire if the match is not struck. But since the match is struck, the spirit does nothing. In w₂, the counterfactual (1) is false. (This is of course just a Frankfurt case.)

Thus physicalist theories where counterfactual connections are essential are incompatible with supervenience of the mental upon the physical.

I suppose one could insist that the supervenience base has to include counterfactual facts, and not just physical facts. But this is problematic. Even in purely physical worlds, counterfactual facts are not grounded in physical facts, but in physical facts combined with the absence of spirits, ghosts, etc. And in worlds that are only partly physical, counterfactual connections between physical facts may be grounded in the dispositions of non-physical entities.

Normative powers

A normative power is a power to change a normative condition. Raz says the change is not produced “causally” but “normatively”.

Here is a picture on which this is correct. We exercise a normative power by exercising a natural power in such a context that the successful exercise of the natural power is partly constitutive of a normative fact. For instance, we utter a promise, thereby exercising a natural power to engage in a certain kind of speech act, and our exercise of that speech act is partly constitutive of, rather than causal of, the state of affairs of our being obligated to carry out the promised action.

There are two versions of the above model. On one version, there is an underlying fundamental conditional normative fact C, such as that if I have promised something then I should do it, and my exercise of normative power supplies the antecedent A of that conditional, and then the normative consequent of C comes to be grounded in C and A. On another version, there there are some natural acts that are directly constitutive of a normative state of affairs, not merely by supplying the antecedent of a conditional normative fact. I think the first version of the model is the more plausible in paradigmatic cases.

But why not allow for a causal model? Why not suppose that a normative power is a causal power to make an irreducible normative property come to be instantiated in someone? Thus, my power to promise is the power to cause myself to be obligated to do what I have promised.

I think the difficulty with a causal model is the fact that in paradigm cases of normative power, there is a natural power that is being exercised, and we have the intuition that the exercise of the natural power is necessary and sufficient for the normative effect. But on a causal model, why couldn’t I cause a promissory-type obligation without promising, simply causing the relevant property of being obligated to come to be instantiated in me? And why couldn’t I engage in the speech act while yet remaining normatively unbound, because my normative power wasn’t exercised in parallel with the natural power?

Maybe the answer to both questions is that I could, but only metaphysically and not causally. In other words, it could be that the laws of nature, or of human nature, make it impossible for me to exercise one of the powers without the other, just as I cannot wiggle my ring finger without wiggling my middle finger as well. On this view, if there is a God, he could cause me to acquire promissory-type obligations without my promising, and he could let me engage in the natural act of promising while blocking the exercise of normative power and leaving me normatively unbound. This doesn’t seem particularly problematic.

Perhaps the real problem for a lot of people with a causal view of normative powers is that it tends to lead to a violation of supervenience. For if it is metaphysically possble to have the exercise of the normative power without the exercise of the natural power, or vice versa, then it seems we don’t have supervenience of the normative on the non-normative. But supervenience does not seem to me to be inescapable.

Failures of supervenience on Lewis's system

Start with the concept of “narrowly physical” for facts about the arrangement of physical entities and first-order physical properties such as “charge” and “mass”.

Here are two observations I have not seen made:

1. On Lewis-Ramsey accounts of laws, laws of nature concerning narrowly physical facts do not supervene on narrowly physical facts.

2. On Lewis’s account of causation, causal facts about narrowly physical events do not supervene on narrowly physical facts.

This means that in a Lewisian system we have at least four things we could mean by “physical”:

3. narrowly physical

4. grounded in the laws of narrowly physical facts and/or the narrowly physical facts themselves

5. grounded in the causal facts about narrowly physical events and/or the narrowly physical facts themeselves

6. grounded in the causal facts about narrowly physical events, the laws concerning narrowly physical facts and/or the narrowly physical facts themselves.

Here’s a corollary for the philosophy of mind:

7. On a Lewisian system, we should not even expect the mental properties of purely narrowly physical beings to supervene on narrowly physical facts.

Argument for (1): The laws are the optimal systematization of particular facts. But now imagine a possible world where there is just a coin that is tossed a trillion times, and with no discernible pattern lands heads about half the time. In the best systematization, we attribute a chance of 1/2 to the coin landing heads. But now imagine a possible world with the same narrowly physical facts, but where there is an angel that thought about ℵ₃ about a million times—each time, with a good prior mental explanation of the train of thought—and each of these times was a time just before the coin landed heads. Then the best systematization of the coin tosses will no longer make them simply have a chance of 1/2 of landing heads. Rather, they will have a chance 1/2 of landing heads when the angel didn’t just think about ℵ₃.

Argument for (2): Add to the world in the above argument some cats and suppose that on any day when the fattest cat in the world eats n mice, that leads the angel to think about ℵ_n, though there are other things that can get the angel to think about ℵ_n. We can set things up so that the fattest cat’s eating three mice in a day causes the coin to land heads on the Lewisian counterfactual account of causation, but if we subtract the angel from the story, this will no longer be the case.

Naturalism and property dualism

It is generally taken that a view on which there are mental properties that do not supervene on the properties of physics is a non-naturalistic view: it is a form of property dualism.

But now imagine that we find out that:

1. There are chemical properties that do not supervene on the properties physics speaks of.

That would be a really exciting discovery, but it wouldn’t be a discovery incompatible with naturalism. The new chemical properties would presumably be just as natural as the physical ones.

So, why would we call non-supervenient mental properties non-natural, if we wouldn’t call non-supervenient chemical properties non-natural? It can’t be just because chemical properties are the province of a science, namely chemistry. For mental properties are the province of a science, too, namely psychology.

While we’re exploring this corner of logical space, consider this view:

2. Chemical properties do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, physical and chemical properties.

I’ve never met an advocate of (2). It would be a very strange view. But here is one that, I think, is not actually all that strange:

3. Biological properties do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, biological properties.

I think view (3) is worth thinking about. Most of the people who have tried to reduce the mental have tried to reduce it to the physical, but perhaps a reduction to an irreducible biological level would be more promising.

Will dogs live forever?

Suppose a dog lives forever. Assuming the dog stays roughly dog-sized, there is only a finite number of possible configurations of the dog’s matter (disregarding insignificant differences on the order of magnitude of a Planck length, say). Then, eventually, all of the dog’s matter configurations will be re-runs, as we will run out of possible new configurations. Whatever the dog is feeling, remembering or doing is something the dog has already felt, remembered or done. It will be literally impossible to teach the dog a new trick (without swelling the dog beyond normal dog size).

But a dog’s life is a material life, unlike perhaps the life of a person. Plausibly, a dog’s mental states are determined by the configuration of the dog’s (brain) matter. So, eventually, every one of the dog’s mental states will be a re-run, too.

And then we will run out of states re-run once, and the dog will only have states that are on their second or later re-run. And so on. There will come a day when whatever the dog is feeling, remembering or doing is something the dog has felt, remembered or done a billion times: and there is still eternity to go.

Moreover, we’re not just talking about momentary re-runs. Eventually, every day of the dog’s life will be an identical re-run of an earlier day of the dog’s life (at least insofar as the dog is concerned: things beyond the power of the dog’s sensory apparatus might change). And then eventually every year of the dog’s life will be a re-run of an earlier year. And then there will come a year when every coming year of the dog’s life will already have been done a billion times already.

This doesn’t strike me as a particularly flourishing life for a dog. Indeed, it strikes me that it would be a more flourishing life for the dog to cut out the nth re-runs, and have the dog’s life come to a peaceful end.

Granted, the dog won’t be bored by the re-runs. In fact, probably the dog won’t know that things are being re-run over and over. In any case, dogs don’t mind repetition. But there is still something grotesque about such a life of re-runs. That’s just not the temporal shape a dog’s life should have, much as a dog shouldn’t be cubical or pyramidal in spatial shape.

If this is right, then considerations of a dog’s well-being do not lead to the desirability of eternal life for the dog. As far as God’s love for dogs goes, we shouldn’t expect God to make the dogs live forever.

This is, of course, the swollen head argument, transposed to dogs, from naturalist accounts of humans.

But maybe God would make dogs live forever because of his love for their human friends, not because of his love for the dogs themselves? Here, I think there is a better case for eternal life for dogs. But I am still sceptical. For the humans would presumably know that from the dog’s point of view, everything is an endless re-run. The dog has already taken a walk that looked and felt just like this one a billion times, and there is an infinite number of walks that look and feel just like this one to the dog ahead. Maybe to the human they feel different: the human can think about new things each time, because naturalism is false of humans, and so differences in human mental states don’t require differences in neural states (or so those of us who believe in an eternal afterlife for humans should say). But to the dog it’s just as before. And know that on the dog’s side it’s just endless repetition would, I think, be disquieting and dissatisfying to us. It seems to me that it is not fitting for a human to be tied down for an eternity of a friendship with a finite being that eventually has nothing new to exhibit in its life.

So, I doubt that God would make dogs live forever because of his love for us, either. And the same goes for other brute animals. So, I don’t think brute animals live forever.

All this neglects Dougherty’s speculative suggestion that in the afterlife animals may be transformed, Narnia-like, so that they become persons. If he’s right, then the naturalistic supervenience assumption will be no more true for the animals than for us, and the repetition argument above against dogs living forever will fail. But the argument above will still show that we shouldn’t expect brute animals to live forever. And I am dubious of the transformation hypothesis, too.

At the same time, I want to note that I think it is not unlikely that there will be brute animals on the New Earth. But if so, I expect they will have finite lifespans. For while an upper temporal limit to the life of a human would be an evil, an upper temporal limit to the life of a brute animal seems perfectly fitting.

Supervenience and omniscience

Problem: It seems that if God necessarily exists, then the moral automatically supervenes on the non-moral. For, any two worlds that differ in moral facts also differ in what God believes about moral facts, and presumably belief facts are non-moral. This trivializes the mechanism of supervenience for theists.

Potential Solution: Divine simplicity makes God’s beliefs about God-external facts be externally constituted. Thus, a part of what makes it true that God believes that there are sheep are the sheep. If so, then perhaps a part of what makes it true that God believes a moral fact is that very moral fact. Thus, God’s beliefs about moral facts are partly constituted by the moral facts, and hence are not themselves non-moral.

Anti-reductionism and supervenience

In the philosophy of mind, those who take anti-reductionism really seriously will also reject the supervenience of the mental on the non-mental. After all, if a mental property does not reduce to the non-mental, we should be able to apply a rearrangement principle to fix the non-mental properties but change the mental one, much as one can fix the shape of an object but change its electrical charge, precisely because charge doesn’t reduce to shape or shape to charge. There might be some necessary connections, of course. Perhaps some shapes are incompatible with some charges, and perhaps similarly some mental states are incompatible with some physical arrangement. But it would be surprising, in the absence of a reduction, if fixing physical arrangement were to fix the mental state.

Yet it seems that in metaethics, even the staunchest anti-reductionists tend to want to preserve the supervenience of the normative on the non-normative. That is surprising, I think. After all, the same kind of rearrangement reasoning should apply if the normative properties do not reduce to the non-normative ones or vice versa: we should be able to fix the non-normative ones and change the normative ones at least to some degree.

Here’s something in the vicinity I’ve just been thinking about. Suppose that A-type properties supervene on B-type properties, and consider an A-type property Q. Then consider the property Q^B of being such that the nexus of all B-type properties is logically compatible with having Q. For any Q and B, having Q^B is necessary for having Q. But if Q supervenes on B-type properties, then having Q^B is also sufficient for having Q. Moreover, Q^B seems to be a B-type property in our paradigmatic cases: if B is the physical properties, then Q^B is a physical property, and if B is the non-normative properties, then Q^B is a non-normative property. (Interestingly, it is a physical or non-normative property defined in terms of mental or normative properties.)

But now isn’t it just as weird for a staunch anti-reductionist to think that there is a non-normative property that is necessary and sufficient for, say, being obligated to dance as it is for a staunch anti-reductionist to think there is a physical property that is necessary and sufficient for feeling pain?

Supervenience and natural law

The B-properties supervene on the A-properties provided that any two possible worlds with the same A-properties have the same B-properties.

It is a widely accepted constraint in metaethics that normative properties supervene on non-normative ones. Does natural law meet the contraint?

As I read natural law, the right action is one that goes along with the teleological properties of the will. Teleological properties, in turn, are normative in nature and (sometimes) fundamental. As far as I can see, it is possible to have zombie-like phenomena, where two substances look and behave in exactly the same way but different teleological properties. Thus, one could have animals that are physically indistinguishable from our world’s sheep, and in particularly have four legs, but, unlike the sheep, have the property of being normally six-legged. In other words, they would be all defective, in lacking two of their six legs.

This suggests that natural law theories depend on a metaphysics that rejects the supervenience of the normative. But I think that is too quick. For in an Aristotelian metaphysics, the teleological properties are not purely teleological. A sheep’s being naturally four-legged simultaneously explains the normative fact that a sheep should have four legs and the non-normative statistical fact that most sheep in fact have four legs. For the teleological structures are not just normative but also efficiently causal: they efficiently guide the embryonic development of the sheep, say.

In fact, on the Koons-Pruss reading of teleology, the teleological properties just are causal powers. The causal power to ϕ in circumtances C is teleological and dispositional: it is both a teleological directedness towards ϕing in C and a disposition to ϕ in C. And there is no metaphysical way of separating these aspects, as they are both features of the very same property.

Our naturally-six-but-actually-four-legged quasi-sheep, then, would differ from the actual world’s sheep in not having the same dispositions to develop quadrapedality. This seems to save supervenience, by exhibiting a difference in non-normative properties between the sheep and the quasi-sheep.

But I think it doesn’t actually save it. For the disposition to develop four (or six) legs is the same property as the teleological directedness to quadrapedality in sheep. And this property is a normative property, though not just normative. We might say this: The sheep and the quasi-sheep differ in a non-normative respect but they do not differ in a non-normative property. For the disposition is a normative property.

Perhaps this suggests that the natural lawyer should weaken the supervenience claim and talk of differences in features or respects rather than properties. That would allow one to save a version of supervenience. But notice that if we do that, we preserve supervenience but not the intuition behind it. For the intuition behind the supervenience of the normative on the non-normative is that the normative is explained by the non-normative. But on our Aristotelian metaphysics, it is the teleological properties that explain that actual non-normative behavior of things.

Brute necessities and supervenience

There is something very unappealing about unexplained, i.e., brute, metaphysical necessities that are “arbitrary”. For instance, suppose that someone said that some constant in a law of nature had the precise value it does by metaphysical necessity. If that contant were 1 or π or something like that, we could maybe buy that. But if the constant couldn’t be put in any neat way, could not be derived from deeper metaphysical necessities, but just happened necessarily to be exactly 1.847192019... (in a natural unit system) for some infinite string of digits? Nah! It would be much more satisfactory to posit a theory on which that constant has that value contingently. “Arbitrariness” of this sort is evidence of contingency, though it is a hard question exactly why.

Here is an application of this epistemic principle. It seems very likely that any view on which mental properties supervene of metaphysical necessity on physical ones will involve brute metaphysical necessities that are “arbitrary”.

For instance, consider a continuum of physical arrangements, starting with a paradigmatic healthy adult human and ending with a rock of the same mass. The adult human has conscious mental properties. The rock does not. Given metaphysically necessary supervenience, there must be a necessary truth as to where on the continuum the transition from consciousness to lack of consciousness occurs or, if there is vagueness in the transition, then there must be a necessary truth as to how the physical continuum maps to a vagueness profile. But it is very likely that any such transition point will be “arbitrary” rather than “natural”.

Or consider this. The best naturalist views make mental properties depend on computational function. But now consider how to define the computational function of something, say of a device that has two numerical inputs and one numerical output. We might say that if 99.999% of the time when given two numbers the device produces the sum of the numbers, and there is no simple formula that gives a higher degree of fit, then the computational function of the device is addition. But just how often does the device need to produce the sum of the numbers to count as an adder? Will 99.99% suffice? What about 99.9%? The reliability cut-off in defining computational function seems entirely arbitrary.

It may be that there is some supervenience theory that doesn’t involve arbitrary maps, arbitrary cut-offs, etc. But I suspect we have no idea how such a theory would go. It’s just pie in the sky.

If supervenience theories appear to require “arbitrary” stuff, then it is reasonable to infer that any supervenience is metaphysically contingent—perhaps it is only nomic supervenience.

This line of argument is plausible, but to make it strong one would need to say more about the notion of the “arbitrary” that it involves.

Relativity, simultaneity, minds and brains

This is very much a thinking-in-progress post rather than a finished argument. But I've been toying with this line of thought:

1. The simultaneity relations between conscious mental states of an ordinary human (e.g., "itching while feeling cold") are not relative to reference frame.
2. The simultaneity relations of spatially extended states of an object are relative to a reference frame.
3. If conscious mental states are identical with or wholly constituted by brain states, then they are spatially extended states.
4. So, conscious mental states of an ordinary human are neither identical with nor wholly constituted by brain states.

The restriction to ordinary people rules out cases where someone has two or more centers of consciousness at a given time (e.g., due to brain-splitting, time travel, or multiple personalities). In the case of such a non-ordinary person, we can run the argument for each center of consciousness and conclude that the center's states are not identical with or constituted by brain states.

What makes this argument tricky—and this is the part I need think more about—is that of course the relativistic effects between different bits of the brain are practically negligible. The kind of time difference that would be involved in trying to see whether I started itching before starting to feel cold or whether it was the other way around would be so minuscule that I couldn't tell the difference as to which state started earlier or whether they started simultaneously. Nonetheless, there is some plausibility in thinking that there is a fact of the matter as to which state started earlier or whether they started simultaneously. Moreover, maybe we could imagine beings with bigger and faster brains where the effects would be real--and (1) plausibly isn't just a fact about us, but about any discursive agents with a single center of consciousness.

Here's an interesting thing. Suppose that one responds to the argument by saying that there is an absolute reference frame, despite relativity theory, much as defenders of the A-theory of time hold. That response doesn't get one completely out of the argument. We can argue: the absolute frame is insignificant for physics; yet it is significant for mind; so mind doesn't reduce to physics.

I also think the argument (though perhaps not the absolute-frame variant) may lead to some problems for supervenience theories of mind. But that's for future research.

Another notion of supervenience

Say that the A-facts cs-supervene on the B-facts iff a computer simulation of the B-facts, based on the actual world's B-laws and initial conditions for B-facts, would necessarily also correctly simulate the A-facts.

Thesis: A-facts are problematic for physicalists iff A-facts do not cs-supervene on physical facts.

Corollary: There is a debate in the philosophy of biology on whether the apparent irreducibility of biological facts to physical facts is a problem for physicalism, and if not, why not. If the Thesis is true, then as long as biological facts cs-supervene on physical facts, then whether or not there is a reduction, biology does not present a problem for physicalism. I suspect that typical non-reductionist philosophers of biology would accept the cs-supervenience of the biological on the physical—for instance, they would agree that simulated natural selection would show up in the physical simulations—and hence their non-reductionism is not a problem for physicalism.

What about my argument against reductionism in biology, based on the instantaneousness of coming-into-being and the gradualness of chemical processes? I guess in the present setting the thing to say is that we wouldn't be able to tell from the computer simulation exactly when a new animal came into existence—just as we can't tell from empirical observation of the world—and so the computer simulation would not be simulating the coming into existence of animals.

A problem with the notion of cs-supervenience is the imprecision of the notion of "simulating".

The knowability paradox and supervenience

The Knowability Paradox is the surprisingly easy argument that if there are unknown truths, there are unknowable truths. Use "Kp" to mean that p is known (say, to humans). Then, suppose p is an unknown truth and let q be the proposition (p and ~Kp). Then q is true, but cannot be known, since if q were known, its first conjunct, namely p, would also be known, and both of its conjuncts would be true (since knowledge entails truth), so that we would have both Kp and ~Kp, which is absurd. For reasons I don't quite understand, some people think this is a paradox rather than just a perfectly good, and highly intuitive ("if p is an unknown truth, then that p is an unknown truth is an unknowable truth"—isn't that obvious?) argument that the existence of unknown truths entails that of unknowable ones.

Here's something less trivial—a reductio of an interesting quintuple of premises.

1. (Premise) Human epistemic states concerning natural states of the world, including knowledge of natural states of the world, supervene on natural states of the world.
2. (Premise) Every true proposition reporting only natural states of the world can be known (by humans).
3. (Premise) Some true proposition reporting only natural states of the world is not known.
4. (Premise) There is a true proposition p reporting solely natural states of the world is such that any world in which p holds is an exact duplicate of our world in respect of natural states.
5. (Premise) The conjunction of propositions reporting solely natural states of the world reports solely natural states of the world.
6. Let q be a true proposition reporting only natural states of the world that is not known. (3)
7. Let r be the conjunction of p and q. (4 and 6)
8. r is true. (4, 6 and 7)
9. r reports only natural states of the world. (4, 5, 6, 7)
10. r is knowable. (2, 8 and 9)
11. Let w be a world at which r is known. (10)
12. At w, r is true. (11: knowledge entails truth)
13. At w, p is true. (7 and 12)
14. w is an exact duplicate of the actual world in respect of natural states. (4 and 13)
15. At w, Kr. (11)
16. Actually, Kr. (1, 14, 15)
17. Therefore, Kq. (7 and 16: if a conjunction is known, so are its conjuncts)
18. Therefore Kq and ~Kq. (6 and 17)

If we take 2-5 to be very plausible, this gives us a nice argument against 1. I think there are some technical difficulties with 4. To make 4 work, a description of natural states of the world has to be able to use not only first order naturalistic vocabulary ("electrons", "equids", etc.) but also "natural", so it can, after giving a complete catalog of natural states, say: "And there are no other natural states." This reading of "reporting natural states" is not the standard, I think. This broader reading of "reporting natural states" only makes 1 and 3 more plausible, though it makes 2 a bit less plausible.

The other way to get 4 working with only first order naturalistic vocabulary is to have an infinite proposition that inter alia denies the existence of all possible natural kinds other than the ones that are exemplified. This has some problems, but can be defended (how well?).

Vagueness about existence of substances

I suspect that pressure to believe in vagueness about the existence of material substances comes from a belief that facts about the existence of material substances supervene on facts about the physical arrangement of matter in the universe. The most plausible arguments for such vagueness is questions like this: What time t₀ in the history of the union of the gametes of Bambi's parents is such that were the world annihilated at t, Bambi would not have existed? Given that the union of gametes is a physically continuous process, there seems to be an interval of time (perhaps several hours long) such that drawing a line at a particular point of that interval and asserting that it is precisely at that time that Bambi came into existence seems arbitrary.

But if one does not believe that facts about when Bambi came into existence supervene on facts about the physical arrangement of matter in Bambi's history, then an epistemic solution on which some particular point in that interval that we cannot scientifically determine exactly has the property of being such that Bambi came into existence precisely at that point is not that implausible. The fact that points slightly before and slightly t₀ would seem to be just as physically fitting for Bambi's existence is irrelevant, since Bambi's existence does not supervene on whether there is a physical state fitted out for Bambi's existence. Compare the fact that when an atom decays at t₀, it could just as easily have decayed shortly before t₀ or shortly after t₀—there is a real sense in which its decaying at t₀ rather than shortly before or after (or maybe even a long time before or after) was arbitrary (unless Providence has some special reason for t₀, which quite possibly it does). That doesn't trouble us that much, I suspect because we accept that when the atom decays is contingent. Well, likewise, if we accept that even given all the physical facts, it is contingent when Bambi comes into existence, we shouldn't be worried about the fact that nearby times are such that they would have done just as well as far as we can tell (though Providence might have some special reason for choosing one time rather than another).

The same issue comes up with regard to those like Trenton Merricks who believe in limited composition theories: some bunches of things compose a whole but not all bunches of things compose wholes. There seems to be vagueness as to composition. We can imagine a continuous sequence of hypothetical biological/physical situations, starting with what are clearly two trees and ending with what is clearly one tree (with in-between cases which, depending on whom you ask, look like two trees grown together or one tree with a bit of a divide down its trunk). It seems arbitrary to suppose that at some point in the sequence we have one tree, and very shortly before in that sequence we had two. But again, this intuition depends on a supervenience claim: the supervenience of facts about composition on facts about physical arrangement of matter. Granted such supervenience, we do seem to get arbitrariness. But why not, instead, deny supervenience, and simply say that what we get is contingency: given given a particular biological/physical arrangement of matter, there is a contingent fact whether all this matter composes a whole or not.

Of course one might worry about the Principle of Sufficient Reason (PSR) here. But if we believe in quantum mechanics (QM), then presumably we either think the PSR is compatible with QM or we deny the PSR. If we deny the PSR, then the problem that the story I gave is alleged to be incompatible with the PSR shouldn't worry us. But if we think that the PSR is compatible with QM, then I suspect that whatever story we give about the compatibility of QM and the PSR will also have an analogue here. (I defend the compatibility of QM and the PSR in my book on the PSR.) For instance, if we say that God providently chooses which otherwise random results of a quantum experiment will happen, then we can say the same here: God providently chooses when exactly Bambi comes into existence and whether there is one tree or a pair of trees. Or if we say that effects caused stochastically under probabilistic laws are not violations of the PSR, then we can say that there are probabilistic laws about the arising of substances or about composition.