On two problems for non-Humean accounts of laws

There are three main views of laws:

• Humeanism: Laws are a summing up of the most important patterns in the arrangement of things in spacetime.

• Nomism: Laws are necessary relations between universals.

• Powerism: Laws are grounded in the essential powers of things.

The deficiencies of Humeanism are well known. There are also deficiencies in nomism and powerism, and I want to focus on two.

The first is that they counterintuitively imply that laws are metaphysically necessary. This is well-known.

The second is perhaps less well-known. Nomism and powerism work great for fundamental laws, and for those non-fundamental laws that are logical deductions from the fundamental laws. But there is a category of non-fundamental laws, which I will call impure laws, which are not derivable solely from the fundamental laws, but from the fundamental laws conjoined with certain facts about the arrangement of things in spacetime.

The most notorious of the impure laws is the second law of thermodynamics, that entropy tends to increase. To derive this from the fundamental laws, we need to add some fact about the initial conditions, such as that they have a low entropy. The nomic relations between universals and the essential powers of things do not yield the second law of thermodynamics unless they are combined with facts about which universals are instantiated or which things with which essential powers exist.

A less obvious example of an impure law seems to be conservation of energy. The necessary relations between universals will tell us that in interactions between things with precisely such-and-such universals energy is conserved. And it might well be that the physical things in our world only have these kinds of energy-conserving universals. But things whose universals don’t conserve energy are surely metaphysically possible, and the fact that such things don’t exist is a contingent fact, not grounded in the necessary relations between universals. Similarly, substances with causal powers that do not conserve energy are metaphysically possible, and the non-existence of such things is at best a contingent fact. Thus, to derive the law of conservation of energy, we need not only the fundamental laws grounded in relations between universals or essential powers, but we also need the contingent fact that conservation-violators don’t exist.

Finally, the special sciences (geology, biology, etc.) are surely full of impure laws. Some of them perhaps even merely local ones.

One might bite the bullet and say that the impure laws are not laws at all. But that makes the nomist and powerist accounts inadequate to how “law” gets used in science.

The Humean stands in a different position. If they can account for fundamental laws, impure laws are easy, since the additional grounding is precisely a function of patterns of arrangement. The Humean’s difficulty is with the fundamental laws.

There is a solution, and this is for the nomist and powerist to say that “law of nature” is spoken in many ways, analogically. The primary sense is the fundamental laws that the theories nicely account for. But there are also non-fundamental laws. The pure ones are logical consequences of the fundamental laws, and the impure ones are particularly important consequences of the fundamental laws conjoined with important patterns of things in nature. In other words, impure laws are to be accounted for by a hybrid of the non-Humean theory and the Humean theory.

Now let’s come back to the other difficulty: the necessity worry. I submit that our intuitions about the contingency of laws of nature are much stronger in the case of impure laws than fundamental laws or pure non-fundamental laws. It is not much of a bullet to bite to say that matching charges metaphysically cannot attract—it is quite plausible that this is explained by thevery nature of charge. It is the impure laws where contingency is most obvious: it is metaphysically possible for entropy to decrease (funnily enough, many Humeans deny this, because they define the direction of time in terms of the increase of entropy), and it is metaphysically possible for energy conservation to be violated. But on our hybrid account, the contingency of impure laws is accounted for by the Humean element in them.

Of course, we have to check whether the objections to Humeanism apply to the hybrid theory. Perhaps the most powerful objection to a Humean account of laws is that it only sums up and does not explain. But the hybrid theory can explain, because it doesn’t just sum up—it also cites some fundamental laws. Moreover, it may be the case that the patterns that need to be added to get the impure laws could be initial conditions, such as that the initial entropy is law or that no conservation-violators come into existence. But fundamental law plus initial conditions is a perfectly respectable form of explanation.

An observation about the backwards-infinity branching view of possibility

In my dissertation, I defended a causal power account of modality on which something is possible just in case either it’s actual or something can bring about a causal chain leading to its being actual. I noted at the time that unless there is a necessary first cause, this leads to an odd infinite branching view on which any possible world matches our world exactly once you get far enough back, but nonetheless every individual event is contingent, because if you go back far enough, you get a causal power to generate something else in its place. Rejecting this branching view yields a cosmological argument for a necessary being. To my surprise when I went around giving talks on the account, I found that some atheists were willing to embrace the branching view. And since then Graham Oppy has defended it, and Schmid and Malpass have cleverly used it to attack certain cosmological arguments.

I want to note a curious, and somewhat unappealing, probabilistic feature of the backwards-infinite branching view. While it is essential to the view that it be through-and-through contingentist, assuming classical probabilities can be applied to the setup, then the further back you go on a view like that, the closer it gets to fatalism.

For let S_t be a proposition describing the total state of our world at time t. Let Q_t be the conjunction of S_u for all u ≤ t: this is the total present and past at t. Here is what I mean by saying that the further back you go, the closer you get to fatalism on the backwards-infinite branching view:

1. lim_{t→− ∞} P(Q_t) = 1.

I.e., the further back we go, the less randomness there is. In our time, there are many sources of randomness, and as a result the current state of the world is extremely unlikely—it is unlikely that I would be typing this in precisely this way at precisely this time, it is unlikely that the die throws in casinos right now come out as they do, and so on. But as we go back in time, the randomness fades away, and things are more and more likely.

This is not a completely absurd consequence (see Appendix). But it is also a surprising prediction about the past, one that we would not expect in a world with physics similar to ours.

Proof of (1): Let t_n be any decreasing sequence of times going to  − ∞. Let Q be the infinite disjunction Q_t1 ∨ Q_t2 ∨ .... The backwards-infinite branching view tells us that Q is a necessary truth (because any possible world has Q_t is true for t sufficiently low). Thus, P(Q) = 1. But now observe that Q_t1 implies Q_t2 implies Q_t3 and so on. It follows from countable additivity that lim_n→∞ P(Q_tn) = P(Q) = 1.

Appendix: Above, I said that the probabilistic thesis is not absurd. Here is a specific model. Imagine a particle that on day  − n for n > 0 has probability 2⁻ⁿ of moving one meter to the left and probability 2ⁿ of moving one meter to the left, and otherwise it remains still. Suppose all these steps are independent. Then with probability one, there is a time before which the particle did not move (by the Borel-Cantelli lemma). We can coherently suppose that necessarily the particle was at position 0 if you go far enough back, and then the system models backwards-infinite branching. However, note an unappealing aspect of this model: the movement probabilities are time-dependent. The model does not seem to fit our laws of nature which are time-translation symmetric (which is why we have energy conservation by Noether’s theorem).

Do particles have a self-concept?

Of course not.

But consider this. A negatively charged substance has the power to attract other substances to itslf. Its causal power thus seems to have a centeredness, a de se character. The substance’s power somehow distinguishes between the substance itself and other things.

Put this way, Leibniz's (proto?)panpsychism doesn’t seem that far a departure from a more sedate commitment to causal powers.

Motivating panpsychism

There is something attractive about an ontology where all the properties are powers, but it seems objectionable.

First, a power is partly defined by the properties it can produce. But if these in turn are powers, then we have a vicious regress or circularity.

At the same time, mental properties do not seem to be purely powers: they seem to have a categorical qualitative character that is not captured by the power to produce something else.

What is attractive about a pure powers ontology is the conceptual simplicity, and the fact that categorical properties seem really mysterious.

There is, however, a modification we can make to a pure powers ontology that gets us out of the problem. There are two kinds of properties: powers and qualia. The mysteriousness objection does not apply to qualia, because we experience them. On this ontology, powers bottom out in the ability to produce qualia.

For this to avoid implausible anthropocentrism, we need panpsychism—only then will there be enough qualia outside of living things for the powers of fundamental physics to bottom out in. So we have an interesting motivation for panpsychism: it yields an attractive ontology for reasons that have nothing to do with the usual concerns in the philosophy of mind.

It’s worth noting that this ontology is similar to Leibniz’s. Leibniz had two kinds of properties: appetitions and perceptions. The appetitions are (deterministic) powers. Perceptions are similar to qualia, but not quite the same, because (a) perceptions need not be conscious, and (b) perceptions are always representational. Unfortunately, the representational aspect leads to a regress or circularity problem, much as the power powers ontology did, since representationality will define a perception in terms of other appetitions and perceptions.

An argument against a giant multiverse

Tariq Nazeem emailed me a really cool and simple argument against certain kinds of gigantic multiverses. I’ve tweaked the argument a little, and here it is.

Start with this, as the target of the reductio ad absurdum:

1. Every metaphysically possible kind of substance exists.

But:

2. It is metaphysically possible to have a substance that has the causal propensity to turn every colorable object red every second.

(Colorable objects are things are like trees and dogs, but not numbers, photons or electromagnetic fields.)

Well, it follows from (1) and (2) that:

3. So, there is a substance that has the causal propensity to turn every colorable object red every second.

4. So, every colorable object turns red every second.

5. But I am a colorable object that does not turn red every second. (Empirical observation)

6. Contradiction!

My initial objection to Nazeem’s argument was that in a typical philosophical giant multiverse theory, the multiverses exist in separate spacetimes. (I think Nazeem’s own target was a view where they were in a single spacetime, but that is a less common view.) But then I realized that there is nothing absurd about a substance affecting things that are not spatiotemporally connected to it—classical theists think God is like that. Substances have causal propensities that specify the types of things they affect and the circumstances in which they affect them, and there is nothing absurd about a specification of these things and circumstances that makes no reference to a spatiotemporal connection. Therefore, (2) is pretty plausible, notwithstanding the fact that the colorable objects might exist in other spacetimes than the substance making them red does.

A different objection to this argument is what to say about conflict. What if reality included a substance that constantly made everything colorable red and another substance that constantly made everything colorable blue? Would I then be red all over and blue all over at the same time? But that’s impossible.

I am not completely clear on what to say to this objection.

One thought is: So much the worse for our giant multiverse—there are metaphysically possible pairs of kinds of substances, like the constant-reddenner and the constant-bluer, that simply cannot both be exemplified.

But on the other hand, maybe the possibility of conflict suggests that when we fully specify the causal propensities of a substance, we need to specify how they would interact with other causal propensities. Thus, we might have a constant-reddener that in the absence of other color-setters turns everything red, but in the presence of a constant-bluer, turns everything purple. However, it seems metaphysically possible to also have an overriding-reddener which makes everything red notwithstanding whatever other things exist. Then there could also be an overriding-bluer which makes everything blue notwithstanding whatever other things exist. And again this refutes (1).

"In the right way"

When I was in grad school, we were taught that one should abandon all hope of solving “in the right way” problems, such as the problem of how exactly an intention has to result in an action in order for the action to be done from that intention.

I think that with a robust metaphysics of causation, the problem is soluble.

Solution 1: Causal powers have a teleology: to produce a certain effect in a certain way. That teleology is metaphysically written into the causes. The “in the right way” condition may be infinitely complex, but it has a metaphysical home: it is found in the causal power. What makes it be the case that William James’ mountaineer who intended to kill his buddy by dropping the rope, and then dropped the rope because of the nervousness resulting from the intention did not intentionally drop the rope is because the outcome of events is a mismatch to the description in the teleology of the causal powers constituting the intention.

Solution 2: It is a Thomistic maxim that the effect is the actuality of the cause qua cause. This maxim I suspect needs a qualification: the proper effect—the one that happens in the right way—is the actuality of the cause qua cause. So now we have a neat and simple criterion for when a cause C has caused an effect E in the right way: this happens precisely when E is the actuality of C qua cause. (See here for more discussion.)

I think the reason we were taught to eschew the problem of “in the right way” conditions was because of an implicit reductionistic metaphysics. If we think that the cause is just an arrangement of particles, it is hopeless to have a distinction between proper and improper effects.

Cats versus nothing

Suppose I insisted that the Big Bang happened due to a cat generating an extremely high energy hairball. You would think I’m crazy. But why is the cat theory any worse than a theory on which the Big Bang happened for no reason at all?

Granted, we haven’t ever seen such a high energy hairball coming from a cat. But we likewise haven’t seen something come from nothing.

Granted, we know something about the causal powers of cats, namely that they lack the power to originate high energy hairballs. But likewise we know about the causal power of nothing, namely that where there is nothing, there is no causal power.

However, this last response is too quick. For when we talk of the universe coming from nothing versus the universe coming from a cat, we are equivocating on “coming from”. When the atheist says the universe came from nothing, they don’t mean that nothing was something that originated the universe. Rather, they simply deny that there was something that originated the universe. Cats don’t have the power to generate universes, so universes don’t get generated by cats. Similarly, where there is nothing, there is no power to generate universes, so universes don’t get generated by nothing. But the atheist doesn’t say that the universe is generated by (a?) nothing—they simply deny that it was generated by something.

Thus, the problem with the universe coming from a cat is with the origination: cats just aren’t the sorts of things to originate universes.

I guess that’s right, but I still feel the pull of the thought that a cat comes closer to making it possible for a universe to come into being than nothingness does. After all, where there is a cat, there are some causal powers. And where there is nothing, there aren’t any.

Perhaps another way to make the argument go through is to say this: There is nothing less absurd about the universe appearing causelessly ex nihilo than there is about a cat causelessly ex nihilo gaining a universe-creating power.

Joint powers

Suppose neither Alice nor Bob has the power to budge the sofa, but together they can lift it. Causal powers belong to substances, and Alice and Bob do not compose a substance, so it seems the causal power to lift the sofa does not belong to the pair as a pair. Rather, the power must belong to the pair in virtue of the substances composing it. But how can that work?

Here is what I used to think. Causal powers come with actuation conditions. So we can say:

1. Alice has the power to lift the sofa when Bob is helping.

2. Bob has the power to lift the sofa when Alice is helping.

But now suppose both are working together. Then both causal powers’ actuation conditions are met. But when each of two causal powers for an effect E is actuated, then E is overdetermined. Thus, the sofa’s upward movement is overdetermined. But that is clearly false. So something is wrong.

Maybe we just need a better account of overdetermination? Or maybe there need to be irreducibly joint powers?

Energy conservation

On a Humean metaphysics, energy conservation implies a vast conspiracy in the arrangement of things throughout spacetime, somewhat like this:

1. Wherever there is a change in energy in one region there is a corresponding balancing change in another region.

In an Aristotelian causal powers metaphysics, energy conservation implies a fact like the following about every physical substance x:

2. Every causal power of x whose content includes an effect on the energy of one or more substances also includes a balancing reverse effect on x’s own energy.

That no physical substance simply has a power to affect the energy of another substance, without the content of that power having to include a balancing effect on one’s own energy, is deeply surprising. It is a conspiracy almost as surprising as (1).

These conspiracies strongly suggest that neither the Humean nor the Aristotelian metaphysics is the whole story about energy conservation. The conspiracies desperately call for explanation. I know of two putative explanations: an optimalist one (on which reality strives for value, and mathematically expressible patterns are a part of the value) and a theistic one. Both of these explanations, however, really do great violence to the spirit behind Humean metaphysics. But Aristotelian metaphysics with optimalism or theism explaining the conspiracy in (2) works just fine.

Of course, the problem can also be solved by a different metaphysics, one on which the behavior of objects is explained by pushy global laws. But it is harder to fit human freedom and agency into that metaphysics than into the Aristotelian one.

A pre-established harmony with genuine mind-world causation

Molinists have the ability to give a distinctive pre-established harmony account of how the exceptionless truth of deterministic laws of nature could be made compatible with libertarianism.

Here is the story. God considers possible worlds where dualistic agents have the causal power to miraculously contradict the physical laws in their free choices, but where outside of exercises of free will, there are elegant deterministic mathematical laws governing the world. Call such worlds Candidate Worlds.

God then narrows his consideration to Finalist Worlds, which are Candidate Worlds that are feasible—i.e., compatible with the Molinist conditionals—and where as it happens the agents’ free choices accord with the elegant deterministic mathematical laws that govern the rest of the world.

And then God wisely and prudently chooses one of the Finalist Worlds for actualization.

On this story, there are elegant deterministic mathematical laws of nature which are true even of the agents’ choices, but they are true of the agents’ choices because the agents freely chose as they did. The agents had the causal power to violate, say, the conservation of momentum, but in fact freely did not do so.

There is an ambiguity in the concept of “exceptionless laws”. “Exceptionless laws” could mean: laws that allow no exception (they are pushy laws that are so strong as to make no exception possible) and laws that in fact have no exception. The deterministic laws in this story are exceptionless in the sense of having no exception, which is why I am talking of their exceptionless truth rather than their exceptionless power.

In this story, there is a dual explanation of the agents’ choices. On the one hand, there is a standard libertarian story about the agents’ free causality. On the other hand, the laws have explanatory power, because God chose the Finalist Worlds because they are worlds where the laws have exceptionless truth.

The big difficulty with the above story is Molinism. Also, it is worth noting that it is metaphysically possible that there turn out not to be any (feasible) Finalist Worlds: in that scenario, God wouldn’t be able to create a world where there is freedom and elegant deterministic mathematical laws holding exceptionlessly. But for reasons similar to why many people think Transworld Depravity is unlikely to be true, I think it is unlikely that there would be no Finalist Worlds.

It is also interesting to note that there are two more views that could be plugged into the story that can do the same job: Thomism and compatibilism.

On Thomism, God can use primary causation to make agents freely choose as he desires. Then we can suppose that God surveys the same Candidate Worlds as on the Molinist story. Then he chooses Finalist Worlds as those Candidate Worlds where the agents’ free choices in fact do not contradict the mathematical laws. And then God uses primary causation to actualize one of the Finalist Worlds. Again, the agents have the power to contradict the laws, but freely choose not to exercise it.

Finally we have straightforward compatibilism. A dualist can just as easily be a compatibilist as a materialist. On this story, we skip the Candidate Worlds, and the Finalist Worlds are worlds with compatibilist agents, with a deterministic non-physical mental life, who have the power of contradict the physical laws of the world but who are mentally determined, in a way compatible with freedom, never to exercise such a power. And then God chooses one of the Finalist Worlds. The agents then are as free as any compatibilist agents.

The compatibilist version of this story is close to Leibniz’s pre-established harmony, except that it has real mind-world causation, which is a big improvement.

Of course, the non-theist can’t make any of these moves. And, alas, neither can I, since my mere foreknowledge view denies Molinism, Thomism (about free will) and compatibilism.

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.

Causal powers, imperfection, free will and divine simplicity

Here is a plausible connection between normativity and causal powers:

1. If x has a power to ϕ in C, and x is in C but does not ϕ, then x qua having that power imperfect.

2. x is imperfect simpliciter if x is imperfect qua having ϕ for some ϕ that x has in virtue of its nature.

(I think one can make biconditionals out of these.)

But here is a problem. By omnipotence, God has the power to make reality be such that there are horses and they are all green, and he has the power to make reality be such that there are horses and they are all red. And he has these powers in the same circumstance C, namely that of creation. He exercises only one of these two powers. So it seems that God is imperfect qua having at least one of these powers. But he has these powers in virtue of his omnipotence and hence in virtue of his nature. Hence it seems that God is imperfect simpliciter.

Here is my best solution. Revise 1 to:

3. If x has a power P such that P is a power to ϕ in C, and x is in C but does not successfully exercise P, then x qua having P is imperfect.

This sounds like it is equivalent to 1. After all, this seems like a necessary truth:

4. If P is a power to ϕ in C and x successfully exercises P in C, then x must ϕ.

But actually 4 need not be true. For the same entity, P, could be both a power to ϕ in C and a power to ψ in C. And if so then when the possessor of P ψs in C, that would be a successful exercise of P.

This fits really well with divine simplicity on which all of God’s causal powers are ontologically the same, and indeed are identical to God. Given that, God’s powers are always fulfilled as long as God exercises one of them. (And perhaps even ensuring that God is alone would count as an exercise of God’s creative power.)

Here is another interesting thought. When I exercise free will, I have the power to ϕ and the power to ψ where ϕing and ψing are incompatible. It seems at first sight that one of these powers is unexercised, and hence thus far I am imperfect by 1. But perhaps sometimes the power to ϕ and the power to ψ are ontologically the same entity, either my nature or a single accident of me, in virtue of which entity I can ϕ and I can ψ. If so, then either ϕing or ψing could suffice for perfection qua having that power.

And now here is a very speculative thought. When we choose between right and wrong on earth, maybe the power to choose the right and the power to choose the wrong are distinct entities. Thus, we are imperfect even if we choose the right, for the power to do the wrong is unexercised. However, this sort of imperfection is not found in heaven, because there we lack the power to choose the wrong, due to the perfection of our character. But the same question will still come up in heaven when we choose between two incompatible goods, say reciting a piece of prose or reciting a piece of verse. However, perhaps, our mind will have such a deep internal unity in heaven that our abilities to choose between the various incompatible goods will be grounded in a single entity, and so no matter what we choose, we will thus far be perfect. (Not that I think it is disastrous to admit certain kinds of imperfections in heaven, so perhaps we don’t need recourse to this.)

Emergence and the epistemological gap

After reading O’Connor and Churchill’s piece on emergence, one of my very smart undergraduate students commented that it follows from such emergentist views that one could know the mental facts from the physical facts. Here I will argue for this and discuss an unhappy consequence for the causal emergentist.

The causal emergentist thinks that mental properties are not physical, but they causally emerge from complexes of physical properties of a physical entity.

So, now, suppose that physical entity e has a causal power C to produce mental property M when it has a complex P of physical properties. This causal power C will then either be a physical or a non-physical property of e. If it is a physical property of e, then by knowing the physical properties of e, one can know that e has the causal power to produce M. And that, in turn, means M is knowable from physical properties. On the other hand, if C is non-physical, then we do not have emergence of the mental from the physical: we have emergence of the mental from the physical and non-physical. So, if we have genuine emergence of the mental from the physical, then in knowing the physical, we will know the mental.

The unhappy consequence of this is that qualia-based epistemological gap arguments against physicalism apply against causal emergence, since we could suppose M is a quale, and then knowing all about C will include knowing all about M.

Causal emergence may fare a little better with respect to zombie-type arguments. If an entity has an exact duplicate of your physical properties, it will have an exact duplicate of the physically-based causal powers, and hence it will have the causal power to make mental properties emerge. However, it is logically possible that these mental properties will in fact fail to emerge, because it is logically possible that some external causal power blocks the causal powers of the duplicate from achieving their effects. One could even imagine a whole world that is an exact physical duplicate of this one but where nobody physical has mental powers, because some non-physical entity blocks the mental-emergence powers of all the physical beings. So I guess this does some justice to zombie intuitions. But note that if the possibility-of-zombies intuition is satisfied by a non-physical entity blocking mental powers, then a dispositional functionalist could do justice to the zombie intuition by imagining a world just like this one, but where a non-physical entity changes our dispositional properties in the way of Frankfurt’s neurosurgeon. And it’s not clear that that really does justice to the zombie intuition. Maybe.

The above argument against causal emergentism supposes that knowing a cause implies knowing the range of its effects. That is correct on causal powers views of causation. It is not true on Humean views of causation. So a causal emergentist could simply adopt a Humean view of causation. It is also not true on views on which causation depends on laws of nature extrinsic to the particular things in the world. But the causal powers view is the correct one. (And it is one that O’Connor and Churchill embrace.)

What if the emergence relation is not causal in nature? Then it is still a dispositional fact about our physical entity e that it comes to have mental property M when it comes to have a complex P of physical properties. This fact seems like it should be grounded in the properties of e. These properties had better be physical, because the motivation for the theory seems to be that our non-physical properties emerge from our physical ones. And now we still have the danger that by knowing these physical grounds, one can come to know the dispositional fact, and hence come to know M. Perhaps there is a way out of this danger.

Perhaps the best way out for the emergentist, causal or not, is to acknowledge a non-emergent non-physical property in each minded entity grounding the emergence dispositions.

Of course, none of this is a problem if one is unimpressed by qualia-based epistemological gap arguments.

A reductive account of parthood in terms of causal powers

Analytic philosophers like to reduce. But not much work has been done on reduction of parthood. Here’s an attempt, no doubt a failure as most reductive accounts are. But it’s worth trying.

Suppose that necessarily everything has causal powers. Then we might be able to say:

1. x is a part of y if and only if every (token) causal power of x is a causal power of y.

Some consequences:

2. Transitivity

3. Reflexivity

4. If nothing other than x shares a token causal power with x, then x is mereologically simple and does not enter into composition. Plausibly nothing shares a token causal power with God, so it follows that God is mereologically simple and does not enter into composition.

How does this work for hard cases where parthood is controversial?

Suppose I lose a leg and get a shiny green prosthesis. If the prosthesis is a part of me, then the prosthesis’ power of reflecting green light is a power I have. It seems about as hard to figure out whether the power of reflecting green light is a power that I have as it is to figure out whether the prosthesis is a part of me. So here it is of little help.

Suppose I am plugged into a room-size heart-lung machine. Is the machine a part of me? Well, the machine has the power of crushing people by its weight. It seems intuitively right to say that by being plugged into that machine, I have not acquired the power of crushing people. So it seems that it’s not a part of me.

Is a fetus a part of the mother? Here, maybe the story is some help. The fetus eventually acquires certain powers of consciousness. These do not seem to be powers of the mother—she can be conscious while the fetus is awake. So, once consciousness is acquired, the fetus is not a part of the mother. But earlier, the fetus as the power to acquire these instances of consciousness, and the mother does not seem to, so earlier, too, the fetus does not seem to be a part of the mother. Here the story is of some help, maybe.

However, one doesn’t need all of (1) for some of the applications. The “only if” part of in (1) is sufficient for the heart-lung machine and pregnancy cases.

Zero chance events

A standard thing in the philosophy of science to say such stochastic explanation questions is that one can given an answer in terms of the objective chance of the event, even when these chances are less than 1/2.

But consider the question: Why did this atom decay exactly at t₁?

Here, the objective chance may well be zero. And surely that an event had zero chance of happening does nothing to explain the event. After all, that the decay at t₁ had zero chance does not distinguish the atom’s decaying at t₁ from the atom’s turning into a square circle at t₁. And to explain something we minimally need to say something that distinguishes it from an impossibility.

Here, I think, the causal powers theorist can say something (even though I may just want to reject the presuppositions; see the Response to Objection 2, below). Stochastic systems have a plurality of causal powers for incompatible outcomes. The electron in a mixed-spin state may have both a causal power to have its spin measured as up and to have its spin measured as done. Normally, some of the causal powers are apt to prevail more than others, and hence have a greater chance than others. But even the weaker causal powers are there, and we can explain the event by citing them. The electron’s spin was measured as, say, up because it had a causal power to that outcome; had it been measured as, say, down, that would have been because it had a causal power to that outcome. We can give further detail here: we can say that one of these causal powers is stronger than the other. And the stronger causal power has, because it is stronger, a higher chance of prevailing. But even the weaker causal power can prevail, and when it does, we can explain the outcome in terms of it.

This story works just fine even when the chances are zero. The weaker causal power could be so weak that the chance associated with it has to be quantified as zero. But we can still explain the activation of the weaker causal power.

So, going back to the decay, we can say that the atom had a causal power to decay at t₁, and that’s why it decayed at t₁. That causal power was of minimal strength, and so the chance of the decay has to be quantified as zero. But we still have an explanation.

The causal powers story about the atom encodes information that the chances do not. The chances do not distinguish the atom’s turning into a square circle from the atom’s decaying exactly at t₁. The causal powers do, since it has a power to decay but no power to turn into a square circle.

Objection 1: Let’s say that the atom has twice as high a chance of decaying over the interval of times [0, 2] as over the interval of times [0, 1]. How do we explain that in terms of causal powers, given that there are equally many (i.e., continuum many) causal powers to decay at precise times in [0, 2] as there are causal powers to decay at precise times in [0, 1]?

Response: It could be that just as the causal power story carries information the chance story does not, the chance story could carry information the causal power story does not, and both stories reflect aspects of reality.

Another story could be that there are causal powers associated with intervals as well as points of times, and the causal power to decay at a time [0, 2] is twice as strong as the causal power to decay at a time in [0, 1]. There are difficulties here, however, with thinking about the fundamentality relations between the powers associated with different intervals. I fear that there is no avoiding an infinite sequence of causal powers that violates causal finitism, and I am inclined to reject the possibility of exact decay times—and hence reject the explanatory question I started this post with. I don’t see much hope for a measurement of an exact time after all. But someone with other commitments about finitism could have a story.

Objection 2: This is just like a dormitive power explanation of opium making someone sleepy.

Response: Opium’s dormitive power is fundamental or not. If opium has a fundamental dormitive power, then the dormitive power explanation is perfectly fine. That’s just the kind of explanation we have to have at the fundamental level. If the dormitive power explanation is not fundamental, then the explanation is correct but not as informative as an explanation in terms of more fundamental things would be.

Likewise, the power to decay at t₁ either is or is not fundamental. If it is fundamental, then the explanation in terms of the power is perfectly fine. If it is not, then there is a more fundamental explanation. But probably the more fundamental explanation will also involve minimal strength powers with zero activation chances, too.

A serious difficulty for some powers accounts of modality

On my causal powers account of modality, p is possible provided that either p is true, or something has an nth order power to make p true for some n. Here, a first order power to make p true is just a power to make p true. A second order power to make p true is a power to make there be a first order power to make p true. A third order power to make p true is a power to make there be a second order power to make p true. And so on.

Here's a serious problem. It seems quite possible that there is a sequence of false propositions p₁,p₂,p₃,... with the following properties:

1. It is possible that all the propositions are true.
2. For each n, something has an nth order power to make p_n true, but nothing has a lower order power to do so.

Now, let P be the proposition that all the p_n are true. Then P is false. But for every n it is true that nothing has an nth order power to make P true, as nothing has an nth order power to make p_n+1 true.

For concreteness, we might suppose that there are infinitely many planets, and on the nth planet there is a fertile asexually reproducing person x_n who has no children. Let p_n be the proposition that x_n has nth level descendants (where first level descendants are children, second level descendants are grandchildren, and so on).

What should I do? I can think of one option I don't like and two I can live with.

The option I don't like is to adopt strong assumptions about the nature of time that rule out the above story, such as an open future view plus discreteness assumptions.

The two I can live with both involve my scrapping the nth order power stuff. The first option is to make my thesis more modest: causal powers are the ground of metaphysical possibility, but I eschew giving an account of metaphysical modality in terms of causal powers. Then I can say that the possibility of P is grounded in powers, without giving a specific account. This is unattractive because it's unambitious.

The second option I can live with is to say that a thing can have a causal power to produce an effect even when it cannot directly produce the effect. Thus, I not only have a causal power to have children, but a causal power to have grandchildren. Then in the infinitely many planets scenario, the childless people jointly have a power to make P true. This seems to be the best option, but I really liked the iterated account.

Causation in the right way and actualization of causal powers

Consider William James' murderous mountaineer. His buddy is hanging on a rope that our antihero is holding, and our antihero decides to murder him by letting go. The thought of what he's about to do makes him so nervous that his hands start shaking and let go of the rope. The intention, and by extension the reasons behind the intention, caused the murderous mountaineer to let go, just as he intended to. But although the reasons and the intention cause the letting go, he didn't intentionally let go and his letting go wasn't done for a reason, though it was because of a reason.

This is a famous example where we need the idea of "causation in the right way". Not every intention that causes an action according with intention causes it in the right way, in the way that makes the action intentional. The problem of having to add a "non-aberrancy" or "in the right way" condition plagues a lot of philosophy. A usual thought about such cases is that there is a messy story, beyond our ability to specify all the details. Perhaps that story includes various messy exceptions for various kinds of accidentality, or perhaps it has fairly onerous conditions on the details of the causal chain.

But what if in some--it's too much to hope that in all--cases instead of a long and messy story, we just have a bit of irreducible (or relatively so?) metaphysics. It's just a metaphysical feature of some instances of causation that they are intrinsically non-aberrant.

How could that be? Think of a causal power for an effect as something that can be actualized partially or completely. When a causal power is actualized completely, that causal power automatically causes its actualization, and everything constitutive of that actualization, in the right way. When it fails to actualize completely, it falls short of causing in the right way, though perhaps we can say something more (here's one place serious work would need to be done) about the degree of aberrancy in its partial causes.

It's a medieval dictum that causes contain their effects. But that needs qualification. Causes in a sense contain their proper effects. They contain those proper effects as telê, and then some aspect of the effect--perhaps with cooperation or thwarting from other causes--just is an actualization of the cause with that telos. When all goes well, the whole of the teleologically specified effect is an actualization of the cause, but in aberrant cases, very little is. For instance, in the case of the murderous mountaineer, thinking about how to drop the buddy is an actualization of the intention, but the dropping of the rope is not. There is no further messy reductive story. The one event just is an actualization of the causal power and the other just is not.

But there is something incredible about this story. Sam leaves money for her grandchildren invested wisely in some investments locked up for twenty years after her death. All goes according to plan: the investments rise in value and eventually enrich her grandchildren. But how could the enriching of her grandchildren twenty years after her death somehow have as an irreducible feature its being the actualization of her intention? (Quick thought: It'd be very hard to get a presentist story about this. But presentism is false.) By the time the enrichment happens, her intention is long past. (Does it matter that it's long past? Probably not, but the story is more vivid then.)

There are, I think, three things I can say about the incredulity objection. First, I could bite the bullet. Her intention in some sense lives on in the effects. Yes, these intended effects in the future really just are actualizations of her intention. That's just a metaphysical feature of them. This isn't all that crazy if one believes in the essentiality of origins. For if one believes in the essentiality of origins, then the enrichment's having this cause is an essential feature of the enrichment. Somehow this makes it less surprising if in fact the enrichment is an actualization (or part of the actualization) of the intention. We could even think that the very being of an effect is its having-been-caused.

Second, we could say that when x causes y in the right way, then being-an-actualization-of-x is an intrinsic feature of y, a feature that is causally involved in everything y does, and so when y causes z in the right way, z has the intrinsic feature of being-an-actualization-of-y, and we can go back down the chain to x. Perhaps this is what Aquinas means by per se ordered causal series.

Third, I could go the road of caution. I could say that this metaphysical "actualized by x" feature only is found in immediate effects. Thus, we would in the first instance only have a story about causation-in-the-right way for immediate effects. And then we would use this feature to help construct messier account of causation in the right way for remote effects.

All of this, though, requires a fairly non-reductive metaphysics of human beings.

A world abuzz in activity

I sometimes think that the phrase "causal power" doesn't quite convey what the causal powers theorist means or should mean. When I hear the phrase, it makes me think of a mere potentiality, a disposition which needs separate activation. But this is a mistaken image.

A causal power should be seen as active. It is a striving, a conatus. I lie on a bed typing this post. The elasticity of the springs strives to lift me up. The gravitation attraction between my body and the earth strives to press me down. There is not much motion, as the forces have balanced out, but both forces are constantly active. If gravity suddenly disappeared, the bed's springs would eject my upward, and if the springs suddenly disappeared, I would slump down.

The world is abuzz in activity. It trembles with action. Objects strive in various directions in their causal powers, pulling hither and yon (cf. Amjum and Mumford).

Aristotle talks of two levels of potentiality. I am in first potentiality for speaking German—I would have to learn it in order to speak it—and in second potentiality for speaking English—I can do it whenever I wish to. Second potentiality is also first actuality—the general human potential for speaking languages is realized in me in respect of English. And then there is second actuality—I am now in second actuality for writing in English. So we have a three point scale of actuality:

1. first potentiality
2. second potentiality = first actuality
3. second actuality.

Having a causal power, a conatus or a striving is something intermediate between the first and second actuality. When unopposed, the causal power causes second actuality—actual action. When opposed, we just have a tense striving, a pull.

The world, both physical and mental, is a world of tension. Forces push against forces, reasons push against reasons. Or, more precisely, substances with forces or reasons push against the same or other substances with opposed forces or reasons.

Sometimes an image helps develop good metaphysics. That's all the above is: an image.

Possibility, probability and propensity

I have defended at length the idea that metaphysical possibility is grounded in the causal powers of things. It just occurred to me that this view is very naturally connected to the view that objective probability is grounded in causal propensities. We can think of probability as a measure of the degree of possibility, and of possibility as an attenuated kind of probability. If we see things in this very natural way—and hopefully its naturalness isn't just due to alliteration—then we have a unified and mutually supporting story about probability and possibility. Both are grounded in causal powers, but differently. Possibility is grounded in the bare existence of causal powers. Probability is grounded in the propensities of causal powers. If we have reason to accept one view, that tends to give us reason to accept the other.

Clearly anything that's made possible by the causal powers account of possibility—let's call this "causally possible"—is possible. So the only question about the causal powers account of possibility is whether it captures all possibilities. Suppose some things are possible but not causally possible. Then we can ask about their probabilities. If probabilities are propensities, then we should say that such things have zero probability, since nothing has a propensity to produce them. And not just the kind of "numerical zero" that classical probability assigns to a sequence of infinitely many heads, but the deep kind of zero that is had by the probability that one equals two. It's plausible, though, that things with this deep zero probability just can't happen. So the propensity account of probability neatly suggests the causal powers account of possibility.

And the converse is also plausible. If all possibilities are causal possibilities, it is very natural to measure the degree of their possibility by the causal propensities.

Of course the above is very vague. It may be that particular details of how one works out a causal powers account of possibility don't sit well with the particular details of a propensity account of objective probability.