We have systematic overdetermination in our movements

The causal exclusion argument requires us to deny that there is systematic overdetermination between mental and physical causes.

But it is interesting to note that in the real world there is systematic overdetermination of physical movements. Suppose I raise my arm. My muscle contraction is caused by a bunch of electrons moving in the nerves between the brain and the muscle. Suppose there are N electrons involved in the electrical flow, for some large number N. But now note that except in extremely rare marginal cases, any N − 1 of the electrons are sufficient to produce the same muscle contraction. Thus, my muscle contraction is overdetermined by at least N groups of electrons. Each of these groups differs from the original N electron group by omitting one of the electrons. And each group is sufficient to produce the effect.

One might try to defend the no-systematic-overdetermination view by saying that what doesn’t happen is systematic overdetermination by non-overlapping causes. There are two problems with this approach. First, it is not empirically clear that there isn’t systematic overdetermination by non-overlapping causes. It could turn out that typically twice as many electrons are involved in nerve impulses as are needed, in which case there are two non-overlapping groups each of which is sufficient. Second, the anti-physicalist can just say that there is overlap between the mental cause and the physical cause—the mental cause is not entirely physical, but is partially so.

Alternately, one might say that there may be systematic overdetermination of physical events by physical events, but not of physical events by physical and mental events. This would need an argument.

Overdetermining causation and prevention

Overdetermination seems to work differently for prevention and positive causation.

Suppose Timmy the turtle is wearing steel armor over his shell, because it looks cool. Alice shoots an arrow at Timmy’s back from the side, which glances off the armor. Let us assume that arrows shot at the back of an unarmored turtle from the side also harmlessly glance off the shell. Then we have two questions:

1. Did the armor prevent Timmy’s death?

2. Did the armor cause the arrow to glance off?

My intuition is that the answers are “no” and “yes”, respectively. You only count as preventing death if you are stopping something lethal. But I assumed that an arrow aimed at the back of an ordinary turtle from the side glances off the shell and is not lethal. On the other hand, it is clear that the arrow glanced off the armor, not the shell, and so it was the armor that redirected the flight.

Why the difference?

I think it may be this. There is a particular token flight-redirection event f₀ that the the armor caused. When you cause a token of a type, you automatically count as having cause an event of that type. So by causing f₀, the armor caused a flight-redirection event, a glancing-off.

However, it does not seem right to say that in preventing an event, one is causing a token non-occurrence. There would be too many non-occurrences in the ontology! Prevention is prevention of a type.

Having multiple sufficient causes

It would be useful for discussions of causal exclusion arguments for physicalism to have a full taxonomy of the kinds of cases in which one effect E can have two sufficient causes C₁ and C₂.

Here is my tentative list of the cases:

1. Overdetermination: C₁ and C₂ overdetermine E

2. Chaining: C_i sufficiently causes C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1)

3. Constitution: C_i sufficiently causes E by being partly constituted by C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1)

4. Parthood: C_i sufficiently causes E by having the part C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1).

If parthood is a special case of constitution, then (4) is a special case of (3). Moreover (2)–(4) are all species cases of:

5. Instrumentality: C_i sufficiently causes E by means of C_j sufficiently causing E (where i = 1 and j = 2 or i = 2 and j = 1).

Note that the above cases are not mutually exclusive. We can, for instance, imagine a case where we have both chaining and overdetermination. Let’s say I aim a powerful heat gun at a snowball. Just in front of the snowball is a stick of dynamite. The heat melts the snowball. But it also triggers an explosion which blows the snowball apart. Thus, we have overdetermination of the destruction of the snowball by two causes: heat and explosion. However, we also have chaining because the heat causes the explosion.

I wonder if we can come up with an argument that (1)–(4), or maybe (1) and (5), are the only options. That seems right to me.

Ways out of the closure argument for physicalism

One of the main arguments for physicalism is based on the closure principle:

1. Any physical event that has a cause has a physical cause.

It is widely thought that it follows from (1) that:

2. If a physical event has a nonphysical cause, the event is overdetermined.

And hence in the absence of systematic overdetermination, mental causes must be physical.

But (2) doesn’t follow from (1). There are at least three ways for an event E to have two sufficient causes A and B:

• overdetermination

• chaining: A causes B which causes E or B causes A which causes E

• parthood: A causes E by having B as a part which causes E, or B causes E by having a part A which causes E.

Let’s think a bit about how the chaining and parthood options might avoid physicalism in the case of mental causation and yet allow for closure.

Option I: Nonphysical-physical-physical chaining: A nonphysical event M causes a physical event P which causes a physical event E. This can’t be the whole story for how we respect closure. For by closure, P will need a physical cause P₂, and so it is looking like P is going to be overdetermined, by M and P₂. But that does not follow without further assumptions. For we could have the following scenario:

• E is caused by an infinite chain of physical causes which chain is causally preceded by M, namely: P ← P₂ ← P₃ ← ... ← M, with infinitely many physical events in the “…”.

This scenario requires the possibility of an infinite sequence of causal means, contrary to causal finitism, and hence is unacceptable to me. But those who are less worried about infinite chains of causes should take this option seriously. Note that this option is reminiscent of Kant’s view on which our noumenal selves collectively cause the physical universe as a whole.

Option II: Physical-nonphysical-physical chaining: Here, the physical event P causes E by having a mental event as an intermediate cause. This option exploits a loophole in the closure principle as it is normally formulated: nothing in the closure principle says that the physical cause can’t operate by means of a nonphysical intermediary. Granted, that’s not how we normally think of physical causes as operating. But there is nothing incoherent about the story.

Option III: Physical parts of larger events: A physical event E is caused by a physical event P, and the physical event P is itself a part of a larger event M which is only partly physical. One might object that in this case it’s only P and not the larger event that counts as the cause. But that’s not right. If someone dies in the battle of Borodino, then at least three causes of death can be given: a shot being fired, the battle of Borodino, and the War of 1812. The shot is a part of the battle, and the battle is a part of the war. One particular way to have Option III is this: a quale Q is constituted by two components, a brain state B (say, a state of the visual cortex) and a soul state S of paying attention to the brain system that exhibits B, with B being the causally efficacious part of the Q. So a physical event—say, an agent’s making an exclamation at what they saw—counts as caused by the physical event B and the event Q which is not physical, or at least not completely physical.

One might object, however, that by “nonphysical”, one means entirely nonphysical, so Q’s having a nonphysical part S does not make Q nonphysical. If so, then we have one last option.

Option IV: Some or all physical causes cause their effects by having a nonphysical part that causes the event. That nonphysical part could, for instance, be an Aristotelian accidental or substantial form. Thus, here a physical event E is caused by a physical event by means of its nonphysical part M.

What if one objects that “physical” and “nonphysical” denote things that are purely physical and nonphysical, and neither can have a part that is the other? In that case, we have two difficulties. First, the closure principle is now stronger: it requires that a physical event that has a cause always has a purely physical cause. And we have a serious gap at the end of the argument. From closure at most we can conclude that a physical event doesn’t have a purely nonphysical cause. But what if it has a partly physical and partly nonphysical cause? That would be enough to contradict physicalism.

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?

Nitpicking about the causal exclusion argument

Exclusion arguments against dualism, and sometimes against nonreductive physicalism, go something like this.

1. Every physical effect has a sufficient microphysical cause.

2. Some microphysical effects have non-overdetermined mental causes.

3. If an event E has two distinct causes A and B, with A sufficient, it is overdetermined.

4. So, some mental causes are identical to microphysical causes.

But (3) is just false as it stands. It neglects such cases of non-overdetermining distinct causes A and B as:

5. A is a sufficient cause of E and B is a proper part of A, or vice versa. (Example: E=window breaking; A=rock hitting window; B=front three quarters of rock hitting window.)

6. A is a sufficient cause of B and B is a sufficient cause of E, or vice versa, with these instances of sufficient causation being transitive. (Example: E=window breaking; A=Jones throwing rock at window; B=rock impacting window.)

7. B is an insufficient cause of A and A is a sufficient cause of B, with these instances of causation being transitive. (Example: E=window breaking; B=Jones throwing rock in general direction of window; A=rock impacting window.)

8. A and B are distinct fine-grained events which correspond to one coarse-grained event.

To take care of (6) and (7), we could replace “cause” with “immediate cause” in the argument. This would require the rejection of causation by a dense sequence of causes (e.g., the state of a Newtonian system at 3 pm is caused by its state at 2:30 pm, its state at 2:45 pm, at 2:52.5 pm, and so on, with no “immediate” cause). I defend such a rejection in my infinity book. But the price of taking on board the arguments in my infinity book is that one then has very good reason to accept the Kalaam argument, and hence to deny (1) (since the first physical state will then have a divine, and hence non-microphysical, cause).

We could take care of (5) and (8) by replacing “distinct” with “non-overlapping” in (3). But then the conclusion of the argument becomes much weaker, namely that some mental causes overlap microphysical causes. And that’s something that both the nonreductive physicalist and hylomorphic dualist can accept for different reasons: the nonreductive physicalist may hold that mental causes totally overlap with microphysical causes; the hylomorphist will say that the form is a part of both the mental cause and of the microphysical cause. Maybe we still have an argument against substance dualism, though.

Change in transubstantiation

The two main parts of the doctrine of transubstantiation that get philosophically discussed are that after consecration we have:

• Real Presence: Christ's body and blood is really there.
• Real Absence: bread and wine is no longer there.

But there may be another part: that the bread and wine change into the body and blood rather than simply being replaced by the body and blood. Certainly the Council of Trent uses the language of "conversion" of bread and bread wine, but it is not completely clear to me that they mean to define there to be something more than replacement. Aquinas talks unclearly (to me) of the substantial change as a kind of "order" in the two substances.

Besides the general puzzle of how change differs from replacement, there are at least two philosophical difficulties about the change. The first is that on some versions--not mine--of Aristotelian metaphysics, what makes substantial change be a change is the persistence of matter. But there is no matter persisting here (indeed, Aquinas' remark emphasizes this). The second is that what the bread and wine change into, namely Christ's body, is already there. But it seems that if x changes into y, then y doesn't exist prior to the change.

Leibniz considers a theory on which the bread and wine change into new parts of Christ's body. This solves the second problem, but at the expense of having to say that the bread changes into a mere part of Christ's body, which does not appear to be what the Church means. Trent does say that whole Christ comes to be present. I suppose one could have a hybrid theory on which the bread and wine change into new parts of Christ's body, and the rest of Christ's body then additionally comes to be present, but not by conversion. While I do not have decisive textual evidence, this does not seem to me to be what Trent means. And it is grotesque to think that Christ gets fatter at transubstantiation.

While it could well be that the Council doesn't mean anything beefy about the "conversion", and perhaps all it is an "order" between the two substances (cf. Aquinas), an order constituted by by non-coincidental replacement in the same location. That would simplify things metaphysically. But I want to try for something metaphysically thicker.

Here's the thought. On my Aristotelian metaphysics, nothing persists in substantial change. But when a change of substance x into substance y, a rather special causal power is triggered in x, the causal power of giving rise to y while perishing. The exercise of such a causal power is what makes it be the case that x has changed into y. There isn't any matter persisting in the change, so the first of the two philosophical problems with the Eucharistic change disappears. What about the second? Here's my suggestion. Normally, the existence of Christ's body at later times is caused by its existence at earlier times. But what if we say that the bread miraculously gets a special causal power, the power of causing Christ's body to exist just as the bread perishes? Then the existence of Christ's body after consecration will be causally overdetermined by two things: the bread's exercising that causal power and Christ's body exercising its ordinary causal power to make itself persist.

The bread in perishing is an overdetermining cause of the existence of Christ's body, and that is exactly how substantial change happens on my view. The main metaphysical difference here is that normally substantial change is not overdetermined, while here it is.

Grounding overdetermination

Consider:

1. The sky is blue or snow is white.

This is grounded by:

2. The sky is blue.

But's it's also grounded by:

3. Snow is white.

This is a case of grounding overdetermination. I was tempted to characterize this as follows:

4. p is grounding overdetermined iff p is grounded by q and grounded by r, and q≠r, and neither q grounds r nor r grounds q.

The proviso at the end ensures that grounding chains do not count as cases of overdetermination. But (4) isn't good enough. Consider this:

5. The sky is blue or the sky has a color.

This seems to be grounding overdetermined by:

6. The sky is blue.
7. The sky has a color.

But (6) grounds (7), so the proviso in (4) kicks in. Oops!

This odd phenomenon is related to a deficiency of the causal analogue of (4):

8. E is causally overdetermined iff there are C₁ and C₂, with C₁≠C₂, and each of them is a full cause of E and neither of which is a full cause of the other.

But counterexamples akin to (5) are easy to manufacture. Boff is a trainee exterminator and Biff is his boss. Biff tells Boff to imitate everyting he does. Biff pours a lethal dose of crocodile poison into the customer's pond. Boff imitates him and pours another lethal dose. While Biff poured first, Boff poured closer to the crocodile, and as a result both doses arrived at the crocodile simultaneously, each sufficient to kill it. The alligator's death was overdetermined by the pouring of the two doses, even though one pouring caused the other.

We could try this:

9. p is directly grounding overdetermined iff p is directly grounded by q and directly grounded by r and q≠r.

And then we could say that:

10. p is grounding overdetermined iff it is either directly grounding overdetermined or it is grounded in something directly grounding overdetermined.

(And there is an obvious analogue for causation.) But this is only plausible if grounding is transitive. Maybe what we need to add to (10) something like "in a way that doesn't generate a relevant failure of the transitivity of grounding"?

Another difficulty with (9) is that the notion of direct grounding is not so easy to define. The tempting definition of direct grounding is, after all:

11. p is directly grounded by q iff p is grounded by q and there is no r such that p is grounded by r and r is grounded by q.

But cases of overdetermination like (5) are counterexamples to (11), since (5) is directly grounded by its first disjunct, even though the first disjunct grounds the second and the second grounds all of (5). So one wants to say:

11. p is directly grounded by q iff p is grounded by q and there is no r such that p is grounded by r and r is grounded by q and this is not a case of grounding overdetermination.

But of course then we have circularity.

All this suggests to me that we need a notion not reducible to grounding to make the above distinctions. We might, for instance, take direct grounding to be primitive. Or overdetermination. Or maybe we could use some version of my grounding graph approach.