Force-realism and simultaneous causation

If a charged particle is an electromagnetic field, the field exerts a Lorentz force F = qE + qv × B, where q and v are the charge and velocity of the particle, E is the electric field and B is the magnetic field. All of these quantities are taken at one location in spacetime. Thus, if realism about forces is correct, we have simultaneous causation: the electromagnetic field simultaneously causes the force.

Not everyone is a realist about forces, though. One might think that the electromagnetic field directly causes the subsequent change in velocity instead of causing a force which in turn causes the change in velocity.

Simultaneous causation and occasionalism

In an earlier post, I said that an account that insists that all fundamental causation is simultaneous but secures the diachronic aspects of causal series by means of divine conservation is “a close cousin to occasionalism”. For a diachronic causal series on this theory has two kinds of links: creaturely causal links that function instantaneously and divine conservation links that preserve objects “in between” the instants at which creaturely causation acts. This sounds like occasionalism, in that the temporal extension of the series is entirely due to God working alone, without any contribution from creatures.

I now think there is an interesting way to blunt the force of this objection by giving another role to creatures using a probabilistic trick that I used in my previous post. This trick allows created reality to control how long diachronic causal series take, even though all creaturely causation is simultaneous. And if created reality were to control how long diachronic causal series take, a significant aspect of the diachronicity of diachronic causal series would involve creatures, and hence the whole thing would look rather less occasionalist.

Let me explain the trick again. Suppose time is discrete, being divided into lots of equally-spaced moments. Now imagine an event A₁ that has a probability 1/2 of producing an event A₂ during any instant that A₁ exists in, as long as A₁ hasn’t already produced A₂. Suppose A₁ is conserved for as long as it takes to produce A₂. Then the probability that it will take n units of time for A₂ to be produced is (1/2)^n + 1. Consequently, the expected wait time for A₂ to happen is:

• (1/2)⋅0 + (1/4)⋅1 + (1/8)⋅2 + (1/16)⋅3 + ... = 1.

We can then similarly set things up so that A₂ causes A₃ on average in one unit of time, and A₃ on causes A₄ on average in one unit of time, and so on. If n is large enough, then by the Central Limit Theorem, it is likely that the lag time between A₁ and A_n will be approximately n units of time (plus or minus an error on the order of n^1/2 units), and if the units of time are short enough, we can get arbitrarily good precision in the lag time with arbitrarily high precision.

If the probability of each event triggering the next at an instant is made smaller than 1/2, then the expected lag time from A₁ to A_n will be less than n, and if the probaility is bigger than 1/2, the expected lag time will be bigger than n. Thus the creaturely trigger probability parameter, which we can think of as measuring the “strength” of the causal power, controls how long it takes to get to A_n through the “magic” of probabilistic causation and the Central Limit Theorem. Thus, the diachronic time scale is controlled precisely by creaturely causation—even though divine conservation is responsible for A_i persisting until it can cause A_i + 1. This is a more significant creaturely input than I thought before, and hence it is one that makes for rather less in the way of occasionalism.

This looks like a pretty cool theory to me. I don’t believe it to be true, because I don’t buy the idea of all causation being simultaneous, but I think it gives a really nice.

Simultaneous causation and determinism

Consider the Causal Simultaneity Thesis (CST) that all causation is simultaneous. Assume that simultaneity is absolute (rather than relative). Assume there is change. Here is a consequence I will argue for: determinism is false. In fact, more strongly, there are no diachronic deterministic causal series. What is surprising is that we get this consequence without any considerations of free will or quantum mechanics.

Since there is a very plausible argument from presentism to CST (a non-simultaneous fundamental causal relation could never obtain between two existent things given presentism), we get an argument from presentism to indeterminism.

Personally, I am inclined to think of this argument as a bit of evidence against CST and hence against presentism, because it seems to me that there could be a deterministic world, even though there isn’t. But tastes differ.

Now the argument for the central thesis. The idea is simple. On CST, as soon as the deterministic causes of an effect are in place, their effect is in place. Any delay in the effect would mean a violation of the determinism. There can be nothing in the deterministic causes to explain how much delay happens, because all the causes work simultaneously. And so if determinism is true—i.e., if everything has a deterministic cause—then all the effects happen all at once, and everything is already in the final state at the first moment of time. Thus there is no change if we have determinism and CST.

The point becomes clearer when we think about how it is an adherent of CST explains diachronic causal series. We have an item A that starts existing at time t₁, persists through time t₂ (kept in existence not by its own causal power, as that would require a diachronic causal relation, but either by a conserver or a principle of existential inertia), then causes an item B, which then persists through time t₃ and then causes an item C, and so on. While any two successive items in the causal series A, B, C, ... must overlap temporally (i.e., there must be a time at which they both exist), we need not have temporal overlap between A and C, say. We can thus have things perishing and new things coming into being after them.

But if the causation is deterministic, then as soon as A exists, it will cause B, which will cause C, and so on, thereby forcing the whole series to exist at once, and destroying change.

In an earlier post, I thought this made for a serious objection to CST. I asked: “Why does A ‘wait’ until t₂ to cause B?” But once we realize that the issue above has to do with determinism, we see that an answer is available. All we need to do is to suppose there is probabilistic causation.

For simplicity (and because this is what fits best with causal finitism) suppose time is discrete. Then we may suppose that at each moment of time at which A exists it has a certain low probability p_AB of causing B if B does not already exist. Then the probability that A will cause B precisely after n units of time is (1 − p_AB)ⁿp_AB. It follows mathematically that “on average” it will cause B after p_AB/(1 − p_AB) fundamental units of time.

It follows that for any desired average time delay, a designer of the universe can design a cause that has that delay. Let’s say that we want B to come into existence on average u fundamental units of time after A has come into existence. Then the designer can give A a causal power of producing B at any given moment of time at which B does not already exist with probability p_AB = 1/(1 + u).

The resulting setup will be indeterministic, and in particular we can expect significant random variation in how long it takes to get B from A. But if the designer wants more precise timing, that can be arranged as well. Let’s say that our designer wants B to happen very close to precisely one second after A. The designer can then ensure that, say, there are a million instants of time in a second, and that A has the power to produce an event A₁ with a probability at any given instant such that the expected wait time will be 0.0001 seconds (i.e., 100 fundamental units of time), and A₁ the power to produce A₂ with the same probability, and so on, with A₁₀₀₀₀ = B. Then by the Central Limit Theorem, the average wait time between A and B can be expected to be fairly close to 10000 × 0.0001 = 1 seconds, and the designer can get arbitrarily high confidence of an arbitrarily high precision of delay by inserting more instants in each second, and more intermediate causes between A and B, with each intermediate cause having an average delay time of 100 fundamental units (say). (This uses the fact that the geometric distribution has a finite third moment and the Barry-Esseen version of the Central Limit Theorem.)

Thus, a designer of the universe can make an arbitrarily precise and reliable near-deterministic changing universe despite CST. And that really blunts the force of my anti-deterministic observation as a consideration against CST.

Substantial change and simultaneous causation

Some philosophers hold that all fundamental instances of causal relations are simultaneous. Many of these philosophers are Aristotelians, though presentism provides a plausible route to this simultaneity doctrine independently of (other) Aristotelian considerations. I think the phenomenon of substantial change shows that this simultaneity doctrine is false.

When a horse changes into a carcass (or an electron-positron pair changes into a pair of photons) we have substantial change. Clearly, in such a case, the horse is the cause of the carcass.

Notice, however, that there is never a time at which both the horse and the carcass exists. This means that substantial change involves properly diachronic rather than simultaneous causation. And while there is a way of building a diachronic causal explanation out of simultaneous causation and persistence, I don’t see any way of doing that here. The trick in that way was to use the persistence of one or both of the relata of simultaneous causation to extend the relationship temporally. But here adding the earlier persistence of the horse or the later persistence of the carcass does not help, because it is still not the case that the horse and carcass have any moment of co-existence.

I think that this is where an Aristotelian will try to bring in matter. The horse has matter. When the horse perishes, its matter persists and comes to make up a carcass. We have a simultaneous relation between the horse and its matter, and then we have a simultaneous relation between the matter and the carcass.

But this doesn’t solve the problem. For the horse doesn’t just cause a heap of matter—it causes a carcass of a particular sort, made up of substances other than the substance of the horse. What persists in substantial change, on a classic Aristotelian view, is at most the prime matter. And the prime matter does not explain the form had by the carcass (or the parts of the carcass, if the carcass counts as a heap of substances).

We can even see the problem at the level of the accidents. Take the horse’s shape S_h and the carcass’s very similar shape S_c. Then, clearly, S_h causes S_c. One can see this empirically: if one rearranges the legs of the dying horse, the carcass’s shape changes correspondingly. But the only relevant thing that on the Aristotelian story persists across the change from horse to carcass is the matter: S_h does not persist, nor does anything that grounds S_h.

On reflection, the last line of thought shows that there could be a problem even for accidental change. For it seems likely to the case that a substance has an accident A which partially causes itself to be replaced by an accident B incompatible with itself. For instance, consider my current shape S₁. In a moment, my body will shift into a new shape S₂. The shape S₁ partially causes the shape S₂. Yet there is never a moment where I have both shapes. Indeed, at any time where I have shape S₁, that’s the only shape I have. So, the shape S₁ cannot cause any different future shape of me, assuming causation is always simultaneous.

This problem may be less serious than for substantial change, however, because one might say that S₁ does not cause S₂, but there is some deeper persisting accident that first causes me to have S₁ and then causes me to have S₂, so that there is no more a causal relationship between S₁ and S₂ than between a shadow of a moving person first appearing in one place and then in another. I think it is implausible to think that all cases where an accident A partially causes its immediate replacement by an accident B can be accounted by positing A and B to be mere epiphenomena, but I am not sure I have as good an argument against this as I do against the substantial change case.

I conclude from all this that while simultaneous causation is possible, it is not the case that all diachronic causation reduces to simultaneous causation.

Divine conservation, existential inertia, presentism and simultaneous causation

As a four-dimensionalist, I have been puzzled both by the arguments that divine conservation is necessary secure the persistence of substances and the idea of existential inertia as a metaphysical principle.

Temporal extent seems little different metaphysically to me from spatial thickness, the “problem of persistence” seems to me to be a pseudo-problem, and both solutions to this pseudo-problem seem to me to be confused.

On the existential inertia side, a metaphysical principle that objects continue to exist unless their existence is interrupted by some other cause seems as ridiculous to me as a principle that objects are maximally thick (and long and deep) unless and until their thickness (or length or depth) is stopped by other causes. And divine action is needed to secure persistence only to the extent that it is needed to secure thickness (and length or depth). That said, I do think divine action is needed to secure thickness, as well as all other accidents of a thing, because substances are in some sense causes of their accidents, but all creaturely causation requires divine cooperation. But that, I think, is a slightly different line of argument from the arguments for persistence of substances (in particular, I don’t have a good argument for it that doesn’t already presuppose theism, while the arguments for conservation are supposed to provide reasons for accepting theism).

However, I now see how it is that presentism yields a real problem of persistence. Here’s the line of thought. First, note that contrary to the protestations of some presentists, it is very plausible that:

1. Presentism implies that all causation is simultaneous.

For something that exists, at least at the time at which it is caused, cannot have as its cause something that doesn’t exist. But given presentism, only something present exists. So at a time at which E is caused, if the cause of E did not exist, we would have the exercise of a non-existent causal power, which is absurd.

But even if all causation is simultaneous, nonetheless:

2. There is diachronic causal explanation.

Setting the alarm at night explains why it goes off in the morning, even if by the simultaneity thesis (1), setting the alarm cannot be the cause of the alarm going off. Diachronic causal explanation cannot simply be causation. So what is it? Here is the best presentist story I know (and it’s not original to me).

First, we can get some temporal extension by the following trick. Imagine a thing A persists over an interval of time from t₁ to t₂. At t₂ is causes a thing B that persists over an interval of time from t₂ to t₃. The existence of A at t₁ then causally explains the existence of B at t₃. Note, however, that the existence of A at t₁ does not cause the existence of B at t₃. Causation happens at t₂ (or perhaps over an interval of times—thus, A might persist until some time t_2.5 < t₃, and be causing B over all of the interval from t₂ to t_2.5), but not at any earlier time, since at earlier times A doesn’t exist. Thus, by supplementing the simultaneous causal relation between A and B at t₂ with the persistence of A before t₂ and/or the persistence of B after t₂, we have, we can extend the relation into what one might call a fundamental instance of diachronic causal explanation.

Thus, a fundamental link in diachronic causal explanation consists of an instance of causation preceded and/or followed by an instance of persistence of the causing thing and/or the caused thing respectively. And a non-fundamental instance of diachronic causal explanation is a chain of fundamental links of diachronic causal explanations. (It may be that these diachronic causal explanations are very close to what Aquinas calls per accidens causal sequences.)

But for this to be genuine explanation, the persistence of the cause and/or effect needs to have an explanation. Divine conservation provides a very neat explanation: God necessarily exists eternally, and is simultaneous with everything (there may be some complications, though, with a timeless being given presentism), so God can cause A to persist from t₁ to t₂ and B to persist from t₂ to t₃. Thus, fundamental links in diachronic causal explanations depend on divine conservation.

An existential inertia view also gives a solution, but a far inferior one. For existential inertia requires the earlier existence of A, together with the metaphysical principle of existential inertia, to explain the later existence of A. But such a cross-time explanatory relation seems too much like the already rejected idea of cross-time causation. For it’s looking like A qua existing at t₁ explains A existing at t₂. But at t₂, according to presentism A qua existing at t₁ is in the unreal past, and it is absurd to suppose that what is in the unreal past can explain something real now.

In summary, given presentism, all fundamental explanatory relations need to be simultaneous. But it is an evident fact that there are diachronic causal explanatory relations. The only way to build those out of simultaneous explanatory relations is by supposing a being that can be simultaneous with things that exist at more than one time—a timelessly eternal being—whose causal efficacy provides the diachronic aspects of the explanatory linkage.

That said, I think there are two serious weaknesses in this story. The first is that it’s a close cousin of occasionalism. For there is no purely non-divine explanatory chain from the setting of the alarm at night to the alarm going off in the morning—divine action explains the persistences that make the chain diachronic.

A second problem is the puzzle of what explains why A causes B at t₂ rather than as soon as A comes into existence. Why does A “wait” until t₂ to cause B? Crucial to the story is that A is the whole cause, which then persists from t₁ to t₂. But why doesn’t it cause B right away, with B then causing whatever effect it has right away, and with everything in the whole causal history of the universe happening at once? Again, one might give this an occasionalist solution—A causes B only because God cooperates with creaturely causation, and God might hold off his cooperation until t₂. But this makes the story even more occasionalist, by making God involved in the timing of causation.

Simultaneous actualization of potentiality

I will argue, on Aristotelian grounds, for the following thesis:

• There are cases of actualization of potentials that are simultaneous with the possession of the potentials.

In particular, it follows that Aristotelian arguments against eternalism on the grounds that eternalism makes potentials co-real with their actualities fail, because every Aristotelian has to admit that there are potentials that are co-real with their actualities.

Here is the argument for the thesis.

1. All ordinary substances have first moments of existence.

It follows from Causal Finitism that all temporal substances have a first moment of existence. By “ordinary” substances, I mean things like dogs, cats and oak trees. I am excluding weirder candidates like the wavefunction of the universe or the universe itself, as well as extraordinary substances such as angels.

Now we add this premise:

2. Every ordinary substance always actualizes a potential of itself.

For instance, ordinary substances are always emitting electromagnetic radiation, and on Aristotelian grounds such activity had better be the actualization of a potential.

Now, while time travel and backwards causation might turn out to be possible, they are extraordinary. Thus:

3. An ordinary substance never actualizes a future potential.

Moreover, transsubstantiation is also extraordinary and:

4. Every potential that an ordinary substance has is one that it has at a time at which it exists.

From 1-4, it follows that:

5. An ordinary substance in the first moment of its existence actualizes a potential that it has then.

For suppose Alice is an ordinary substance and it’s now the first moment of her existence (she has such a moment by (1)). Alice actaulizes a potential of herself by (2). That potential which she is actualizing must be had by her in the present or the future by (4), since this is the first moment of her existence. She isn’t actualizing a future potential by (3). So she must be actualizing a present one.

And (5) gives us the thesis about potentiality being sometimes simultaneous with its actuality.

Is eternalism compatible with the actualization of potentiality?

Every so often, someone claims to me that there is a difficulty in reconciling the Aristotelian idea of the actualization of potential with eternalism, the view that past, present and future are equally real. I am puzzled by this question, because I can’t see the difficulty. On the contrary, there is a tension between presentism, the view that only present things exist, and this Aristotelian thesis:

1. Some present events are the actualization of a no-longer present potentiality.

2. A non-existent thing is not actualized.

3. Therefore, some no-longer present potentialities exist.

4. Therefore, something that is no longer present exists.

5. Therefore, presentism is false.

One might say: Yes, the potentiality doesn’t exist, but it did exist, and it was actualized. But then:

6. Some present potentialities are actualized in not yet present events.

7. A non-existent thing does not actualize anything.

8. So, there exist some not yet present things.

9. So, presentism is false.

Of course, this is the old problem of transtemporal relations for presentism as applied to the actualization relation.

So, what about the question whether eternalists can have actualization of potentials? Here may be the problem. On eternalism plus Aristotelianism, it seems that the past unactualized potential exists even though it is now actualized. This seems to be a contradiction: how can an unactualized potential be actualized?

A first answer is that a potential is actualized at a time t provided that its actualization exists at t. Thus, the potential is unactualized at t₁ but actualized at a later time t₂, because its actualization exists at t₂ but not at t₁. But, the objector can continue, by eternalism at t₁ isn’t it the case that the actualization exists? Yes: but the eternalist distinguishes:

10. It is true at t₁ that B exists.

11. B exists at t₁.

Claim (11), for spatiotemporal objects, means something like this: the three-dimensional spacetime hypersurface corresponding to t = t₁ intersects B. Claim (10) means that B exists simpliciter, somewhere in spacetime (assuming it’s a spatiotemporal object). There is no contradiction in saying that the actualization doesn’t exist at t₁, even though it is true at t₁ that it exists simpliciter.

The second answer is that Aristotelianism does not need actualizations of unactualized potentials. Causation is the actualization of a potential. But Aristotle and Aquinas both believed in the possibility of simultaneous causation. In simultaneous causation, an event B is the actualization of a simultaneous potential A. At the time of the simultaneous causation, nobody, whether presentist or eternalist, can say that B is the actualization of unactualized potential, since then the potential would be actualized and unactualized at the same time. Thus, one can have causation, and actualization of potential, where the potential and the actualization are simultaneously real, and hence where the actualization is not of an unactualized potential. The eternalist could—but does not have to—say that transtemporal cases are like this, too: they are actualizations of a potential, but not of an unactualized potential.

Simultaneous and diachronic causation

The main problem with the idea that all causation is simultaneous is to make sense of the obvious fact of diachronic causation, as when setting an alarm in the evening causes it to go off in the morning. Here is a theory that has both simultaneity and diachronicity that bears further examination:

• All causation between substances is simultaneous

• There is diachronic causation within a substance.

We now have a model of how setting the alarm works, on the simplifying assumption that the alarm clock is a substance. In the evening, by simultaneous causation, I cause the clock to have a certain state. A sequence of diachronic causal interactions within the clock—accidents of the clock causing other accidents of the clock, say—then causes the alarm to go off. The alarm’s going off then, by means of simultaneous causation between substances, causes particles in the air to move, etc. In other words, the diachronicity of the causation is all internal to the substances.

An even more interesting theory would hold that:

• All causation between substances is simultaneous

• All causation within a substance is diachronic.

If we were willing to swallow this, then we would have a very elegant account of the internal time of a substance as constituted by the causal relations within the substance (presumably, the causal relations between the accidents of the substance).

A version of the cosmological argument from preservation

Suppose that all immediate causation is simultaneous. The only way to make this fit with the obvious fact that there is diachronic causation is to make diachronic causation be mediate. And there is one standard way of making mediate diachronic causation out of immediate synchronic causation: temporally extended causal relata. Suppose that A lasts from time 0 to time 3, B lasts from time 2 to time 5, and C lasts from time 4 to time 10 (these can be substances or events). Then A can synchronically cause B at time 2 or 3, B can synchronically cause C at time 4 or 5, and one can combine the two immediate synchronic causal relations into a mediate diachronic causal relation between A and C, even though there is no time at which we have both A and C.

The problem with this approach is explaining the persistence of A, B and C over time. If we believe in irreducibly diachronic causation, then we can say that B’s existence at time 2 causes B’s existence at time 3, and so on. But this move is not available to the defender of purely simultaneous causation, except maybe at the cost of an infinite regress: maybe B’s existence from time 2.00 to time 2.75 causes B’s existence from time 2.50 to time 3.00; but now we ask about the causal relationship between B’s existence at time 2.00 and time 2.75.

So if we are to give a causal explanation of B’s persistence from time 2 to time 5, it will have to be in terms of the simultaneous causal efficacy of some other persisting entity. But this leads to a regress that is intuitively vicious.

Thus, we must come at the end to at least one persisting entity E such that E’s persistence from some time t₁ to some time t₂ has no causal explanation. And if we started our question with asking about the persistence of something that persists over some times today, then these times t₁ and t₂ are today.

Even if we allow for some facts to be unexplained contingent “brute” facts, the persistence of ordinary objects over time shouldn’t be like that. Moreover, it doesn’t seem right to suppose that the ultimate explanations of the persistence of objects involve objects whose own persistence is brute. For that makes it ultimately be a brute fact that reality as a whole persists, a brute and surprising fact.

So, plausibly, we have to say that although E’s persistence from t₁ to t₂ has no causal explanation, it has some other kind of explanation. The most plausible candidate for this kind of explanation is that E is imperishable: that it is logically impossible for E to perish.

Hence, if all immediate causation is simultaneous, very likely there is something imperishable. And the imperishable entity or entities then cause things to exist at the time at which they exist, thereby explaining their persistence.

On the theory that God is the imperishable entity, the above explains why for Aquinas preservation and creation are the same.

(It’s a pity that I don’t think all immediate causation is simultaneous.)

Problem: Suppose E immediately makes B persist from time 2 to time 4, by immediately causing it to exist at all the times from 2 to 4. Surely, though, E exists at time 4 because it existed at time 2. And this “because” is hard to explain.

Response: We can say that B exists at time 4 because of its esse (or act of being) at time 2, provided that (a) B’s esse at time 2 is its being caused by E to exist at time 2, and (b) E causes B to exist at time 4 because (non-causally because) E caused B to exist at time 2. But once we say that B exists at time 4 because of its very own esse at time 2, it seems we’ve saved the “because” claim in the problem.

Instantaneous Newtonian gravitational causation at a distance?

It’s widely thought that Newtonian gravity, when causally interpreted, involves instantaneous causation at a distance. But I think this is technically not right.

Suppose we have two masses m₁ and m₂ with distance r apart at time t₁. The location of m₂ at t₁ causes m₁ to accelerate at t₁ towards m₂ of magnitude Gm₂/r². And this sure looks like instantaneous causation at a distance.

But this isn’t an instance of instantaneous causation. For facts about what m₁’s acceleration is at t₁ are not facts about how the mass is instantaneously at t₁, but facts about how the mass is at t₁ and at times shortly before and after t₁: acceleration is the rate of change of velocity over time. Suppose that a poison ingested at t₁ caused Smith to be dead at all subsequent times. That wouldn’t be a case of instantaneous causation, even though we could say: “The poison caused t₁ to be the last moment of Smith’s life.” For the statement that t₁ is the last moment of Smith’s life isn’t a statement about what the world is instantaneously like at t₁, but is a conjunctive statement that at t₁ he’s alive (that part isn’t caused by the poison) and that at times after t₁ he’s dead (that part is caused by the poison, but not instantaneously). Similarly, m₁’s velocity (and position) at times after t₁ is caused by m₂’s location at t₁, but m₁’s velocity (or position) at t₁ itself is inot.

Let’s call cases where a cause at t₁ causes an effect at interval of times starting at, but not including, t₁ a case of almost instantaneous causation. In the gravitational case, what I have described so far is only almost instantaneous causation. Of course, people balking at instantaneous action at a distance are apt to balk at almost instantaneous action at a distance, but the two are different.

The above is pretty much the whole story about instantaneous Newtonian causation if one is not a realist about forces. But if one is a realist about forces, then things will be a bit more complicated. For m₂’s location at t₁ causes a force on m₁ at t₁, which complicates the causal story. On the bare story above, we had m₂’s location causing an acceleration of m₁. When we add realism about forces, we have an intermediate step: m₂’s location causes a force on m₁, which force then causes an acceleration of m₁. (There might even be further complications depending on the details of the realism about forces: we may have component forces causing a net force.) Now, when the force-at-t₁ causes an acceleration-at-t₁, this is, for the reasons given above, a case of almost instantaneous causation. But the causing of the force-at-t₁ by the location-at-t₁ of m₂ is a case of genuinely instantaneous causation.

But is it a case of causation at a distance? It seems to be: after all, the best candidate for where the force on m₁ is located is that it is located where m₁ is, namely at distance r from m₂. (There are two less plausible candidates: the force acting on m₁ is located at m₂, and almost instantaneously pulls on m₁; or it’s bilocated between the two locations; in any case, those candidates won’t improve the case for instantaneous action at a distance.) But here is another problem. The force on m₁ is not produced by m₂. It is produced by m₁ and m₂ together. After all, the Newtonian force law is Gm₁m₂/r². (It is only when we divide the force by m₁ to get the acceleration that m₁ disappears.) Rather than m₂ pulling on m₁, we have m₁ and m₂ pulling each other together. Thus, m₂ instantaneously partially causes the force on m₁ at a distance. But the full causation, where m₁ and m₂ cause the force on m₁, is not causation at a distance, because m₂ is at the location of that force.

In summary, the common thought that Newtonian gravitation involves instantaneous causation at a distance is wrong:

• If forces are admitted as genuine causal intermediates (“realism about forces”), then we have almost instantaneous causation of acceleration by force (moreover, not at a distance), and instantaneous partial causation of force at a distance.

• Absent force realism, we have almost instantaneous causation at a distance.

Naturalism and second-order experiences

My colleague Todd Buras has inspired this argument:

1. A veridical experience of an event is caused by the event.
2. Sometimes a human being is veridically experiencing that she has some experience E at all the times at which E is occurring.
3. If (1) and (2), then there is intra-mental simultaneous event causation.
4. If naturalism about the human mind is true, there is no intra-mental simultaneous causation.
5. So, naturalism about the human mind is not true.

In this argument, (4) is a posteriori: if naturalism is true, mental activity occurs at best at the speed of light. I am sceptical about (2) myself.

Experiencing present events and simultaneous causation

When I look at a rock, I see the rock and not just its outside surface. Of course, it is the outside layer that is causally responsible for my perception: a typical rock would look the same (except when intense light was shining through it) if suddenly all but the outer one millimeter of it disappeared. Similarly, when I see an event like a ball flying through the air, I see an event that includes the ball's presently flying through the air, even though it is only the temporal parts of the event fractions of a second prior to my perception that are causally responsible for my perception, since it takes light a few of nanoseconds to get to me from the ball and then it takes my visual apparatus rather longer to process it, and I need to process data from two different times in order to get the perception of motion. In both cases the data is processed without my being aware of it, and a rock or an event that includes the present is presented to me. If all goes well, this is veridical, though it could happen that there is no rock but a mere shell or that the ball was annihilated just before I had the perception.

So, in these experiences, when things go well, I have an experience of something extended through space and/or time caused by a very small proper part of the object of the experience. But veridical experiences must be caused by their objects (and in the right way). This means that a whole can count as causing something that is only caused by a proper part. (There are, of course, plenty of non-perceptual examples.) Moreover, notice that the case of the ball flying through the air, then, is a case of something like simultaneous causation when all goes well: a temporally extended event of the ball flying--including its flying now--causes my present perception, and the two events temporally overlap.

But this instance of simultaneous causation seems grounded in a case of non-simultaneous causation: a past temporal part of the ball's flight causing a present experience. That may be so. However, for all we know this non-simultaneous causation could be grounded in a finite sequence of fundamental simultaneous causations between temporally-extended temporally-simple events.