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.

Two theories of divine conservation

Here are two theories of divine conservation, tendentiously labeled:

• Occasionalist conservation: That a creature that previously existed continues to exist is solely explained by God’s power.

• Concurrentist conservation: That a creature that previously existed continues to exist is explained by God’s power concurring with creaturely causal powers (typically, the creature’s power to continue to exist).

It is usual in classical theism to say that divine conservation is very similar to divine creation. This comparison might seen to favor occasionalist conservation. However, that is not so clear once we realize that classical theism holds that all finite things are created by God, and hence creation itself comes in two varieties:

• Creation ex nihilo: God creates something by the sole exercise of his power.

• Concurrentist creation: God creates things by concurring with a creaturely cause.

Most of the objects familiar to us are the product of concurrentist creation. Thus, an acorn is produced by God in concurrence with an oak tree, and a car inconcurrence with a factory. (The human soul is an exception according to Catholic tradition.)

Because of this, even if we opt for concurrentist conservation, we can still save the comparison between conservation and creation, as long as we remember that often creation is concurrentist creation.

Which of the two theories of conservation should we prefer?

On general principles, I think we have some reason to prefer concurrentist conservation, simply because it preserves the explanatory connections within the natural world better.

However, if we insist on presentism, then we may be stuck with occasionalist conservation, because presentism makes cross-time causal relations problematic.

[Edited Nov. 4 2020 to replace "cooperation" with the more usual term "concurrence".]

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.

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.

What's so bad about species extinction?

A couple of weeks ago, an article in BMC Biology argued that there may be six reproductively isolated species of giraffes: "By analyzing mitochondrial DNA sequences and nuclear microsatellite loci, we show that there are at least six genealogically distinct lineages of giraffe in Africa, with little evidence of interbreeding between them." Reproductive isolation is, of course, the primary feature of species as defined in a modern biological way. Let's grant, for the sake of the argument, that the geneticists did their job correct, and that there are six biological species of giraffes (if not, the following will be hypothetical, but the same conclusions will follow).

So far, then, so good. But the The BBC says:

Mr Brown [the first author of this study] also highlighted the conservation implications of this study: "Lumping all giraffes into one species obscures the reality that some kinds of giraffe are on the brink.
"Some of these populations number only a few hundred individuals and need immediate protection."

Here is one place where things get philosophically interesting. The idea is that once we find out that, e.g., the Nigerian giraffe, of whom the BBC says "[t]he last 160 individuals are found in West and Central Africa", is a species, we have strong reason to prevent the extinction of the Nigerian giraffe.

Let K be a kind, natural or not, of organism. For some kinds K, we do not think there is anything bad about the extinction of Ks. Granted, the deaths of the individual members of K may be bad, but whether a kind K goes extinct or not, each individual has exactly one death to die (the last point I got from a comment by Jeff Schloss at a workshop we both attended; he may not endorse the use I make of the remark). Suppose K is the kind Dalmatian with exactly one spot shaped like in the diagram on right. There really is nothing bad about K ceasing to have members, over and beyond the individual members' deaths (note that one way for K to go extinct would be for the descendants of Dalmatians that have exactly one such spot to have two such spots, and there never again be any Dalmatians with exactly one such spot). Or maybe for diversity reasons, we think that in the best of all possible worlds all non-bad kinds are realized, and so there is something bad about the Ks dying out over and beyond the individual deaths, but it is a very minor bad.

I suspect what is going on here is that there is an equivocation between two senses of species: an intuitive non-scientific one (at least in the post-Aristotelian sense of "scientific") that understands a species as a kind of organism distinguished in a significant way from other organisms (the normative term "significant" is what marks this as non-scientific in the modern sense), and the modern scientific one in terms of reproductive isolation. For while there is something bad about a species in the intuitive sense going extinct, it is not at all clear what is so bad about a species in the reproductive-isolation sense going extinct. In particular, it is not clear why one of the giraffe species going extinct would be worse than Dalmatians with exactly one spot of some precise shape going extinct.

All this suggests that there is a need for a notion of species going distinct from the biological one. I rather hope that the Aristotelian notion of species as defined by qualitative identity of essence will do the job here.

Let me end with a question: Suppose that some kind of subatomic particle were to cease to exist forever, with no way of bringing it back. Would there be any non-instrumental bad in that (there might be an instrumental bad, if there is some use for the particle, or if studying it empirically might help with the progress of science)? (I am inclined to say yes.)