More on God causing infinite regresses

In my previous two posts I focused on the difficulty of God creating an infinite causal regress of indeterministic causes as part of an argument from theism to causal finitism. In this post, I want to drop the indeterministic assumption.

Suppose God creates a backwards infinite causal regress of (say) chickens, where each chicken is caused by parent chickens, the parent chickens by grandparent chickens, and so on. Now, I take it that the classical theist tradition is right that no creaturely causation can function without divine cooperation. Thus, every case where a chicken is caused by parent chickens is a case of divine cooperation.

Could God’s creative role here be limited to divine cooperation? This is absurd. For then God would be creating chickens by cooperating with chickens!

So what else is there? One doubtless correct thing to say is this: God also sustains each chicken between its first moment of life and its time of death. But this sustenance doesn’t seem to solve the problem, because the sustenance is not productive of the chickens—it is what keeps each chicken in existence after it has come on the scene. So while there is sustenance, it isn’t enough. God cannot create chickens by cooperating with chickens and by sustaining them.

Thus God needs to have some special creative role in the production of at least some of the chickens, fulfilling a task over and beyond cooperation and sustenance. Furthermore, this special task must be done by God in the case of an infinite number of the chickens, since otherwise there would be a time before which that task was not fulfilled—and yet God created infinitely the chickens before that time, too, since we’re assuming an infinite regress of chickens.

What happens in these cases? One might say is that in these special cases, God doesn’t cooperate with the parent chickens. But since no creaturely causation happens without divine cooperation, in these cases the parent chickens don’t produce their offspring, which contradicts our assumption of the chickens forming a causal regress. So that won’t do.

So in these cases, we seem to have two things happening: divine cooperation with chicken reproduction and divine creation of the chicken. Since divine cooperation with chicken reproduction is sufficient to produce the offspring, and divine creation of the chicken is also sufficient, it follows that in these cases we have causal overdetermination.

Now, we have some problems. First, does this overdetermination happen in all cases of chicken reproduction or only in some? It doesn’t need to happen in all of them, since it is overdetermination after all. But if it happens only in some, then it is puzzling to ask how God chooses which cases he overdetermines and which he does not.

Second, when there is overdetermination, the overdetermination is not needed for the effect. So it seems that if God’s additional role is that of overdetermining the outcome, that role is an unnecessary role, and the chickens could be produced by mere divine cooperation, which we saw is absurd. This isn’t perhaps the strongest of arguments. One might say that while in each particular case the overdetermining divine creative action is not needed, it is needed that it occur in some (indeed, infinitely many) cases.

Third, just as it is obviously absurd if God creates chickens merely by cooperating with chickens, it seems problematic, and perhaps absurd, that God creates chickens merely by cooperating with chickens and overdetermining that cooperation.

Famously, Aquinas thinks that God could have created an infinite regress of fathers and sons, and hence presumably of chickens as well. At this point, I can think of only one plausible way of getting Aquinas out of the above arguments, and it’s not a very attractive way. Instead of saying that God cooperates with the production of offspring, we can say that occasionalism holds in every case of substantial causation, that all causation of one substance’s existence by another is a case of direct divine non-cooperative causation, with the creaturely causation perhaps only limited to the transmission of accidents. Like all occasionalism, an occasionalism about substance causation is unappealing philosophically and theologically.

From theism to causal finitism

Causal Finitism—the thesis that nothing can have an infinite causal history—implies that there is a first cause, and our best hypothesis for what a first cause would be is God. Thus:

1. If Causal Finitism is true, God exists.

But I think one can also argue in the other direction:

2. If God exists, Causal Finitism is true.

Aquinas wouldn’t like this since he thought that God could create a per accidens ordered backwards-infinite causal series.

In this post, I want to sketch an argument for (2). The form of the argument is this.

3. God cannot create a sequence of beings ..., A₋₃, A₋₂, A₋₁, A₀ where each being causes the next one.

4. If God cannot create such a sequence, such a sequence is impossible.

5. The best explanation of the impossibility of such a sequence is Causal Finitism.

Claim (4) comes from omnipotence. Claim (5) is I think the weakest part of the argument. Causal Finitism follows logically from the conjunction of two theses, one ruling out backwards-infinite causal chains and the other ruling out infinite causal cooperation (a precise statement and a proof is given in Chapter 2 of my Infinity book). But I am now coming to think that there is a not crazy view where one accepts the anti-chain part of Causal Finitism but not the anti-cooperation part. However, (a) the main cost of Causal Finitism come from the anti-chain part (the anti-chain part is what forces either a discrete time or a discrete causal reinterpretation of physics), (b) there are significant anti-paradox benefits to maintaining the anti-cooperation part, and (c) the theory may seem more unified in having both parts.

Now let’s move on to (3). Here is an argument. Say that an instance of causation is chancy provided that the outcome has a probability less than one.

6. If God can create a backwards-infinite causal sequence of beings, he can create a backwards-infinite chancy causal sequence of beings as the only thing in creation.

7. Necessarily, if God creates a backwards-infinite chancy causal sequence of beings as the only thing in creation, then there is no creature x such that God determines x to exist.

8. Necessarily, if God creates, he acts in a way that determines that something other than God exists.

9. Necessarily, if God determines that something other than God exists then there is a creature x that God determines x to exist.

10. Necessarily, if God creates a backwards-infinite chancy causal sequence of beings, then there is a creature x such that God determines x to exist. (8,9)

11. Hence, God cannot create a backwards-infinite chancy causal sequence of beings. (7,10)

12. Hence, God cannot create a backwards-infinite causal sequence of beings. (6,11)

The thought behind (6) is an intuition about modal uniformity. I think (6) is probably the most vulnerable part of the argument, but I don’t think it’s the one Aquinas would attack. What I think Aquinas would attack would most likely be (7). I will get to that shortly.

But first a few words about (8). In theory, it is possible to determine that something exists without determining any particular thing to exist. One can imagine a being with a chancy causal power such that if it waves a wand necessarily either a bunny or a pigeon is caused to exist, with the probability of the bunny being 1/2 and the probability of the pigeon being 1/2. But God is not like that. God’s will is essentially efficacious and not chancy. God can play dice with the universe, but only by creating dice. Thus, if God wanted to ensure there is a bunny or a pigeon without ensuring which specific one exists, he would have to create a random system that has chancy propensities for a bunny and for a pigeon and that must exercise one of the two propensities.

In fact, I think divine simplicity may imply this. For by divine simplicity, any two possible worlds that differ must differ in something outside God. Now consider a world w₁ where God determines a bunny to exist, and a world w₂ where God merely determines that a bunny or a pigeon exists and in fact a bunny is what comes about. There seems to be no difference outside God between these two worlds (one might wonder about the relation of being-created: could there be an relation of being-created-chancily and being-created-non-chancily? this seems fishy to me, and suggests a regress—how are the two relations differently related to God? and do we want to multiply such relations, saying there is such a thing as being-created-chancily-with-probability-0.7?). If both worlds are possible, by divine simplicity they must be the same, which is absurd. So at least one must be impsosible. And w₂ is a better candidate for that than w₁.

That still doesn’t establish (8). For I admitted that God can play dice if he creates dice. Thus, it seems that God could determine that something exists without determining where it’s A or B or C (say) by determining there to be dice that decide whether A or B or C are produced. But on this story, God still determines there to be dice, so there is an x—a die—that God determines to exist. I think a bit more could be said here, but as I said, I don’t think this is the main thing Aquinas would object to.

Back to (7). Why can’t God create a chancy backwards-infinite causal sequence while determining some item A_n in it to exist? Well, the sequence is chancy, so the probability that A_n − 1 causes A_n given that A_n − 1 exists is some p < 1. But, necessarily, if one creature causes another, it does so with divine cooperation (Aquinas will not disagree), and conversely if God cooperates with one creature to cause another, the one creature does cause the other. That the probability that God cooperates with A_n − 1 to cause A_n is equal to the probability that A_n − 1 causes A_n, because necessarily one thing happens if and only if the other does. Thus, the probability that God cooperates with A_n − 1 to cause A_n, given that A_n − 1 exists, is p. But p < 1, so it sure doesn’t look like a case of God determining A_n to exist!

But perhaps there is something like overdetermination, but between determination and chanciness (so not exactly over-determination). Perhaps God both determines A_n to exist and chancily cooperates with A_n − 1 to produce A_n. One problem with this hypothesis is with divine simplicity: it does not seem that there is any difference outside God between a world where God does both and God merely cooperates or concurs. But Aquinas may respond: “Yes, exactly. Necessarily, when one creature chancily causes another, God’s primary causation determines which specific outcome results. Thus there is no world where God merely cooperates.” So now the view is that whenever we have chancy causation, necessarily God determines the outcome. But suppose I chancily toss a coin, and it has chance 1/2 of heads and chance 1/2 of tails. Then on this view, I get heads if and only if God determines that I get heads. Hence the chance that God determines I get heads is 1/2. But it seems plausible that God’s determinations are not measured by numerical probabilities, and in any case that they are not measured by numerical probabilities coming from our world’s physics!

Distant collaboration

Suppose mereological universalism is true, and that I make a pizza and an alien a long time ago in galaxy far, far away (or even in another universe) makes a sandwich. Then I and the alien have engaged in an amazing collaboration spanning time and space, and maybe even across universes, and produced a fusion of a pizza and a sandwich. Surely I cannot so very easily collaborate in the production of things with beings so far off!

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 hiddenness as a problem for atheists

One might think that divine hiddenness is a problem for the theist but not at all for the atheist. That is not so clear to me. Consider the plausible evolutionary psychology stories about theistic belief, such as that social animals as smart as us will be sufficiently able to outwit the social enforcement of cooperative behavior and the best evolutionary solution is to have us believe in a being who misses nothing and whose judgment cannot be escaped. But given such good evolutionary stories about theistic belief, why are there so many who do not believe?

I am not saying the problem has no good answer, just that there is still a problem there, even if theism is false.

Thomism, chance and cooperative providence

Thomists have two stories about how God can act providentially in the world. First, God can work simply miraculously, directly producing an effect that transcends the relevant created causal powers. Second, God can work cooperatively: whenever any finite causal agency is exercised, God intentionally cooperates with it through his primary causation, in such a way that it is up to God which of the causal agents natural effects is produced.

I think there is a difficult problem for cooperative divine agency. Suppose Alice is desperate for food for her children. She finds an indeterministic alien device which has the following property. If she presses the big button on it, the machine has probability 1/2 of producing enough food for a month for her family, and probability 1/2 of giving her a mild shock and turning off for a month.

Alice says a quick but sincerely prayer and presses the button. Then, presumably:

1. The probability that the machine will produce food is 1/2 conditionally on God not working miraculously.

But now notice:

2. Necessarily, if God does not work miraculously, the machine will produce food if and only if God intentionally connaturally cooperates with the machine to produce food.

From (1) and (2) we can conclude:

3. The probability that God will intentionally cooperates with the machine to produce food is 1/2 conditionally on God not working miraculously.

But imagine a different machine, where pressing the button has probability 1/2 of producing enough round pizza for a week and probability 1/2 of producing enough square pizza for a week. If Alice pressed the button on that machine, God, in acting cooperatively, would not have any significant reason to make the output of the machine come out one way or another.

In the round-or-square-pizza machine, we would expect the probability that God would cooperate to produce a particular outcome to be 1/2. But in the food-or-nothing machine, God does have a good reason to make the output of the machine be food: namely, God loves Alice and her family. We would expect the statistics for divine intentional cooperation to be different in the case of the two machines. But they are the same. In other words, it seems that God’s cooperative providence cannot depart from the statistics built into the natures of creatures. Yet that providence is fully under God’s voluntary control according to Thomism. This is puzzling.

If the Thomist says that God’s special providence is always exercised miraculously rather than cooperatively, the problem disappears. Absent special providential reasons, God has reason to follow the natural statistics of the machines. But if we allow that God sometimes exercises his special providence cooperatively, that should skew the statistics, and it cannot do that given the argument from (1) and (2) to (3).

Restricting special providence to miracles is a real option, but it destroys one of the advantages that Thomism has over competing theories.

Competitive sports

We think of competitive team sports as involving two groups of people, with cooperation within each group but competition between the groups. However, there is a better picture. We can think of the two teams as part of a larger cooperating group, which is subdivided into two subgroups. The two subgroups cooperate with each other for the goods that the sport achieves. The means by which the two subgroups cooperate for the goods of the sport is competition, much as when lawyers for two sides (normatively speaking) cooperate for the sake of truth and justice by competitively each giving the best rendition of one side of the case. Central among the goods in the sport case will presumably be athletic excellence (I am grateful to Dan Johnson for pointing out this good to me), but there will be other goods such as health, fun, entertainment of others, etc.

Of course, something similar happens in competitive individual sports: the individuals cooperate with each other in order that they achieve the goods of the sport.

From this high vantage point, all competitive sports--as well as other games--are a cooperative human activity. I think one can feel this particularly well when one wants to play a sport or another kind of game and an opponent becomes only available after some difficulty. There is a gratitude one has to the opponent for making the game possible.

Yet, paradoxically, the cooperation can involve each pursuing an incompatible end: their own victory. But ideally each pursues that end because the pursuit (but not necessarily achievement) of that end is what makes the joint goods possible.

Epistemic self-sacrifice and prisoner's dilemma

In the fall, I attended a really neat talk by Patrick Grim which reported on several computer simulation experiments by Grim. Suppose you have a bunch of investigators who are each trying to find the maximum ("the solution to the problem") of some function. They search, but they also talk to one other. When someone they are in communication with finds a better option than their own, they have a certain probability of switching to that. The question is: How much communication should there be between investigators if we want the community as a whole to do well vis-a-vis the maximization problem?

Consider two models. On the Local Model (my terminology), the investigators are arranged around the circumference of a circle, and each talks only to her immediate neighbors. On the Internet Model (also my tendentious terminology), every investigator is in communication with every investigator. So, here's what you get. On both models, the investigators eventually communally converge on a solution. On the Internet Model, community opinion converges much faster than on the Local Model. But on the Internet Model the solution converged on is much more likely to be wrong (to be a local maximum rather than the global maximum).

So, here is a conclusion one might draw (which may not be the same as Grim's conclusion): If the task is satisficing or time is of the essence, the Internet Model may be better—we may need to get a decent working answer quickly for practical purposes, even if it's not the true one. But if the task is getting the true solution, it seems the Local Model is a better model for the community to adopt.

Suppose we're dealing with a problem where we really want the true solution, not solutions that are "good enough". This is more likely in more theoretical intellectual enterprises. Then the Local Model is epistemically better for the community. But what is epistemically better for the individual investigator?

Suppose that we have a certain hybrid of the Internet and Local Models. As in the Local Model, the investigators are arranged on a circle. Each investigator knows what every other investigator is up to. But the investigator has a bias in favor of her two neighbors over other investigators. Thus, she is more likely to switch her opinion to match that of her neighbors than to match that of the distant ones. There are two limiting cases: in one limiting case, the bias goes to zero, and we have the Internet Model. In the other limiting case, although she knows of the opinions of investigators who aren't her neighbors, she ignores it, and will never switch to it. This is the Parochial Model. The Parochial Model gives exactly the same predictions as the Local Model.

Thus, investigators' having an epistemic bias in favor of their neighbors can be good for the community. But such a bias can be bad for the individual investigator. Jane would be better off epistemically if she adopted the best solution currently available in the community. But if everybody always did that, then the community would be worse off epistemically with respect to eventually getting at the truth, since then we would have the Internet Model.

This suggests that we might well have the structure of a Prisoner's Dilemma. Everybody is better off epistemically if everybody has biases in favor of the local (and it need not be spatially local), but any individual would be better off defecting in favor of the best solution currently available. This suggests that epistemic self-sacrifice is called for by communal investigation: people ought not all adopt the best available solution—we need eccentrics investigating odd corners of the solution space, because the true solution may be there.

Of course, one could solve the problem like this. One keeps track of two solutions. One solution is the one that one comes to using the biased method and the other is the best one the community has so far. The one that one comes to using the biased method is the one that one's publications are based on. The best one the community has so far is the one that one's own personal opinion is tied to. The problem with this is that this kind of "double think" may be psychologically unworkable. It may be that investigation only works well when one is committed to one's solution.

If this double think doesn't work, this suggests that in some cases individual and group rationality could come apart. It is individually irrational to be intellectually eccentric, but good for the community that there be intellectual eccentrics.

My own pull is different in this case than in the classic non-epistemic Prisoner's Dilemma. In this case, I think one should individually go for individual rationality. One should not sacrifice oneself epistemically here by adopting biases. But in the classic Prisoner's Dilemma, one has very good reason to sacrifice oneself.

Cooperating with evil

Here is an interesting case raising the question of when it is permissible to cooperate with evildoers.

Benefiting from evil

A topic on which there has been some, but not enough, written is that of complicity after the fact. A standard case is the question whether it is permissible to use the small amount of usable Nazi concentration camp medical "research" data (apparently some of the typhus and hypothermia data is useful). Is there any reason to avoid benefiting from the evils of others? I've made a distinction between two sorts of benefits: those benefits that the original evildoer intended, and other benefits. For instance, the Nazi camp doctors may have intended to benefit medical science. If so, then by using their data, one is "playing along" with their plan—one is, in some sense, complicit. It does not follow that the action is wrong, but it does follow that one has a reason (perhaps not conclusive) to refrain from it. On the other hand, the police officer who gets promoted for catching a criminal benefits from crime in a way that the criminal did not intend. This kind of benefiting from an evildoer's action is not a case of complicity, and there is no prima facie reason to refrain from it.

It has hit me that an exactly parallel issue comes up for benefiting from one's own past evil activity. If one has lied on one's resume and as a result got a job, then one's continuing to have the job is a way of benefiting from one's own past ill deed, and, moreover, the benefit is one that was intended by oneself when one lied. It seems to me that one can and should say very similar things about benefiting from one's own past evil deeds as about benefiting from others' evil deeds. In other words, when the benefit is not an intended one, and especially if it was not even hoped for or expected, one is not playing along, and one need have no qualms. For instance, when one benefits from one's past sins by becoming more humble through reflection on one's past weakness, that is not something one has any reason against. On the other hand, one does have prima facie reason not to continue in the job when one got it illicitly. Nonetheless, ultima facie, one might have reason to remain in the job—for instance, if one's employer could not replace one without significant loss to the employer (for instance, because one's employer has put significant effort into training one), one may have sufficient reason to continue in the job.

I think that the parallel between complicity in one's own past sins and in the past sins of others is illuminating and worth plumbing further.