## Tuesday, November 20, 2012

### Barr on chance and design

Stephen Barr has an article in First Things where he argues that there is no conflict at all between chance and divine design. The position seems to hinge on two claims:

1. A series of events is chancy if and only if the secondary (i.e., finite, non-divine) causes of the events are independent of one another.
2. God controls series of events by primary causation.
Given (1) and (2), there is no conflict between divine design, since (1) says nothing about dependencies among events induced by primary causation.

I wish Barr's account worked. I'd love for there to be a good account of the interplay of chance and design. But there are a number of serious problems with Barr's proposal.

I. The account of chanciness does not work in the case of a single event. Depending on how we read (1), a single event will either trivially count as chancy (since its cause is independent of the causes of all other events in the series, there being no others) or it will never count as chancy. But single events can be chancy (imagine a universe where there is only one quantum collapse happening) or non-chancy.

II. Chance is explanatory, both in gambling and in evolution. But independence of causes has no explanatory force--without probabilities or chances, it generates no useful statistic predictions or explanations (here is a very technical way to make the point). So Barr's account needs something more, something like objective tendencies of the secondary causes that give rise to probabilities. I will assume in some of the following criticisms that something like this has been added.

III. Suppose I go to the casino and I play the slot machine a thousand times, and each time win, due to independent secondary causes, because God so arranged it. It seems absurd to say that I won by chance, and yet on Barr's definition my winning is a matter of chance.

IV. The preceding case shows that it is difficult to see how one can make any probabilistic predictions about a chancy series of events. Consider an infinite sequence of coin tosses where the limiting frequency of heads is 1/2. God can just as easily make this infinite sequence of heads come out in the case of an ordinary fair coin as in the case of a coin heavily biased in favor of heads. When God controls series of events by primary causation—and as far as Barr's position goes, this could be always—it is not clear why we should expect frequencies to match the probabilities arising from the tendencies of secondary causes. The frequencies of events will be precisely what God needs them to be for his purposes. Why think his purposes match the probabilistic tendencies of secondary causes? Now it could be that God wills to ensure that the actual frequencies usually match the secondary causal tendencies, in order that the universe be simpler and more predictable. That is a reasonable hypothesis. But then the it seems that it isn't the secondary causal tendencies that are directly explanatorily of the observed frequencies, but rather the explanation of the observed tendencies is God's will. I.e., in the case of a fair coin, the reason the limiting frequency comes out as heads is because God willed to ensure that the limiting frequency match the secondary causal tendency of the coin. The secondary causal tendency of the coin is still explanatorily responsible for this outcome (because God willed to match the frequency to it), but it isn't causally responsible for this outcome (unless we take an occasionalist analysis of secondary causation).

V. In light of III and IV, no statistical prediction can be made from probabilistic facts about the causal tendencies of secondary causes without an implicit auxiliary hypothesis that God through primary causation willed a particular series of events whose statistical features match the stochastic features of the causes. This is not entirely special to Barr's account—-probably every theistic account requires an implicit auxiliary hypothesis that God works no miracle here. But in Barr's case there is a difference—it's not just a hypothesis that God works no miracle here, since in the case where God makes me win the slot machine a thousand times in a row, on Barr's view no miracle has occurred, just the ordinary chancy operation of secondary causes and God's primary causal oversight. So Barr's view needs two auxiliary hypotheses to generate empirical predictions from scientific data: a no-miracles hypothesis like in every theistic case and a hypothesis of stochastic-to-statistical match.

VI. Random processes need not involve independent causes. Take, for instance Markov chains or exchangeable sequences of random variables.

VII. The elliptical orbits of the planets in our solar system and of the planets in another solar system have independent causes—the gravitational influences of different bodies—and hence by Barr's criterion the two events are chancy. But it's not chance that the orbits are elliptical. Now maybe Barr will count these cases as not independent because they are governed by the same laws of nature. True, they are. But so are paradigmatically chancy events, like the results of successive quantum collapse experiments.

#### 12 comments:

Brandon said...

I'm not sure I follow your (I); (1) is based on independence of causes of events, not independence of events. Or are you assuming that the single event has no causes or only one cause, and thus can't have independent causes? I feel like I'm missing something.

I find the list of problems interesting, though; I can't read the article, but your response suggests that Barr has a Molinist account of primary and secondary causation. Would you regard these as generalizing to Molinism in general?

Alexander R Pruss said...

(1) works something like this. Events E1,...,En are chancy iff their secondary causes C1,...,Cn are independent of each other. Well, if there is one event, then we either trivially have independence of its cause from the other causes in the set, since there aren't any, or we can insist that trivially there is no independence as there are no other causes in the set.

I am lumping all the (proximate?) causes of Ei into Ci here.

I don't see Barr's account as Molinist. It's more Thomist.

Alexander R Pruss said...

But you're right that my formulation of (I) was bad in that I should have talked of independence of causes rather than of events. I fixed it.

Brandon said...

OK, that definitely makes sense.

I suppose it was (IV) that suggested Molinism to me; Molinists can more easily accommodate the possibility of divergences between frequencies and secondary-cause tendencies because they think of primary causation in terms of choice of sequences (orders of nature, world histories, or what have you) and can make sense of such a divergence at the 'deliberation' stage of divine action, where those sequences are considered. Whereas part of the point of Banez-style Thomism is that there are no tendencies of secondary causes except as arising from the action of the first cause -- such tendencies already presuppose primary causation.

William said...

Barr may assume that the overall probability distribution of his series of events may follow a probabilistic law, but that God may be able to determine the specific temporal ordering of individual events in that series.

So for example in a world defined by 10000 sequential independent quantum events that can be either spin up or spin down, the total number of up events might approach over time to be about the same as the total down events, but God might still determine the order (down, up, up,down,down,...) in which they occur so as to, for some reason, for example, in a way unknown to other observers, make sure that events 100 and 101 are "up," yet not change overall probabilities in the process.

This would be sort of the difference between a pseudo-random and a truly random series, except that our analysis would not be expected to see a difference.

So a single event would not need to have a specifically readable meaning, since only the sequence would matter.

Alexander R Pruss said...

That would take care of some of the criticisms, but I think the divine control he was supposing was more ambitious--individual control of each event.

Also, reordering will keep overall frequency fixed, but will disturb other statistics. Suppose you reorder a more random-looking sequence of heads-and-tails to: HHHHHHTTTT. Then while the overall frequency of heads and tails is a reasonable 60%, if you break it up into pairs: HH HH HH TT TT you have unlikely frequencies: HH occurs three times and TT occurs twice, while HT and TH never occur.

You could get around this by having only a few shifts, so few that they are statistically insignificant in the full sequence. I defend that option, among others, in this paper (subscription required). But I think Barr wants God micromanaging, albeit with primary causation (that distinction plays a big role for Barr, though it is not clear how it does it), all the outcomes.

Heath White said...

I am rather partial to Barr’s sort of view, and I think it can be defended against many of these worries. Start by attributing objective tendencies as per your II, which entities have because God wills it. That will take care of objections I and II, I think.

Now treat natural laws as situations involving entities where these objective tendencies are (close to) 100% effective. I think if we construct “parodies” of the further objections we see where Barr might push back.

III. Suppose I go to the casino and play the slots 1000 times. Each time, the arm of the slot machine remains rigid, due to the natural laws of metallurgy, which God has willed the substance composing the arm have. Does it seem absurd to say that the arm remains rigid due to the natural laws of metal, rather than to God’s will? Not to me; they are just different kinds of explanation.

IV. Is it difficult to see how natural laws can allow one to make definite predictions of events they cover? I don’t think so. God can just as easily make metal bars non-rigid as rigid, but we can rely on their natural-law property of rigidity. Why? Presumably because God likes an orderly and intelligible universe, where such predictions are possible. Similarly for statistical predictions. The explanation of statistical regularity can appeal to whatever we like at the secondary level (objective tendencies, or whatever) just as the explanation of complete regularity can appeal to natural laws. In both cases such regularities obtain because God wills them to.

V. This objection (and the next post) seem to me to revolve around a false dichotomy: either the real explanation of a chancy event is some objective secondary tendency, or the real explanation is God’s primary causal activity. But the Thomist should say that what God primarily causes just is the operation of the objective secondary tendency, so these explanations do not compete. (This is also the reply I would give to the argument of the next post.)

(V cont’d.) You are right that Barr’s view needs the two auxiliary hypotheses you mention, assuming we take ‘miracle’ to mean something like “suspension or prevention of the operation of ordinary secondary causes.” But the only reason we aren’t making two such hypotheses in the natural-law case is that a failure of the statistical-to-stochastic match in that case (i.e. one counterexample) would entail a suspension or prevention of the ordinary secondary cause. In the case of statistical explanations, this entailment fails, so the hypotheses come apart.

I do not think I understand VI and VII well enough to reply to them; they seem to be worries about the definition of ‘chance’ and those may already have been taken care of. Not sure.

Alexander R Pruss said...

Heath:

Regarding III: To make this a better analogy, you need to suppose that God also willed that there be a chancy process that almost all the time results in the arm being rigid and very rarely--maybe once in 10^1000 times--in the arm being soft. Now, suppose that each time you play the arm is soft, because God so willed it for some purpose. By the Barr account, that's a matter of chance. Likewise, by the Barr account, if the arm is rigid every time, that's also a matter of chance.

IV. The picture I am getting is that God wants to make sure that the statistics we get from the chancy processes match the objective tendencies of the chancy processes. So the objective tendencies of the chancy processes do explain the statistics. But they seem to me to explain it in the wrong way.

Suppose I have a superpower of determining how a coin you toss will land. Moreover, suppose it's a superpower I can't help exercising: whenever you toss a coin, I have to make a choice of how the coin will land. You're going to toss a coin a thousand times. I want to hide this superpower from you, and so I make the coins land in a sequence that statistically matches the objective tendencies of the coin. So about 500 of the tosses are heads. In this case, the explanation of why about 500 of the tosses were heads does include the objective tendencies of the coin, because I was intentionally acting to ensure that the statistics match the objective tendencies. But the objective tendencies of the coin enter the wrong way into the explanation.

To see that they enter the wrong way, consider a different case, where I deliberately choose to make heads come out half as often as the objective tendency makes it come out. (I.e., there'll be about 250 heads.) In that case, the objective tendency of the coin flips does explain the results, but clearly it does so in the wrong way. But I think it's also in the wrong way if instead of choosing to make heads come out half as often I choose to make heads come out exactly as often. For in neither case is the result explained by the tendency in the stochastic-explanation way.

V. As for competition, I think stochastic explanations can be trumped, as in my superpower case. The stochastic facts are still true, but they are no longer explanatory.

Here's perhaps another way to see this. Suppose that I have that superpower and I have an intention to ensure that coin flip results match the tendencies. Now rewind stuff, erase my memory of the experiment, but give me the same desires, and run the experiment again and again. Each time you run the rewound experiment, the result will be that about half of the coin flips will be heads. But that's not how it is with a real stochastic explanation. With a real stochastic explanation, if you rewind enough times (of the order of 2^1000 times), you will eventually have a case where all the coins end up heads. In other words, you get different probabilistic predictions when you condition on my plans and when you condition on just the tendencies of the coins. And the plans trump the coins.

Heath White said...

Alex,

I think the root of the issue, roughly, is that on your model of the Barr/Thomist view, what God causes is the state of affairs “the coin lands heads,” and that this is normally in some kind of pre-established harmony with the objective tendencies of coins to land heads. But then you point out that God can will whatever he likes about coins and therefore the tendencies and God’s will can come apart, so that the real explanation is God’s will not the tendencies.

My model of this view is a little different. What God causes, inter alia, is “the objective tendencies of the coin cause the coin to land heads.” God could cause these tendencies to result in heads 1000x in a row. But then, it is possible for fair coins to land heads 1000x in a row. That is a chancy result in exactly the same sense that everyone else uses the term. On the Barr/Thomist view, there is no option of God NOT causing any particular sequence of heads/tails.

Re III: My analogy was, if anything, not extreme enough; I put in “close to” to avoid definitional questions about natural law. Suppose some universe were described by Newtonian mechanics and therefore subject to complete Laplacean determinism. Every event could be completely explained by citing some prior event plus the natural laws. Is it then puzzling how God’s will could also explain events? Or does the deterministic explanation compete with the divine voluntarist explanation? I don’t think so. Now if you just make the laws chancy, you get a similar result.

Here is a way to think about it. Consider the universe as a four-dimensional block of space-time. Included in it are whatever causal relations obtain: determinisms, objective tendencies, or whatever you like. Now simply add the thought that God intentionally creates THAT universe down to the detail, including all the causal relations it contains. The object of his creation is whatever you were thinking of initially, so that whatever explanations held initially should still hold. And yet we can also attribute the result to the divine will.

Alexander R Pruss said...

I don't think it matters for my arguments whether God causes the state of affairs of the coin landing heads or the state of affairs of the coin's tendencies causing it to land heads.

"But then, it is possible for fair coins to land heads 1000x in a row. That is a chancy result in exactly the same sense that everyone else uses the term."

But I don't think many would say that it's chancy when God on purpose made it land heads 1000 times in a row.

"Or does the deterministic explanation compete with the divine voluntarist explanation? I don’t think so. Now if you just make the laws chancy, you get a similar result."

You get to preserve, in both cases, causal non-competing causal explanations. But what I think you don't get to preserve in the stochastic case is non-competition between the probabilistic explanation and the agential explanation.

Take my superpower case, but make it more similar to the case at hand. I have the power to direct the causal influence from the coin's tendency in such a way as to intentionally bring it about that the coin's tendency causes it to land heads or so as to intentionally bring it about that the coin's tendency causes it land tails. Suppose, as before, that I cannot refrain from exercising my superpower.

Then while it is true as a matter of causal explanation that the coin's landing heads (say) is caused by the coin's causal tendencies, it is no longer correct to say that the coin landed heads about half the time because this was likely given the coin's tendencies, where the "because" is the because of stochastic explanation. It is now desires that are the real explanation of the statistical results. This is clear in the case where my desires are independent of the choice of the coin's causal tendencies.

But we can consider two sub-cases.

Subcase 1: I first wanted half of the coin flips to land heads, and so I gave the coin the relevant tendencies. In this case, the coin's tendencies don't explain the statistical features: rather, there is a common-cause explanation of the coin's tendencies and the statistical features.

Subcase 2: I wanted half of the coin flips to land heads because the coin had the relevant tendencies. In this case, the coin's having the relevant tendencies does explain the statistical result, but does not do so in the right way--it does it through my desires.

Alexander R Pruss said...

I would also like to know what you think of my newer post. Would you agree that P(God wills coin to land heads) = 1/2?

Alexander R Pruss said...

Maybe a way to highlight the difference in explanations is to say that there is a difference between the case when the number of heads, in a thousand tosses, is close to 1000 and the case where it's close to 500. When it's close to 1000 and when it's close to 500, we can give an explanation in terms of the chancy phenomena. But only when it's close to 500 can we give an additional explanation--an explanation in terms of the result being very likely given the chancy phenomena. It is this something like kind of explanation that underlies the explanation of why casinos make money. (The Darwinian case is weaker but similar: we now have an explanation in terms of the result being not very unlikely given the chancy phenomena.) And it is this additional kind of explanation (or perhaps the additional strength of explanation) that I think is undercut by Barr-type accounts.