Friday, November 23, 2012

Prayer and Thomistic accounts of chance and design

On Thomistic accounts of chance and design, God micromanages the outcomes of chancy processes by means of primary causation, ensuring that the processes secondarily cause precisely the results that God wants. (Thomists often say a similar thing about free will, too.) On such accounts we can distinguish between two different ways that God can achieve a result, which I will call the miracle and natural methods. In the miracle method, God suspends the causal powers of the chancy process and directly cause the specific outcome he wants. If he does this on a die toss (I'll assume that die tosses are indeterministic), then the hand tosses the die, but somewhere there will be a break in the natural chain of causes. In the natural method, God causes the the causal powers of the chancy process to cause, in the way proper to them, the specific outcome he wants. Presumably, given that the natural method preserves the value of finite causes' activity, much of the time God providentially acts using the natural rather than the miracle method.

Now suppose that I am about to toss a die. And suppose that I pray, for all the right reasons (say, a good to a friend will result from non-six, and nobody will be harmed by it) and in the right way, that the die should show a non-six, while no one else prays that it should show a six. Moreover, suppose that God in fact does not have any significant counterbalancing reasons in favor of the die showing six. Let C be a complete description of the state of the world--including all the facts about the universe on which God's reasons are based--just before the die toss result. This seems a paradigmatic case for God to be moderately likely to exercise providential control. Moreover, let us suppose with the typical Thomist that almost all the time, excepting cases of particularly spectacular demonstrations, God exercises providential control by the natural method. Suppose then:

  • P(God wills non-six | C and no miracle) > 0.95.
And since God wills non-six if and only if non-six occurs on the Thomistic view:
  • P(non-six occurs | C and no miracle) > 0.95.

Suppose that in fact three occurs. It is then obviously correct to explain the non-six by adverting to the above 0.95 probability. The question of interest to me is this: Can we also explain the non-six by the fact that natural causes described in C, in isolation from the facts about prayer and the like, had a probability of 5/6 of producing a non-six?


Heath White said...

Well, a ‘no’ answer has (what strike me as) implausible consequences. People often pray for outcomes which I suppose have some objective probability: that their side will win the battle, that their child will be healed, that they will get a toy train for Christmas, etc. Secular people often propose explanations of such events: the Union had a stronger military, the medicine worked, Mom and Dad knew you wanted a train and bought one, etc. But if the prayers are even a little efficacious, and your question is answered in the negative, then these explanations fail, for (on this hypothesis) unless we invoke the divine primary-causal explanation we lack (not merely ‘the’ explanation but) any explanation. It would be quite likely, for instance, that secular historians lack any explanation of the outcome of any battle involving Western forces in the last thousand years or so.

Alexander R Pruss said...

That sounds convincing in cases of probability boosting like this.

I want to note a few things.

1. Many of these explanations are merely causal rather than properly stochastic. I don't know exactly how to characterize the properly stochastic case. I am not even sure the case I gave is properly stochastic. My paradigm of a properly stochastic case is one that involves long-run probabilities of the sort involved in limit theorems like the law of large numbers, the central limit theorem, Bayesian convergence theorems, etc. So I am now more inclined to agree with you in cases that aren't like that.

2. Outside of lab situations and gambling, probabilistic explanations are not given with much numerical precision, but are things like "moderate" and "high". It will still be true that given the conditions, the probability of a non-six is "high".

3. Often the explanations are only causal. Those may be OK.

4. I think the best move in these kinds of cases--but I am sceptical that it will work in the "properly stochastic" cases though I could be wrong and it will--is a move I've advocated previously on the blog about the nature of probabilistic explanation. Suppose you toss non-six and explain it by saying that this had probability 5/6. "This had probability 5/6" is equivalent to a conjunction of two claims: (p) "This had probability at least 5/6" and (q) "This had probability at most 5/6."
Now (p) by itself explains why you got non-six, but (q) by itself does nothing at all to explain why you tossed non-six. If anything, it makes it harder to see why you tossed non-six. Moreover, while (p) by itself explains, this explanation does not get any better if you conjoin (q) to it. So (q) is by itself non-explanatory of the result, and doesn't improve the explanation given by (p). But we should remove irrelevancies from explanations. ("The coin was fair and green" is not an explanation of why it came up heads half the time, unless greenness somehow makes it more fair.) So the correct explanation of why we got non-six is: "The probability was at least 5/6." And that's true in my example, where it was 0.95.

5. Go back now to the properly stochastic cases of our previous discussions. I wonder now if what the Thomist couldn't say is this. God intends that about half of the coin tosses cause heads, and he intends this because of the causal tendency of heads and his desire for an orderly universe where statistics match tendencies. (He could also intend that a quarter of the tosses coin heads, but then he wouldn't be intending it because of the causal tendency of heads.) The secular scientist is wrong in thinking that the causal tendency directly and in the causal tendency way explains the statistics. But she is right in thinking that the causal tendency explains the statistics. And that's all we need for a reconciliation of science and theology. We don't need the scientists' metaphysics to come out right, but only their science.

It still seems to me that this isn't a chance-based explanation, though. This isn't chance either in the sense the scientist means nor in the sense the ordinary person means. It is only chance in a highly technical Thomistic sense. So it would be incorrect to talk of this as a reconciliation of chance and design, but it might be correct to talk of this as a reconciliation of probabilistic science and design.

Of course, I am still inclined to reject it because of what I think about the free will analogue, but that's a different kettle of fish, perhaps.

Heath White said...

I would not put a lot of weight on my own intuitions in this area, but I have some notion that what you are calling properly stochastic or chance-based explanations are more like mathematical explanations than causal explanations. (Formal not efficient causes, in Aristotelian lingo.)

If there is anything to that, then perhaps we can split up the puzzle into (roughly) “[how] can God primary-cause events with indeterministic secondary causes?” and “[how] can God primary-cause events which have certain probability distributions?”

My thought is that the connection between “x is a fair coin” and “x comes down heads about 50% of the time in a long series of trials” is synthetic when are focusing on causal explanations. Thus there is room to ask why are we so sure God will make the outcomes match the causal tendencies. The answer we are coming up with is that God is interested in an orderly universe and this interest of his doesn’t undercut secondary-causal explanations after all. But, I want to say, the connection is analytic when we are focusing on properly statistical explanations. In that sense, if a coin comes down heads 100% of the time, it is not a fair coin. Thus it is impossible for God’s primary causation to undercut properly statistical explanations.

Like I said, I would not put a lot of weight on my intuitions in this area.