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.
- 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?