The Thomistic reconciliation of design with chance—of which Barr's reconciliation is a special case—holds that, necessarily, each particular chancy event occurs precisely because God causes it with primary causation. Now, if p and q are propositions that have the property that, necessarily, p is true if and only q is true, then P(p)=P(q) and P(p|r)=P(q|r) for any proposition r such that P(r)>0 and, in fact, intuitively, for any possibly true r for which the conditional probabilities are defined. Suppose:
- P(the coin lands heads)=1/2.
- P(God primarily causes the coin to land heads)=1/2.
If the probabilities are epistemic, there may be less of a problem. For typically we have no reason to think God prefers the coin to land heads than to land tails or vice versa, and so the epistemic probability of his causing it to land heads may be 1/2. (Generalizing this to other cases may be problematic. How would this work for a Poisson or Gaussian distribution? To suppose a Poisson or Gaussian distribution on God's preferences would be weird.)
But if the probability in (1) is merely epistemic, then it isn't going to be useful for explaining why of a hundred tosses about fifty landed heads. Maybe one could still explain it by saying that God's preferences are likely to be randomly or quasi-randomly distributed, because of the great diversity of factors that affect God's choices about different coin flips. But then it is (2) rather than (1) that is the real explanation of why about fifty tosses landed heads: our explanation essentially involves a random distribution on the factors that God's decision is made on the basis of.
A non-Thomist (and by that I just mean someone who doesn't accept this reading of Thomas and the corresponding reconciliation—she might be a Thomist in all sorts of other ways) could say that God doesn't specifically choose which way each coin toss goes, but cooperates with the coin-tosses in a way that does not determine the specific outcome. Of course, God can still work a miracle and specifically choose a coin outcome, but then that outcome will be miraculous (in a weak sense of the word not implying God's self-revelation in the event) and not random. Such a non-Thomist will then say:
- P(the coin lands heads | no miracle)=1/2
- P(God cooperates in a way that results in the coin landing heads | no miracle)=1/2.
I do not think this is available to the Molinist: I suspect it only works on simple foreknowledge (or open theist, for that matter) views.
Mike Almeida has told me that he has worried about the coincidence between (1) and (2) as well.