Suppose that a Molinist God creates a world where there is a sequence of 1000 indeterministic throws of a fair coin, and suppose that middle knowledge extends to stochastic non-agential events. (My argument will also apply in the case of Thomist God who determines indeterministic events.) Suppose 514 of the coin throws, let us suppose, are heads and 486 are tails. Consider the fact p that approximately half of the throws landed heads. A standard scientific explanation of p would involve the following facts:
- The coin was fair: heads and tails each had probability 1/2.
- The individual throws of the coin were independent of one another.
- If (1) and (2) hold, then by an appropriate version of the Law of Large Numbers, it is likely that a sequence of 1000 throws of the coin would have approximately half of them be heads.
Fact (3) is a mathematical fact. Facts (1) and (2) are concrete facts about the situation at hand, and both are essential. If (1) is false, we might well expect a different heads-to-tails ratio. If (2) is false, then the Law of Large Numbers need not apply.
But this scientific explanation is unlikely to be correct if Molinism holds. For if Molinism holds, then God in effect controls what sequences of throws come up, by choosing the antecedents of counterfactuals. God makes the choice of sequence based on global providential considerations. Since the sequence is chosen on the basis of considerations of the sequence as a whole, it seems unlikely that the items in the sequence will be independent.
Suppose we say, as I suggested in the previous thread in response to Mike’s related concern, that God deliberately chooses a sequence of events that is statistically apparently random. Then p will still be true–about half of the throws will land heads. However, (2) will not be true, at least not if we condition on God’s choosing a sequence of events that is statistically apparently random. For, if (1) and (2), hold we have a non-zero probability that all the throws will be heads. But conditionally on of (1) and the claim that God chose a sequence of events that was statistically apparently random, we get a zero probability that all the throws will be heads, since if all the throws were heads, the sequence could not be statistically apparently random.
Perhaps we shouldn’t condition on God’s choosing a sequence of events that is statistically apparently random. But if we don’t condition on that, then to check whether (1) and (2) we need to compute the probabilities of all the possible choices God could have made. And we have little reason to think (1) and (2) will hold then.