Molinism and statistical explanation
June 7, 2008 — 0:38

Author: Alexander Pruss  Category: Molinism  Tags: ,   Comments: 6

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:

1. The coin was fair: heads and tails each had probability 1/2.
2. The individual throws of the coin were independent of one another.
3. 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.

• By “the individual throws” in (2), I meant “the outcomes of the individual throws”.

June 7, 2008 — 10:11
• Alex,
Because (2) is not true (as I also mention in the comments to my post) I argue (in the paper from which my post is excerpted) that rational and cautious agents will not be responsible for their choices. This is another bad outcome of Molinist assumptions and this bad outcome holds whether God chooses a sequence of events that appears random or not. To take a simple example, for each roll of a fair die, God chooses a die D such that, were D rolled in C, it would come up N. Rational agents should use the Principal Principle (given certain provisos) to adjust credence to chance. A rational agent will put his credence that N occurs at 1/6 and act accordingly. Unfortunately, the probability of N is not 1/6 (though the chance of N is 1/6) and behavior based on that assumption will often lead to very bad results. This is not the fault of the rational agent, who is doing just what he ought to do. So he cannot be held responsible for his choices.

June 7, 2008 — 11:11
• I don’t see why this bad outcome happens if God chooses a sequence that appears random. Behavior based on the Principal Principle will only go badly if the frequencies depart from those predicted by the Principal Principle. But if God chooses a sequence that appears random, the frequencies will not thus depart.

June 7, 2008 — 13:22
• Could you explain the distinction between chances and probabilities? Thanks!

June 7, 2008 — 13:22
• Alex,
Take the fair die D. Assume that the die has a 1/6 propensity to land on 2. But God chooses D in such a way that, were it rolled in C, it would land 5. Suppose I’m very short on resources, I’m trying to keep my familiy alive and my last best hope is to wager on what D will land in C. How do I set my credence for D landing on 2? I use the Principal Principle (in its standard form), using ‘E’ for admissible evidence, ‘Cr’ for credence and ‘Ch’ for chance,
1. Cr(2/E & Ch(2)= 1/6) = 1/6
Credence values should be set to chance values in the absence of “inadmissible evidence”. If I have spoken to a fortune teller about the future or, better, if I spoke with God about what would happen, then I set my credence NOT to chance, but to chance + the additional, inadmissible evidence.
If Molinists are right, there is always inadmissible evidence! There is always evidence such as “God has chosen D in such a way that it is certain to land 3 if rolled in C”. If I add that information, E*, to (1), then we get,
2. Cr(2/ Ch(2) = 1/6 & E*) = 0
I was using ‘probability’ to refer to the credence of rational agents on all of the stochastically relevant evidence. So here’s the problem. God is constantly picking and choosing undetermined events in ways that upset my decisions. Keep in mind: God is NOT choosing the die randomly! He only APPEARS to be doing so!
Suppose I set my credence to the chance of rolling 2 and wager on 2 appropriately. God makes certain, in his own choice of D to have rolled in C, that I lose. So He is responsible for the suffering my family endures as a result of that loss. I am certainly not responsible. I would be responsible if I lost fair and square, but I did not lose fair and square.

June 7, 2008 — 13:54
• Maybe double effect can help the Molinist to get out of this problem? Thus, God doesn’t intend your family’s suffering, though he does intend the particular dice outcome that leads to your family’s suffering.

June 8, 2008 — 21:59