Let’s grant that if sceptical theism is true, then for any evil E, we have no reason to think that the prevention of E will lead to an overall better result than letting E happen, so the fact that we do not see God preventing E is not evidence against the existence of God, since we have no more reason to think that God would prevent E than that he would not. The standard objection is that then we have no reason to prevent E, since we have no reason to think that the overall result will be better if we prevent E.
This objection is mistaken. Suppose I offer you a choice of two games–you must play the one or the other. Each game lasts forever. In Game A, you get pricked in the foot with a thorn on the first move. In Game B, nothing happens to you on the first turn. And that’s all you know. (You don’t know if God exists or anything like that.) Which game should you choose?
You should probably say you have the same probability of doing better by playing Game A as by playing Game B. Why? Well, let Games A* and B* be Games A and B minus their first steps. You know nothing about Games A* and B*. (You don’t know if the first step is a sign of what it is to come, or maybe the sign of the opposite of what is to come, or completely uncorrelated with what comes later.) Now given a pair of infinitely long games about which you know nothing, the overall difference in outcome utility can be minus infinity, plus infinity, undefined, or finite. The likelihood that this difference would be within a pinprick is zero. But if the difference is not within a pinprick, then A is better than B iff A* is better than B*, and B is better than A iff B* is better than A*. Since we know nothing about A* and B*, we should not say that it’s more likely that A* is better than B*, nor the other way around. So, the probability that A would give a better result than B is the same as the probability that B would give a better result than A. (This calculation assumes Molinism. Without Molinism, it only works for deterministic games, or as an intuition-generator.)
Now if the reasoning in the anti-sceptical-theism argument is sound, you have no reason to choose Game B over Game A, since you have equal probabilities of doing better with A as with B. But in fact, despite this equality, you should choose Game B. For since you know nothing about what Games A* and B* are like, the expected value of Games A* and B* should be the same–even if it’s infinite, or even if it’s undefined. (Think of doing this with non-standard arithmetic.) So you have two options: first a pinprick, and then something with a certain (perhaps undefined) expected value; or just something with that same (perhaps undefined) expected value. And of course you should choose the latter–you should avoid the pinprick. The lesson here is that while beliefs are guided by probabilities, action is guided by expected values.
Next, let’s consider an analogy to the sceptical theism case. Suppose we observe Fred beginning to play. We are told by a friend that p, where p is the proposition that Fred is an omniscient and perfectly self-interestedly rational being, who in particular knows exactly what the outcomes of every step in Games A and B would be. (Maybe the games are deterministic, or maybe Fred has middle knowledge.) We observe that Fred chooses Game A. He gets the pinprick. And at that point we stop being able to observe. Now, if we knew that Fred chose the game that overall paid off less well, we would have good reason to deny p. Does the fact that Fred chose the pinprick give us any evidence against p? No! For the probability that Game B is better than Game A is no greater than the probability that Game A is better than Game B. So we have, in fact, no evidence that Fred chose the game that paid off less well, and no evidence against p. Nonetheless if we were asked to choose between the games, without having been able to observe Fred’s choice, we would have been irrational to choose Game A.
The same is true if we are dealing with non-self-interested rationality. Suppose that in Game A, an innocent person loses a leg on the first move, and in Game B, nothing happens on the first move. We have good moral reason to choose Game B. Nonetheless, if we know nothing more about the two games, we have no reason to think that Game B is more likely to result in a better overall outcome than Game A. But that Patricia chooses Game A is no evidence against the claim that she is an omniscient and a maximizer of the good. Nor can we say anything Roweian like: “We have no reason to think there is a reason to prefer Game A* over Game B*, so we should assume that there is no reason to prefer A* over B*, in which case Patricia is not both omniscient and a maximizer of the good.” For that is mistaken.
The same reasoning shows that even if our world is deeply chaotic, so that any tiny event might have enormous consequences (I break to avoid hitting a pedestrian, and that causes an earthquake in Japan next week, say), still we will have reason to prevent evils.
I should make one qualification. When I said that the probability that Game A is better than Game B is no less than the probability that B is better than A, one might object that the probability that B is better is infinitesimally greater. That may in fact be right. But the sceptical theist can agree that it is infinitesimally less likely that God would permit the evil E than that God would allow it. For while that admission will make the inductive argument from evil decrease the probability of the existence of God, it will only decrease it infinitesimally. And since we have in fact only observed a finite number of evils, even if one adds up all the decreases from all the evils, the total decrease will only be literally infinitesimal. Hence, if before the argument from evil, the probability of God’s existence was non-infinitesimally greater than 0.5 (say, it was 0.51), it will still be non-infinitesimally greater than 0.5 (if it originally was 0.51, it will now be 0.51-epsilon, where epsilon is an infinitesimal, and 0.51-epsilon is greater than, say, 0.509999), since an infinitesimal is smaller than every standard positive real number. The only time a finite number of infinitesimal disconfirmations could make a real difference is if the initial probability was exactly 0.5, or within an infinitesimal of 0.5, and even then the difference shouldn’t be that significant, I think.