The goal of this post is to layout various skeptical theistic theses. Skeptical theism is the position that we should be leery of our ability to limn the limits of God's reasons for permitting some cases of horrendous evils. Bergmann casts skeptical theism as responding to Rowe's noseeum inference: (P) No good we know of justifies God in permitting E1 and E2 (the bambi and sue cases) to (Q) No good at all justifies God in permitting E1 and E2. From (Q) one deduces that there's no God (~G).
Here's a list of various skeptical theistic theses in the order of strongest to weakest.
First group: evidential irrelevance
1. Necessarily, for any evil, P(G|e)=P(G).
(1) claims that necessarily evil is evidentially irrelevant to the existence of God. (1) is clearly subject to counterexample: let e be a trillion sentient creatures suffer endless torment. Skeptical theism need not be committed to denying that this would be evidence against theism.
2. For any evil, necessarily, P(G|e)=P(G).
(2) restricts the evils to evils that occur in the actual world and claims that they are such that necessarily they are evidentially irrelevant to the existence of God.
3. For any evil, P(G|e)=P(G).
(3) drops the embedded necessity operator. Depending on how one understands the nature of the P function and the nature of evil, 2 and 3 could be equivalent.
4. For E1 and E2 (and similar evils), P(G|E1&E2)=P(G).
This further restricts the evils in our world to those like the Bambi and Sue cases. One advantage of this restriction is that it allows skeptical theism to be viewed as a special case defense and not a general strategy defense. (Also, we can add back in the necessity operator to get further distinctions here).
Second group: Relevance but not significance (my gloss: "evil isn't a game changer")
An evil is a game-changer if it can tip the balance of evidence in favor of atheism or agnosticism. A no-game changer version of skeptical theism says that while evil can detract from the probability of God it can't be the proverbial straw that brought the camel's back. I shall represent the 'no-game changer thesis' by using '≈'. This represents that the probabilities are closely similar.
5. Necessary, for any evil, P(G|e)≈P(G).
6. For any evil, necessarily, P(G|e)≈P(G).
7. For any evil, P(G|e)≈P(G).
8. For E1 and E2 (and similar evils), P(G|e)≈P(G).
To undermine Rowe's inference all Bergmann and company need is 8. Thus, the skeptical theist can easily recognize that there are many evils that could occur that would significantly distract from the probability of theism. Also, 8 is interesting because it allows skeptical theism to be viewed as a special case defense that can be run along with other defenses--the free will defense, the soul-making defense, the value of natural laws, etc.