Say that a "God-disproving evil" is an evil that God, if he existed, would have no justification in permitting. Here is an argument:
- (Premise) If there are God-disproving evils, then pain in childbirth is a God-disproving evil.
- (Premise) If a pain is a God-disproving evil, then probably significant numbers of theists who suffer this pain thereby become atheists.
- (Premise) Very few theists who give birth and suffer the pain of childbirth thereby become atheists.
- Therefore, probably, the pain of childbirth is not a God-disproving evil. (2 and 3)
- Therefore, probably, there are no God-disproving evils. (1 and 4)
But if one wants more than soundness, I am not happy with (1). Maybe a better version would be: The sort of reasoning that makes one think that there are God-disproving evils makes one think that pain in childbirth is one. And then (2) and (3) serve to make one more suspicious of that sort of reasoning.
If one does like (1)-(5), we can add two fun steps:
- (Premise) Probably, if there is no God, there are God-disproving evils.
- Therefore, probably there is a God. (5 and 6)