The Existence of God I agree that free will is a good start (though not more than that) that there can be compensating goods for evils. I'm still not sure that's the best defense of evils brought about free will. I take free will as a given. By definition, God is not responsible for evil caused by free will (though he could be expected to sometimes intervene to soften its evil results--that's what a lot of petitionary prayer is about). It seems unnecessary to show that there are compensating goods for free will. Are you saying that, because of the evil it allowed, God would not have given us free will if it did not contribute to greater good that non-free will? Then you're faced with the same computational problem as with natural evil. I'm more inclined to just give God a pass on free will evil and not do any computations. I'm not entirely sure we'd even be having a discussion like this if we didn't have free will--or at least the mental capacity that results in free will. We're having this discussion at least in part because we have free will about whether to believe that God exists. Hence we're morally culpable if God exists and we don't believe s/he exists.
I'm inclined to proceed like this. The starting point is that an all-powerful and perfectly good God would not permit evil. However, we then realize evil results in part from human free will--which we consider good. We also see the good that comes from at least some of the natural challenges that we face. They can help us develop and grow.
But then I have two serious problems: (1) even if all evils are outweighed by the good they create, aren't the means God uses often immoral? I don't think many of us would say that we should murder an innocent person so that several other innocent people can harvest her organs and continue to live. We can't defend the use of immoral means in order to create a greater good. Yet the argument, even if it doesn't necessitate the use of immoral means, clearly permits God to use immoral means. The only consideration is whether the means create greater good. Natural evil results in all kinds of death and suffering that is neither deserved nor fairly distributed. It sounds like God is thought of as an act utilitarian--though maybe not just in reference to humans. Through natural evil, God does countless things that we would put people in jail for.
(2) While some degree of natural suffering might be good for an individual, it seems implausible that hideous amounts of pain are good for that individual. It's "pointless" at least so far as that individual goes. Either the good result could have been achieved with much less pain, or the treatment destroys the patient, or the pain is an immoral means of obtaining the good result.
Anyway, I'm inclined to say that, for natural evil, any non-trivial amount of evil that meets the criteria in (1) or (2) above falsifies the proposition that God is perfectly good unless and until the theist can show (or at least make a plausible case) both that the natural evil is not immoral and that it is not pointless. The burden of proof shifts to the theist. That's how science works. It's an empirical argument. The skeptic has not "proven" deductively that God is not perfectly good, but s/he's overcome whatever evidence the theist has for saying that God is perfectly good. The logical possibility that God is perfectly good is not evidence that God is perfectly good.
How would you argue against the claim that God is a completely malevolent being who uses good to increase the amount of evil? The atheist could say that it's logically possible and therefore s/he does not need to show that there are compensating evils for the good that exists.
I wonder if the main point of saying it's logically possible that God is perfectly good is to allow room for faith, ie, simply believing that God is perfectly good without any reasons--except perhaps revelation in the Bible. Many theists don't want to be irrational in the sense of believing things that are formal contradictions, like God creating a round square. Using a noseeum argument to show it's logically possible that God is perfectly good, despite widespread evil, keeps theists from having to believe a formal contradiction. Then faith/belief enters the scene.