See William Rowe, “The Problem of Evil,” in Philosophy of Religion (Belmont: CA, Wadsworth, 2007), 112-31.
Rowe makes a strong positive case for why atheism is true. He supposes that, as especially in the absence of other arguments, anyone who observes the amount of human and animal suffering in the world and the truth of premise 1 in the evidential argument (that there are probably pointless evils) then this person would be rationally justified in believing atheism to be true. He presents two basic forms of the argument: the logical and the evidential problems of evil. The logical problem of evil argues that the existence of God and the existence of evil are logically contradictory claims. However, these aren’t explicitly contradictory—they are implicit (i.e. a married bachelor is an implicit contradiction and a married non-married person is an explicit contradiction). Rowe recognizes that we must abandon the logical problem of evil because the contradiction has yet to be proved (though he states that just because it has yet to be demonstrated doesn’t necessarily mean there isn’t one).
The evidential problem is a probabilistic argument, which argues that given the apparent [pointless] evil it is more probable that God does not exist than if God does exist. He uses the example of a fawn suffering for no apparent reason. Given that God would prevent this from happening and the fact that it does happen then God doesn’t seem to exist. Rowe seems to favor this form of the problem of evil over the logical problem.
Each of the arguments is countered with theistic objections to the problem of evil such as the free will defense and other theodicies. Rowe gives fair attention and representation of the competing explanations. He concedes that there are certainly rational grounds for believing in theism and advocates a form of friendly agnosticism or atheism and discourages any unfriendly forms of agnosticism or atheism.