Greg lays out a classic argument that God does not exist, which he calls "The Problem of Evil." He distinguishes two versions of that argument, which are sometimes called "the deductive" and "the evidential" version. He goes into some details on the deductive version.
Greg gives a response to the deductive version of the Problem of Evil on behalf of someone who believes that God exists. In thinking about this response, we need to think about whether God can make contradictions true, and whether God can have good reasons for allowing bad things to happen.
Greg considers the evidential version of the Problem of Evil, and gives a response on behalf of someone who believes that God exists. This involves considering whether God might have a good reason to allow bad things to happen.