In an earlier post I mentioned the importance of making distinctions when approaching the problem of evil, one being the distinction between the logical problem and the evidential problem. This distinction informs our response to each, helping us to see what's "in play" and what's not. And when it comes to the logical argument we discover that the theist cannot respond by accusing the atheist of presupposing some objective standard of goodness by which to measure evil. Let me explain.
When making the logical argument the atheist is trying to point out a logical contradiction within the theist's worldview. If he succeeds in demonstrating the contradiction then one or more or the propositions in question, again within the theist's worldview, is false. But notice, this does not commit the atheist to the actual existence of the things in question (e.g. evil, an omnibenevolent God). The atheist is standing outside of our worldview so to speak, looking in on it, and examining it. He sees two or more contradictory propositions and so he points them out: "Hey, you theists believe an all-good, all-powerful God exists but you also believe that evil exists--that's a contradiction. It's like saying 2 + 2 = 4 and 2 + 2 = 5 at the same time."
Merely pointing out the logical contradiction does not commit the atheist to the actual existence of evil. Indeed, it does not matter what the atheist thinks about evil in order for him to show logical inconsistencies in another individual's worldview and this is what he is attempting to do in the logical problem of evil. He is basically saying, "This is what you theists believe but it is contradictory, so this is a problem for you, not me." Thus the theist cannot respond that the atheist is presupposing the existence of an objective moral standard of goodness. However, when we come to the evidential problem of evil the atheist is commited in this manner, as we shall see in an upcoming post.