Is the existence of evil compatible with the existence of an omnipotent god with the ability to desire to eliminate evil? That seems unlikely and many antitheological arguments have been based upon just that. A solid argument makes the existence of the traditional God unlikely at best - and belief in it unreasonable.

John at Fake Barn Country offers a reconstruction of such an argument from John Mackie:

(1) A good thing always eliminates evil as far as it can. (Premise)
(2) There is no limit to what an omnipotent thing can do. (Premise)
(3) If there is no limit to what an omnipotent thing can do, then it can eliminate evil completely. (Implicit Premise)
(4) A good omnipotent thing eliminates evil completely. (By 1 - 3)
(5) The existence of a good omnipotent thing is inconsistent with the existence of evil. (By 4)
(6) God is wholly good. (Premise)
(7) God is omnipotent. (Premise)
(8) Therefore, the existence of God is inconsistent with the existence of evil. (By 5 - 7).

As this argument demonstrates, it isn’t enough to simply say that omnipotence and the existence of evil are contradictions. We must add a number of things: that good and evil are opposed to each other, that good eliminates evil whenever possible, and that omnipotence doesn’t allow for any limits. A theist might try to challenge any or all of these premises, but they are completely consistent with the beliefs of traditional theists in the western religions. Thus, this is not only a logically valid argument but also an effective argument against typical forms of theism.

Read More:

• Religion 101
• Theism 101
• Does God Exist?