God, Über-God, and Unter-God

I examine two related arguments for the claim that if God is omnipotent, God cannot lack abilities such as the ability to do evil or to act irrationally. Both arguments concern the idea that omnipotence is inconsistent with being dominated with respect to abilities. I raise new issues in the formulation of such dominance principles about ability, and attempt to solve them. I also discuss and reject existing objections to these arguments. I conclude that these arguments are promising but not conclusive, and that important work remains to be done in formulating the relevant dominance principles.