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.

There is a rich tradition within game theory, decision theory, economics, and philosophy correlating practical rationality with impartiality, and spatial and temporal neutrality. I argue that in some cases we should give priority to people over both times and places, and to times over places. I also show how three plausible dominance principles regarding people, places, and times conflict, so that we cannot accept all three. However, I argue that there are some cases where we should give priority to times over people, suggesting that there is impersonal value to the distribution of high quality life over different times.