Infinite Power and Finite Powers

Alexander Pruss and I have proposed an analysis of omnipotence which makes no use of the problematic terms 'power' and 'ability'. However, this raises an obvious worry: if our analysis is not related to the notion of power, then how can it count as an analysis of omnipotence, the property of being all-powerful, at all? In this paper, I show how omnipotence can be understood as the possession of infinite power (general, universal, or unlimited power) rather than the possession of particular powers. I then argue that the ordinary notions of particular powers or abilities can be understood as applying vague limitations to the notion of infinite power. The vagueness of these limitations is the source of the well-known difficulties in the analysis of ability.