Peter Geach

• How does traditional interpretations of God leave us with problems?

  "God is absolutely omnipotent" means that God can do everything absolutely. Everything that can be expressed in a string of words even if it can be shown to be self-contradictory. This position is advanced by Descartes. It has the theological advantage of making God prior to the laws of logic. However, it gives rise to the philosophical disadvantage of making God's nature potentially self-contradictory, rather than philosophically coherent and is left in the air as an unsolvable paradox.
• What is another way traditional interpretations of God leave us problems?

  "God is omnipotent" means “God can do X" is true if and only if X is a logically consistent description of a state of affairs. This position was advocated by Thomas Aquinas. This definition of omnipotence solves some of the paradoxes associated with omnipotence, but this brings about a new problem that if God is bound by logic he therefore cannot be the author of logic.
• What is another way traditional interpretations of God leave us problems?

  "God is omnipotent" means "God can do X" is true if and only if "God does X" is logically consistent. Here the idea is to exclude actions which would be inconsistent for God to do but might be consistent for others. Again sometimes it looks as if Aquinas takes this position. However, this account may still have problems with temporal issues like X = "brings it about that Rome was never founded."
• What is another way traditional interpretations of God leave us problems?

  "God is omnipotent" means whenever "God will bring about X" is logically possible, then "God can bring about X" is true. This sense also does not allow the paradox of omnipotence to arise, and unlike definition 3 avoids any temporal worries about whether or not an omnipotent being could change the past. However, even this sense of omnipotence misunderstands the nature of God's promises.
• What is Peter Geach's personal view on omnipotence?

  I believe that the only acceptable solution is to define God’s omnipotence as meaning  "God is almighty", which entails that God is not only more powerful than any creature; it means that no creature can compete with God in power, even unsuccessfully. In this account nothing like the omnipotence paradox arises, because God is seen as all-powerful in the sense of ‘having undisputed power over all’ rather than as being capable of doing absolutely anything.