I am sick to death of people defining God's omnipotence by the capacity to do all that is logically possible. That is not a logically self-consistent idea. We can prove it right now.
- God is omnipotent (definition).
- Omnipotence is the capacity to perform any logically possible task (definition).
- Therefore, God has the capacity to perform any logically possible task (from 1, 2).
- If I can imagine some logically possible world wherein some task is being performed, then that task is logically possible to perform (definition of a logically possible action/task).
- Given any finite rock, I can imagine a logically possible world wherein it is being lifted (definition of possible worlds---the proposition is self-consistent so it is necessarily possible to imagine).
- Therefore, it is logically possible to lift any finite rock (from 4,5).
- Therefore, God can lift any finite rock (from 3,6).
- I can create a finite rock such that its own creator cannot lift it (observation---I can only lift so much weight).
- If I can create a finite rock such that its own creator cannot lift it, then it is logically possible to create a finite rock such that its own creator cannot lift it (modal axiom B---actual implies necessarily possible).
- Therefore, God can create a finite rock such that its own creator cannot lift it (from 3,9).
- If a rock is created by God, then God is the creator of that rock (definition of "creator").
- If God can create a finite rock such that its own creator cannot lift it, then God can create a finite rock such that God cannot lift it (from 11).
- If God can create a finite rock such that God cannot lift it, then there exists a finite rock such that God cannot lift it (definition of create---to bring into existence; the rock does not have to be actual, either; I can simply imagine an element of that set, and the set is officially nonempty).
- If there exists a finite rock such that God cannot lift it, then God cannot lift any finite rock (from set theory---there exists an element of the set of finite rocks that is outside of the set of things that God can lift).
- Contradiction with 6: (God can lift any finite rock) and (God cannot lift any finite rock).
The logic has spoken, guys. Just give it up already and find another definition for omnipotence. I defy anyone to explain which premise they disagree with.