All of the extant definitions of omnipotence are missing what seems to me to be an important ingredient. A typical definition says something like: "God can do anything that's logically possible." But that's not quite enough. One needs to specify that God can do everything effortlessly. This is an easy emendation, of course, but an important one.
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I wonder if the latter is contained in the former, and whether the latter can stand on its own.
If it was impossible to do anything without some effort, then God could do anything possible, but wouldn't be able to do so without effort. If you were pedantic wouldn't you have to say "God can do anything possible" and "Anything that's possible can possible be done effortlessly", or "God can do anything possible, effortlessly" Merely saying "God can do anything effortlessly" might not be enough, because if there was a possible thing that could be done, that did require some effort (Christ's sacrifice perhaps), then that would suggest that there would be something God couldn't do.
If we specify that God can do everything effortlessly, are we really prepared to deal with this reality? Most of us can handle easily enough God doing anything that's logically possible. That is called God being providential. But what if God were to do something that's not logically possible? I would say most of us would be baffled, perplexed, and perhaps more than a little scared. This is why most of us do not experience God doing the things that are not logically possible. And when He does something that is not logically possible, for most of us he does it as a small thing because we are too fragile for Him to subject us to the really really big things out there.
What would it even mean to say the contrary?
What would it mean to say that God is unable to accomplish P effortlessly? How does the meaning of, God does P, change when we add, 'with effort'. What is added?
In the case of the human agent, such additions might function by denoting some psychological characteristics of the agent at the time of action, something like frustration or discontent resulting from failed attempts.
"By the seventh day God completed His work which He had done, and He rested on the seventh day from all His work which He had done." (Genesis 2:2)
That doesn't sound like a being who acts "effortlessly" to me.
Here's a simple proof that omnipotence entails effortlessness. Let the completion of task T require effort E to complete. Possibly, T requires effort E' < E to complete. And generally, for any T, if the completion of T takes E to complete, then it is possible that T takes E' < E to complete. So, if it takes effort E for an omnipotent being to complete task T, then there is some being from whom it takes less effort. That's not possible. So it takes God no effort.
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