I’ve addressed this in a much earlier post, and a little bit in passing on multiple occasions, but lots of people are for some reason convinced that it raises a problem with the Christian account of God, so here goes.
The omnipotence paradox consists of a question such as “Can God make a rock that’s so heavy He can’t lift it?” or, in my favorite formulation, “Can Jesus microwave a burrito so hot that even He can’t eat it without burning His mouth?” In either case, the paradox is supposed to point to an inherent contradiction in the concept of omnipotence, the ability to do anything. When formulated syllogistically, it looks like this:
P1 An omnipotent God can do anything, even bring about a state of affairs in which He is unable to do something.
P2 A state of affairs in which an omnipotent entity is unable to do something is a logical contradiction.
C Therefore, omnipotence results in logical contradiction.
This is a valid argument, but it accomplishes nothing (I’ll get to why this is in a sec). There are two ways to define omnipotence, henceforth referred to as Omni-1 and Omni-2.
Omni-1 omnipotence is defined as the ability to bring about any state of affairs that is not inherently logically contradictory. So God can create the world and turn water into wine, but He can’t make a square circle or a married bachelor, or cause colorless green ideas to sleep furiously, since those sets of concepts are contentless when combined in those ways. This is the view of omnipotence that I and many of the more rationalist Christian thinkers hold.
Omni-2 omnipotence is a bit stranger, and it holds that God can do absolutely anything, even bring about states of affairs that contradict themselves. On this view, God can make a square circle, whatever that means. If concepts can be combined into a proposition, God can cause the proposition to be true. This was Martin Luther’s view of God’s omnipotence and was shared by many Christian irrationalists.
So how do we get out of the paradox with these definitions?
If Omni-1 is what it means that God is omnipotent, the argument is unsound because P1 is false. It is a logical contradiction with the definition of omnipotence for a state of affairs to exist in which an omnipotent entity is unable to do something, where the ‘something’ is a logically coherent act. Therefore, an omnipotent entity can exist without contradiction, even though it is unable to bring about a state of affairs that contradicts its omnipotence.
If Omni-2 is what it means for God to be omnipotent, the argument becomes irrelevant. Sure, omnipotence is a logically contradictory category, but the bounds of possibility have already been expanded outside of logic by the definition of omnipotence. Even though an omnipotent God is not logically possible on Omni-2, He is still actually possible, since possibility no longer depends on logic.
The appeal of the paradox to popular audiences comes with a kind of conflation of the two definitions of omnipotence, using each at different points of the argument where it suits the arguer. The presenter of the paradox uses Omni-2 to support P1, where he claims that omnipotence is not bound by logical concerns, and he employs Omni-1 to support the conclusion’s importance, where possibility is bounded by logic. Thus, the argument proves the impossibility of an odd hybrid omnipotence that is simultaneously bound and not bound by the demands of logical possibility, which I will join in rejecting in favor of either consistent definition of omnipotence (but of course, Omni-1 is much nicer.)