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The omnipotence paradox is an argument that an omnipotent being cannot exist due to the following lines of argument. An omnipotent being is one that can do anything. Assuming there is such a being, one can then pose a question like the following: "Can an omnipotent being create a stone that is too heavy for him to lift? If he can create it, then there is one thing he can't do: lift the stone. If he can't create it, then there is one thing he can't do: create such a stone. Either way, there is something he can't do, which contradicts the assumption that he is omnipotent. This is a paradox."
Philosophical responses
One common response points out that this question makes implicit assertions that are inconsistent and self-contradictory. The phrase omnipotent being implicitly states that any phrase such as a stone too heavy for him to lift is meaningless. Thus, one solution to this type of paradox is to say that it is logically impossible for both entities to exist at the same time. So, there cannot be both an omnipotent God and an unliftable rock.
Therefore, a response is available if it is already accepted that God cannot do what is logically impossible:
- God cannot do what is logically impossible.
- It is logically impossible for there to be a stone God cannot move.
- So, God cannot create such a stone.
This necessarily accepts the view that even an omnipotent God cannot violate the laws of logic, and indeed this whole paradox can be seen as a strong reason for such a view. The philosopher Averroes advanced the omnipotence paradox for this reason (for which he was condemned by Bishop Tempier), although instead of phrasing it in terms of stones, he asked whether God could create a triangle whose internal angles did not add up to 180 degrees. (Note that the later discovery of non-Euclidean geometry does not resolve this question. One might as well ask, "If given the axioms of Riemannian geometry, can God create a triangle whose angles do not add up to less than 180 degrees?" In either case, the real question is whether, once God has decided to establish a system of axioms, can He evade the consequences which follow logically from them?)
However, the answer above can be restated even if one does not already accept that God cannot do logically impossible things: one can answer that the question is literally meaningless, and therefore there is not even a logically impossible task being set.
This is a useful distinction if one wants to hold (as some, including René Descartes, have held), that God can do even some logically impossible things, such as making 2+2=4 false.
Another solution is simply that an omnipotent being can create a stone too heavy for him to lift. The being's omnipotence depends on the nonexistence of such a stone, but his omnipotence also implies that the being can give up his unlimited power if he wishes. If he were to create such a stone, then he would in effect be relinquishing his omnipotence, but no logical contradiction would arise. (But in this "solution" may lie yet another problem: if God is omnipotent at any given point in time, he must also be omnipotent at any other time since he can manipulate the time axis arbitrarily without losing his omnipotence. Thus, God cannot choose to give up his omnipotence at any time.)
Yet another solution would be to say that creating a stone too heavy for God to lift is impossible, as God can do anything. But because God can do anything he must therefore be able to create a stone so heavy that he cannot lift it: God must be able to do the impossible if he is truly omnipotent. Once the stone is created, logically, it is impossible for God to lift. However, God can do the impossible, so he can lift a stone so heavy that he cannot lift it. In the words of Harry Frankfurt, "If an omnipotent being can do what is logically impossible, then he can not only create situations which he cannot handle but also, since he is not bound by the limits of consistency, he can handle situations which he cannot handle."
It could also be argued that with omnipotence comes omniscience. If God knew that he would be needing to lift the stone in the future, why would he create that stone?
See Omnipotence for a discussion on the various positions regarding the meaning of omnipotence.
Pop-culture and humorous responses
The omnipotence paradox has infiltrated popular culture. In an episode of The Simpsons, Homer asks rhetorically, "Could Jesus microwave a burrito so hot that He Himself could not eat it?"
One cheeky solution invokes a theory of physics called "quantum superposition". Quantum superposition refers to when an object appears to possess two states that would otherwise be mutually exclusive, simultaneously. It continues to appear this way until we attempt to observe it. The famous example of this is Schrödinger's cat: a cat is placed in a box with a radioactive atom that may or may not decay, and a detector (say a Geiger counter) is arranged so that if the atom decays, the cat is killed. Without opening the box, we do not know whether the cat is alive or dead, and for that time it is both alive and dead, in a state of superposition.
Thus, if we can never observe God, God may be able to both create a stone he cannot lift and lift it at the same time, and in this way resolving the paradox (albeit rather sneakily) and retaining his omnipotence. Of course, an omnipotent God could forever prevent us from observing him, and thus prevent us ever undoing the state of superposition.
This kind of tongue-in-cheek "scientific explanation" is often used for humorous effect, as in the proof that Heaven is hotter than Hell (http://www.lhup.edu/~dsimanek/hell.htm). It is also strongly reminiscent of Greg Egan's science fiction novel Quaratine.
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