The omnipotence paradox is a family of paradoxes that arise with some understandings of the term omnipotent. The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, even a logically contradictory one such as creating a square circle. Atheological arguments based on the omnipotence paradox are sometimes described as evidence for countering theism. Other possible resolutions to the paradox hinge on the definition of omnipotence applied and the nature of God regarding this application and whether omnipotence is directed toward God Himself or outward toward his external surroundings.
The omnipotence paradox has medieval origins, dating at least to the 10th century, when the Saadia Gaon responded to the question of whether God's omnipotence extended to logical absurdities. It was later addressed by Averroes and Thomas Aquinas. Pseudo-Dionysius the Areopagite (before 532) has a predecessor version of the paradox, asking whether it is possible for God to "deny Himself".
The best-known version of the omnipotence paradox is the paradox of the stone: "Could God create a stone so heavy that even he could not lift it?" This is a paradoxical question because if God could create something he could not do, then he would not be omnipotent. Similarly, if God was able to lift the stone then that would mean he was unable to create something he could not do, leading to the same result. Alternative statements of the paradox include "If given the axioms of Euclidean geometry, can an omnipotent being create a triangle whose angles do not add up to 180 degrees?" and "Can God create a prison so secure that he cannot escape from it?".
Overview
A common modern version of the omnipotence paradox is expressed in the question: "Can [an omnipotent being] create a stone so heavy that it cannot lift it?" This question generates a dilemma. The being can either create a stone it cannot lift, or it cannot create a stone it cannot lift. If the being create a stone that it cannot lift, then it is not omnipotent because there is a weight threshold beyond its own power to lift. If the being create a stone it cannot lift, then there is something it cannot create, and is therefore not omnipotent. In either case, the being is not omnipotent.
A related issue is whether the concept of "logically possible" is different for a world in which omnipotence exists than a world in which omnipotence does not exist.
The dilemma of omnipotence is similar to another classic paradox—the irresistible force paradox: "What would happen if an irresistible force were to meet an immovable object?" One response to this paradox is to disallow its formulation, by saying that if a force is irresistible, then by definition there is no immovable object; or conversely, if an immovable object exists, then by definition no force can be irresistible. Another response to this that the only way out of this paradox is if the irresistible force and immovable object never meet. However this does not hold up under scrutiny, because an object cannot in principle be immovable if a force exists that can in principle move it, regardless of whether the force and the object actually meet.
Types of omnipotence
Augustine of Hippo in his City of God writes "God is called omnipotent on account of His doing what He wills" and thus proposes the definition that "Y is omnipotent" means "If Y wishes to do X then Y can and does do X".
The notion of omnipotence can also be applied to an entity in different ways. An essentially omnipotent being is an entity that is necessarily omnipotent. In contrast, an accidentally omnipotent being is an entity that can be omnipotent for a temporary period of time, and then becomes non-omnipotent. The omnipotence paradox can be applied to each type of being differently.
In addition, some philosophers have considered the assumption that a being is either omnipotent or non-omnipotent to be a false dilemma, as it neglects the possibility of varying degrees of omnipotence. Some modern approaches to the problem have involved semantic debates over whether language—and therefore philosophy—can meaningfully address the concept of omnipotence itself.