The omnipotence paradox is a family of related paradoxes addressing the question of whether the existence of an omnipotent entity is logically possible. The paradox states that if a being can perform any action, then it should be able to create a task it is unable to perform, and hence, it cannot perform all actions. Yet, on the other hand, if it cannot create a task it is unable to perform, then there exists something it cannot do.
One version of the omnipotence paradox is the so-called paradox of the stone: "Could an omnipotent being create a stone so heavy that even that being could not lift it?" If so, then it seems that the being could cease to be omnipotent; if not, it seems that the being was not omnipotent to begin with.
The argument is medieval, dating at least to the 12th century, addressed by Averroës (1126–1198) and later by 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".
Answers to the paradox include that since God is supposedly omnipotent, the phrase "could not lift" does not make sense and the paradox is meaningless, and that logical impossibilities do not fall under the omnipotence of God. The omnipotence paradox is related to the problem of free will, because an omnipotent being should have the ability to freely choose to alter any laws that might hinder omnipotence.
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 which it cannot lift, or it cannot create a stone which it cannot lift. If the being can create a stone that it cannot lift, then it seems that it can cease to be omnipotent. If the being cannot create a stone which it cannot lift, then it seems it is already not omnipotent.
The problem is similar to another classic paradox, the irresistible force paradox: What happens when an irresistible force meets an immovable object? One response to this paradox is that if a force is irresistible, then by definition there is no truly immovable object; conversely, if an immovable object were to exist, then no force could be defined as being truly irresistible. But this way out is not possible in the omnipotence case, because the purpose is to ask if the being's omnipotence makes its own omnipotence impossible.
Types of omnipotence
Peter Geach describes and rejects four levels of omnipotence. He also defines and defends a lesser notion of the "almightiness" of God.
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