The omnipotence paradox is a family of paradoxes that arise with varying understandings of the concept of omnipotence. 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 Saadia Gaon responded to the question of whether God's omnipotence extended to logical absurdities.The Select Book of Beliefs and Convictions, Kafich ed. and translation, p. 114 (retyped online). Corresponding section in Rosenblatt's English translation (The Book of Beliefs and Opinions, Yale Judaica, 1948) p. 134. It was later addressed by AverroesAverroës, Tahafut al-Tahafut (The Incoherence of the Incoherence) trans. Simon Van Den Bergh, Luzac & Company 1969, sections 529–536 and Thomas Aquinas.Aquinas, Thomas Summa Theologica Book 1 Question 25 article 3 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 lift, 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 lift, 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.Savage, C. Wade. "The Paradox of the Stone" Philosophical Review, Vol. 76, No. 1 (Jan., 1967), pp. 74–79 This modern version is referred to as the Paradox of the Stone.
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.Haeckel, Ernst. The Riddle of the Universe. Harper and Brothers, 1900. Some modern approaches to the problem have involved semantic debates over whether language—and therefore philosophy—can meaningfully address the concept of omnipotence itself.Wittgenstein, Ludwig. Tractatus Logico-Philosophicus (6.41 and following)
Proposed answers Omnipotence does not mean breaking the laws of logic A common response from philosophers is that the paradox assumes a wrong definition of omnipotence. Omnipotence, they say, does not mean that God can do anything at all but, instead, that he can do anything that is logically possible; he cannot, for instance, make a square circle. Likewise, God cannot make a being greater than himself, because he is, by definition, the greatest possible being. God is limited in his actions by his nature. The Christian Bible, in passages such as Hebrews 6:18, says it is "impossible for God to lie".https://www.alwaysbeready.com/images/stories/alwaysbeready/geisler%20norman%20-%20how%20to%20approach%20bible%20difficulties%20a.pdf
A good example of a modern defender of this line of reasoning is George I. Mavrodes.Mavrodes, George. "Some Puzzles Concerning Omnipotence " first published 1963, now in The Power of God: readings on Omnipotence and Evil. Linwood Urban and Douglass Walton, eds. Oxford University Press 1978 pp. 131–34 Essentially, Mavrodes argues that it is not a limitation on a being's omnipotence to say that it cannot make a round square. Such a "task" is termed by him a "pseudo-task" as it is self-contradictory and inherently nonsensical. Harry Frankfurt—following from René Descartes—has responded to this solution with a proposal of his own: that God can create a stone impossible to lift and also lift said stone.
For why should God not be able to perform the task in question? To be sure, it is a task—the task of lifting a stone which He cannot lift—whose description is self-contradictory. But if God is supposedly capable of performing one task whose description is self-contradictory—that of creating the problematic stone in the first place—why should He not be supposedly capable of performing another—that of lifting the stone? After all, is there any greater trick in performing two logically impossible tasks than there is in performing one?Frankfurt, Harry. "The Logic of Omnipotence" first published in 1964 in Philosophical Review and now in Necessity, Volition, and Love. Cambridge University Press November 28, 1998 pp.1–2
If a being is accidentally omnipotent, it can resolve the paradox by creating a stone it cannot lift, thereby becoming non-omnipotent. Unlike essentially omnipotent entities, it is possible for an accidentally omnipotent being to be non-omnipotent. This raises the question, however, of whether the being was ever truly omnipotent, or just capable of great power. On the other hand, the ability to voluntarily give up great power is often thought of as central to the Christian doctrine of incarnation.Gore, Charles, "A Kenotic Theory of Incarnation" first published 1891, in The Power of God: readings on Omnipotence and Evil. Linwood Urban and Douglass Walton, eds. Oxford University Press 1978 pp. 165–68
If a being is essentially omnipotent, it can also resolve the paradox. The omnipotent being is essentially omnipotent; therefore, it is impossible to be non-omnipotent. Further, the omnipotent being can do what is logically impossible—just like the accidentally omnipotent—and has no limitations except the inability to become non-omnipotent. The omnipotent being cannot create a stone it cannot lift.
The omnipotent being cannot create such a stone because its power is equal to itself, thus removing the omnipotence, for there can only be one omnipotent being, but it nevertheless retains its omnipotence. This solution works even with definition 2, as long as we also know the being is essentially omnipotent rather than accidentally so. However, non-omnipotent beings can compromise their own powers, which presents the paradox that non-omnipotent beings can do something (to themselves) which an essentially omnipotent being cannot do (to itself). This was essentially the position Augustine of Hippo took in his The City of God:
For He is called omnipotent on account of His doing what He wills, not on account of His suffering what He wills not; for if that should befall Him, He would by no means be omnipotent. Wherefore, He cannot do some things for the very reason that He is omnipotent.
Thus, Augustine argued that God could not do anything or create any situation that would, in effect, make God not God.
In a 1955 article in the philosophy journal Mind, J. L. Mackie tried to resolve the paradox by distinguishing between first-order omnipotence (unlimited power to act) and second-order omnipotence (unlimited power to determine what powers to act things shall have).Mackie, J. L., "Evil and Omnipotence." Mind LXIV, No. 254 (April 1955). An omnipotent being with both first and second-order omnipotence at a particular time might restrict its own power to act and, henceforth, cease to be all-powerful in either sense. There has been considerable philosophical dispute since Mackie about the best way to formulate the paradox of omnipotence in formal logic.The Power of God: Readings on Omnipotence and Evil. Linwood Urban and Douglass Walton, eds. Oxford University Press, 1978. Keene and Mayo disagree p. 145, Savage provides three formalizations pp. 138–41, Cowan has a different strategy p. 147, and Walton uses a whole separate strategy pp. 153–63 More recently, Budaev trivialized the paradox of the stone by converting it to an arithmetic form: "Can a person make such a big number that he/she cannot imagine a number greater than that?"Budaev, S., The Omnipotence Paradox Reduces to the Omniidiota Dilemma. Available at SSRN: https://ssrn.com/abstract=5017222 (November 07, 2024)., apparently resulting in a solution similar to that by SavageSavage, C. Wade. "The Paradox of the Stone" Philosophical Review, Vol. 76, No. 1 (Jan., 1967), pp. 74–79 : "God can create stones of any poundage and God can lift stones of any poundage": "One can imagine any number and always make an even bigger number".
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