Omnipotence paradox

Detail depicting Averroes, who addressed the omnipotence paradox in the 12th century, from the 14th-century Triunfo de Santo Tomás by Andrea da Firenze (di Bonaiuto).

The omnipotence paradox is a family of semantic paradoxes that explores what is meant by 'omnipotence'. If an omnipotent being is able to perform any action, then it should be able to create a task that it is unable to perform. Hence, this being cannot perform all actions (i.e. it is not omnipotent), a logical contradiction. The most well-known version of the omnipotence paradox is the so-called paradox of the stone: "Could an omnipotent being create a stone so heavy that even they could not lift it?" This phrasing of the omnipotence paradox is vulnerable to objections based on the physical nature of gravity, such as how the weight of an object depends on what the local gravitational field is. Alternative statements of the paradox that do not involve such difficulties include "If given the axioms of Riemannian 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?"

The omnipotence paradox is medieval, dating at least to the 12th century. It was 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".

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 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 it cannot lift, then it seems it is already 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. Some claim that the only way out of this paradox is if the irresistible force and immovable object never meet. But this is not a way out, 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

Main article: Omnipotence

Peter Geach describes and rejects four levels of omnipotence. He also defines and defends a lesser notion of the "almightiness" of God.

1. "Y is absolutely omnipotent" means that "Y" can do everything absolutely. Everything that can be expressed in a string of words even if it can be shown to be self-contradictory, "Y" is not bound in action, as we are in thought by the laws of logic." This position is advanced by Descartes. It has the theological advantage of making God prior to the laws of logic. Some claim that it in addition gives rise to the theological disadvantage of making God's promises suspect. On this account, the omnipotence paradox is a genuine paradox.
2. "Y is omnipotent" means "Y can do X" is true if and only if X is a logically consistent description of a state of affairs. This position was once advocated by Thomas Aquinas. This definition of omnipotence solves some of the paradoxes associated with omnipotence, but some modern formulations of the paradox still work against this definition. Let X = "to make something that its maker cannot lift." As Mavrodes points out there is nothing logically contradictory about this. A man could, for example, make a boat that he could not lift. It would be strange if humans could accomplish this feat, but an omnipotent being could not. Additionally, this definition has problems when X is morally or physically untenable for a being like God. But this brings about a new problem that if God is bound by logic he therefore cannot be the author of logic.
3. "Y is omnipotent" means "Y can do X" is true if and only if "Y does X" is logically consistent. Here the idea is to exclude actions that are inconsistent for Y to do, but might be consistent for others. Again sometimes it looks as if Aquinas takes this position. Here Mavrodes' worry about X= "to make something its maker cannot lift" is no longer a problem, because "God does X" is not logically consistent. However, this account may still have problems with moral issues like X = "tells a lie" or temporal issues like X = "brings it about that Rome was never founded."
4. "Y is omnipotent" means whenever "Y will bring about X" is logically possible, then "Y can bring about X" is true. This sense, also does not allow the paradox of omnipotence to arise, and unlike definition #3 avoids any temporal worries about whether or not an omnipotent being could change the past. However, Geach criticizes even this sense of omnipotence as misunderstanding the nature of God's promises.
5. "Y is almighty" means that Y is not just more powerful than any creature; no creature can compete with Y in power, even unsuccessfully. In this account nothing like the omnipotence paradox arises, but perhaps that is because God is not taken to be in any sense omnipotent. On the other hand, Anselm of Canterbury seems to think that almightiness is one of the things that make God count as omnipotent.

St Augustine 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.

Some Philosophers, such as René Descartes, argue that God is absolutely omnipotent. 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.

Proposed resolutions

Thomas Aquinas asserts that the paradox arises from a misunderstanding of omnipotence. He maintains that inherent contradictions and logical impossibilities do not fall under the omnipotence of God. J. L Cowan sees this paradox as a reason to reject the concept of 'absolute' omnipotence, while others, such as René Descartes, argue that God is absolutely omnipotent, despite the problem.

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). 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 omnipotent in either sense. There has been considerable philosophical dispute since Mackie, as to the best way to formulate the paradox of omnipotence in formal logic.

Another common response to the omnipotence paradox is to try to define omnipotence to mean something weaker than absolute omnipotence. This approach entails simply stipulating that omnipotence does not require that the being have abilities that are logically impossible, but only be able to do anything that conforms to the laws of logic. A good example of a modern defender of this line of reasoning is George Mavrodes. Mavrodes argues that it is no limitation on a being's omnipotence to say that it cannot make a round square. Harry Frankfurt responded to this solution with a proposal 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 supposed 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 supposed 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?

It could be assumed to be possible for non-omnipotent beings to compromise their own powers, which presents the paradox that non-omnipotent beings could be assumed to be capable of actions that an 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.

Language and omnipotence

The philosopher Ludwig Wittgenstein is often interpreted as arguing that language is not up to the task of describing the kind of power an omnipotent being would have. In his Tractatus Logico-Philosophicus, he stays generally within the realm of logical positivism until claim 6.4—but at 6.41 and following, he argues that ethics and several other issues are "transcendental" subjects that we cannot examine with language. Wittgenstein also mentions the will, life after death, and God—arguing that, "When the answer cannot be put into words, neither can the question be put into words."

Wittgenstein's work expresses the omnipotence paradox as a problem in semantics—the study of how we give symbols meaning. (The retort "That's only semantics," is a way of saying that a statement only concerns the definitions of words, instead of anything important in the physical world.) According to the Tractatus, then, even attempting to formulate the omnipotence paradox is futile, since language cannot refer to the entities the paradox considers. The final proposition of the Tractatus gives Wittgenstein's dictum for these circumstances: "What we cannot speak of, we must pass over in silence".

Wittgenstein's approach to these problems is influential among other 20th century religious thinkers such as D. Z. Phillips. In his later years, however, Wittgenstein wrote works often interpreted as conflicting with his positions in the Tractatus, and indeed the later Wittgenstein is mainly seen as the leading critic of the early Wittgenstein.

Other versions of the paradox

In the 6th century, Pseudo-Dionysius claims that a version of the omnipotence paradox constituted the dispute between St. Paul and Elymas the Magician mentioned in Acts 13:8, but it is phrased in terms of a debate as to whether or not God can "deny himself" ala 2 Tim 2:13. In the 11th century, St. Anselm argues that there are many things that God cannot do, but that nonetheless he counts as omnipotent.

Thomas Aquinas advanced a version of the omnipotence paradox by asking whether God could create a triangle with internal angles that did not add up to 180 degrees. As Aquinas put it in Summa contra Gentiles:

Since the principles of certain sciences, such as logic, geometry and arithmetic are taken only from the formal principles of things, on which the essence of the thing depends, it follows that God could not make things contrary to these principles. For example, that a genus was not predicable of the species, or that lines drawn from the centre to the circumference were not equal, or that a triangle did not have three angles equal to two right angles.

This can be done on a sphere, and not on a flat surface. The later invention of non-Euclidean geometry does not resolve this question; for one might as well ask, "If given the axioms of Riemannian geometry, can an omnipotent being create a triangle whose angles do not add up to more than 180 degrees?" In either case, the real question is whether or not an omnipotent being would have the ability to evade consequences that follow logically from a system of axioms that the being created.

A version of the paradox can also be seen in non-theological contexts. A similar problem occurs when accessing legislative or parliamentary sovereignty, which holds a specific legal institution to be omnipotent in legal power, and in particular such an institution's ability to regulate itself.

In a sense, the classic statement of the omnipotence paradox — a rock so heavy that its omnipotent creator cannot lift it — is grounded in Aristotelian science. After all, if we consider the stone's position relative to the sun the planet orbits around, one could hold that the stone is constantly lifted—strained though that interpretation would be in the present context. Modern physics indicates that the choice of phrasing about lifting stones should relate to acceleration; however, this does not in itself of course invalidate the fundamental concept of the generalized omnipotence paradox. However, one could easily modify the classic statement as follows: "An omnipotent being creates a universe that follows the laws of Aristotelian physics. Within this universe, can the omnipotent being create a stone so heavy that the being cannot lift it?"

Ethan Allen's Reason addresses the topics of original sin, theodicy and several others in classic Enlightenment fashion. In Chapter 3, section IV, he notes that "omnipotence itself" could not exempt animal life from mortality, since change and death are defining attributes of such life. He argues, "the one cannot be without the other, any more than there could be a compact number of mountains without valleys, or that I could exist and not exist at the same time, or that God should effect any other contradiction in nature." Labeled by his friends a Deist, Allen accepted the notion of a divine being, though throughout Reason he argues that even a divine being must be circumscribed by logic.

In Principles of Philosophy, Descartes tried refuting the existence of atoms with a variation of this argument, claiming God could not create things so indivisible that he could not divide them.

The paradox also appears in popular culture. In an episode of The Simpsons, Homer Simpson asks Ned Flanders, "Could Jesus microwave a burrito so hot that He Himself could not eat it?" In one strip of the webcomic Saturday Morning Breakfast Cereal, a child is seen asking a priest "Could God make an argument so circular that even He couldn't believe it?"

In the Marvel Comics Runaways, Victor Mancha, the technorganic android created by Ultron, is shown as unable to process correctly paradoxes: as such, it's known that a small number of well known paradoxes may force his logic in a permanent loop, shutting his functions down until someone steps in to give Victor the proper solution. As such, his peers stop him once by asking "Could God make a sandwich so big that even he couldn't finish it?", and reboot his mind by explaining him a simplified version of the God as essentially omnipotent solution ("Yes. God could make a sandwich so big that even he couldn't finish it, and eat it all").

In the book Bart Simpson's Guide to Life this question is phrased as, "If God can do anything, could he create a hot dog so big that even he couldn't eat it?"

See also

• Absolute monarchy
• Atlas, the deity responsible for holding the celestial spheres in Greek mythology
• Gödel's incompleteness theorems
• Irresistible force paradox
• Problem of evil
• Russell's paradox
• Semantics
• Theodicy

References

• Allen, Ethan. Reason: The Only Oracle of Man. J.P. Mendum, Cornill; 1854. Originally published 1784. (Accessed on 19 April 2006)
• Augustine. City of God and Christian Doctrine. The Christian Literature Publishing Co., 1890. (Accessed on 26 September 2006)
• Burke, James. The Day the Universe Changed. Little, Brown; 1995 (paperback edition). ISBN 0-316-11704-8.
• Gleick, James. Genius. Pantheon, 1992. ISBN 0-679-40836-3.
• Haeckel, Ernst. The Riddle of the Universe. Harper and Brothers, 1900.
• Hoffman, Joshua, Rosenkrantz, Gary. "Omnipotence" The Stanford Encyclopedia of Philosophy (Summer 2002 Edition). Edward N. Zalta (ed.). (Accessed on 19 April 2006)
• Mackie, J. L., "Evil and Omnipotence." Mind LXIV, No, 254 (April 1955).
• Wierenga, Edward. "Omnipotence" The Nature of God: An Inquiry into Divine Attributes. Cornell University Press, 1989. (Accessed on 19 April 2006)
• Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Available online via Project Gutenberg. Accessed 19 April 2006.