Omnipotence paradox

Omnipotence paradox

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The omnipotence paradox is a family of semantic paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

es which address two issues: Is an omnipotent entity logically possible? and What do we mean by 'omnipotence'?. 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
Averroes
' , better known just as Ibn Rushd , and in European literature as Averroes , was a Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy,...

 (1126–1198) and later by Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...

. Pseudo-Dionysius the Areopagite
Pseudo-Dionysius the Areopagite
Pseudo-Dionysius the Areopagite, also known as Pseudo-Denys, was a Christian theologian and philosopher of the late 5th to early 6th century, the author of the Corpus Areopagiticum . The author is identified as "Dionysos" in the corpus, which later incorrectly came to be attributed to Dionysius...

 (before 532) has a predecessor version of the paradox, asking whether it is possible for God to "deny himself".

Many answers to the paradox have been proposed.

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 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 whether the above question is ad hoc, or, instead, is inherently required by the concept of omnipotence (is a material paradox). If it is ad hoc, then the concept of omnipotence does not include being subject to be exceeded. If it is inherently required, then there is no way to exclude answering the question in either the affirmative or the negative, and, thus, no way to determine whether an omnipotent being is logically possible or impossible. But, if the question is inherently required by the concept of omnipotence, then it seems the logic which allows it to be inherently required is a paradox since the particular concept of omnipotence which requires it is a paradox.

But, whether the concept of omnipotence itself is a material paradox, or is simply too obscure to us to preclude being construed by paradoxical thinking, the central issue of the omnipotence paradox is whether the concept of the 'logically possible' is different for a world in which omnipotence exists from a world in which omnipotence does not exist. The reason this is the central issue is because our sense of material paradox, and of the logical contradiction of which material paradox is an expression, are functions of the fact that we presuppose that there must be something which exists which is inherently meaningful or logical, that is, which is concretely not a compound of other things or other concepts. So, for example, in a world in which exists a materially paradoxical omnipotence, it's very paradoxicality seems either to be a material-paradox-of-a-material-paradox, or to be a non-paradox per the proposition that it exists (i.e., if it exists, then nothing has inherent meaning, including itself). Whereas, a world in which exists non-paradoxical omnipotence, its own omnipotence is coextensive with whatever is the concrete basis of our presupposition that something must be inherently meaningful.

The dilemma of omnipotence is similar to another classic paradox, the irresistible force paradox
Irresistible force paradox
The Irresistible force paradox, also the unstoppable force paradox, is a classic paradox formulated as "What happens when an unstoppable force meets an immovable object?" This paradox is a form of the omnipotence paradox, which is a simple demonstration that challenges omnipotence:...

: 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. The only way out of this paradox is if the irresistible force and the immovable object never meet. But, this way out is not possible in the omnipotence case, because the purpose is to ask if the being's own inherent omnipotence makes its own inherent omnipotence impossible. So, while, prior to any task, it is easy to imagine that omnipotence is in state of coherence with itself, some imaginable tasks are not possible for such a coherent omnipotence to perform without compromising its coherence.

Types of omnipotence


Peter Geach
Peter Geach
Peter Thomas Geach is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.He was educated at Balliol College, Oxford...

 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
    Contradiction
    In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

    , "Y"is not bound in action, as we are in thought by the laws of logic." This position is advanced by Descartes
    René Descartes
    René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

    . It has the theological advantage of making God prior to the laws of logic, but the theological disadvantage of making God's promises suspect. On this account, the omnipotence paradox is a genuine paradox, but genuine paradoxes might nonetheless be so.
  2. "Y is omnipotent" means "Y can do X" is true if and only if
    If and only if
    In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

     X is a logically consistent description of a state of affairs. This position was once advocated by Thomas Aquinas
    Thomas Aquinas
    Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...

    . 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
    George I. Mavrodes
    George I. Mavrodes is Professor Emeritus of Philosophy at the University of Michigan and author of Belief in God: A Study in the Epistemology of Religion. Dr. George Mavrodes is emeritus professor of philosophy at the University of Michigan, Ann Arbor...

     points out there is nothing logically contradictory about this; a man could, for example, make a boat which 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.
  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 which would be 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" will no longer be 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
    Anselm of Canterbury
    Anselm of Canterbury , also called of Aosta for his birthplace, and of Bec for his home monastery, was a Benedictine monk, a philosopher, and a prelate of the church who held the office of Archbishop of Canterbury from 1093 to 1109...

     seems to think that almightiness is one of the things that makes God count as omnipotent.


St Augustine in his City of God writes "God
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....

 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 differently to each type of being.

Some Philosophers, such as René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

, 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
False dilemma
A false dilemma is a type of logical fallacy that involves a situation in which only two alternatives are considered, when in fact there are additional options...

, as it neglects the possibility of varying degrees of omnipotence. Some modern approaches to the problem have involved semantic
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 debates over whether language—and therefore philosophy—can meaningfully address the concept of omnipotence itself.

Proposed answers


A common response is that since God is supposedly omnipotent, the phrase "could not lift" doesn't make sense and the paradox is meaningless. An alternative version would be to assume that a non-corporeal God cannot lift anything, but can raise it (a linguistic pedantry) - or to use the beliefs of Christians and Hindus (that there is one God, who can be manifest as several different beings) that whilst it is possible for God to do all things, it is not possible for all his incarnations to do them. As such, God could create a stone so heavy that, in one incarnation, he was unable to lift it - but would be able to do something that an incarnation that could lift it couldn't.

Isaac Asimov
Isaac Asimov
Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...

, a confirmed atheist, answered a variation of this question: what happens when an irresistible force meets an immovable object? He points out that Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 demonstrated the equivalence of mass-energy. That is, according to relativity theory, mass is simply frozen energy, energy is simply liquid mass. In order to be either "immovable" or "irresistible", the entity must possess the majority of energy in the system. No system can have two majorities. A universe in which there exists such a thing as an irresistible force is, by definition, a universe which cannot also contain an immovable object. And a universe which contains an immovable object cannot, by definition, also contain an irresistible force. So the question is essentially meaningless: either the force is irresistible or the object is immovable, but not both. Asimov points out that this question is the logical fallacy of the pseudo-question. Just because we can string words together to form what looks like a coherent sentence doesn't mean the sentence really makes any sense.

Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...

 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 Rene Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

, argue that God is absolutely omnipotent, despite the problem.

C. S. Lewis
C. S. Lewis
Clive Staples Lewis , commonly referred to as C. S. Lewis and known to his friends and family as "Jack", was a novelist, academic, medievalist, literary critic, essayist, lay theologian and Christian apologist from Belfast, Ireland...

 argues that when talking about omnipotence, referencing "a rock so heavy that God cannot lift it" is nonsense just as much as referencing "a square circle." So asking "Can God create a rock so heavy that even he cannot lift it?" is just as much nonsense as asking "Can God draw a square circle?" The logical contradiction here being God's simultaneous ability and disability in lifting the rock (the statement "God can lift this rock" must have a truth value of either true or false, it cannot possess both). Therefore the question (and therefore the perceived paradox) is meaningless. Nonsense does not suddenly acquire sense and meaning with the addition of the two words, "God can" before it.

John Christian Uy said that it is just the same as someone with double-bladed sword(accidentally omnipotent), or sword and a shield(essentially omnipotent). Therefore, an accidentally omnipotent deity CAN remove it's omnipotence while an essentially omnipotent deity CANNOT do anything that would make it non-omnipotent. Both however, have no limitations so far other than the essential omnipotent being who cannot do anything which will make it non-omnipotent like making someone equal with him, lowering or improving himself(for omnipotence is the highest) etc. It could, however, make someone with a great power, though it cannot be 99% because Omnipotence is infinite, because that created being is not equal with him. Overall, God in the Christian Bible, is essentially omnipotent.

William Jennings Bryan
William Jennings Bryan
William Jennings Bryan was an American politician in the late-19th and early-20th centuries. He was a dominant force in the liberal wing of the Democratic Party, standing three times as its candidate for President of the United States...

 said this is roughly the view espoused by Matthew Harrison Brady, a character in the 1955 play Inherit the Wind
Inherit the Wind (play)
Inherit the Wind is a play by Jerome Lawrence and Robert Edwin Lee. The play, which debuted in 1955, is a parable that fictionalizes the 1925 Scopes "Monkey" Trial as a means to discuss the then-contemporary McCarthy trials.-Background:...

loosely based upon William Jennings Bryan
William Jennings Bryan
William Jennings Bryan was an American politician in the late-19th and early-20th centuries. He was a dominant force in the liberal wing of the Democratic Party, standing three times as its candidate for President of the United States...

. In the climactic scene of the 1960 movie version
Inherit the Wind (1960 film)
Inherit the Wind is a 1960 Hollywood film adaptation of the play of the same name, written by Jerome Lawrence and Robert Edwin Lee, directed by Stanley Kramer....

, Brady argues, "Natural law was born in the mind of the Creator. He can change it—cancel it—use it as he pleases!" But this solution merely pushes the problem back a step; one may ask whether an omnipotent being can create a stone so immutable that the being itself cannot later alter it. But a similar response can be offered to respond to this and any further steps.

In a 1955 article published in the philosophy journal Mind, J. L. Mackie
J. L. Mackie
John Leslie Mackie was an Australian philosopher, originally from Sydney. He made significant contributions to the philosophy of religion, metaphysics, and the philosophy of language, and is perhaps best known for his views on meta-ethics, especially his defence of moral skepticism.He authored six...

 attempted 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, such as definition 3 or 4 above. The paradox can be resolved by simply stipulating that omnipotence does not require the being to have abilities which are logically impossible, but only to be able to do anything which conforms to the laws of logic. A good example of a modern defender of this line of reasoning is George Mavrodes. Essentially, Mavrodes argues that it is no 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 nonsense. Harry Frankfurt
Harry Frankfurt
Harry Gordon Frankfurt is an American philosopher. He is professor emeritus of philosophy at Princeton University and has previously taught at Yale University and Rockefeller University. He obtained his B.A. in 1949 and Ph.D. in 1954 from...

—following from 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 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?


If a being is accidentally omnipotent, then it can resolve the paradox by creating a stone which it cannot lift and 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 or not 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 notion of the Christian Incarnation.

If a being is essentially omnipotent, then it can also resolve the paradox (as long as we take omnipotence not to require absolute omnipotence). The omnipotent being is essentially omnipotent, and therefore it is impossible for it to be non-omnipotent. Further, the omnipotent being can do what is logically impossible and have no limitations just like the accidentally omnipotent but the ability to make oneself non-omnipotent. The creation of a stone which the omnipotent being cannot lift would be an impossibility. The omnipotent being cannot create such a stone because it's power will be equal to him and thus, remove his omnipotence for there can only be one omnipotent being in existence, but 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, it is possible for non-omnipotent beings to 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 taken by Augustine of Hippo
Augustine of Hippo
Augustine of Hippo , also known as Augustine, St. Augustine, St. Austin, St. Augoustinos, Blessed Augustine, or St. Augustine the Blessed, was Bishop of Hippo Regius . He was a Latin-speaking philosopher and theologian who lived in the Roman Africa Province...

 in his The City of God:
Thus Augustine argued that God could not do anything or create any situation that would in effect make God not God.

Some philosophers maintain that the paradox can be resolved if the definition of omnipotence includes Descartes' view that an omnipotent being can do the logically impossible. In this scenario, the omnipotent being could create a stone which it cannot lift, but could also then lift the stone anyway. Presumably, such a being could also make the sum 2 + 2 = 5
Two plus two make five
The phrase "two plus two equals five" is a slogan used in George Orwell's Nineteen Eighty-Four as an example of an obviously false dogma one must believe, similar to other obviously false slogans by the Party in the novel...

 become mathematically possible or create a square triangle. This attempt to resolve the paradox is problematic in that the definition itself forgoes logical consistency
Consistency proof
In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if and only if it has a model, i.e. there exists an interpretation under which all...

. The paradox may be solved, but at the expense of making the logic a paraconsistent logic
Paraconsistent logic
A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent systems of logic.Inconsistency-tolerant logics have been...

. This might not seem like a problem if one is already committed to dialetheism
Dialetheism
Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true...

 or some other form of logical transcendence
Transcendence (philosophy)
In philosophy, the adjective transcendental and the noun transcendence convey the basic ground concept from the word's literal meaning , of climbing or going beyond, albeit with varying connotations in its different historical and cultural stages...

.

St Augustine's definition of omnipotence, i.e. that God can do and does everything that God wishes, resolves all possible paradoxes, because God, being perfectly rational, never wishes to do something that is paradoxical.

If God can do absolutely anything, then God can remove His own omnipotence. If God can remove His own omnipotence, then God can create an enormous stone, remove His own omnipotence, then not be able to lift the stone. This preserves the belief that God is omnipotent because God can create a stone that He couldn't lift. Therefore, in this theory, God would not be omnipotent while not being able to lift the stone. This is a trivial solution because, for example, an omnipotent being could create a boulder that the strongest human could not lift (it needn't do that anyway since such boulders exist) and then give itself the potency of an average human; it would then not be able to lift the stone. This solves nothing as the entity that is unable to lift the stone is not "God" as understood by the paradox, but a very average being with the same potency as a human. The solution only produces a reduced-potency "God"; it does not deal with the matter at hand: God maintaining omnipotence even while performing a task, the success or failure of which seems to imply impotence.

David Hemlock has proposed an incarnational resolution: "On one small planet, lying in a manger, one incarnate babe could not lift the rocks He had made. All the rocks of all of the starfields in Him consist, with their whirling atoms; by Him were and ever-are all things lifted up (Col 1:17; Phil 2:5-8)."

An atheist solution to the paradox is that omnipotence, and hence God, doesn't exist.

The paradox is internally incoherent. If it is assumed that there is e.g. no rock that the being cannot lift, then the category 'rocks so heavy that the being cannot lift' is a category of non-existence. The being is then required to create something that does not exist. This is a nonsense requirement. Hence the paradox is nonsense.

Language and omnipotence


The philosopher Ludwig Wittgenstein
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...

 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
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime. It was an ambitious project: to identify the relationship between language and reality and to define the limits of science...

he stays generally within the realm of logical positivism
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...

, until claim 6.4, but at 6.41 and following the succeeding propositions argue that ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...

 and several other issues are "transcendental" subjects which 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 makes the omnipotence paradox a problem in semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

, the study of how symbols are given 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
D. Z. Phillips
Dewi Zephaniah Phillips , known as D. Z. Phillips, Dewi Z, or simply DZ, was a leading proponent of Wittgensteinian philosophy of religion and had a long academic career spanning five decades...

.

But in his later years, Wittgenstein wrote works which are 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 Elmyas 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
Anselm of Canterbury
Anselm of Canterbury , also called of Aosta for his birthplace, and of Bec for his home monastery, was a Benedictine monk, a philosopher, and a prelate of the church who held the office of Archbishop of Canterbury from 1093 to 1109...

 argues that there are many things that God cannot do, but that nonetheless he counts as Omnipotent.

Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...

 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
Summa contra Gentiles
The Summa contra Gentiles by St. Thomas Aquinas has traditionally been dated to 1264, though more recent scholarship places it towards the end of Thomas’ life, 1270-73 . The work has occasioned much debate as to its purpose, its intended audience and its relationship to his other works...

:
This can be done on a sphere, and not on a flat surface. The later invention of non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...

 does not resolve this question; for one might as well ask, "If given the axioms of Riemannian geometry
Elliptic geometry
Elliptic geometry is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. Elliptic geometry, like hyperbolic geometry, violates Euclid's parallel postulate, which can be interpreted as asserting that there is exactly one...

, 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 the consequences which 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
Parliamentary sovereignty
Parliamentary sovereignty is a concept in the constitutional law of some parliamentary democracies. In the concept of parliamentary sovereignty, a legislative body has absolute sovereignty, meaning it is supreme to all other government institutions—including any executive or judicial bodies...

, 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
Aristotelianism
Aristotelianism is a tradition of philosophy that takes its defining inspiration from the work of Aristotle. The works of Aristotle were initially defended by the members of the Peripatetic school, and, later on, by the Neoplatonists, who produced many commentaries on Aristotle's writings...

 science. After all, if one considers the stone's position relative to the sun around which the planet orbits, one could hold that the stone is constantly being 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
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

 which 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
Ethan Allen
Ethan Allen was a farmer, businessman, land speculator, philosopher, writer, and American Revolutionary War patriot, hero, and politician. He is best known as one of the founders of the U.S...

's Reason addresses the topics of original sin
Original sin
Original sin is, according to a Christian theological doctrine, humanity's state of sin resulting from the Fall of Man. This condition has been characterized in many ways, ranging from something as insignificant as a slight deficiency, or a tendency toward sin yet without collective guilt, referred...

, theodicy
Theodicy
Theodicy is a theological and philosophical study which attempts to prove God's intrinsic or foundational nature of omnibenevolence , omniscience , and omnipotence . Theodicy is usually concerned with the God of the Abrahamic religions Judaism, Christianity, and Islam, due to the relevant...

 and several others in classic Enlightenment
Age of Enlightenment
The Age of Enlightenment was an elite cultural movement of intellectuals in 18th century Europe that sought to mobilize the power of reason in order to reform society and advance knowledge. It promoted intellectual interchange and opposed intolerance and abuses in church and state...

 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
Deism
Deism in religious philosophy is the belief that reason and observation of the natural world, without the need for organized religion, can determine that the universe is the product of an all-powerful creator. According to deists, the creator does not intervene in human affairs or suspend the...

, 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
Principles of Philosophy
Principles of Philosophy is a book by René Descartes. Written in Latin, it was published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long standing friendship. A French version followed in 1647. It set forth the principles of nature—the Laws of Physics--as Descartes...

,
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.

It is even in popular culture. In an episode of The Simpsons
The Simpsons
The Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical parody of a middle class American lifestyle epitomized by its family of the same name, which consists of Homer, Marge, Bart, Lisa and Maggie...

, Homer asks Ned Flanders
Ned Flanders
Nedward "Ned" Flanders, Jr. is a recurring fictional character in the animated television series The Simpsons. He is voiced by Harry Shearer, and first appeared in the series premiere episode "Simpsons Roasting on an Open Fire". He is the next door neighbor to the Simpson family and is generally...

 the question "Could Jesus microwave a burrito so hot that He Himself could not eat it?"

See also

  • Problem of evil
    Problem of evil
    In the philosophy of religion, the problem of evil is the question of how to explain evil if there exists a deity that is omnibenevolent, omnipotent, and omniscient . Some philosophers have claimed that the existences of such a god and of evil are logically incompatible or unlikely...

  • Semantics
    Semantics
    Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

  • Absolute monarchy
    Absolute monarchy
    Absolute monarchy is a monarchical form of government in which the monarch exercises ultimate governing authority as head of state and head of government, his or her power not being limited by a constitution or by the law. An absolute monarch thus wields unrestricted political power over the...

  • Russell's paradox
    Russell's paradox
    In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...

  • Gödel's incompleteness theorems
    Gödel's incompleteness theorems
    Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of...

  • Irresistible force paradox
    Irresistible force paradox
    The Irresistible force paradox, also the unstoppable force paradox, is a classic paradox formulated as "What happens when an unstoppable force meets an immovable object?" This paradox is a form of the omnipotence paradox, which is a simple demonstration that challenges omnipotence:...