- Omnipotence paradox
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The omnipotence paradox is a family of semantic paradoxes 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 (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".
Many answers to the paradox have been proposed.
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: 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 describes and rejects four levels of omnipotence. He also defines and defends a lesser notion of the "almightiness" of God.
- "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, 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.
- "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 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.
- "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."
- "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.
- "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 makes 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 differently to each type of being.
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.
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, 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 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 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, argue that God is absolutely omnipotent, despite the problem.
C. S. Lewis 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 said this is roughly the view espoused by Matthew Harrison Brady, a character in the 1955 play Inherit the Wind loosely based upon William Jennings Bryan. In the climactic scene of the 1960 movie version, 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 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—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).
“ 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.
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 become mathematically possible or create a square triangle. This attempt to resolve the paradox is problematic in that the definition itself forgoes logical consistency. The paradox may be solved, but at the expense of making the logic a paraconsistent logic. This might not seem like a problem if one is already committed to dialetheism or some other form of logical transcendence.
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 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 the succeeding propositions argue that ethics 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, 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.
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 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 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, 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 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 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'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.
- Problem of evil
- Absolute monarchy
- Russell's paradox
- Gödel's incompleteness theorems
- Irresistible force paradox
- ^ a b Savage, C. Wade. "The Paradox of the Stone" Philosophical Review, Vol. 76, No. 1 (Jan., 1967), pp. 74–79 doi:10.2307/2182966
- ^ Averroës, Tahafut al-Tahafut (The Incoherence of the Incoherence) trans. Simon Van Der Bergh, Luzac & Company 1969, sections 529–536
- ^ a b c d Geach, P. T. "Omnipotence" 1973 in Philosophy of Religion: Selected Readings, Oxford University Press, 1998, pp. 63–75
- ^ Aquinas, Thomas Summa Theologica Book 1 Question 25 article 3
- ^ a b 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
- ^ Aquinas Summa Theologica Book 1 Question 25 article 4 response #3
- ^ Anselm of Canterbury Proslogion Chap VII in The Power of God: readings on Omnipotence and Evil. Linwood Urban and Douglass Walton eds. Oxford University Press 1978 pp. 35–36
- ^ a b Hoffman, Joshua, Rosenkrantz, Gary. "Omnipotence" The Stanford Encyclopedia of Philosophy (Summer 2002 Edition). Edward N. Zalta (ed.). (Accessed on 19 April 2006)
- ^ a b Descartes, Rene, 1641. Meditations on First Philosophy. Cottingham, J., trans., 1996. Cambridge University Press. Latin original. Alternative English title: Metaphysical Meditations. Includes six Objections and Replies. A second edition published the following year, includes an additional ‘’Objection and Reply’’ and a Letter to Dinet
- ^ Haeckel, Ernst. The Riddle of the Universe. Harper and Brothers, 1900.
- ^ Wittgenstein, Ludwig. Tractatus Logico-Philosophicus (6.41 and following)
- ^ a b The Problem of Pain, Clive Staples Lewis, 1944 MacMillan
- ^ Loving Wisdom: Christian Philosophy of Religion by Paul Copan, Chalice Press, 2007 page 46
- ^ http://www.ccel.org/a/aquinas/summa/FP/FP025.html#FPQ25A3THEP1
- ^ Cowan, J. L. "The Paradox of Omnipotence" first published 1962, in The Power of God: Readings on Omnipotence and Evil. Linwood Urban and Douglass Walton eds. Oxford University Press 1978 pp. 144–52
- ^ Mackie, J. L., "Evil and Omnipotence." Mind LXIV, No, 254 (April 1955).
- ^ 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 3 formalizations p. 138–41, Cowan has a different strategy p. 147, and Walton uses a whole separate strategy p. 153–63
- ^ 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
- ^ 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
- ^ City of God, Book 5, Chapter 10
- ^ http://katachriston.wordpress.com/2011/04/01/can-god-make-a-stone-he-cannot-lift/
- ^ Wittgenstein, Ludwig. proposition 6.5
- ^ Wittgenstein, Ludwig. proposition 7
- ^ D. Z. Phillips "Philosophy, Theology and the Reality of God" in Philosophy of Religion: Selected Readings. William Rowe and William Wainwright eds. 3rd ed. 1998 Oxford University Press
- ^ Hacker, P.M.S. Wittgenstein's Place in Twentieth-Century Analytic Philosophy. 1996 Blackwell
- ^ Pseudo-Dionysius, "Divine Names" 893B in Pseudo-Dionysius: The Complete Works. trans Colm Luibheid Paulist Press. 1987. ISBN 0-8091-2838-1
- ^ Anselm of Canterbury Proslogion Chap. VII, in The Power of God: readings on Omnipotence and Evil. Linwood Urban and Douglass Walton eds. Oxford University Press 1978 pp. 35–36
- ^ "Cum principia quarundam scientiarum, ut logicae, geometriae et arithmeticae, sumantur ex solis principiis formalibus rerum, ex quibus essentia rei dependet, sequitur quod contraria horum principiorum Deus facere non possit: sicut quod genus non sit praedicabile de specie; vel quod lineae ductae a centro ad circumferentiam non sint aequales; aut quod triangulus rectilineus non habeat tres angulos aequales duobus rectis". Aquinas, T. Summa Contra Gentiles, Book 2, Section 25. trans. Edward Buckner
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- 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).
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