Omnipotence Paradox

1. Introduction

The omnipotence paradox is a family of arguments suggesting that the concept of an all‑powerful being may be internally inconsistent. It focuses on whether the notion of omnipotence—having unlimited power—is logically coherent when subjected to certain self‑referential or limit‑setting tasks.

The best‑known formulation is the Paradox of the Stone: “Can an omnipotent being create a stone so heavy that it cannot lift it?” This question appears to force a dilemma:

• If the being can create such a stone, there is something it cannot do (lift it).
• If it cannot create such a stone, there is something it cannot do (create that stone).

On either option, omnipotence seems to fail, leading some philosophers to claim that traditional theistic conceptions of God are conceptually problematic.

The paradox sits at the intersection of:

• Philosophy of religion, because it tests the coherence of a central divine attribute;
• Logic and metaphysics, because it concerns what is possible, impossible, or contradictory;
• Philosophy of language, because it raises questions about whether some apparent “tasks” are genuine tasks or linguistic illusions.

Responses diverge sharply. Some treat the paradox as a decisive objection to classical theism. Others hold that a refined understanding of omnipotence—typically restricting it to what is logically possible or compatible with an essential divine nature—dissolves the problem. Yet others interpret the paradox as revealing limits or revisions needed in our concepts of power, possibility, or even logic itself.

This entry surveys the origins of the paradox, its standard formulations and logical structure, key assumptions and debates, and the main strategies for resolving or reframing it within both theistic and non‑theistic frameworks.

2. Origin and Attribution

Discussion of questions that anticipate the omnipotence paradox appears in medieval Jewish, Christian, and Islamic philosophy, though the now‑standard “stone” formulation is a product of 20th‑century analytic philosophy.

Medieval roots

Medieval theologians addressed whether an omnipotent God could perform seemingly impossible acts (e.g., make a square circle, sin, change the past). For example:

• Thomas Aquinas in Summa Theologiae I, q.25, a.3 explicitly asks “Whether God is omnipotent?” and considers whether God can do the logically impossible, answering negatively.
• Moses Maimonides, in Guide of the Perplexed, also restricts divine power to what is logically possible.
• Islamic theologians such as al‑Ghazālī debate whether God can break causal regularities or alter the past, implicating early forms of omnipotence puzzles.

Although these thinkers do not use the exact stone example, they confront structurally similar worries about whether omnipotence entails the power to undermine itself or contradict logic.

Emergence of the stone paradox

The explicit “Can God create a stone so heavy that he cannot lift it?” question gained currency in the 20th century. It appears in mid‑century English‑language discussions:

Neither Mackie nor Mavrodes claims original authorship; the example appears to have been part of earlier informal discourse. Its precise historical source remains uncertain, and scholars generally regard it as an anonymous, widely circulated puzzle rather than traceable to a single originator.

Thus, while the core issue is commonly traced to Aquinas and other medievals, the canonical modern formulation—the “Paradox of the Stone”—is usually associated with mid‑20th‑century analytic discussions by Mackie, Mavrodes, and their contemporaries.

3. Historical Context in Medieval and Modern Thought

The omnipotence paradox developed within broader debates about divine attributes and the nature of logical and metaphysical possibility.

Medieval scholastic context

In medieval scholastic theology, omnipotence was one element in a systematic account of God as necessary, simple, immutable, omniscient, and omnibenevolent. Philosophers examined tensions among these attributes.

Key themes included:

• Whether God can do the logically impossible.
• Whether divine power is limited by God’s own nature (e.g., inability to lie or sin).
• The difference between God’s absolute power (potentia absoluta) and ordered power (potentia ordinata), especially in late medieval debates (e.g., Ockhamist traditions).

These discussions created a conceptual backdrop for later omnipotence paradoxes, by sharpening distinctions between genuine possibilities and contradictions, and between absolute and self‑limiting powers.

Early modern and Enlightenment shifts

In early modern philosophy, the focus broadened to include:

• The relationship between divine omnipotence and laws of nature (e.g., Descartes, Leibniz).
• Skepticism about traditional theism (e.g., Hume’s critiques of miracles and divine attributes).

Questions about whether God could change necessary truths or violate logic remained live, though not always framed in the precise paradox form.

19th–20th century and analytic philosophy

The consolidation of modern logic and modal logic in the late 19th and 20th centuries provided tools to formalize debates about omnipotence. Within analytic philosophy of religion, omnipotence became a central test case for:

• The coherence of classical theism;
• The adequacy of various modal systems;
• The analysis of paradoxes and self‑referential tasks.

From the 1950s onward, the omnipotence paradox, particularly the Paradox of the Stone, appears alongside discussions of the problem of evil and other challenges to theism. Thinkers such as Mackie, Mavrodes, Plantinga, Kretzmann, Swinburne, and Leftow embed the paradox in sophisticated debates about necessity, possible worlds, and divine attributes.

4. The Omnipotence Paradox Stated

In its most familiar form, the omnipotence paradox presents a dilemma intended to show that the notion of an omnipotent being leads to contradiction.

Core formulation

The canonical version, the Paradox of the Stone, is stated as:

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Can an omnipotent being create a stone so heavy that the being cannot lift it?

The paradox proceeds by considering the two possible answers:

1. Yes, the being can create such a stone.
   Then there exists at least one task the being cannot perform: lifting that stone. The being would therefore not be omnipotent.

2. No, the being cannot create such a stone.
   Then there exists at least one task the being cannot perform: creating that stone. Again, the being would not be omnipotent.

On either horn, omnipotence seems to be undermined.

General form

Many authors abstract from the stone example to a more general self‑limitation pattern:

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Can an omnipotent being bring about a state of affairs in which it is no longer omnipotent (or in which there is some task it cannot perform)?

If the answer is yes, omnipotence appears self‑defeating; if no, omnipotence appears limited from the outset.

Variants of the statement

Although details belong to later sections, several common restatements appear in the literature:

• “Can an omnipotent being bind itself so that it cannot act?”
• “Can an omnipotent being create a rule it cannot break?”
• “Can an omnipotent being make itself weak or destroy itself?”

These restatements preserve the key structure: omnipotence is challenged by tasks that purport to put limits on the omnipotent being’s own power. Advocates maintain that, if such tasks must fall within omnipotence, the concept is self‑contradictory; if they do not, omnipotence is already restricted in a problematic way.

5. Logical Structure and Reductio Form

Philosophers typically interpret the omnipotence paradox as a reductio ad absurdum argument: assuming that an omnipotent being exists (or that omnipotence is a coherent attribute) and deriving a contradiction.

Basic logical structure

A simplified formalization is as follows:

1. Assume that omnipotence is the property of being able to do anything (often: anything logically possible).
2. Define a task T: creating a stone so heavy that the omnipotent being cannot lift it.
3. Either the being can perform T or cannot perform T.
4. If it can perform T, there is something it cannot do (lift the stone).
5. If it cannot perform T, there is something it cannot do (create that stone).
6. Therefore, there is at least one task the being cannot perform.
7. Therefore, the being is not omnipotent, contradicting the initial assumption.

This structure exhibits classic reductio features: starting with a plausible definition of omnipotence and, via uncontroversial logical steps, deriving that no omnipotent being is possible or that the concept is inconsistent.

Disjunctive dilemma

The argument centers on a dilemma structured around a disjunction:

Both conditional branches are intended to yield the same type of conclusion: the existence of a limitation.

Target of the reductio

Different authors emphasize different targets:

• The coherence of the concept of omnipotence itself (conceptual analysis).
• The coherence of a particular definition (e.g., “can do absolutely anything whatsoever”).
• The existence of a classical theistic God possessing such omnipotence.

In all cases, the paradox functions as a logical tool: by embedding the initial claim within a formally valid argument, it seeks to show that the claim leads to contradiction unless certain assumptions are modified or rejected.

6. Premises and Key Assumptions Examined

The force of the omnipotence paradox depends on several substantive assumptions. Philosophical debate often focuses on whether these assumptions should be accepted, revised, or rejected.

Assumptions about omnipotence

A central premise is:

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P1. An omnipotent being can do anything (or anything that is logically possible).

This raises issues about:

• Whether “anything” includes self‑referential or self‑limiting tasks.
• Whether omnipotence should be defined relative to the being’s essential nature (e.g., cannot cease to be omnipotent).
• Whether omnipotence is time‑indexed (power at each time) or global (power over all times taken together).

Assumptions about tasks and possibilities

Another crucial assumption is:

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P3. “Creating a stone so heavy that an omnipotent being cannot lift it” describes a genuine task or possible state of affairs.

Critics question whether this is a pseudo‑task (like making a square circle), arguing that its description embeds a contradiction: “an unliftable object for a being that can lift anything.” If so, the paradox may trade on a category mistake rather than a real limitation on power.

Modal and logical assumptions

The argument presupposes standard principles of classical logic:

• Law of non‑contradiction (no proposition is both true and false).
• Law of excluded middle (for any task T, either the being can do T or cannot do T).
• Closure principles about what follows from being unable to do some T (that inability negates omnipotence).

Some responses question whether omnipotence should be evaluated within classical modal frameworks or whether non‑classical logics might be relevant, though this is a minority approach.

Assumptions about divine attributes

For theistic applications, additional assumptions often operate implicitly:

• That God is essentially omnipotent (cannot lose omnipotence without ceasing to be God).
• That omnipotence coheres with other attributes (goodness, rationality, necessity).

These assumptions affect whether “making oneself non‑omnipotent” is counted as a relevant test of power or as an incoherent demand.

7. The Paradox of the Stone and Related Variations

The Paradox of the Stone is the standard case used to illustrate the omnipotence paradox, but a family of related puzzles employs similar self‑referential structures.

The canonical stone formulation

The basic question:

"

Can an omnipotent being create a stone so heavy that it cannot lift it?

This involves:

• An agent characterized as omnipotent.
• An object defined relative to that agent’s powers (unliftable by that agent).
• A task whose performance appears to generate a new limitation.

Common variations

Philosophers often recast the puzzle with different objects or actions to avoid accidental features of the stone example:

All variants follow the same basic template: a task whose success would seem to undermine omnipotence, and whose failure would likewise suggest a limit.

Structural generalizations

Some authors abstract to a schematic form:

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For any omnipotent being O, consider the task T(O) = “bring about a state of affairs S such that O cannot bring about S or some related outcome.”

The paradox then appears as a general claim that any self‑referential limit‑setting task for omnipotence generates inconsistency. This allows philosophers to analyze the paradox in more formal terms, independent of particular imagery like stones or prisons.

Others note connections to broader self‑reference puzzles (e.g., liar sentences, Russell’s paradox), seeing the stone paradox as one instance of a wider class of paradoxical definitions constructed by reference to an all‑encompassing property (here, unlimited power).

8. Definitions of Omnipotence and Logical Possibility

How one understands the omnipotence paradox depends heavily on how omnipotence and logical possibility are defined.

Competing definitions of omnipotence

Several influential definitions appear in the literature:

Debate centers on whether a satisfactory definition must include self‑referential tasks, allow for self‑limitation, or be constrained by other divine attributes.

Logical possibility and pseudo‑tasks

The phrase “can do all things that are logically possible” requires a notion of logical impossibility:

• Logically impossible: entails a contradiction; cannot obtain in any logically possible world (e.g., round squares, married bachelors).
• Logically possible: does not entail contradiction; can be described consistently within a logical system.

The status of “creating a stone an omnipotent being cannot lift” turns on whether this description conceals a contradiction. On one view, it is akin to “creating a round square”—a pseudo‑task that does not represent a real possibility. On another, it is taken as a coherent specification of a possible limitation, pressing the paradox.

Modal frameworks

Modern analyses often use modal logic and possible worlds semantics:

• An omnipotent being might be said to have the power to actualize any metaphysically possible world consistent with its nature.
• Disagreement persists over whether logical possibility alone suffices, or whether additional metaphysical or essential‑nature constraints must be incorporated.

These definitional and modal choices significantly shape whether the omnipotence paradox is seen as a devastating incoherence, a trivial confusion, or a spur to refine our understanding of power and possibility.

9. Standard Theistic Responses and Objections

Theistic philosophers have developed several influential strategies to resist the omnipotence paradox while preserving a robust doctrine of divine power.

Logical‑impossibility restriction

This response holds that omnipotence ranges over all logically possible tasks, not contradictions. On this view:

• Tasks like “create a stone an omnipotent being cannot lift” are logically impossible because they entail the coexistence of “can lift anything” and “cannot lift this.”
• Failing to perform such pseudo‑tasks does not limit omnipotence, any more than being unable to make 2+2=5 counts as a weakness.

Aquinas, C. S. Lewis, and many contemporary theists adopt versions of this restriction.

Pseudo‑task / category‑mistake objection

Relatedly, some argue that the paradox involves a category mistake:

• “Create a stone an omnipotent being cannot lift” is not a single coherent action‑type, but a contradictory description.
• It is analogous to “drawing a round square”: grammatically well‑formed but semantically empty.

Mavrodes and Plantinga, among others, frame the stone task as a pseudo‑task that simply does not belong to the domain of things‑that‑can‑be‑done.

Time‑indexed and essential omnipotence

Another line distinguishes between:

• Being omnipotent at each time (time‑indexed omnipotence);
• Bringing about states where one is no longer omnipotent.

On essential omnipotence views, an omnipotent being has omnipotence as an essential property and cannot lose it. Creating a state in which it lacks omnipotence would be incompatible with its nature and thus not a genuine possibility for that being. Plantinga and Swinburne develop versions of this approach.

Essential‑nature constraints

Some theists maintain that divine omnipotence is limited by God’s essential attributes (e.g., perfect goodness, rationality, necessary existence):

• God cannot act contrary to these attributes (e.g., cannot sin, cannot cease to exist).
• Therefore, demands that God be able to annihilate or weaken himself are seen as misunderstandings of what divine power involves.

On this view, the paradox is resolved not by weakening omnipotence, but by clarifying that omnipotence is always exercised in harmony with an unchangeable divine nature.

10. Alternative Theological and Philosophical Resolutions

Beyond standard theistic replies that retain classical omnipotence with refinements, some approaches resolve the paradox by reconceptualizing divine power or rejecting traditional omnipotence.

Limited‑power theisms

Some theologies explicitly deny that God is omnipotent in the classical sense:

• Finite‑God views depict God as powerful but not all‑powerful, often to address the problem of evil.
• Open theism and some contemporary models portray God’s power as significantly constrained by creaturely freedom or by the structure of reality.

For these positions, the omnipotence paradox loses much of its force because unlimited power is not attributed in the first place.

Process theism

Process theism typically conceives divine power as persuasive rather than coercive:

• God influences but does not unilaterally determine all events.
• Divine power is relational and interacts dynamically with the world’s own powers.

Because God is not taken to be able to actualize any logically possible state of affairs at will, classic omnipotence paradoxes are often regarded as misdirected.

Revisionary perfect‑being theology

Some philosophers modify perfect‑being analyses:

• Instead of treating unrestricted power as a great‑making property, they treat maximal compossible power as great‑making.
• This may exclude self‑contradictory or self‑destructive powers from the set of perfections, not as limits but as clarifications of what “greatness” entails.

Non‑theistic resolutions

From non‑theistic perspectives:

• Some conclude that the paradox shows the concept of omnipotence is incoherent, and thus no such being exists.
• Others regard the paradox as a case study in conceptual analysis, using it to refine modal and logical notions without focusing on theological implications.

These resolutions typically treat the paradox as indicating that certain intuitive but naïve pictures of unlimited power must be abandoned, either by revising the concept of God or by dispensing with it.

11. Implications for Conceptual Coherence of God

Because many theistic traditions define God as necessarily omnipotent, the omnipotence paradox has significant implications for the conceptual coherence of God.

Perfect‑being and maximal greatness

In perfect‑being theology, God is “that than which no greater can be conceived.” Omnipotence is often treated as a central great‑making property. The paradox raises questions such as:

• Is unlimited power genuinely a coherent or great‑making attribute?
• Should the divine attribute list be revised to some form of maximal but constrained power?

These questions influence whether God’s essential nature can be expressed without contradiction.

Necessary existence and essential attributes

If God is said to possess omnipotence essentially and necessarily:

• Any incoherence in omnipotence threatens the intelligibility of a being whose essence includes it.
• Some philosophers argue that if even one essential divine attribute is conceptually incoherent, the classical theistic conception of God is undermined.

Others respond by refining omnipotence so that it is compatible with necessity, immutability, and other attributes.

Unity and compatibility of attributes

The paradox also intersects with broader concerns about the mutual compatibility of divine attributes:

• Whether omnipotence can coexist without contradiction with omniscience, perfect goodness, and immutability.
• Whether constraints on omnipotence (e.g., inability to do evil or contradict logic) are limitations or simply aspects of a coherent nature.

These debates influence assessments of whether the traditional theistic concept of God passes tests of conceptual coherence, independently of questions about factual existence.

12. Connections to Other Divine Attribute Paradoxes

The omnipotence paradox is part of a wider network of puzzles concerning the coherence and compatibility of divine attributes.

Omniscience and foreknowledge

Questions about omniscience parallel the omnipotence paradox:

• Can an omniscient being know future free actions without undermining freedom?
• Is it possible for an omniscient being to learn or forget anything?

Like the stone paradox for power, “can God know a future that is genuinely open?” functions as a self‑referential challenge to the coherence of unlimited knowledge.

Omnibenevolence and the problem of evil

The problem of evil raises tensions among omnipotence, omniscience, and omnibenevolence:

• If God is able (omnipotent), aware (omniscient), and willing (omnibenevolent) to prevent evil, why does evil exist?

Although structurally different, this problem also hinges on whether certain combinations of attributes yield contradictions or surprising limitations.

Immutability and impassibility

Paradoxes involving immutability (unchangeability) and impassibility (incapacity for suffering) include:

• Can an immutable God respond to prayer or act differently at different times?
• Can an impassible God genuinely love or be affected by creatures?

These problems, like the omnipotence paradox, question whether traditional attributes can be jointly instantiated without conceptual tension.

Divine simplicity and modal paradoxes

The doctrine of divine simplicity—that God has no parts and is identical with divine attributes—raises further puzzles:

• How can a simple being have distinct properties (power, knowledge, goodness)?
• How does such a being relate to different possible worlds?

The omnipotence paradox interacts with these issues by challenging whether an all‑powerful, simple, immutable, and omniscient being is metaphysically possible.

13. Use in Contemporary Analytic Philosophy of Religion

In contemporary analytic philosophy of religion, the omnipotence paradox serves as a standard tool for testing and refining theories of God, logic, and modality.

Conceptual analysis and definitions

Philosophers use the paradox to probe:

• Competing definitions of omnipotence and their consequences.
• The distinction between logical and metaphysical possibility.
• Whether some apparent tasks are linguistic illusions rather than genuine possibilities.

Work by Mavrodes, Plantinga, Kretzmann, Swinburne, Leftow, and others exemplifies this analytic approach.

Testing modal frameworks

The paradox motivates detailed use of modal logic and possible worlds semantics:

• To formalize claims such as “God can actualize any possible world.”
• To analyze self‑referential tasks in terms of accessibility relations and world‑indexed powers.

These analyses contribute to broader discussions about the adequacy of various modal systems for theological purposes.

Role in debates about theism

Within debates about the rationality of theism:

• Some non‑theistic philosophers cite the omnipotence paradox as evidence that classical theism posits an incoherent being.
• Theistic philosophers aim to show that, once clarified, omnipotence is coherent, thereby neutralizing this line of objection.

The paradox is thus frequently discussed alongside the problem of evil, divine hiddenness, and miracle debates as one of the main philosophical challenges to traditional theism.

Pedagogical and illustrative role

In teaching and introductory texts, the paradox often functions as:

• An accessible illustration of reductio ad absurdum reasoning.
• A way to introduce students to philosophy of language, logic, and philosophy of religion through a vivid puzzle.

Its simplicity of formulation and depth of implication make it a staple example in contemporary analytic literature.

14. Critiques of the Paradox as a Linguistic Confusion

A prominent line of criticism holds that the omnipotence paradox arises from misuse of language rather than from any real incoherence in the idea of omnipotence.

Pseudo‑task diagnosis

Critics argue that the stone paradox describes a pseudo‑task:

• The phrase “a stone an omnipotent being cannot lift” implicitly combines “can lift anything” with “cannot lift this,” yielding a concealed contradiction.
• As with “draw a round square,” the grammatical form suggests a coherent request, but the underlying description is impossible.

On this view, the paradox mistakenly elevates a nonsense specification to a purported test of power.

Category mistakes

Some characterize the paradox as involving a category mistake:

• It treats “being unable to perform contradictory tasks” as a limitation of power, when it is actually a reflection of the nature of logical consistency.
• It confuses the category of genuine abilities with that of “performing contradictions,” which is not an ability at all.

Thus, the paradox is seen as misclassifying tasks and then inferring spurious limits.

Semantic and logical analysis

More detailed critiques focus on:

• The semantics of “can” and “able to,” distinguishing ability relative to description from ability relative to real tasks.
• Ambiguities in quantifying over “all tasks,” suggesting that the domain should exclude inconsistent descriptions.
• The role of context in determining which counterfactuals and tasks are meaningful.

These analyses often leverage tools from philosophy of language and formal semantics to show how the paradox might dissolve once linguistic confusions are clarified.

Evaluative stance

Proponents of the linguistic‑confusion critique typically maintain that:

• The paradox does not reveal a flaw in omnipotence but in certain informal ways of speaking about it.
• Careful attention to logical form and conceptual categories suffices to defuse the apparent dilemma.

Others, however, contend that even if some versions are linguistically flawed, deeper questions about self‑limitation and essential attributes remain, so the paradox cannot be entirely dismissed as mere wordplay.

15. Legacy and Historical Significance

The omnipotence paradox has had a lasting impact on philosophy of religion, systematic theology, and discussions of logic and modality.

Influence on doctrinal development

Historically, puzzles about divine power—including precursors to the omnipotence paradox—have contributed to:

• The articulation of logical‑possibility restrictions on omnipotence (e.g., Aquinas, Maimonides).
• Distinctions between absolute and ordered divine power in medieval thought.
• Later refinements of doctrines of divine attributes, especially in relation to necessity, immutability, and goodness.

These developments have shaped major theological traditions in Christianity, Judaism, and Islam.

Impact on modern and contemporary debates

In the 20th and 21st centuries, the paradox:

• Became a standard test case for evaluating classical theism in analytic philosophy.
• Stimulated detailed work on modal logic, possible worlds, and the semantics of ability.
• Informed alternative theological models (e.g., process theism, open theism) that modify or reject classical omnipotence.

It also appears frequently in introductory texts, shaping popular as well as academic understandings of divine power.

Broader philosophical significance

Beyond theology, the omnipotence paradox has:

• Served as an example of how self‑reference and limit concepts (e.g., “all‑powerful,” “set of all sets”) can generate paradoxes.
• Illustrated the importance of conceptual analysis and careful definition in metaphysics and logic.
• Provided a testing ground for theories of conceptual coherence and for the boundaries of meaningful discourse.

As a result, the omnipotence paradox remains a prominent and enduring topic, continuing to influence how philosophers and theologians think about the nature and limits of power, possibility, and divine attributes.