Logical Problem of Evil

1. Introduction

The logical problem of evil is a family of deductive arguments claiming that the existence of evil is logically incompatible with the existence of a God who is omnipotent, omniscient, and perfectly good. It asks whether the traditional theistic picture of God can be coherently maintained once the reality of suffering, wrongdoing, and seemingly pointless harms is acknowledged.

Unlike the evidential problem of evil, which focuses on how probable God’s existence is given the amount and kinds of evil, the logical problem presents itself as a strict incompatibility claim: it maintains that certain core theistic propositions and the proposition that evil exists cannot all be true together. If the argument succeeds, then no possible world contains both such a God and evil, making classical theism logically impossible.

Most canonical formulations center on an inconsistent triad:

1. God is omnipotent.
2. God is perfectly good.
3. Evil exists.

Advocates argue that when these claims are supplemented with certain principles about what a good and powerful being would do, a contradiction can be derived. Critics respond by challenging either the divine attributes as traditionally defined, the nature and scope of evil, or the connecting principles that produce the alleged inconsistency.

The logical problem of evil has played a central role in the philosophy of religion, shaping debates about divine attributes, free will, and the rationality of theism. It also functions as a point of contact between metaphysics (what sorts of beings and powers are possible), ethics (what perfect goodness involves), and logic (what follows from which premises). Subsequent sections examine its origins, formal statements, and the major responses it has generated.

2. Origin and Attribution

The logical problem of evil has deep historical roots but acquires its canonical analytic form in the twentieth century.

Ancient and Early Sources

The problem is often traced to Epicurus (4th–3rd century BCE), via a later report by Lactantius. The famous trilemma asks, in effect, whether a powerful and benevolent deity is compatible with the persistence of evil:

"

“God either wishes to take away evils, and is unable; or He is able, and unwilling; or He is neither willing nor able, or He is both willing and able.”

— Lactantius, De Ira Dei

Some scholars question whether this reflects Epicurus’ own wording, but it has nonetheless shaped later formulations. In the early modern period, David Hume gives a widely cited version in the voice of Philo:

"

“Is he willing to prevent evil, but not able? then is he impotent.
Is he able, but not willing? then is he malevolent.
Is he both able and willing? whence then is evil?”

— David Hume, Dialogues Concerning Natural Religion, Part X–XI

Hume’s dialogue is often treated as a precursor to modern logical and evidential treatments.

Modern Analytic Attribution

The argument’s classic modern formulation is typically attributed to J. L. Mackie, especially his 1955 paper “Evil and Omnipotence” in Mind. Mackie casts the issue in explicitly logical terms, speaking of the “paradox of omnipotence” and the “inconsistent set” of statements comprising theism plus evil.

Subsequent philosophers, including Alvin Plantinga, William Rowe, and others, treat Mackie’s paper as the standard reference point for the “logical” version, whether to refine, defend, or reject it.

3. Historical Context

The logical problem of evil emerges within broader philosophical and theological efforts to reconcile divine attributes with empirical reality.

Ancient and Classical Context

In the ancient world, debates over the gods’ goodness and power took place against the backdrop of polytheism and fate. The alleged Epicurean trilemma confronts popular beliefs in divine benevolence with the obvious presence of suffering. Stoic and other philosophical theologies developed strategies for explaining evil (e.g., as a byproduct of cosmic order), but the problem of consistency between divine perfection and evil was already present.

Medieval and Early Modern Context

In medieval Christian, Jewish, and Islamic thought, classical theism developed a robust doctrine of an all-powerful, all-knowing, perfectly good Creator. Thinkers such as Augustine, Aquinas, Maimonides, and Al-Ghazālī discussed evil extensively, often treating it as a privation or as permitted for wise reasons. While they did not present the problem in modern symbolic form, they recognized a tension between God’s attributes and the reality of sin and suffering.

In the early modern period, with the rise of scientific explanations and skepticism, the problem took on new force. Hume’s Dialogues situate the issue in a context of empiricism and critical scrutiny of natural theology. Disasters (such as the 1755 Lisbon earthquake) sparked intense debates about providence and evil, further foregrounding questions about coherence.

Twentieth-Century Analytic Context

The explicitly logical version crystallizes in the mid-twentieth century, as analytic philosophy of religion begins to formalize traditional debates. Mackie’s 1955 article, written in an environment shaped by logical positivism and rigorous analysis of language and modality, frames the problem as one of formal inconsistency among propositions.

This context also includes the development of modal logic and possible-world semantics, which later become crucial for Plantinga’s response. The logical problem of evil thus sits at the intersection of long-standing theological concerns and newly precise logical tools.

4. The Argument Stated

Formulations of the logical problem of evil vary in detail, but most share a common core: they aim to derive a contradiction from affirming both traditional theism and the existence of evil.

A Canonical Formulation

One widely discussed version can be presented as:

1. God is omnipotent (able to do anything that is logically possible).
2. God is omniscient (knows all truths, including all evils that occur or might occur).
3. God is perfectly good (omni­benevolent).
4. Evil exists.
5. A perfectly good being always eliminates evil as far as it can.
6. An omnipotent being can eliminate any evil it knows about, unless doing so is logically impossible.

From (1)–(3), (5), and (6), proponents infer:

1. If such a God exists, then there would be no evil.

From (4) and (7), they derive:

1. Therefore, such a God does not exist, or at least one of these propositions must be rejected or suitably modified.

Variants

Different authors adjust these premises. Some focus on a shorter inconsistent triad—omnipotence, perfect goodness, and evil—leaving implicit the principles that connect these to a contradiction. Others make the premises about divine goodness more specific, for example by claiming that a perfectly good being must always prevent any gratuitous or unnecessary evil.

Some formulations explicitly distinguish between:

• arguments targeting all evil; and
• arguments targeting certain especially severe or apparently pointless evils.

Despite these differences, what unifies the logical problem is the claim that, once the relevant concepts are analyzed, theism and evil are logically incompatible, not merely improbable or surprising.

5. Logical Structure and Inconsistent Triad

The logical problem of evil is presented as a deductive argument. Its proponents maintain that, given certain premises, the conclusion that a traditional theistic God does not exist follows with logical necessity.

Deductive Form

Abstractly, the structure can be represented as:

• Let T = “There exists an omnipotent, omniscient, perfectly good God.”
• Let E = “Evil exists.”

By adding certain connecting principles C (about what such a God would or must do), the argument aims to show:

• From T ∧ C, it follows that ¬E.
• But E is true.
• Therefore, T ∧ C is false.

If C is taken to be analytic or necessary given standard understandings of goodness and power, then the set {T, E} is claimed to be inconsistent.

The Inconsistent Triad

A popular heuristic is the inconsistent triad:

1. God is omnipotent.
2. God is perfectly good.
3. Evil exists.

Advocates hold that no more than two of these can be true simultaneously, assuming certain plausible background principles. The triad can be summarized:

The logical problem of evil targets a position that affirms all three while also endorsing the connecting principles (typically versions of “a good being eliminates evil it can”).

Compatibility vs. Incompatibility

The core dispute concerns logical compatibility: whether there is any possible world in which an omnipotent, omniscient, perfectly good God coexists with evil. Defenders of the logical problem claim no such world is possible; critics attempt to describe at least one coherent possible scenario where both God and evil exist, thereby resolving the purported inconsistency.

6. Key Premises and Hidden Assumptions

Most of the philosophical work surrounding the logical problem of evil focuses on the linking premises rather than on the bare claims that God is omnipotent, omniscient, and good, or that evil exists. Critics and defenders identify several crucial assumptions.

Central Connecting Premises

Two premises frequently singled out are:

1. Goodness Principle: A perfectly good being always eliminates evil as far as it can.
2. Power Principle: An omnipotent being can eliminate any evil it knows about, unless doing so is logically impossible.

These are often seen as the engine of the argument: they connect divine attributes to the alleged conclusion that there should be no evil at all.

Hidden Assumptions about Evil and Goods

Commentators identify additional, sometimes tacit, assumptions:

• That preventing evil is always better, morally speaking, than allowing it, other things being equal, and that there are no goods that logically require the existence or possibility of evil.
• That there exist possible worlds in which free creatures never do wrong, and that such worlds are available for God to actualize.
• That there is no logical necessity for particular evils (or types of evils) as conditions for greater goods or for a well-ordered, law-governed universe.

These assumptions are contested by various theistic responses, which hold that some evils may be logically tied to outweighing goods or necessary structures.

Assumptions about Divine Attributes and Freedom

Further debated assumptions include:

• That omnipotence involves control over all contingent truths, including free choices, rather than being constrained by the free will of creatures or by necessary truths.
• That omniscience includes knowledge of all future free actions in such a way that God can guarantee outcomes while creatures remain significantly free.
• That perfect goodness is best modeled as a simple maximization or elimination principle, rather than as a more complex value structure (e.g., including respect for autonomy, justice, or aesthetic order).

The viability of the logical problem of evil often turns on whether these background premises and interpretations are accepted as necessary truths or rejected as oversimplifications.

7. Concepts of Omnipotence, Omniscience, and Goodness

The logical problem of evil depends heavily on how the divine attributes are understood. Different conceptions yield different assessments of logical compatibility with evil.

Omnipotence

Standard theistic accounts define omnipotence as the ability to do anything that is broadly logically possible.

• Maximal power view: God can actualize any logically possible state of affairs. On this view, if a world with free creatures and no evil is logically possible, God can create it.
• Logically constrained view: Some argue that God’s power is constrained not only by logic but also by necessary moral truths or by the nature of created freedom; God cannot, for example, strongly determine libertarian free agents always to do right without thereby undermining their freedom.

Debate centers on whether “making free creatures who never sin” is logically possible and available to omnipotence.

Omniscience

Omniscience is commonly taken as knowledge of all truths, including:

• past, present, and future facts;
• counterfactuals of creaturely freedom (what free agents would do in any circumstances).

Some views (e.g., open theism) modify this by denying definite future truths about free choices, thereby altering what omniscience covers. How omniscience interacts with free will and providence affects whether God could foresee and prevent all evils.

Perfect Goodness (Omnibenevolence)

Omnibenevolence is variously interpreted:

• Simple benevolence model: A perfectly good being always prevents any evil it can, unless preventing it would lead to something worse.
• Complex value model: Goodness includes multiple values—justice, mercy, respect for autonomy, virtue formation, beauty—such that allowing some evils may be part of the best overall order.

Some philosophers distinguish between:

Different models of goodness yield different expectations about what a perfectly good being “must” do in the face of possible evils, and thus about whether the existence of evil entails a contradiction with such goodness.

8. Types of Evil: Moral, Natural, and Horrendous

Discussions of the logical problem of evil usually distinguish among several types of evil, since different arguments and responses may apply differently to each.

Moral Evil

Moral evil refers to suffering or harm resulting from the free actions or omissions of moral agents (typically humans, sometimes angels or other rational beings). Examples include murder, war, cruelty, deception, and oppression.

• Proponents of free-will-based responses often focus on moral evil, arguing that it is tied to the existence of significantly free agents.
• Critics sometimes ask whether all such evils really follow from or are required by creaturely freedom, especially in extreme cases.

Natural Evil

Natural evil consists of suffering not directly caused by the free choices of moral agents: earthquakes, tsunamis, diseases, congenital disorders, and many animal harms.

• Some argue that natural evils pose a distinctive challenge because they cannot be straightforwardly explained by human misuse of freedom.
• Others attempt to connect natural evils to overall laws of nature, soul-making, or non-human freedom.

Horrendous Evil

The category of horrendous evils, developed notably by Marilyn McCord Adams, designates evils so severe that they prima facie threaten to make a person’s life not worth living (e.g., genocide, extreme torture, abuse).

"

“By ‘horrendous evils’ I mean those evils the participation in which (that is, the doing or suffering of which) constitutes prima facie reason to doubt whether the participant’s life could (given their inclusion in it) be a great good to him/her on the whole.”

— Marilyn McCord Adams, Horrendous Evils and the Goodness of God

While horrendous evils figure more prominently in evidential and existential discussions, some formulations of the logical problem focus on whether the existence of such extreme evils is compatible with perfect goodness and power at the level of logical possibility, not just probability.

Relevance to the Logical Problem

The logical problem, in principle, can be framed using any of these categories. Some versions are global (any evil at all is incompatible with God), while others single out particular kinds—especially natural and horrendous evils—as providing sharper tests of logical compatibility.

9. Mackie’s Classic Formulation

J. L. Mackie’s 1955 article “Evil and Omnipotence” in Mind is often regarded as the definitive modern statement of the logical problem of evil. Mackie presents the problem explicitly as a set of claims that are “inconsistent” or at least “positively irrational” when held together.

Mackie’s Inconsistent Set

Mackie focuses on the following propositions:

1. God is omnipotent.
2. God is wholly good.
3. Evil exists.

He argues that, taken together with certain “quasi-logical rules,” these form an inconsistent set. The crucial connecting principles are:

• A good being always eliminates evil as far as it can.
• There are no limits to what an omnipotent being can do.

On this basis, Mackie contends that if God is both able and willing to eliminate evil, evil should not exist. Since evil does exist, at least one member of the set must be rejected.

Mackie’s Analysis of Theistic Responses

Mackie also examines common theistic strategies and argues that they either implicitly modify the divine attributes or introduce further inconsistencies:

• Appeals to free will: Mackie considers these and argues that, if free will is a great good, God could have created beings who always freely choose the good, or could at least prevent many evils without infringing freedom.
• Appeals to good requiring evil: Mackie grants that some goods logically presuppose certain evils (e.g., courage presupposes danger) but maintains that this does not justify the overall amount or distribution of evil.

Mackie concludes that traditional theism is “positively irrational” unless it revises or abandons some of these claims. His article set the agenda for subsequent debates, especially by inviting more precise analyses of omnipotence, goodness, and the notion of logical possibility.

10. Plantinga’s Free Will Defense

Alvin Plantinga’s Free Will Defense is the most influential response to the logical problem of evil. It does not attempt to explain why God in fact permits evil; instead, it aims to show that the existence of evil is logically compatible with the existence of an omnipotent, omniscient, perfectly good God.

Aim and Strategy

Plantinga’s goal is to refute the claim of strict inconsistency. He argues that there is at least one possible scenario in which God and evil coexist without contradiction. This suffices, on his view, to undermine the logical problem, even if we do not know whether the scenario is true.

Significant Freedom and Moral Evil

Plantinga posits:

• Significant freedom: creatures are significantly free if they can perform morally good or bad actions, and no one determines which they choose.
• It may be that God values significant freedom so highly that he prefers to create free creatures even though they may sometimes do wrong.

He then suggests that it may be logically impossible for God to cause or determine that free creatures always do right while they remain significantly free.

Transworld Depravity

A key technical notion is transworld depravity:

"

A person suffers from transworld depravity if, in any possible world in which that person is significantly free and God strongly actualizes that world, the person goes wrong at least once.

If it is logically possible that all significantly free creatures suffer from transworld depravity, then God could not have created a world with free creatures and no moral evil, despite being omnipotent.

Logical Outcome

Plantinga concludes that the set:

• “God exists and is omnipotent, omniscient, and perfectly good”
• “Evil exists”

is not logically inconsistent, since there is at least a possible world in which both are true under his scenario. Many philosophers— including some who reject theism—have taken this to show that the strict logical problem of evil, as formulated by Mackie, is unsuccessful, even if evidential concerns remain.

11. Theodicies and Greater-Good Explanations

While the Free Will Defense is a defense (aiming only at logical consistency), many philosophers and theologians develop theodicies: more ambitious accounts proposing actual or probable reasons why God permits evil. In the context of the logical problem, these theodicies function by challenging the crucial premise that a good God would eliminate all evil he can.

Soul-Making Theodicies

John Hick famously develops an “Irenaean” or soul-making theodicy:

• The world is seen as a vale of soul-making, where moral and spiritual virtues—courage, patience, compassion—are developed through struggle, risk, and suffering.
• Certain evils may be logically necessary conditions for these goods; a world without danger, temptation, and hardship might be unable to produce mature, morally significant persons.

On this view, a perfectly good God may permit evils as part of a fitting environment for character formation.

Law-and-Order and Regularity Theodicies

Philosophers such as Richard Swinburne stress the value of a world governed by stable natural laws:

• Predictable laws enable meaningful action, responsibility, and long-term projects.
• However, such regularities inevitably permit harmful outcomes (e.g., falling rocks, diseases), giving rise to natural evil.

Proponents argue that God cannot both have a law-governed world and individually intervene to prevent every instance of suffering without undermining the goods associated with regularity and responsibility.

Greater-Good Patterns

These and other theodicies share a structure: they posit goods G such that:

• G is of great value;
• G logically requires allowing evil E or the possibility of E;
• God, being perfectly good, may rationally permit E for the sake of G.

In the setting of the logical problem, theodicies are invoked to show that the premise “a good being always eliminates evil as far as it can” is too strong, because some evils may be logically tied to greater goods.

12. Skeptical Theism and Epistemic Limits

Skeptical theism is not a theodicy but a stance about human epistemic limitations regarding God’s reasons for permitting evil. In relation to the logical problem of evil, skeptical theism challenges the assumptions needed to infer a contradiction from the existence of evil.

Core Claims

Skeptical theists maintain that:

• Our cognitive capacities, moral understanding, and access to the total set of goods and evils in the universe are severely limited.
• From our limited perspective, we are not justified in claiming that there are no morally sufficient reasons God could have for allowing the evils we observe.

"

“We have no good reason for thinking that the possible goods we know of are representative of the possible goods there are.”

— Stephen J. Wykstra, “The Humean Obstacle to Evidential Arguments from Suffering”

Application to the Logical Problem

For a strict logical inconsistency to be established, critics argue, one must show that:

• It is impossible that God has morally sufficient reasons to permit the actual evils.

Skeptical theists contend that such a claim overreaches our epistemic position. Even if certain evils appear utterly pointless, this appearance does not entail that they are in fact pointless, or that no logically possible justifying reasons exist.

Varieties of Skeptical Theism

Different authors emphasize different aspects:

In the context of the logical problem, skeptical theism undercuts the move from “we see no sufficient reasons” to “there are no possible sufficient reasons,” thereby blocking the derivation of strict inconsistency between God and evil.

13. Shift to the Evidential Problem of Evil

Over the late twentieth century, many philosophers came to regard the logical problem of evil as less central than the evidential or probabilistic problem. This shift is closely tied to the perceived success of Plantinga’s Free Will Defense and related arguments.

Perceived Resolution of the Logical Problem

After Plantinga’s work, a substantial number of philosophers—including some atheists—conceded that theism and evil are not strictly logically incompatible. They held that:

• Defenders of theism can describe possible scenarios (involving free will, greater goods, or unknown reasons) under which God and evil coexist coherently.
• Therefore, the ambitious claim that theism is logically impossible given evil is hard to sustain.

Emergence of Evidential Formulations

Attention thus turned to evidential arguments, which do not claim inconsistency but argue instead that evil makes God’s existence unlikely. William L. Rowe’s influential 1979 paper articulates this shift, focusing on apparently gratuitous evils (suffering that appears to serve no greater good).

Evidential discussions often employ inductive or Bayesian reasoning, considering the total evidence of suffering rather than a priori logical relations among propositions.

Continuing but Changed Role

The logical problem remains important for clarifying concepts and logical relations, but many contemporary debates about evil now proceed within evidential frameworks. The shift reflects a move from questions about mere possibility to questions about plausibility and probability.

14. Alternative Theistic Responses and Modifications

Beyond free-will defenses, theodicies, and skeptical theism, some responses address the logical problem of evil by revising or reinterpreting traditional doctrines about God.

Finite and Modified Theisms

Some thinkers propose limiting divine attributes:

• Finite God theologies (e.g., certain strands influenced by John Stuart Mill or process thought) hold that God is morally perfect but not omnipotent in the classical sense. Evil is then not logically incompatible with God, because God lacks the power to unilaterally eliminate all evils.
• Open theism modifies omniscience, suggesting that future free choices are not yet determinate truths, so God does not (and cannot) know them as fixed. This can alter the expectations about God’s ability to prevent certain evils.

Process Theism

Process theism (inspired by Alfred North Whitehead and Charles Hartshorne) reconceives God as:

• Not an omnipotent coercer but a persuasive agent working within an evolving universe.
• Experiencing the world and influencing it but not unilaterally determining outcomes.

On process views, the traditional inconsistent triad is replaced by a different set of claims about divine power and goodness, thereby sidestepping the classical logical problem as originally posed.

Reinterpretations of Goodness

Some approaches retain divine omnipotence and omniscience but reinterpret goodness:

• Instead of equating goodness with always minimizing evil, they frame divine goodness in terms of faithfulness, covenant loyalty, or aesthetic order, allowing that a world with some evils might be part of a more valuable whole.
• Others argue that divine goodness may include the willingness to share vulnerability and risk with creatures, rather than guaranteeing a world without suffering.

These alternative responses aim to retain some form of theism while dissolving the specific logical inconsistency targeted by traditional formulations of the problem.

15. Status in Contemporary Philosophy

In contemporary philosophy of religion, the logical problem of evil is widely regarded as having mainly pedagogical and clarificatory significance, though not all authors agree on its complete resolution.

Broad Scholarly Consensus

Many philosophers— including theists, atheists, and agnostics—hold that:

• The strong claim that theism and evil are strictly logically inconsistent is difficult to sustain in the face of coherent possible scenarios (such as those offered by Plantinga and others).
• Consequently, the more pressing issues now concern the probability or plausibility of theism given evil, rather than pure logical compatibility.

Textbooks and introductory courses often present the logical problem as a starting point, quickly moving to evidential formulations.

Ongoing Debates and Refinements

However, there is no absolute unanimity:

• Some critics contend that even sophisticated defenses do not adequately address certain formulations, especially those involving specific kinds of evil or more nuanced principles of divine goodness.
• Others explore new logical models, using modal and deontic logics to refine the structure of the argument and the meaning of “logical impossibility.”

Scholars also continue to debate the adequacy of key concepts—omnipotence, omniscience, and justice—partly motivated by the challenges raised by the logical problem.

Role in Current Discourse

Today, the logical problem of evil serves as:

• A tool for analyzing the internal coherence of different theistic systems.
• A framework for exploring how divine attributes interrelate.
• A historical and conceptual backdrop to more empirically and probabilistically oriented discussions of suffering and theism.

Thus, while its ambitious original aim (deriving a contradiction) is often seen as unmet, the logical problem continues to shape and structure philosophical inquiry into God and evil.

16. Legacy and Historical Significance

The logical problem of evil has left a substantial legacy in both philosophy and theology, influencing conceptions of God, methods of argument, and the broader intellectual landscape.

Impact on Philosophy of Religion

The problem played a major role in establishing analytic philosophy of religion as a rigorous field:

• It prompted detailed analyses of modal logic, possible worlds, and counterfactuals, particularly in Plantinga’s work.
• It encouraged precise definitions of divine attributes and led to extensive debates about free will, determinism, and moral responsibility.

The controversy between Mackie and Plantinga is often used to illustrate the evolution from mid-twentieth-century atheistic critiques to more nuanced theistic defenses.

Shaping Theological and Doctrinal Reflection

Within theology, the logical problem:

• Pressed classical theists to articulate more carefully how God’s goodness and power relate to creation, providence, and human freedom.
• Stimulated renewed interest in traditional doctrines (such as Augustine’s privation theory of evil) and in alternative frameworks like process theology and open theism.

It has also contributed to ongoing reassessments of what it means to affirm a “perfect being” and whether classical attributes should be qualified or reinterpreted.

Broader Cultural and Intellectual Influence

The logical problem of evil has permeated:

• Public debates about the rationality of religious belief, often serving as a central argument in popular atheistic and apologetic literature.
• Literature and art, where the tension between divine goodness and suffering is a recurring theme.

Even where its strongest formulations are contested, the logical problem of evil has functioned as a catalyst for deeper reflection on the nature of God, evil, and rational belief, securing its place as a central episode in the intellectual history of theism and atheism.