The logical problem of evil claims that the existence of an omnipotent, omniscient, and omnibenevolent God is logically incompatible with the existence of evil in the world. The argument's inferential structure is deductive: it attempts to demonstrate that the propositions "God exists" and "evil exists" form a logical contradiction when God is defined as possessing the traditional divine attributes. The argument typically proceeds by asserting that an omnipotent being could eliminate all evil, an omniscient being would know about all evil, and an omnibenevolent being would want to eliminate all evil. Since evil demonstrably exists, the argument concludes that such a God cannot exist. This formulation seeks to establish atheism as a matter of logical necessity rather than empirical probability.
The logical problem of evil has ancient roots in Epicurus (341-270 BCE), whose formulation is preserved in Lactantius's De Ira Dei. David Hume revived the argument in his Dialogues Concerning Natural Religion (1779), presenting it through the character Philo. The modern formulation received its most influential treatment from J.L. Mackie in "Evil and Omnipotence" (Mind, 1955), where he argued that theism involves a logical contradiction. H.J. McCloskey's "God and Evil" (Philosophical Quarterly, 1960) further developed the logical incompatibility thesis. Earlier in the 20th century, John Stuart Mill had pressed similar concerns in his Three Essays on Religion (1874). The argument gained particular prominence in analytic philosophy of religion during the 1950s-1970s, becoming a centerpiece of philosophical atheology.
The strongest theistic reply came from Alvin Plantinga's free will defense, articulated in God, Freedom, and Evil (1974) and The Nature of Necessity (1974). Plantinga argues that it is logically possible that God could not create a world containing moral good without also permitting moral evil, if that good requires libertarian free will. His defense employs possible world semantics to show that there is no formal contradiction between God's existence and evil's existence. Most philosophers, including former proponents like William Rowe, now accept that Plantinga successfully refuted the logical problem. However, proponents maintain that the logical problem retains force against specific conceptions of God, particularly those involving divine determinism or those that deny genuine free will. Some argue that natural evil remains logically problematic even if moral evil can be explained.
The logical problem of evil differs from the evidential problem of evil in claiming logical impossibility rather than evidential improbability. While the evidential version (defended by Rowe and Draper) argues that evil makes God's existence unlikely, the logical version claims it makes God's existence impossible. Unlike theodicies such as soul-making (Hick) or free will theodicy (Swinburne), which attempt to explain why God permits evil, the logical problem denies that any explanation could succeed given the logical contradiction. It also differs from the problem of divine hiddenness, which focuses on God's apparent absence rather than evil's presence.