paradox

logic

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June 17, 2026

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A paradox is a statement that appears self-contradictory but reveals a deeper meaning upon closer examination. These statements are designed to capture attention and stimulate thought, such as "Less is more". Paradoxes can be found in literature, like in George Orwell's Animal Farm, where a revised commandment states, "All animals are equal, but some animals are more equal than others". In poetry, paradoxes are integral to language, expressing simultaneous tensions of error and truth.1

A well-known example is the liar paradox, stemming from the statement "This sentence is false." If the sentence is true, it must be false, and if it's false, it must be true. This type of paradox highlights challenges in logical theories of truth. Other paradoxes, like Zeno's paradoxes, question motion and plurality, while the sorites paradox deals with vagueness in predicates. These logical puzzles have stimulated significant philosophical inquiry throughout history.23

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complexity
Paradox
Paradoxes typically arise from false assumptions, which then lead to inconsistencies between observed and expected behavior. Sometimes paradoxes occur in simple logical or linguistic situations, such as the famous Liar Paradox (“This sentence is false.”). In other situations, the paradox comes from the peculiarities…
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Paradoxes typically arise from false assumptions, which then lead to inconsistencies between observed and expected behavior. Sometimes paradoxes occur in simple logical or linguistic situations, such as the famous Liar Paradox (“This sentence is false.”). In other situations, the paradox comes from the peculiarities…
Read More

number game
Paradoxes and fallacies
Mathematical paradoxes and fallacies have long intrigued mathematicians. A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. A mathematical fallacy, on the other hand, is an instance…
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Mathematical paradoxes and fallacies have long intrigued mathematicians. A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. A mathematical fallacy, on the other hand, is an instance…
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history of logic
The Megarians and the Stoics
Many paradoxes have been attributed to them, including the “liar paradox” (someone says that he is lying; is his statement true or false?), the discovery of which has sometimes been credited to Eubulides of Miletus, a pupil of Euclid of Megara. The Megarians also discussed how…
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Many paradoxes have been attributed to them, including the “liar paradox” (someone says that he is lying; is his statement true or false?), the discovery of which has sometimes been credited to Eubulides of Miletus, a pupil of Euclid of Megara. The Megarians also discussed how…
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set theory
Essential features of Cantorian set theory
…in order to prevent certain paradoxes. See below Cardinality and transfinite numbers.) Because of the principle of extension, the set A corresponding to S(x) must be unique, and it is symbolized by {x | S(x)}, which is read “The set of all objects x such that S(x).” For instance, {x…
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…in order to prevent certain paradoxes. See below Cardinality and transfinite numbers.) Because of the principle of extension, the set A corresponding to S(x) must be unique, and it is symbolized by {x | S(x)}, which is read “The set of all objects x such that S(x).” For instance, {x…
Read More