List of paradoxes: Encyclopedia II - List of paradoxes - Logical except mathematical

List of paradoxes - Logical except mathematical

• Paradox of entailment: Inconsistent premises always make an argument valid.
• Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens being black.
• Horse paradox: All horses are the same colour.
• Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise.
• Russell's paradox: Does the set of all those sets that do not contain themselves contain itself?
• Barber paradox: The adult male barber who shaves all men who do not shave themselves, and no-one else. (A close relative of Russell's paradox.)
• Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory.

List of paradoxes - Semantic paradoxes

These form a well-known (and well-studied) class having in common that any permissible assignment of semantic value (truth, reference) to an expression immediately implies the assignment of a different value.

• Berry paradox: What is "The first number not nameable in under ten words"? (And has it not just been named in nine?)
• Curry's paradox: "If this sentence is true, the world will end in a week."
• Epimenides paradox: A Cretan says "All Cretans are liars".
• Exception paradox: "If there is an exception to every rule, is there an exception to the rule that states that there is an exception to every rule?"
• Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? (Another close relative of Russell's paradox.)
• Hegel's paradox: "Man learns from history that man learns nothing from history."
• Liar paradox: "This sentence is false."
• Missing dollar paradox: Faulty logic makes it appear as if a dollar from a restaurant bill has gone missing. Not in the same class as the others.
• The Y combinator in the lambda calculus and combinatory logic has been called the paradoxical combinator since it is related to the self-referential antinomies.
• Petronius' paradox: "Moderation in all things, including moderation."
• Quine's paradox: "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

List of paradoxes - Vagueness

• Ship of Theseus/George Washington's axe: When every component of the ship has been replaced at least once, is it still the same ship?
• Sorites paradox: At what point does a heap stop being a heap as I take away grains of sand? Alternately, at what point does someone become bald?

Adapted from the Wikipedia article "Logical except mathematical", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki