Paradox

"I find that the quietest times of my life speak the loudest."

List of Paradoxes

Logic

  • Grandfather paradox:The grandfather paradox is a proposed paradox of time travel first described (in this exact form) by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (The Imprudent Traveler). The paradox is this: suppose a man travelled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which means the grandfather would still be alive, and the traveller would have been conceived allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation.

  • Barbershop paradox: The supposition that if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved leads to paradoxical consequences.

  • What the Tortoise Said to Achilles "Whatever Logic is good enough to tell me is worth writing down...", also known as Carroll's paradox, not to be confused with the physical paradox of the same name.

  • Crocodile Dilemma: If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?

  • Catch-22 (logic): In need of something which can only be had by not being in need of it.

  • Drinker paradox: In any pub there is a customer such that, if he or she drinks, everybody in the pub drinks.

  • Paradox of entailment: Inconsistent premises always make an argument valid.

  • Horse paradox: All horses are the same color.

  • Lottery paradox: There is one winning ticket in a large lottery. It is reasonable to believe of a particular lottery ticket that it is not the winning ticket, since the probability that it is the winner is so very small, but it is not reasonable to believe that no lottery ticket will win.

  • Raven paradox (or Hempel's Ravens): Observing a green apple increases the likelihood of all ravens being black.

  • Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise. The surprise examination and Bottle Imp paradox use similar logic.

  • Self-reference

  • Barber paradox: A male barber shaves all and only those men who do not shave themselves. Does he shave himself? (Russell's popularisation of his set theoretic paradox.)

  • Berry paradox: The phrase "the first number not nameable in under eleven words" appears to name it in nine words.

  • Paradox of the Court: A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.

  • Curry's paradox: "If this sentence is not true, then Santa Claus exists."

  • Epimenides paradox: A Cretan says: "All Cretans are liars". This paradox works in mainly the same way as the Liar paradox.

  • Exception paradox: "If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule — which is, in of itself, an accepted exception of the rule."

  • Grelling–Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? (Another close relative ofRussell's paradox.)

  • Kleene–Rosser paradox: By formulating an equivalent to the liar paradox, untyped lambda calculus is shown to be inconsistent.

  • Liar paradox: "This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question no?" And "I'm lying."

  • Card paradox: "The next statement is true. The previous statement is false." A variant of the liar paradox that does not use self-reference.

  • The Pinocchio paradox: What would happen if Pinocchio said "My nose will be growing"?[1]

  • Quine's paradox: "'Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation." Shows that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals.

  • Yablo's paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. Uses neither self-reference nor circular reference.

  • Opposite Day: "It is opposite day today."

  • Petronius's Paradox: "Practice moderation in all things. Including moderation."

  • Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.

  • Socratic paradox: "I know that I know nothing at all."