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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 in which neither of the sentences employs (direct) self-reference, instead this is a case ...
In literature, the paradox is an anomalous juxtaposition of incongruous ideas for the sake of striking exposition or unexpected insight. It functions as a method of literary composition and analysis that involves examining apparently contradictory statements and drawing conclusions either to reconcile them or to explain their presence.
One example occurs in the liar paradox, which is commonly formulated as the self-referential statement "This statement is false". [16] Another example occurs in the barber paradox, which poses the question of whether a barber who shaves all and only those who do not shave themselves will shave himself. In this paradox, the barber is a self ...
Trying to assign a truth value to either of them leads to a paradox. If the first statement is true, then so is the second. But if the second statement is true, then the first statement is false. It follows that if the first statement is true, then the first statement is false. If the first statement is false, then the second is false, too.
Since Jaakko Hintikka's seminal treatment of the problem, [7] it has become standard to present Moore's paradox by explaining why it is absurd to assert sentences that have the logical form: "P and NOT(I believe that P)" or "P and I believe that NOT-P." Philosophers refer to these, respectively, as the omissive and commissive versions of Moore's paradox.
Polanyi's paradox, named in honour of the British-Hungarian philosopher Michael Polanyi, is the theory that human knowledge of how the world functions and of our own capability are, to a large extent, beyond our explicit understanding.
In summary, Parrondo's paradox is an example of how dependence can wreak havoc with probabilistic computations made under a naive assumption of independence. A more detailed exposition of this point, along with several related examples, can be found in Philips and Feldman. [9]
Littlewood's pack of cards is infinitely large and his paradox is a paradox of improper prior distributions. Martin Gardner popularized Kraitchik's puzzle in his 1982 book Aha! Gotcha, in the form of a wallet game: Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets.