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Movement paradox: In transformational linguistics, there are pairs of sentences in which the sentence without movement is ungrammatical while the sentence with movement is not. Sayre's paradox : In automated handwriting recognition, a cursively written word cannot be recognized without being segmented and cannot be segmented without being ...
Self-reference occurs when a sentence, idea or formula refers to itself. Although statements can be self referential without being paradoxical ("This statement is written in English" is a true and non-paradoxical self-referential statement), self-reference is a common element of paradoxes.
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.
The problem of the liar paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules. The simplest version of the paradox is the sentence:
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.
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. [1] It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals (i.e. it does not explicitly refer to itself).
The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters). Bertrand Russell , the first to discuss the paradox in print, attributed it to G. G. Berry (1867–1928), [ 1 ] a junior librarian at Oxford 's Bodleian Library .
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything.