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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 ...
This category contains paradoxes in mathematics, but excluding those concerning informal logic. "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction". "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction".
The paradox follows from this analysis. The analysis consists of two steps. First, common natural-language proof techniques can be used to prove that the example sentence is true [steps 1–4 below]. Second, the truth of the sentence can be used to prove that Germany borders China [steps 5–6]: The sentence reads "If this sentence is true ...
Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly. [14] Informally, the term paradox is often used to describe a counterintuitive result.
In philosophy and mathematics, Newcomb's paradox, also known as Newcomb's problem, is a thought experiment involving a game between two players, one of whom is able to predict the future. Newcomb's paradox was created by William Newcomb of the University of California 's Lawrence Livermore Laboratory .
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics .
Thus the seeming contradiction is that a model that is itself countable, and which therefore contains only countable sets, satisfies the first-order sentence that intuitively states "there are uncountable sets". A mathematical explanation of the paradox, showing that it is not a true contradiction in mathematics, was first given in 1922 by Skolem.
Hofstadter points to Bach's Canon per Tonos, M. C. Escher's drawings Waterfall, Drawing Hands, Ascending and Descending, and the liar paradox as examples that illustrate the idea of strange loops, which is expressed fully in the proof of Gödel's incompleteness theorem. The "chicken or the egg" paradox is perhaps the best-known strange loop ...
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