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Epimenides Paradox
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Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Russell's paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished. The study of self-reference led to important developments in logic and mathematics in the twentieth century.
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This is known as the Epimenides Paradox. The subject of self-reference is treated in great detail in Douglas Hofstadter's book of 1979: Gödel, Escher, Bach: An Eternal Golden Braid. In this book, Hofstadter explains the mathematical theorems of Kurt Gödel, by drawing on illustrations from the art of M. C. Escher, and the music of J. S. Bach. The briefest statement of Gödel's Incompleteness Theorem is: "All consistent axiomatic formulations of number theory include undecidable propositions." But let's eschew obfuscation. Put more simply, Gödel's work showed that any mathematical system that is powerful enough to be useful is necessarily incomplete. His proof of this is similar to Turing's non-computability proof in its use of self-reference.
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As opposed to the Epimenides paradox, this is a true paradox: assuming that the statement is true, then it must be false; assuming it is false, then it must be true. No truth value can be consistently assigned to the statement.
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In that article, Russell uses the Epimenides paradox as the point of departure for discussions of other problems, including the Burali-Forti paradox and the paradox now called Russell's paradox. Since Russell, the Epimenides paradox has been referenced repeatedly in logic. Typical of these references is Gödel, Escher, Bach by Douglas Hofstadter, which accords the paradox a prominent place in a discussion of self-reference.
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Goffman takes a more psychological approach to Frame, basing his work in Bateson and the Epimenides' Paradox. Burke develops the more sociological approach, looking at how grand narratives stretch and adapt to compete with emergent frames. Burke views this as a dialectic process between Frames of Acceptance and Frames of Rejection. The old frame makes a net that its transvaluations will allow it to hang on for a while longer. Frames can experience a "cultural lag" where people facing situations located outside the attitudes of the frame (Burke, 1937: 40). No frame is "broad enough to encompass all the necessary attitudes" (1937: 40).
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Een versimpelde én verscherpte versie van Epimenides' paradox is de leugenaarsparadox. Deze luidt: "Deze bewering is onwaar." Aannemende dat de voorgaande bewering middels de frase "deze bewering" naar zichzelf verwijst, dan is ze noch waar, noch onwaar (of beide tegelijk; zie paraconsistente logica).
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Epimenides Paradox