liar paradox

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Related to Liar's paradox: Russell's paradox

liar paradox

(philosophy)
A sentence which asserts its own falsity, e.g. "This sentence is false" or "I am lying". These paradoxical assertions are meaningless in the sense that there is nothing in the world which could serve to either support or refute them. Philosophers, of course, have a great deal more to say on the subject.

["The Liar: an Essay on Truth and Circularity", Jon Barwise and John Etchemendy, Oxford University Press (1987). ISBN 0-19-505944-1 (PBK), Library of Congress BC199.P2B37].
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The Liar's Paradox, the paradox analogous to the diagonal lemma
The paradox that forms the basis of a crucial step in the proof, the diagonal 'lemma' or argument, is what is commonly known as the Liar's Paradox. It is altered somewhat by Godel in the process.
(Students can be advised to keep this description in mind when studying the summary and to refer back to it as they follow the logic of the proof.) At this point a discussion about Russell's theory of sets, the paradox he found, and the Liar's Paradox would set the historical scene.
A representational version of the liar's paradox, here the "real" is false, since the tampon version of the letters is reversed, and the "true" is unreal, since their correct, printed version is forever locked within the bubble of virtual space: Duchamp's "mirroric return." Yet if this were all the painting were, it would be merely clever and brittle, a bright piece of Conceptual art.
Buridan's treatment of the liar's paradox in part two is sometimes referred to as the Peirce-Buridan solution.