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In philosophy and logic, the classical liar paradox or liar's paradox is the statement of a liar who states that they are lying: for instance "I am lying" or "everything I say is false". If they are indeed lying, they are telling the truth, which means they are lying... In "this sentence is a lie" the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar himself. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. If "this sentence is false" is true, then the sentence is false, but if the sentence states that it is false, and it is false, then it must be true, and so on. ==History== The Epimenides paradox (circa 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythical seer Epimenides, a Cretan, reportedly stated that "All Cretans are liars."〔Epimenides paradox has "All Cretans are liars." 〕 However, Epimenides' statement that all Cretans are liars can be resolved as false, given that he knows of at least one other Cretan who does not lie. It is precisely in order to avoid uncertainties deriving from the human factor and from fuzzy concepts that modern logicians proposed a "strengthened" liar such as the sentence "this sentence is false". The paradox's name translates as ''pseudómenos lógos'' (ψευδόμενος λόγος) in Ancient Greek. One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the 4th century BC. Eubulides reportedly asked, "A man says that he is lying. Is what he says true or false?" The paradox was once discussed by St. Jerome in a sermon: The Indian grammarian-philosopher Bhartrhari (late fifth century CE) was well aware of a liar paradox which he formulated as "everything I am saying is false" (sarvam mithyā bravīmi). He analyzes this paradox together with the paradox of "unsignifiability" and explores the boundary between statements that are unproblematic in daily life and paradoxes.〔Jan E.M. Houben, "Bhartrhari's solution to the Liar and some other paradoxes." Journal of Indian Philosophy 23 (1995): 381-401; Jan E.M. Houben, "Paradoxe et perspectivisme dans la philosophie de langage de Bhartrhari: langage, pensée et réalité." Bulletin d'Études Indiennes 19 (2001):173-199. www.academia.edu/6169499/〕 In early Islamic tradition liar paradox was discussed for at least five centuries starting from late 9th century apparently without being influenced by any other tradition. Naṣīr al-Dīn al-Ṭūsī could have been the first logician to identify the liar paradox as self-referential. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Liar paradox」の詳細全文を読む スポンサード リンク
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