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The barbershop paradox was proposed by Lewis Carroll in a three-page essay titled "A Logical Paradox," which appeared in the July 1894 issue of ''Mind''. The name comes from the 'ornamental' short story that Carroll uses to illustrate the paradox (although it had appeared several times in more abstract terms in his writing and correspondence before the story was published). Carroll claimed that it illustrated "a very real difficulty in the Theory of Hypotheticals" in use at the time. Modern logicians would not regard it as a paradox but simply as a logical error on the part of Carroll. ==The paradox== Briefly, the story runs as follows: Uncle Joe and Uncle Jim are walking to the barber shop. There are three barbers who live and work in the shop—Allen, Brown, and Carr—but not all of them are always in the shop. Carr is a good barber, and Uncle Jim is keen to be shaved by him. He knows that the shop is open, so at least one of them must be in. He also knows that Allen is a very nervous man, so that he never leaves the shop without Brown going with him. Uncle Joe insists that Carr is ''certain'' to be in, and then claims that he can prove it logically. Uncle Jim demands the proof. Uncle Joe reasons as follows. Suppose that Carr is out. If Carr is out, then if Allen is also out Brown would have to be in, since ''someone'' must be in the shop for it to be open. However, we know that whenever Allen goes out he takes Brown with him, and thus we know as a general rule that if Allen is out, Brown is out. So if Carr is out then the statements "if Allen is out then Brown is in" and "if Allen is out then Brown is out" would both be true at the same time. Uncle Joe notes that this seems paradoxical; the two "hypotheticals" seem "incompatible" with each other. So, by contradiction, Carr must logically be in. However, the correct conclusion to draw from the incompatibility of the two "hypotheticals" is that what is hypothesised in them (that Allen is out) must be false under our assumption that Carr is out. Then our logic simply allows us to arrive at the conclusion "If Carr is out, then Allen must necessarily be in". 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「Barbershop paradox」の詳細全文を読む スポンサード リンク
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