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In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is true. The law is also known as the law (or principle) of the excluded third, in Latin ''principium tertii exclusi''. Yet another Latin designation for this law is ''tertium non datur'': "no third (possibility) is given". The earliest known formulation is Aristotle's principle of non-contradiction, first proposed in ''On Interpretation,''〔Geach p. 74〕 where he says that of two contradictory propositions (i.e. where one proposition is the negation of the other) one must be true, and the other false.〔''On Interpretation'', c. 9〕 He also states it as a principle in the ''Metaphysics'' book 3, saying that it is necessary in every case to affirm or deny,〔''Metaphysics 2, 996b 26–30〕 and that it is impossible that there should be anything between the two parts of a contradiction.〔''Metaphysics 7, 1011b 26–27〕 The principle was stated as a theorem of propositional logic by Russell and Whitehead in ''Principia Mathematica'' as: . The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. == Classic laws of thought == The principle of excluded middle, along with its complement, the law of contradiction (the second of the three classic laws of thought), are correlates of the law of identity (the first of these laws). 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「Law of excluded middle」の詳細全文を読む スポンサード リンク
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