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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Function and Concept ： ウィキペディア英語版 Function and Concept "On Function and Concept" ((ドイツ語:Über Funktion und Begriff)) is an article by Gottlob Frege, published in 1891. The article involves a clarification of his earlier distinction between concepts and objects. In general, a concept is a function whose value is always a truth value (139). A relation is a two place function whose value is always a truth value (146). Frege draws an important distinction between concepts on the basis of their level. Frege tells us that a first-level concept is a one-place function that correlates objects with truth-values (147). First level concepts have the value of true or false depending on whether the object falls under the concept. So, the concept $F$ has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept $F$ (or is in the extension of F). Second order concepts correlate concepts and relations with truth values. So, if we take the relation of identity to be the argument $f$, the concept expressed by the sentence: $\backslash forall\; x\; \backslash forall\; y\; f(x,\; y)\; \backslash rightarrow\; \backslash forall\; z\; (f\; (x,\; z)\; \backslash rightarrow\; y=z\; )$ correlates the relation of identity with the True. The conceptual range (Begriffsumfang) follows the truth value of the function: * x2 = 1 and (x + 1)2 = 2(x + 1) have the same conceptual range. ==Works cited== In English: "On Function and Concept" in The Frege Reader, ed. Michael Beaney 1997, pp. 130–148 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「Function and Concept」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.