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A genus–differentia definition is a type of intensional definition, and it is composed of two parts: # a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus. # the differentia: The portion of the definition that is not provided by the genus. For example, consider these two definitions: * ''a triangle'': A plane figure that has 3 straight bounding sides. * ''a quadrilateral'': A plane figure that has 4 straight bounding sides. Those definitions can be expressed as one genus and two ''differentiae'': # ''one genus'': # * ''the genus for both a triangle and a quadrilateral'': "A plane figure" # ''two differentiae'': # * ''the differentia for a triangle'': "that has 3 straight bounding sides." # * ''the differentia for a quadrilateral'': "that has 4 straight bounding sides." == Differentiation and Abstraction == The process of producing new definitions by ''extending'' existing definitions is commonly known as differentiation (and also as derivation). The reverse process, by which just part of an existing definition is used itself as a new definition, is called abstraction; the new definition is called ''an abstraction'' and it is said to have been ''abstracted away from'' the existing definition. For instance, consider the following: * ''a square'': a quadrilateral that has interior angles which are all right angles, and that has bounding sides which all have the same length. A part of that definition may be singled out (using parentheses here): * ''a square'': (a quadrilateral that has interior angles which are all right angles), and that has bounding sides which all have the same length. and with that part, an abstraction may be formed: * ''a rectangle'': a quadrilateral that has interior angles which are all right angles. Then, the definition of ''a square'' may be recast with that abstraction as its genus: * ''a square'': a rectangle that has bounding sides which all have the same length. Similarly, the definition of ''a square'' may be rearranged and another portion singled out: * ''a square'': (a quadrilateral that has bounding sides which all have the same length), and that has interior angles which are all right angles. leading to the following abstraction: * ''a rhombus'': a quadrilateral that has bounding sides which all have the same length. Then, the definition of ''a square'' may be recast with that abstraction as its genus: * ''a square'': a rhombus that has interior angles which are all right angles. In fact, the definition of ''a square'' may be recast in terms of both of the abstractions, where one acts as the genus and the other acts as the differentia: * ''a square'': a rectangle that is a rhombus. * ''a square'': a rhombus that is a rectangle. Hence, abstraction is crucial in simplifying definitions. 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「Genus–differentia definition」の詳細全文を読む スポンサード リンク
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