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A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).〔Bickenbach, Jerome E., and Jacqueline M. Davies. Good reasons for better arguments: An introduction to the skills and values of critical thinking. Broadview Press, 1996. p. 49〕 Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which list every single object that a term describes).〔Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on.〕 A term may have many different senses and multiple meanings, and thus require multiple definitions.〔Dooly, Melinda. Semantics and Pragmatics of English: Teaching English as a Foreign Language. Univ. Autònoma de Barcelona, 2006. p.48 and on〕 In mathematics, a definition is used to give a precise meaning to a new term, instead of describing a pre-existing term. Definitions and axioms are the basis on which all of mathematics is constructed.〔Richard J. Rossi (2011) Theorems, Corollaries, Lemmas, and Methods of Proof. John Wiley & Sons p.4〕 ==Intensional definitions vs extensional definitions== An ''intensional definition'', also called a ''connotative'' definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set.〔 Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition. An ''extensional definition'', also called a ''denotative'' definition, of a concept or term specifies its ''extension''. It is a list naming every object that is a member of a specific set. 〔 Thus, the "seven deadly sins" can be defined ''intensionally'' as those singled out by Pope Gregory I as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation. An ''extensional'' definition would be the list of wrath, greed, sloth, pride, lust, envy, and gluttony. In contrast, while an intensional definition of "Prime Minister" might be "the most senior minister of a cabinet in the executive branch of government in a parliamentary system", an extensional definition is not possible since it is not known who future prime ministers will be. 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「Definition」の詳細全文を読む スポンサード リンク
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