V2EX extensionality

Extensionality

释义 Definition

extensionality(外延性 / 外延原则):逻辑、哲学与数学中常用的概念,强调以对象“所指向的范围/集合(外延)”来判定其是否相同。常见表述是:如果两个表达式在所有情况下指向同一对象或具有同一外延(例如同一集合、同一真值函数结果),就可视为相同(或可互换)。
(在一些语境中也与“内涵性 intension”相对,属于较偏学术的用法。)

发音 Pronunciation (IPA)

/kstnnlti/

例句 Examples

Extensionality means two sets are equal if they have the same elements.
外延性表示:如果两个集合拥有相同的元素,那么它们就是相等的。

In an extensional language, you can replace one term with another that has the same reference without changing the truth of the sentence.
在外延性的语言中,如果两个词指向同一对象,你可以用其中一个替换另一个,而不改变句子的真假。

词源 Etymology

来自 extension(外延) + -ality(……性质)。其中 extension 源自拉丁语 extendere(“伸展、扩展”),在逻辑/语义学中引申为“一个词或表达式所涵盖的对象范围(外延)”。因此 extensionality 字面义就是“外延性的性质/原则”。/p>

相关词 Related Words

文学与名著用例 Literary Works

  • W. V. Quine, From a Logical Point of View(《从逻辑的观点看》)
  • Alonzo Church, Introduction to Mathematical Logic(《数理逻辑导论》)
  • Bertrand Russell & Alfred North Whitehead, Principia Mathematica(《数学原理》)
  • Elliott Mendelson, Introduction to Mathematical Logic(《数理逻辑导论》)
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