Extensional and intensional definitions: Difference between revisions

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In [[logic]], '''extensional and intensional definitions''' are two key ways in which the [[Object (philosophy)|objects]], [[concept]]s, or [[referent]]s a [[terminology|term]] refers to can be [[definition|defined]]. They give [[Meaning (linguistic)|meaning]] or denotation to a term.

An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used.

An extensional definition gives meaning to a term by specifying every [[object (philosophy)|object]] that falls under the definition of the term in question.

For example, in set theory one would extensionally define the set of [[Square number|square numbers]] as {0, 1, 4, 9, 16, <math>\dots</math>}, while an intensional definition of the set of the square numbers could be {<math>x \mid x</math> is the square of an integer}.

==Intensional definition==

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An extensional definition gives meaning to a term by specifying its [[Extension (semantics)|extension]], that is, every [[object (philosophy)|object]] that falls under the definition of the term in question.

ForgetFor example, an extensional definition of the term "nation of the world" might be given by [[List of sovereign states|listing all of the nations of the world]], or by giving some other means of recognizing the members of the corresponding class. An explicit listing of the extension, which is only possible for [[finite sets]] and only practical for relatively [[Small set (category theory)|small sets]], is a type of ''[[enumerative definition]]''.

Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a [[set (mathematics)|set]] tells the questioner enough about the nature of that set.

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An extensional definition possesses similarity to an [[ostensive definition]], in which one or more members of a set (but not necessarily all) are pointed to as examples, but contrasts clearly with an [[intensional definition]], which defines by listing properties that a thing must have in order to be part of the set captured by the definition.

==HistoryEtymology==

The terms "[[intension]]" and "[[Extension (semantics)|extension]]" were introduced before 1911 by [[Constance Jones]]<ref>{{cite web

| title =Emily Elizabeth Constance Jones: Observations on Intension and Extension

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== See also ==

* [[{{annotated link|Comprehension (logic)]]}}

* [[{{annotated link|Extension (predicate logic)]]}}

* [[{{annotated link|Extension (semantics)]]}}

* [[{{annotated link|Extensional context]]}}

* [[{{annotated link|Extensionalism]]}}

* [[{{annotated link|Extensionality]]}}

* [[{{annotated link|Intension]]}}

* [[{{annotated link|Intensional logic]]}}

* [[{{annotated link|Ostensive definition]]}}

== References ==