Extensional and intensional definitions: Difference between revisions

Revision as of 16:08, 16 July 2020

Revision as of 23:58, 24 July 2020

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In [[logic]] and [[mathematics]], '''Extensionalextensional and intensional definitions''' are two key ways in which the [[wikt:entity|object(s)]] or [[concept]](s) a [[terminology|term]] refers to can be [[definition|defined]].

==Intensional definition==

InAn [[logic]] and [[mathematics]], an '''intensional definition''' gives the [[Meaning (linguistic)|meaning]] of a term by specifying necessary and sufficient conditions for when the term should be used. In the case of [[nouns]], this is equivalent to specifying the [[Property (philosophy)|properties]] that an [[Object (philosophy)|object]] needs to have in order to be counted as a [[referent]] of the term.

For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.<ref name="Cook">Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155.</ref>

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==Extensional definition==

An '''extensional definition''' of a concept or term formulates its meaning by specifying its '''extension''', that is, every [[object (philosophy)|object]] that falls under the definition of the concept or term in question.

For example, an extensional definition of the term "nation of the world" might be given by 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 sets, is a type of ''[[enumerative definition]]''.

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This is similar to an [[ostensive definition]], in which one or more members of a set (but not necessarily all) are pointed out as examples. The opposite approach is the [[intensional definition]], which defines by listing properties that a thing must have in order to be part of the set captured by the definition.

==History==

The terms "[[intension]]" and "[[Extension (semantics)|extension]]" were introduced by [[Rudolf Carnap]].<ref>{{cite SEP |url-id=logic-intensional |title=Intensional logic |last=Fitting |first=Melvin}}</ref>

== See also ==

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* [[Extensionality]]

* [[Intension]]

* [[Intensional logic]]

* [[Ostensive definition]]