Extensional and intensional definitions: Difference between revisions

Revision as of 03:51, 6 October 2021

Revision as of 04:02, 6 October 2021

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==Intensional definition==

{{also|Intension}}

An intensional definition gives the meaning toof 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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[[Genus–differentia definition|Definition by genus and difference]], in which something is defined by first stating the broad category it belongs to and then distinguished by specific properties, is a type of intensional definition. As the name might suggest, this is the type of definition used in [[Linnaean taxonomy]] to categorize living things, but is by no means restricted to [[biology]]. Suppose one defines a miniskirt as "a skirt with a hemline above the knee". It has been assigned to a ''genus'', or larger class of items: it is a type of skirt. Then, we've described the ''differentia'', the specific properties that make it its own sub-type: it has a hemline above the knee.

Intensional definition may also consistapplies ofto rules or sets of [[axiom]]s that define a [[set (mathematics)|set]] by describing a procedure for generating all of its members. For example, an intensional definition of ''[[square number]]'' can be "any number that can be expressed as some integer multiplied by itself". The rule—"take an integer and multiply it by itself"—always generates members of the set of square numbers, no matter which integer one chooses, and for any square number, there is an integer that was multiplied by itself to get it.

Similarly, an intensional definition of a game, such as [[chess]], would be the rules of the game; any game played by those rules must be a game of chess, and any game properly called a game of chess must have been played by those rules.

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==Extensional definition==

{{also|Extension (semantics)}}

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

ThisAn isextensional similardefinition possesses some similarity to an [[ostensive definition]], in which one or more members of a set (but not necessarily all) are pointed outto as examples., Thebut oppositecontrasts approachclearly iswith thean [[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==