Definition - Intension and Extension

Intension and Extension

An intensional definition, also called a coactive 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 intentionally 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 a list of the seven. 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.

One important form of the extensional definition is ostensive definition. This gives the meaning of a term by pointing, in the case of an individual, to the thing itself, or in the case of a class, to examples of the right kind. So you can explain who Alice (an individual) is by pointing her out to me; or what a rabbit (a class) is by pointing at several and expecting me to 'catch on'. The process of ostensive definition itself was critically appraised by Ludwig Wittgenstein.

An enumerative definition of a concept or term is an extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.