# Intensional Definition

An Intensional Definition is a Definition of a Concept Class that is based on a description of the (Necessary and Condition) Conditions that a Concept must satisfy to be a member of the Concept Class.

## References

• Misc
• An intensional definition lists the attributes or characteristics of the concept.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Intensional_definition
• In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.
• For example, an intensional definition of "bachelor" is "unmarried man." Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor.
• This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition — an extensional definition of "bachelor" would be a listing of all the unmarried men in the world.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Definiendum#Intension_and_extension
• An intensional definition, also called a connotative 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.

### 2002

• (Cruse, 2002) ⇒ D. Alan Cruse. (2002). “Hyponymy and its Varieties.” In: (Green et al., 2002).
• Taking a logical approach, we can define hyponymy either extensionally or intensionally.
• One extensional definition is the following, after Cann (1994), but modified to exclude synonymy:
• X is a hyponym of Y iff there exists a meaning postulate relation X' and Y' of the form:
• `∀x[X'(x) → Y'(x)]`, but none of the form: `∀x[Y'(x) → X'(x)]`.
• (Here, X' and Y' are the logical constants corresponding to the lexical items X and Y, and the definition states, effectively, that for X to be a hyponym of Y, the extension of X' must be included in the extension of Y'.)
• An example of an intensional definition is the following:
• X is a hyponym of Y iff F(X) entails, but is not entailed by F(Y).