Extensional and intensional definitions

In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give 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 that falls under the definition of the term in question.

For example, in set theory one would extensionally define the set of square numbers as {0, 1, 4, 9, 16, ${\displaystyle \dots }$}, while an intensional definition of the set of the square numbers could be {${\displaystyle x\mid x}$ is the square of an integer}.