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.Cook, Roy T. "Intensional Definition." In A Dictionary of Philosophical Logic. Edinburgh: Edinburgh University Press, 2009. 155.

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.

As becomes clear, intensional definitions are best used when something has a clearly defined set of properties, and it works well for sets that are too large to list in an extensional definition. It is impossible to give an extensional definition for an infinite set, but an intensional one can often be stated concisely — there is an infinite number of even numbers, impossible to list, but they can be defined by saying that even numbers are integer multiples of...
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