Definition

1. Adjective:
   • Relating to or characterized by extension: In logic and philosophy, "extensional" describes a way of defining a term by specifying the set of all objects to which the term applies. It contrasts with "intensional" definitions, which specify the meaning or essential properties of a term.
   • Concerned with the actual objects in a set, not their descriptions or meanings: An extensional context is one where the truth value depends only on the objects referred to, not on the way they are described.

Usage Examples

• Adjective:
  • An extensional definition of "planet" would list all the planets in our solar system.
  • The statement "Mark Twain is Samuel Clemens" is true in an extensional context because both names refer to the same person.
  • Set theory is fundamentally extensional; a set is defined by its members.

Advanced Usage

• Extensionality (Axiom of): A principle in set theory stating that two sets are identical if and only if they have exactly the same members.

  • The axiom of extensionality is a foundational concept in Zermelo-Fraenkel set theory.

• Extensional Context: A context where substituting co-referential terms (terms that refer to the same thing) does not change the truth value of a statement.

  • "Hesperus is Phosphorus" is true in an extensional context because both names refer to the planet Venus.

Variants and Related Words

• Extension (n): The set of all things to which a term applies.

  • The extension of the word "cat" includes all individual cats.

• Extensionalism (n): The philosophical emphasis on extension over intension.

• Extensionality (n): The quality or principle of being extensional.

Synonyms

• Denotative: Concerned with the direct reference or denotation of a term.
• Referential: Pertaining to the objects a term refers to.

Antonyms

• Intensional: Concerned with the meaning, sense, or connotation of a term, rather than its reference.
  • An intensional definition of "bachelor" is "an unmarried man."

Adjective

1. defining a word by listing the class of entities to which the word correctly applies