coextensional

Coextensional is a term used in philosophy of language, logic, and semantics to describe two terms, predicates, or concepts that designate the same set of objects within a given domain. If two expressions are coextensional, their extensions coincide; in other words, for every object in the domain, one expression applies to that object if and only if the other does. In this way, the expressions are interchangeable with respect to reference and truth conditions, assuming the surrounding context remains constant.

Common examples involve descriptive phrases or synonyms. For instance, the morning star and the evening star are coextensional in modern astronomy because both terms pick out the planet Venus as their extension. Similarly, synonyms or narrowly paraphrased descriptions that designate the exact same set of objects, such as “bachelors” and “unmarried men,” tend to be coextensional in typical usage.

Coextensionality is a semantic notion, focused on reference rather than sense or connotation. Two coextensional terms may differ in meaning, emphasis, or presuppositions, yet still refer to exactly the same objects. It also applies to proper names or definite descriptions that refer to a single individual under standard conditions; for example, “Neil Armstrong” and “the first man to walk on the Moon” may be coextensional in a context where Armstrong is that unique individual.

Limitations include domain dependence and the potential for empty or shifting extensions in different possible worlds or contexts. In such cases, coextensional relationships can break down or require careful handling within formal theories.

See also: extension, intension, extensionality, reference, synonymy.