What does extensional mean?
"Extensional" is an adjective used mainly in logic, semantics, mathematics, and computer science to describe approaches that define or evaluate something by its actual members or referents rather than by its underlying concept or properties. An extensional definition of a set, for instance, simply lists its elements, whereas an intensional definition states the rule that determines membership. Two expressions are extensionally equivalent when they apply to exactly the same things, even if they differ in meaning. The word derives from Latin extendere, "to stretch out", and in older or more general use can also relate to outward spatial extent. Because it forms a minimal pair with "intensional", distinguished by a single letter, precision in spelling and usage matters: confusing the two reverses the sense entirely. The adverb "extensionally" also exists for qualifying statements about denotation.
(Logic, semantics) Of or relating to the extension of a term: determined by or expressed in terms of the objects to which the term applies, rather than by its intension or defining properties.
"An extensional approach to set theory identifies a set entirely with its members."
Almost always used in explicit or implicit contrast with "intensional"; the pair is standard terminology across analytic philosophy, model theory, and programming-language theory.
Relating to outward or spatial extension; pertaining to extent.
"The sculpture was praised for the extensional qualities of its sweeping horizontal lines."
A rarer, more general sense; most modern readers will encounter the word only in its technical logical use.
Swap one letter — 'i' for 'e' — and you flip a philosopher's world upside down: intensional is about meaning, extensional is about the things themselves.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of extensional
"Extensional" comes from "extension", which traces back through Late Latin extensio to Latin extendere, meaning "to stretch out", formed from ex- ("out") + tendere ("to stretch"). English adopted "extension" in the late Middle English period with senses of both spatial stretching and scope or range, and "extensional" arose later as its adjective form, becoming prominent in nineteenth- and twentieth-century philosophical and logical writing. It shares its root with words such as "extend", "extensive", and "extent".
Related word forms
How extensional is actually used
A technical term found chiefly in philosophy, formal logic, linguistics, mathematics, and computer science. It carries no informal register and is almost always used contrastively with 'intensional', its near-opposite. Outside academic writing it is rare.
Easily confused with extensional
"Extensional" concerns the actual objects or members a term refers to, while "intensional" concerns the concept or defining properties behind it — two terms that are near-perfect opposites in logic despite differing by only one letter.
"Extentional" is simply a common misspelling of extensional; no separate word exists.