What does extensionally mean?
Extensionally is a formal adverb meaning “in an extensional manner,” especially in logic and philosophy. It describes a comparison that depends on the range of cases, entities, or situations covered by a term, description, or rule rather than merely on similar wording or an apparent shared idea. For example, two predicates can be extensionally equivalent when they are true of exactly the same objects, even if one is expressed more simply. In less specialized prose, the word can also convey “by extension,” applying a statement or analogy beyond its original scope. The term is uncommon in everyday English, where “by extension” is usually clearer and more natural. Its value for a general reader lies in showing that concepts can be compared according to what they actually include. “Extensionally” contrasts with “intensionally,” which concerns the internal meaning or character of something, and it should not be confused with the adjective “extensional.”
adverbIn an extensional manner, especially with respect to the range of cases, entities, or situations covered by a term, description, or rule. It can also mean by extension, in an extended or analogous sense.
- With respect to extension or the range of cases covered by a term, description, or rule; in an extensional manner.
- By extension, in an extended or analogous sense.
"The two predicates are extensionally equivalent because they apply to exactly the same objects."
"The definitions are extensionally equivalent even though one contains considerably more words."
"The reasoning applies extensionally to related systems that were not explicitly discussed."
Two claims can be extensionally equivalent without being phrased alike: in logic, what matters is the cases they cover.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does extensionally come from?
The word was formed in English from extension, ultimately from the Latin extēnsiō, a noun of action derived from extendere, “to stretch out.” The Latin verb combines ex-, meaning “out,” with tendere, meaning “to stretch.” The adverbial ending -ally was added to express the manner of acting extensionally.
How extensionally is actually used
Rare and formal, chiefly used in logic, philosophy, and related technical discussion. In general prose, “by extension” is usually clearer and more natural.
Easily confused with extensionally
Extensional is an adjective meaning relating to extension, whereas extensionally is the corresponding adverb.
An intensionally equivalent claim agrees in internal meaning or character, whereas an extensionally equivalent one covers the same cases.