intensión

Intensión, often rendered as intension in English, is a term used in philosophy of language and semantics to denote the internal content, concept, or sense associated with a linguistic expression. It contrasts with its extension, the set of objects or events to which the expression applies in a given context. In this view, intension captures what a term means beyond its concrete referents and is closely related to the notion of sense in classic Fregean analysis.

Historically, the distinction between sense and reference was introduced by the German logician and philosopher Gottlob Frege in the late 19th century. Frege’s Sinn (sense) and Bedeutung (reference) laid the groundwork for later uses of intension in semantics. In the 20th century, intensional logic and possible-world semantics formalized the idea that intensions can be modeled as context- or world-dependent content, rather than fixed extensions alone.

In modern formal semantics, the intension of a term or predicate is often represented as a function from possible worlds to extensions: for each possible world, the function returns the set of objects that satisfy the predicate in that world. This makes intensions sensitive to modality, context, and propositional attitude. Accordingly, intensional contexts include belief, necessity, knowledge, and obligation, where substitution of co-extensional terms can fail.

Examples illustrate the distinction. The phrases “the morning star” and “the evening star” refer to Venus in the actual world (same extension) but have different intensions because they present Venus under different modes of presentation. Another example concerns necessity: “Necessarily, 2+2=4” expresses a truth that holds across all possible worlds, reflecting the intensional nature of necessity. Intension remains a central concept across linguistics, cognitive science, and artificial intelligence for analyzing meaning beyond direct reference.