An intension is the rule, concept, or mode of presentation that determines what a term refers to. Where extension is the actual referent a term picks out, intension is the criterion that does the picking.
Consider the term “the tallest building in the world.” Its intension is the descriptive rule: find the building that exceeds all others in height. Its extension — the building that satisfies that rule — changes over time as taller buildings are constructed. The intension stays fixed even as the extension shifts.
Gottlob Frege drew an early version of this distinction with his concept of “Sinn” (sense), which he contrasted with “Bedeutung” (reference). Two expressions can have the same reference but different senses: “the morning star” and “the evening star” both refer to Venus, but they present Venus differently. The sense of each expression is what a competent speaker grasps when understanding it.
In possible-worlds semantics, an intension is modeled as a function from possible worlds to extensions. The intension of “water” maps each possible world to whatever substance fills the water-role in that world. This formalization makes intension precise enough for compositional semantic theories, where the intension of a sentence is built from the intensions of its parts.
David Chalmers developed the distinction further by separating primary intension (the epistemic component, sensitive to how things turn out) from secondary intension (the metaphysical component, fixed by how things actually are). This two-dimensional framework addresses puzzles that arise from terms like “water,” which refers to H2O in the actual world but might refer to different substances in counterfactual scenarios.
Related terms
- extension — what a term actually refers to in a given world
- primary intension — the epistemic dimension of intension
- secondary intension — the metaphysical dimension of intension
- rigid designation — terms whose intension yields the same extension in every world