The extension of a term is the actual object or set of objects that the term picks out in a given world. Where intension concerns how a term determines its referent, extension concerns what that referent turns out to be.
For example, the extension of “the morning star” is the planet Venus. The extension of “dog” is the set of all dogs that exist. Two terms can share the same extension while differing in intension: “the morning star” and “the evening star” both refer to Venus, but they present Venus through different descriptive routes.
Extension depends on context. A term may have different extensions in different possible worlds, at different times, or relative to different speakers. The extension of “the president of the United States” changes with each administration, even though its intension — the descriptive rule for picking out a referent — stays the same.
In formal semantics, extension is often modeled as a function from a world (or world-time pair) to the set of objects satisfying the term in that world. This connects extension to the broader apparatus of model theory, where truth conditions for sentences depend on the extensions assigned to their component terms.
The distinction between extension and intension is foundational in the philosophy of language. Gottlob Frege introduced a version of it through his sense/reference distinction, and it remains central to debates about meaning, reference, and rigid designation.
Related terms
- intension — the mode of presentation that determines extension
- primary intension — the epistemic component of intension
- secondary intension — the metaphysical component of intension
- rigid designation — terms whose extension does not vary across possible worlds