Intentio

Intentio is a Latin noun meaning intention, purpose, or aim. In scholarly contexts, it is used to denote the intension of a term—the inherent concept or mental content that a word expresses—contrasted with its extents (extensio), the actual things to which the term applies. The distinction between intentio and extensio has roots in medieval scholastic logic and remained influential in the history of semantics.

Etymology: From the Latin intendere, meaning to intend or stretch toward. In modern English translations, intentio is often rendered as intension, especially in discussions of semantic theory.

Historical usage: In medieval philosophy, intentio referred to the concept or meaning associated with a term, while the extensio referred to the set of things under the term. This dichotomy informed debates about universals, predication, and conceptual analysis.

Modern relevance: In contemporary philosophy of language and logic, the pair intension and extension serves to separate concept from reference. An intension is the condition under which a term applies, often modeled as a function from possible worlds to truth values; its extension is the actual collection of objects satisfying the term in a given world. Although modern texts typically use intension instead of intentio, the Latin term appears in historical writing and in discussions of medieval logic.

See also: Intension, Extension, Semantics, Predicate logic, Scholasticism.

Examples: The term "dog" has a broad extension, but its intension—the concept of a domesticated canid—explains the criteria common to all dogs. The term "unicorn" has an empty extension in the real world, yet its intension describes a horned horse-like creature.