The extension of a linguistic expression is the class of elements that the expression denotes. Therefore, an extensional definition is based on counting all objects to which the expression applies, in contrast with intension (‘sense’), which is determined according to the features by which the concept is defined. Two predicates have the same extension if they apply to the same class of elements, in this sense both expressions evening star and morning star are extensionally identical, since they both denote the planet Venus, even though they both have a different intensional content. In formal logic extension is defined depending on the different categories of expressions.
The extension of a singular term (=individual constant) t is the individual to which t refers (e.g. the extension of Mozart is the ‘composer of the “Magic Flute”’). The extension of a predicate p is the set of elements to which this predicate applies, e.g. the extension of larger than is the set of all pairs x, y for which it is true that x is larger than y. The extension of a sentence is its truth value. The extension of a complex sentence can be conveyed truth-functionally, if the following is true: if in sentence S an element e is replaced by an element of the same extension as e, then the extension of S is unchanged (principle of compositionality).
