1. the entity or set of entities to which an expression refers. The extension of a proper name or definite description is one entity; the extension of a predicate is a set of entities. The extension of an expression is determined by its intension (the meaning or concept of the expression). This is formalized in intensional logic and Montague Grammar by taking the intension of an expression as a function which yields the extension of that expression in every possible world. The distinction between extension and intension is close to Frege's distinction between reference (Bedeutung) and sense (Sinn) and is also related to the distinction between denotation and connotation.
2. a general constraint on determiners in Generalized Quantifier Theory. A determiner D has extension if it is context independent: extension of the number of elements in the domain has no influence on its interpretation. Formally, a determiner D has extension if and only if for all the subsets X and Y of the domains of entities E and E', condition (i) holds.
(i) if D(X,Y) in E and E a subset of E', then D(X,Y) in E'
Some, at least two and not only are examples of determiners which obey extension; many and only are not. Take Only boys dance in a restricted set E and extend E to the set E', then it might be the case that there are dancing girls in E'.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.