extension See INTENSION. extensionalism, a family of ontologies and semantic theories restricted to existent entities. Extensionalist ontology denies that the domain of any true theory needs to include non-existents, such as fictional, imaginary, and impossible objects like Pegasus the winged horse or round squares. Extensionalist semantics reduces meaning and truth to set-theoretical relations between terms in a language and the existent objects, standardly spatiotemporal and abstract entities, that belong to the term’s extension. The extension of a name is the particular existent denoted by the name; the extension of a predicate is the set of existent objects that have the property represented by the predicate. The sentence ‘All whales are mammals’ is true in extensionalist semantics provided there are no whales that are not mammals, no existent objects in the extension of the predicate ‘whale’ that are not also in the extension of ‘mammal’. Linguistic contexts are extensional if: (i) they make reference only to existent objects; (ii) they support substitution of codesignative terms (referring to the same thing), or of logically equivalent propositions, salva veritate (without loss of truthvalue); and (iii) it is logically valid to existentially quantify (conclude that There exists an object such tha. . . etc.) objects referred to within the context. Contexts that do not meet these requirements are intensional, non-extensional, or referentially opaque.
The implications of extensionalism, associated with the work of Frege, Russell, Quine, and mainstream analytic philosophy, are to limit its explanations of mind and meaning to existent objects and material-mechanical properties and relations describable in an exclusively extensional idiom. Extensionalist semantics must try to analyze away apparent references to nonexistent objects, or, as in Russell’s extensionalist theory of definite descriptions, to classify all such predications as false. Extensionalist ontology in the philosophy of mind must eliminate or reduce propositional attitudes or de dicto mental states, expressed in an intensional idiom, such as ‘believes that ————’, ‘fears that ————’, and the like, usually in favor of extensional characterizations of neurophysiological states. Whether extensionalist philosophy can satisfy these explanatory obligations, as the thesis of extensionality maintains, is controversial. See also ABSTRACT ENTITY , INTENSIONAL – ITY , PHILOSOPHY OF LANGUAGE , RUSSELL , THEORY OF DESCRIPTIONS , TRUT. D.J.