Routledge Dictionary of Language and Linguistics.pdf

Dictionary of language and linguistics 398organon model of languageReferencesextension [Lat. extensio ‘stretch, span’] (alsodenotation 2 , designation, referent)The extension of a linguistic expression is the class of elements that the expressiondenotes. Therefore, an extensional definition is based on counting all objects to whichthe expression applies, in contrast with intension (‘sense’), which is determinedaccording to the features by which the concept is defined. Two predicates have the sameextension if they apply to the same class of elements, in this sense both expressionsevening star and morning star are extensionally identical, since they both denote theplanet Venus, even though they both have a different intensional content. In formal logicextension is defined depending on the different categories of expressions. The extensionof a singular term (=individual constant) t is the individual to which t refers (e.g. theextension of Mozart is the ‘composer of the “Magic Flute”’). The extension of a predicatep is the set of elements to which this predicate applies, e.g. the extension of larger than isthe set of all pairs x, y for which it is true that x is larger than y. The extension of asentence is its truth value. The extension of a complex sentence can be conveyed truthfunctionally,if the following is true: if in sentence S an element e is replaced by anelement of the same extension as e, then the extension of S is unchanged ( principleof compositionality).intension, semanticsReferencesextensional [Lat. extendere ‘to stretch’]In formal logic, property of propositional connections whose truth value alone isdependent on the truth values of the elementary propositions, but not on their actualsemantic content. This extensional interpretation is fundamental to the logicalconnections of classical propositional logic and predicate logic, e.g. adjunction,implication, operator, among others.