In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole. Extensional contexts are contrasted with opaque contexts where truth-preserving substitutions are not possible.
Take the case of Clark Kent, who is secretly Superman. Suppose that Lois Lane fell out of a window and Superman caught her. Thus the sentence "Superman caught Lois Lane" is true. Because this sentence is an extensional context, the sentence "Clark Kent caught Lois Lane" is also true. Anybody that Superman caught, Clark Kent caught.
In opposition to extensional contexts are intensional contexts (which can involve modal operators and modal logic), where terms cannot be substituted without potentially compromising the truth-value. Suppose that Lois Lane believes that Clark Kent will investigate a news story with her. Thus, the sentence "Lois Lane believes that Clark Kent will investigate a news story with her" is true. However, the statement, "Lois Lane believes that Superman will investigate a news story with her," is false. This is because 'believes' typically induces an intensional context. Lois Lane doesn't believe that Superman is Clark Kent and the propositional attitude "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.
extensional, context, several, fields, study, that, treat, signs, example, linguistics, logic, mathematics, semantics, semiotics, philosophy, language, extensional, context, transparent, context, syntactic, environment, which, sentential, expression, replaced,. In any of several fields of study that treat the use of signs for example in linguistics logic mathematics semantics semiotics and philosophy of language an extensional context or transparent context is a syntactic environment in which a sub sentential expression e can be replaced by an expression with the same extension and without affecting the truth value of the sentence as a whole Extensional contexts are contrasted with opaque contexts where truth preserving substitutions are not possible Take the case of Clark Kent who is secretly Superman Suppose that Lois Lane fell out of a window and Superman caught her Thus the sentence Superman caught Lois Lane is true Because this sentence is an extensional context the sentence Clark Kent caught Lois Lane is also true Anybody that Superman caught Clark Kent caught In opposition to extensional contexts are intensional contexts which can involve modal operators and modal logic where terms cannot be substituted without potentially compromising the truth value Suppose that Lois Lane believes that Clark Kent will investigate a news story with her Thus the sentence Lois Lane believes that Clark Kent will investigate a news story with her is true However the statement Lois Lane believes that Superman will investigate a news story with her is false This is because believes typically induces an intensional context Lois Lane doesn t believe that Superman is Clark Kent and the propositional attitude believe induces an intensional context so the substitution alters the meaning of the original sentence See also editDe dicto and de re Extension semantics Extensional definition Extensionalism Intensional logic Opaque context Propositional attitude W V QuineFurther reading editFrancis Watanabe Dauer Critical Thinking An Introduction to Reasoning Oxford University Press 1989 p 392 nbsp This philosophy of language related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Extensional context amp oldid 1099491053, wikipedia, wiki, book, books, library,
