# Extensional context

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Extensions with context

In any of several fields of study that treat the use of signs — for example, in [linguistics](/source/Linguistics), [logic](/source/Logic), [mathematics](/source/Mathematics), [semantics](/source/Semantics), [semiotics](/source/Semiotics), and [philosophy of language](/source/Philosophy_of_language) — an **extensional context** (or **transparent context**) is a [syntactic environment](/source/Syntax) in which a sub-sentential expression *e* can be replaced by an expression with the same [extension](/source/Extension_(semantics)) and without affecting the [truth-value](/source/Truth-value) of the sentence as a whole. Extensional contexts are contrasted with [opaque contexts](/source/Opaque_context) where truth-preserving substitutions are not possible.

Take the case of [Clark Kent](/source/Clark_Kent), who is secretly [Superman](/source/Superman). Suppose that [Lois Lane](/source/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](/source/Modal_operator) and [modal logic](/source/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](/source/Propositional_attitude) "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.

## See also

- [De dicto and de re](/source/De_dicto_and_de_re)

- [Extension (semantics)](/source/Extension_(semantics))

- [Extensional definition](/source/Extensional_definition)

- [Extensionalism](/source/Extensionalism)

- [Intensional logic](/source/Intensional_logic)

- [Opaque context](/source/Opaque_context)

- [Propositional attitude](/source/Propositional_attitude)

- [W.V. Quine](/source/W.V._Quine)

## Further reading

- Francis Watanabe Dauer, *Critical Thinking: An Introduction to Reasoning*, Oxford University Press, 1989, p. 392.

v t e Formal semantics (natural language) Central concepts Compositionality Denotation Entailment Extension Generalized quantifier Intension Logical form Presupposition Proposition Reference Scope Speech act Syntax–semantics interface Truth conditions Topics Areas Anaphora Ambiguity Binding Conditionals Definiteness Disjunction Evidentiality Focus Indexicality Lexical semantics Modality Negation Propositional attitudes Tense–aspect–mood Quantification Vagueness Phenomena Antecedent-contained deletion Cataphora Coercion Conservativity Counterfactuals Crossover effects Cumulativity De dicto and de re De se Deontic modality Discourse relations Donkey anaphora Epistemic modality Exhaustivity Faultless disagreement Free choice inferences Givenness Homogeneity (linguistics) Hurford disjunction Inalienable possession Intersective modification Logophoricity Mirativity Modal subordination Opaque contexts Performatives Polarity items Privative adjectives Quantificational variability effect Responsive predicate Rising declaratives Scalar implicature Sloppy identity Subsective modification Subtrigging Telicity Temperature paradox Veridicality Formalism Formal systems Alternative semantics Categorial grammar Combinatory categorial grammar Discourse representation theory (DRT) Dynamic semantics Generative grammar Glue semantics Inquisitive semantics Intensional logic Lambda calculus Mereology Montague grammar Segmented discourse representation theory (SDRT) Situation semantics Supervaluationism Type theory TTR Concepts Autonomy of syntax Context set Continuation Conversational scoreboard Downward entailing Existential closure Function application Meaning postulate Monads Plural quantification Possible world Quantifier raising Quantization Question under discussion Semantic parsing Squiggle operator Strawson entailment Strict conditional Type shifter Universal grinder See also Cognitive semantics Computational semantics Distributional semantics Formal grammar Inferentialism Logic translation Linguistics wars Philosophy of language Pragmatics Semantics of logic

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