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<title>Extensional context</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Extensional context</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In any of several fields of study that treat the use of signs — for example, in <a href="Linguistics" title="Linguistics">linguistics</a>, <a href="Logic" title="Logic">logic</a>, <a href="Mathematics" title="Mathematics">mathematics</a>, <a href="Semantics" title="Semantics">semantics</a>, <a href="Semiotics" title="Semiotics">semiotics</a>, and <a href="Philosophy_of_language" title="Philosophy of language">philosophy of language</a> — an <b>extensional context</b> (or <b>transparent context</b>) is a <a href="Syntax" title="Syntax">syntactic environment</a> in which a sub-sentential expression <i>e</i> can be replaced by an expression with the same <a href="Extension_(semantics)" title="Extension (semantics)">extension</a> and without affecting the <a href="Truth-value" class="mw-redirect" title="Truth-value">truth-value</a> of the sentence as a whole. Extensional contexts are contrasted with <a href="Opaque_context" title="Opaque context">opaque contexts</a> where truth-preserving substitutions are not possible.

</p><p>Take the case of <a href="Clark_Kent" class="mw-redirect" title="Clark Kent">Clark Kent</a>, who is secretly <a href="Superman" title="Superman">Superman</a>. Suppose that <a href="Lois_Lane" title="Lois Lane">Lois Lane</a> 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.

</p><p>In opposition to extensional contexts are intensional contexts (which can involve <a href="Modal_operator" title="Modal operator">modal operators</a> and <a href="Modal_logic" title="Modal logic">modal logic</a>), 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 <a href="Propositional_attitude" title="Propositional attitude">propositional attitude</a> "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.

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<ul><li><a href="De_dicto_and_de_re" title="De dicto and de re">De dicto and de re</a></li>

<li><a href="Extension_(semantics)" title="Extension (semantics)">Extension (semantics)</a></li>

<li><a href="Extensional_definition" class="mw-redirect" title="Extensional definition">Extensional definition</a></li>

<li><a href="Extensionalism" title="Extensionalism">Extensionalism</a></li>

<li><a href="Intensional_logic" title="Intensional logic">Intensional logic</a></li>

<li><a href="Opaque_context" title="Opaque context">Opaque context</a></li>

<li><a href="Propositional_attitude" title="Propositional attitude">Propositional attitude</a></li>

<li><a href="W.V._Quine" class="mw-redirect" title="W.V. Quine">W.V. Quine</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Francis Watanabe Dauer, <i>Critical Thinking: An Introduction to Reasoning</i>, Oxford University Press, 1989, p. 392.</li></ul>

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</style><div id="Formal_semantics_(natural_language)78" style="font-size:114%;margin:0 4em"><a href="Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Central concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Principle_of_compositionality" title="Principle of compositionality">Compositionality</a></li>

<li><a href="Denotation" title="Denotation">Denotation</a></li>

<li><a href="Linguistic_entailment" title="Linguistic entailment">Entailment</a></li>

<li><a href="Extension_(semantics)" title="Extension (semantics)">Extension</a></li>

<li><a href="Generalized_quantifier" title="Generalized quantifier">Generalized quantifier</a></li>

<li><a href="Intension" title="Intension">Intension</a></li>

<li><a href="Logical_form_(linguistics)" title="Logical form (linguistics)">Logical form</a></li>

<li><a href="Presupposition" title="Presupposition">Presupposition</a></li>

<li><a href="Proposition" title="Proposition">Proposition</a></li>

<li><a href="Reference" title="Reference">Reference</a></li>

<li><a href="Scope_(formal_semantics)" title="Scope (formal semantics)">Scope</a></li>

<li><a href="Speech_act" title="Speech act">Speech act</a></li>

<li><a href="Syntax%E2%80%93semantics_interface" title="Syntax–semantics interface">Syntax–semantics interface</a></li>

<li><a href="Truth-conditional_semantics" title="Truth-conditional semantics">Truth conditions</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Areas</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Anaphora_(linguistics)" title="Anaphora (linguistics)">Anaphora</a></li>

<li><a href="Ambiguity" title="Ambiguity">Ambiguity</a></li>

<li><a href="Binding_(linguistics)" title="Binding (linguistics)">Binding</a></li>

<li><a href="Conditional_sentence" title="Conditional sentence">Conditionals</a></li>

<li><a href="Definiteness" title="Definiteness">Definiteness</a></li>

<li><a href="Disjunction" class="mw-redirect" title="Disjunction">Disjunction</a></li>

<li><a href="Evidentiality" title="Evidentiality">Evidentiality</a></li>

<li><a href="Focus_(linguistics)" title="Focus (linguistics)">Focus</a></li>

<li><a href="Indexicality" title="Indexicality">Indexicality</a></li>

<li><a href="Lexical_semantics" title="Lexical semantics">Lexical semantics</a></li>

<li><a href="Modality_(semantics)" title="Modality (semantics)">Modality</a></li>

<li><a href="Negation" title="Negation">Negation</a></li>

<li><a href="Propositional_attitudes" class="mw-redirect" title="Propositional attitudes">Propositional attitudes</a></li>

<li><a href="Tense%E2%80%93aspect%E2%80%93mood" title="Tense–aspect–mood">Tense–aspect–mood</a></li>

<li><a href="Quantifier_(logic)" title="Quantifier (logic)">Quantification</a></li>

<li><a href="Vagueness" title="Vagueness">Vagueness</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Antecedent-contained_deletion" title="Antecedent-contained deletion">Antecedent-contained deletion</a></li>

<li><a href="Cataphora" title="Cataphora">Cataphora</a></li>

<li><a href="Coercion_(linguistics)" title="Coercion (linguistics)">Coercion</a></li>

<li><a href="Conservativity" title="Conservativity">Conservativity</a></li>

<li><a href="Counterfactuals" class="mw-redirect" title="Counterfactuals">Counterfactuals</a></li>

<li><a href="Crossover_effects" title="Crossover effects">Crossover effects</a></li>

<li><a href="Cumulativity_(linguistics)" title="Cumulativity (linguistics)">Cumulativity</a></li>

<li><a href="De_dicto_and_de_re" title="De dicto and de re">De dicto and de re</a></li>

<li><a href="Deontic_modality" title="Deontic modality">Deontic modality</a></li>

<li><a href="Discourse_relation" title="Discourse relation">Discourse relations</a></li>

<li><a href="Donkey_anaphora" class="mw-redirect" title="Donkey anaphora">Donkey anaphora</a></li>

<li><a href="Epistemic_modality" title="Epistemic modality">Epistemic modality</a></li>

<li><a href="Exhaustivity" title="Exhaustivity">Exhaustivity</a></li>

<li><a href="Faultless_disagreement" title="Faultless disagreement">Faultless disagreement</a></li>

<li><a href="Free_choice_inference" title="Free choice inference">Free choice inferences</a></li>

<li><a href="Givenness" title="Givenness">Givenness</a></li>

<li><a href="Homogeneity_(linguistics)" class="mw-redirect" title="Homogeneity (linguistics)">Homogeneity (linguistics)</a></li>

<li><a href="Hurford_disjunction" title="Hurford disjunction">Hurford disjunction</a></li>

<li><a href="Inalienable_possession" title="Inalienable possession">Inalienable possession</a></li>

<li><a href="Intersective_modifier" title="Intersective modifier">Intersective modification</a></li>

<li><a href="Logophoricity" title="Logophoricity">Logophoricity</a></li>

<li><a href="Mirativity" title="Mirativity">Mirativity</a></li>

<li><a href="Modal_subordination" title="Modal subordination">Modal subordination</a></li>

<li><a href="Opaque_context" title="Opaque context">Opaque contexts</a></li>

<li><a href="Performative_utterance" title="Performative utterance">Performatives</a></li>

<li><a href="Polarity_item" title="Polarity item">Polarity items</a></li>

<li><a href="Privative_adjective" title="Privative adjective">Privative adjectives</a></li>

<li><a href="Quantificational_variability_effect" title="Quantificational variability effect">Quantificational variability effect</a></li>

<li><a href="Responsive_predicate" title="Responsive predicate">Responsive predicate</a></li>

<li><a href="Rising_declarative" title="Rising declarative">Rising declaratives</a></li>

<li><a href="Scalar_implicature" title="Scalar implicature">Scalar implicature</a></li>

<li><a href="Sloppy_identity" title="Sloppy identity">Sloppy identity</a></li>

<li><a href="Subsective_modifier" title="Subsective modifier">Subsective modification</a></li>

<li><a href="Subtrigging" title="Subtrigging">Subtrigging</a></li>

<li><a href="Telicity" title="Telicity">Telicity</a></li>

<li><a href="Temperature_paradox" title="Temperature paradox">Temperature paradox</a></li>

<li><a href="Veridicality" title="Veridicality">Veridicality</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalism</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Formal systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Alternative_semantics" title="Alternative semantics">Alternative semantics</a></li>

<li><a href="Categorial_grammar" title="Categorial grammar">Categorial grammar</a></li>

<li><a href="Combinatory_categorial_grammar" title="Combinatory categorial grammar">Combinatory categorial grammar</a></li>

<li><a href="Discourse_representation_theory" title="Discourse representation theory">Discourse representation theory (DRT)</a></li>

<li><a href="Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li>

<li><a href="Generative_grammar" title="Generative grammar">Generative grammar</a></li>

<li><a href="Glue_semantics" title="Glue semantics">Glue semantics</a></li>

<li><a href="Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li>

<li><a href="Intensional_logic" title="Intensional logic">Intensional logic</a></li>

<li><a href="Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li>

<li><a href="Mereology" title="Mereology">Mereology</a></li>

<li><a href="Montague_grammar" title="Montague grammar">Montague grammar</a></li>

<li><a href="Segmented_discourse_representation_theory" class="mw-redirect" title="Segmented discourse representation theory">Segmented discourse representation theory (SDRT)</a></li>

<li><a href="Situation_semantics" title="Situation semantics">Situation semantics</a></li>

<li><a href="Supervaluationism" title="Supervaluationism">Supervaluationism</a></li>

<li><a href="Type_theory" title="Type theory">Type theory</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Autonomy_of_syntax" title="Autonomy of syntax">Autonomy of syntax</a></li>

<li><a href="Context_set" class="mw-redirect" title="Context set">Context set</a></li>

<li><a href="Continuation" title="Continuation">Continuation</a></li>

<li><a href="Conversational_scoreboard" title="Conversational scoreboard">Conversational scoreboard</a></li>

<li><a href="Downward_entailing" title="Downward entailing">Downward entailing</a></li>

<li><a href="Existential_closure" title="Existential closure">Existential closure</a></li>

<li><a href="Function_application" title="Function application">Function application</a></li>

<li><a href="Meaning_postulate" title="Meaning postulate">Meaning postulate</a></li>

<li><a href="Monad_(functional_programming)" title="Monad (functional programming)">Monads</a></li>

<li><a href="Plural_quantification" title="Plural quantification">Plural quantification</a></li>

<li><a href="Possible_world" title="Possible world">Possible world</a></li>

<li><a href="Quantifier_raising" class="mw-redirect" title="Quantifier raising">Quantifier raising</a></li>

<li><a href="Quantization_(linguistics)" title="Quantization (linguistics)">Quantization</a></li>

<li><a href="Question_under_discussion" title="Question under discussion">Question under discussion</a></li>

<li><a href="Semantic_parsing" title="Semantic parsing">Semantic parsing</a></li>

<li><a href="Squiggle_operator" title="Squiggle operator">Squiggle operator</a></li>

<li><a href="Strawson_entailment" title="Strawson entailment">Strawson entailment</a></li>

<li><a href="Strict_conditional" title="Strict conditional">Strict conditional</a></li>

<li><a href="Type_shifter" title="Type shifter">Type shifter</a></li>

<li><a href="Universal_grinder" title="Universal grinder">Universal grinder</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cognitive_semantics" title="Cognitive semantics">Cognitive semantics</a></li>

<li><a href="Computational_semantics" title="Computational semantics">Computational semantics</a></li>

<li><a href="Distributional_semantics" title="Distributional semantics">Distributional semantics</a></li>

<li><a href="Formal_grammar" title="Formal grammar">Formal grammar</a></li>

<li><a href="Inferentialism" class="mw-redirect" title="Inferentialism">Inferentialism</a></li>

<li><a href="Logic_translation" title="Logic translation">Logic translation</a></li>

<li><a href="Linguistics_wars" title="Linguistics wars">Linguistics wars</a></li>

<li><a href="Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></li>

<li><a href="Pragmatics" title="Pragmatics">Pragmatics</a></li>

<li><a href="Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li></ul>

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