Presupposition Projection and Triggering

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presupposition projection context-sensitivity

Core Idea

Presuppositions are content speakers assume and expect hearers to accept without assertion. They project upward through logical operators, though presuppositions can be filtered or accommodated depending on structural position and discourse context.

How It's Best Learned

Study presupposition triggers like definite descriptions and factives in simple sentences, negations, conditionals, and questions to map projection patterns and filtering effects.

Explainer

From your study of Grice's cooperative principle, you know that communication involves more than what is literally said — implicatures arise from the assumption that speakers are being cooperative, informative, and relevant. Presuppositions are a different kind of implicit content: not inferences the hearer draws, but background assumptions the speaker *takes for granted* and *builds into* the utterance as common ground. The sentence "The king of France is bald" presupposes that there is a king of France; the sentence "Maria regrets that she left early" presupposes that Maria did leave early. These presuppositions are not asserted — they are the context the assertion rests on.

Presupposition triggers are linguistic constructions that reliably introduce presuppositions. Definite descriptions ("the X") trigger existence presuppositions. Factive verbs ("know," "realize," "regret") presuppose their complement is true — "John knows it's raining" presupposes it is raining. Change-of-state verbs ("stop," "begin," "continue") carry presuppositions about prior states. Iteratives ("again," "still," "return") presuppose a prior occurrence or state. Each trigger type has a characteristic presupposition that is introduced whenever the construction is used.

The projection problem asks what happens to presuppositions when these triggers appear inside complex sentences — in negations, conditionals, questions, and modal constructions. The surprising fact is that presuppositions often project out of their embedding context, surviving operators that would normally affect assertoric content. "It's not the case that the king of France is bald" still carries the presupposition that France has a king — even though the negation reverses the assertion. "Does Maria regret leaving early?" still presupposes she left early — even though the question doesn't assert it. Your knowledge of possible worlds semantics is relevant here: presuppositions can be understood as constraints on the contexts of utterance — they require the presupposed content to be true in all worlds in the common ground.

But projection is not absolute. Filtering occurs when the embedding context provides information that absorbs or cancels the presupposition. In "If France has a king, the king of France is bald," the presupposition of the consequent ("France has a king") is satisfied by the antecedent and does not project to the whole. Accommodation occurs when a presupposition is not already in the common ground but hearers silently add it rather than reject the utterance — if someone says "My car broke down" to a hearer who didn't know they had a car, the hearer typically accommodates the existence presupposition rather than objecting. Understanding when presuppositions project, get filtered, or get accommodated is crucial for analyzing how information is managed and contested across a discourse: speakers can use presupposition triggers strategically to smuggle contested content into common ground without asserting it openly.

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Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesIntroduction to Graph TheoryPropositional Logic FoundationsLogical Inference and Proof RulesProof Strategies in Discrete MathematicsSoundness and Completeness of Propositional LogicSoundness and Completeness of First-Order LogicCompactness Theorem for First-Order LogicBasic Model TheoryLöwenheim-Skolem TheoremsGödel's Incompleteness TheoremsIntroduction to Intuitionistic LogicIntroduction to Modal LogicModal Semantics: Necessity and PossibilityIntensionality and Possible Worlds SemanticsEvent SemanticsAktionsart (Lexical Aspect)Viewpoint Aspect (Perfective and Imperfective)Formal Semantics of Tense and TimeFormal Semantics of Modality and PossibilityPossible Worlds SemanticsPresupposition Projection and Triggering

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