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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

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Factorial → Permutations → Combinations → Counting Principles: Addition and Multiplication Rules → Introduction to Graph Theory → Propositional Logic Foundations → Logical Equivalences → Boolean Algebra → Introduction to Propositional Logic → Introduction to Predicate Logic (First-Order Logic) → First-Order Logic Syntax → Terms and Atomic Formulas in FOL → Variable Binding and Scope → Open and Closed Formulas in First-Order Logic → Variable Substitution and Capture-Avoidance in First-Order Logic → Quantifier Instantiation Rules in First-Order Proof Systems → Universal Quantification: Meaning and Scope → Free Variables and Bound Variables → Substitution and Instantiation in Predicate Logic → Terms and Atomic Formulas → Formulas and Well-Formed Expressions → Structures and Interpretations → Model Interpretation and Satisfaction → Interpretation, Truth, and Satisfaction of Formulas → Logical Consequence and Entailment → Soundness Theorem and Validity of Proof Systems → Deductive Reasoning and Formal Proof Systems → First-Order Resolution → Propositional Resolution → Semantic Tableaux (Propositional) → Semantic Tableaux (First-Order) → Decidable Fragments of First-Order Logic → Gödel's Completeness Theorem for First-Order Logic → Gödel's Incompleteness Theorems → Introduction to Intuitionistic Logic → Introduction to Modal Logic → Modal Semantics: Necessity and Possibility → Intensionality and Possible Worlds Semantics → Event Semantics → Aktionsart (Lexical Aspect) → Tense and Aspect in Formal Semantics → Viewpoint Aspect (Perfective and Imperfective) → Formal Semantics of Tense and Time → Formal Semantics of Modality and Possibility → Possible Worlds Semantics → Presupposition Projection and Triggering

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