Presupposition

What a presupposition is

Two pieces of information ride together in nearly every utterance. The at-issue piece is what the speaker is asserting and inviting the hearer to evaluate. The not-at-issue piece is what the speaker is treating as background — content the speaker assumes the hearer already accepts. Presuppositions are the canonical case of not-at-issue content.

John regrets eating the cake looks like a single claim, but it carries two distinct pieces:

• Asserted (at-issue): John feels regret about a particular event.
• Presupposed (not-at-issue): John ate the cake.

Negate the sentence — John does not regret eating the cake — and the assertion flips (no regret) but the presupposition survives (John still ate it). This survival under negation is the most reliable diagnostic for presupposition. Robert Stalnaker (1974) characterised presuppositions as part of the conversational common ground: the body of propositions the participants mutually take for granted as the conversation proceeds.

Presupposition triggers

Lauri Karttunen's 1971 catalogue listed roughly thirty triggers — words and constructions that introduce presuppositions reliably. The triggers fall into a small number of principal classes.

Trigger class	Example word/construction	Example sentence	Presupposition
Definite description	the X	The king of France is bald.	There is a unique king of France.
Factive verb	regret, realize, discover, know, forget	John regrets eating the cake.	John ate the cake.
Aspectual verb	stop, continue, start, finish	Mary stopped smoking.	Mary smoked previously.
Iterative	again, another time, return to	Bob came back.	Bob was here before.
Cleft	It was X who Y	It was John who broke the vase.	Someone broke the vase.
Possessive	John's X, his X	John's car is broken.	John has a car.
Wh-question	What/who/where X V?	When did Mary leave?	Mary left.
Implicative verb	manage, fail, dare, bother	John managed to solve it.	It was difficult for John.
Counterfactual	If X had Y, ...	If John had come, ...	John did not come.

The triggers are diverse but the diagnostic is uniform: each presupposition survives under negation, questions, and modal embedding. Did Mary stop smoking? still presupposes Mary smoked. Mary might stop smoking still presupposes she smokes. The triggers are taught as such because their behaviour is regular and the inference patterns are predictable.

The king of France: from Russell to Strawson

The textbook puzzle is the definite description. Bertrand Russell's 1905 paper "On Denoting" treated The king of France is bald as a quantificational paraphrase: there is a unique king of France, and that king is bald. On this analysis the sentence is false when France has no king — there is no unique king to be bald.

P. F. Strawson's 1950 paper "On Referring" objected. The sentence does not seem false, Strawson argued; it seems defective or off. We hesitate to assign it a truth value at all. Strawson proposed that the existence claim is a presupposition, not a conjunct: when the presupposition fails, the question of truth or falsity does not arise. The sentence suffers a truth-value gap, not a falsity.

Modern semantics broadly sides with Strawson. The trihedral table sharpens the contrast:

Sentence	Russell (1905)	Strawson (1950)
The king of France is bald. (no king)	False	Truth-value gap (presupposition failure)
The king of France is not bald. (no king)	True (no unique king)	Truth-value gap
If France has a king, the king is bald.	True (vacuous)	Truth-value gap suspended
The king of France is bald. (king exists, is bald)	True	True

The conditional in row three is a key modern observation: when the presupposition is overtly hypothesised in the antecedent, it does not project to the whole sentence. This was Karttunen's first hint that complex sentences mediate presupposition projection in non-trivial ways.

The projection problem

Lauri Karttunen's 1973 paper "Presuppositions of Compound Sentences" framed the projection problem precisely: given a complex sentence built from simpler clauses, which presuppositions of the parts project to the whole? Karttunen distinguished three behaviours of operators with respect to embedded presuppositions.

• Holes. Let presuppositions through unchanged. Negation, questions, modals, possibility operators. John does not regret eating the cake still presupposes he ate it.
• Plugs. Block presuppositions from projecting. Verbs of saying (say, claim, allege), propositional-attitude verbs in some contexts. John says the king of France is bald does not presuppose a king from the speaker's perspective.
• Filters. Let presuppositions through only conditionally. Conjunction, conditional, disjunction. If France has a king, the king of France is bald filters out the existence presupposition because the antecedent already entails it.

Conjunction is the canonical filter. France has a king and the king of France is bald does not presuppose the existence of a king globally — the first conjunct establishes it, so the second conjunct's presupposition is satisfied locally. Karttunen formalised this: in p and q, the presuppositions of q are filtered by the entailments of p.

Heim's dynamic-semantic solution

Irene Heim's 1983 paper "On the Projection Problem for Presuppositions" reformulated Karttunen's three behaviours within dynamic semantics. Heim treats meanings not as propositions but as context-change potentials — instructions for updating a context (a set of worlds, the common ground). A sentence's presuppositions become definedness conditions: the context must satisfy the presupposition before the update can apply.

On Heim's account, conjunction p and q updates the context with p first, then with q; q's presupposition needs only to be satisfied in the p-updated context, not the original. The filter behaviour falls out for free. Conditional if p, q works similarly: the presupposition of q is evaluated in a hypothetical update where p is true. Negation is a hole because not p still requires the context to satisfy p's presuppositions before computing the negation.

The dynamic approach is now standard in formal pragmatics. Schlenker (2008, 2009) refined it; van der Sandt's (1992) DRT-based "presupposition as anaphora" approach is a competing tradition. The empirical generalisations Karttunen catalogued are robust; the formal explanation is contested.

Accommodation

What happens when a speaker presupposes something the hearer doesn't already know? The expected answer would be: the speaker has misjudged the common ground, and the hearer should object. The actual answer, observed by David Lewis (1979, "Scorekeeping in a Language Game"), is that hearers adjust. They quietly add the presupposed content to the common ground and proceed.

If a stranger says I'm picking up my sister at the airport tomorrow, the listener doesn't object that the existence of a sister hasn't been established. The listener accommodates: the sister is added to the common ground without protest. Accommodation is one of the most efficient communication tools.

It is also routinely exploited. The classic "loaded question" — Have you stopped beating your wife? — uses an aspectual-verb trigger to presuppose prior beating; answering yes or no commits the answerer to the presupposition. Advertising and political rhetoric trade heavily on accommodation. Why did the candidate's tax plan fail? presupposes both that the candidate had a tax plan and that it failed; even posing the question shifts the common ground.

Presupposition vs entailment vs implicature

Presuppositions sit alongside two other inference types. The three differ in projection, cancellation, and source.

	Entailment	Presupposition	Implicature
Source	Truth-conditional content	Lexical/constructional trigger	Gricean maxims
Survives negation?	No	Yes	Often, but can be cancelled
Cancellable?	No (would be contradiction)	Suspendable in some contexts	Yes (\"some, in fact all, ...\")
Failure mode	Falsity	Truth-value gap	Misleading, not false
Example	John ate cake → John ate something	John regrets eating cake → He ate it	Some passed → Not all passed

The cancellation test isolates implicatures from presuppositions. An implicature can be explicitly retracted: Some students passed — in fact, all of them did. A presupposition cannot be retracted in the same easy way: ?John regrets eating the cake — in fact he didn't eat it sounds contradictory, not informative.

Projection puzzles

• The proviso problem. When a conditional has a presupposition trigger only in the consequent — If John writes, his pen will be ready — the predicted weak presupposition is "if John writes, he has a pen", but speakers sometimes infer the stronger "John has a pen". Geurts (1996), Beaver (2001).
• Triggers in attitude reports. Mary believes the king of France is bald — does the speaker presuppose a king, or does the presupposition stay inside Mary's beliefs? The answer is contested and varies by trigger.
• Soft vs hard triggers. Mandy Simons (2001) distinguished triggers that are easy to suspend (discover) from those that are hard to suspend (regret). Soft triggers behave more like Gricean inferences; hard triggers behave more like classical presuppositions.
• The presupposition of disjunction. Either France has no king, or the king of France is bald — does the second disjunct's presupposition project? Conventional wisdom says no, but the data are subtle.
• Local vs global accommodation. Sometimes the listener accommodates the presupposition only inside an embedding (e.g. inside a belief context) rather than globally. Heim (1983), Beaver (2001).

Common pitfalls

• Don't confuse presupposition with assertion. The diagnostic is survival under negation. If negating the sentence kills the inference, it was an assertion, not a presupposition.
• Don't confuse presupposition with implicature. Implicatures derive from Gricean maxims and are cancellable; presuppositions derive from triggers and resist easy cancellation.
• Don't read all triggers as equivalent. Soft triggers (discover) suspend more easily than hard triggers (regret); the projection patterns differ.
• Don't assume Russell is right about definite descriptions. The Strawsonian truth-value-gap analysis is the modern default; Russell's quantificational paraphrase is a competitor, not the consensus.
• Don't ignore filtering by logical context. Conjunction, conditional, and disjunction all filter presuppositions in ways that simple "negation = hole" rules don't capture. If France has a king, the king of France is bald does not presuppose a king globally.
• Don't think accommodation is always silent. When the presupposed content is implausible or contested, hearers do object — Wait, you have a sister? Accommodation is a pragmatic default, not an obligation.