Presupposition Theory

Origin. Frege (1892) on the presuppositions of definite descriptions; Strawson (1950) against Russell; Karttunen (1973, 1974) on projection and plugs, holes, filters; Stalnaker (1973, 1974) on common ground; Heim's file change semantics (1982, 1983); van der Sandt's anaphoric account (1992). Background entailments. Projection problem. Accommodation. Foundation of pragmatic semantics.

Models. Presuppositions as background requirements. Projection through operators. Context update. Accommodation when needed. Pragmatic/semantic interface.

Formalism.

Presupposition: S presupposes P: P backgrounded by S. P survives negation. "The king of France is bald" presupposes France has a king. "The king of France is not bald" still presupposes it.

Presupposition triggers: Definite descriptions: "the X." Factive verbs: "know that P." Change of state: "stop," "continue." Clefts: "It was John who..." Various constructions.

Projection problem: How presuppositions project through operators. "If France has a king, the king is bald" — presupposition satisfied in antecedent. "John doesn't know that P" — P still presupposed. Filtering vs projection.

Stalnaker: Presuppositions in common ground. CG: shared assumptions. Assertion must be compatible. Presupposition = requirement on CG.

Heim's semantics: Context change potential. c[S] = c updated with S. Presupposition = definedness condition. c[S] defined only if c entails presupposition.

Accommodation: Presupposition not in CG? Hearer adds it. "My sister is arriving" (hearer didn't know of sister). Repair mechanism.

Local accommodation: Add presupposition locally. Under operator scope. "If John has a sister, his sister will help." Narrow scope.

Symbols.

Symbol	Unicode	Name	Meaning
∂	U+2202	Partial differential	Beaver's presupposition operator: ∂P is the requirement that P
>>	—	Presupposes	S >> P: S presupposes P
CG	—	Common ground	Stalnaker's set of shared assumptions
c	—	Context	A set of worlds, or a file, updated by assertion
c[S]	—	Context update	The result of updating c with S; undefined if c fails P
S	—	Sentence	The presupposing sentence
P	—	Presupposition	The backgrounded content

Metatheory. Karttunen (1973, 1974) established the descriptive taxonomy — plugs, holes, and filters — and Heim (1983) derived it: if presupposition is a definedness condition on context change and the connectives are defined so that each conjunct or antecedent updates the context for what follows, the filtering conditions are consequences rather than lexical stipulations. The derivation has a known gap, isolated by Soames (1989) and sharpened by Schlenker as the explanatory problem: nothing in the dynamic framework rules out a mirror-image conjunction whose second conjunct filters the first, so the definitions predict the attested left-to-right asymmetry only because they were written left-to-right. Schlenker's local contexts (2008, 2009) recover the same predictions from classical bivalent meanings plus an incrementality requirement, which removes the stipulation. The rival tradition is van der Sandt's (1992), which treats projection as anaphora resolution in DRT, with global accommodation as a last resort and the accessibility relation doing the work of the filters.

Applies to. Definiteness. Factives. Context. Pragmatics.

Limitations. Accommodation is a repair rule with no theory of when it applies, so any prediction the projection algorithm gets wrong can be absorbed by invoking it, which deprives the account of its falsifiability at exactly the point of stress. The proviso problem is the sharpest case: from "If John is scuba diving, he'll bring his wetsuit" the dynamic theory predicts a conditional presupposition, whereas hearers infer the unconditional one that John has a wetsuit, and no principled bridge has been agreed. Triggers do not behave alike — Abusch (2002, 2010) showed that soft triggers such as win suspend under questioning while hard triggers such as too and again do not — and no independent property predicts which class a word falls into. Projection from quantified sentences is unsettled: universal, existential, and presupposition-free predictions are each attested. And no theory derives which lexical items trigger presuppositions in the first place.