Karttunen 1973: Presuppositions of Compound Sentences #
@cite{karttunen-1973}
Linguistic Inquiry 4(2): 169–193.
Core Contributions #
The projection problem: how are presuppositions of constituent sentences inherited (or not) by compound sentences?
Three-way classification of complement-taking predicates (§§2–5):
- Plugs: block all complement presuppositions (say, tell, promise)
- Holes: let all complement presuppositions through (know, regret, stop, force, manage, believe)
- Filters: conditionally cancel some presuppositions (if...then, and, or)
Filtering conditions for logical connectives (§§5–7):
- If A then B (rule 13): A's presuppositions always project; B's presuppositions project unless A's assertion entails them.
- A and B (rule 17): same as conditional.
- A or B (rule 24): A's presuppositions always project; B's presuppositions project unless ¬A entails them.
Classical-logic equivalence (§8): the identical filtering conditions for if...then and and follow from (i) negation preserves presuppositions, (ii) logical equivalents share presuppositions, (iii)
A ⊃ B ≡ ¬A ∨ B ≡ ¬(A ∧ ¬B).
What's Still Live vs Historical #
The plug/hole/filter vocabulary and the filtering connective formulas are still the foundation of presupposition projection theory in 2026. The specific verb inventories, the three-valued logic comparison (§10), the revised filtering conditions with background assumptions (§9), and the internal/external negation distinction (§10) are historical — superseded by CCP (@cite{heim-1983}), local contexts (@cite{schlenker-2009}), and the projective content taxonomy (@cite{tonhauser-beaver-roberts-simons-2013}).
Integration #
The filtering connectives PrProp.impFilter, PrProp.andFilter,
PrProp.orFilter in Core/Semantics/Presupposition.lean are direct
formalizations of Karttunen's rules (13), (17), (24). This study file
proves that correspondence and verifies Fragment verb entries carry the
correct ProjectionBehavior annotations.
Verify that Fragment verb entries carry the correct projectionBehavior
annotations, matching Karttunen's classification (§§3–5).
know is both a presupposition trigger (factive) AND a hole. These are orthogonal properties: trigger = creates presuppositions; hole = passes complement presuppositions through.
manage has a prerequisite presupposition (@cite{nadathur-2024}) and is a hole (presuppositions project through it).
believe has no presupposition trigger but is a hole. Karttunen (§4) initially considers whether attitude verbs are plugs, then argues they are holes — the cumulative hypothesis works for them.
Karttunen's filtering conditions (rules 13, 17, 24) are encoded
directly in the PrProp connectives. These theorems make the
correspondence explicit.
Rule 13a: If A presupposes C (A >> C), then "If A then B" >> C. The antecedent's presupposition always projects.
Rule 13b: If B >> C, then "If A then B" >> C, unless A ⊨ C. When A's assertion entails B's presupposition, the presupposition is filtered out.
Rule 17: filtering condition for conjunction is the same formula as for conditionals. This is Karttunen §6's key observation.
Rule 24: filtering for disjunction uses ¬A instead of A. "A or B" >> C unless ¬A ⊨ C (i.e., ¬A's truth entails C).
Karttunen §8 argues that identical filtering conditions for
if...then and and are consistent with classical logic, given:
(i) negation preserves presuppositions;
(ii) logically equivalent sentences share presuppositions;
(iii) A ⊃ B ≡ ¬A ∨ B ≡ ¬(A ∧ ¬B).
We prove this as a theorem about `PrProp` connectives.
The filtering presupposition of impFilter p q equals that of
andFilter p q. This is the formal content of §8's argument:
the presupposition function for "if A then B" and "A and B" is
identical (both = p.presup ∧ (¬p.assertion ∨ q.presup)).
Negation preserves presupposition (principle (i) of §8).
Finite world models for Karttunen's central examples.
Equations
- One or more equations did not get rendered due to their size.
Instances For
"Jack has children" — no presupposition.
Equations
- One or more equations did not get rendered due to their size.
Instances For
"All of Jack's children are bald" — presupposes Jack has children.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Ex. (11a): "If Jack has children, then all of Jack's children are bald." The presupposition of the consequent ("Jack has children") is filtered because the antecedent entails it.
Ex. (16a): "Jack has children and all of Jack's children are bald." Same filtering as the conditional — the conjunction doesn't presuppose Jack has children.
Karttunen §10 compares four three-valued conjunction tables:
| System | Filtering behavior |
|---------------------|-----------------------|
| Bochvar internal | Hole (cumulative) |
| Bochvar external | Plug |
| Łukasiewicz | Symmetric filter |
| Van Fraassen | Symmetric filter |
The `PrProp` connective zoo covers these:
- `PrProp.and` = Bochvar internal (both must be defined)
- `PrProp.andFilter` = Karttunen's asymmetric filter
- `PrProp.andBelnap` = Belnap's conditional assertion
Łukasiewicz/Van Fraassen use symmetric filtering: when one
operand is # and the other is F, the result is F (not #).
This is not `andFilter` (which is asymmetric/left-to-right).
The Bochvar external connectives correspond to plugs: they
use a "truth operator" `t(A)` that maps # → F, making all
presuppositions invisible.
Bochvar internal conjunction = PrProp.and: both presuppositions
must hold. This is the cumulative hypothesis.
The filtering conjunction is strictly weaker than classical: it can be defined even when q's presupposition fails (if p's assertion is false).
Karttunen distinguishes two senses of not:
- **Internal negation** (choice negation): a hole. Ordinary
negation lets presuppositions through. This is `PrProp.neg`.
- **External negation** (exclusion negation): a plug. Maps
# → F, blocking all presuppositions.
The distinction corresponds to Bochvar's internal vs external
connectives. In 2026 this is subsumed by metalinguistic negation
(Horn 1985) and focus alternatives.
External negation: maps undefined to false (a plug).
Equations
Instances For
External negation is always defined (it's a plug).
Internal negation preserves presupposition (it's a hole).
The two negations agree when the presupposition holds.
Karttunen §9 revises the filtering conditions to handle cases where background assumptions contribute to filtering.
Rule (24b'): If B >> C, then S >> C unless there exists a
(possibly null) set X of assumed facts such that X ∪ {¬A} ⊨ C.
This is superseded by CCP / local contexts (@cite{heim-1983},
@cite{schlenker-2009}), where the context set plays the role
of X automatically. The `LocalCtx` machinery in
`Theories/Semantics/Presupposition/LocalContext.lean` handles
this: the local context at a position already incorporates all
"assumed facts" from the discourse context.
We state the revised condition as a theorem schema showing that
the simple filtering condition is a special case (X = ∅).
The simple filtering condition (rule 13b) is the special case of the revised condition (rule 17b') where X = ∅.