📄 A note on the architecture of presupposition

Summary

The paper examines the Proviso Problem. Most theories of semantic presupposition, which the author calls c-theories, predict that a conditional "If p then q_r" presupposes only the material conditional p ⊃ r. Yet hearers usually take the speaker to presuppose plain r. The standard example is that "If Theo hates sonnets, so does his wife" seems to commit the speaker to Theo having a wife. Defenders of c-theories bridge this gap with pragmatics, in two forms:

• Basic Architecture: the presupposition is strengthened to r when pragmatic plausibility favours it.
• Independence: it is strengthened when r is independent of p.

Mandelkern argues that neither repair works. He offers constructed examples where r depends on p in ordinary ways, yet the unconditional reading is still felt. He then adds a new type of case: there, coherence pressure should push hearers toward the conditional reading, but they still attribute the unconditional one. A minimal contrast (a Ukraine monarchy scenario) shows that conditional readings are sometimes available. Any account must therefore explain both patterns. The paper matters because it challenges the dominant satisfaction-style picture and the minimal-accommodation assumption behind it.

Key points

• C-theory predictions:
  • "If p then q_r" and "p and q_r" presuppose p ⊃ r.
  • "p or q_r" presupposes ¬p ⊃ r.
  • These theories include satisfaction theory (Heim), multivalent theories and others. DRT (van der Sandt, Geurts) is the main exception.
• Two notions of independence are discussed:
  • Probabilistic independence: Pr_c(r) ≈ Pr_c(r|p), following Schlenker and Singh. Lassiter has a ≥ variant.
  • Pérez Carballo's conditional independence, defined through a Stalnaker selection function.
• Novel diabetes case: a speaker says he does not know which illness John has, then utters a conditional that presupposes John has diabetes. A hearer can object "Wait a minute!", which shows the unconditional reading is attributed even though it makes the discourse incoherent.
• Contrast case: "If the monarchist rebellion succeeded, we must contact the new king of Ukraine" allows a merely conditional reading. This holds even though accommodation is non-trivial, since a monarchy may have a queen.
• Ways forward the paper suggests:
  • drop the minimality-of-accommodation assumption;
  • posit a cognitive bias toward unconditional propositions;
  • adopt non-c-theories. Theories that generate both readings and leave the choice to pragmatics still fail on the coherence cases.

Interesting ideas

• I1. Keep two separate layers: what a sentence semantically presupposes, and what the speaker is taken to presuppose, linked by an explicit strengthening step. This keeps the reasoning auditable.
• I2. The "Wait a minute!" challenge is a behavioural probe for whether content is treated as presupposed rather than asserted. It can diagnose commitments without relying on intuitions about truth.
• I3. Build minimal pairs that are structurally alike but differ in whether strengthening happens, such as the diabetes case versus the Ukraine king case. These separate competing theories far better than isolated examples.
• I4. Constructing a context where an expected pressure (here, coherence) pushes the opposite way is a strong way to falsify a pragmatic rule. It exposes whether the rule is really doing the work.
• I5. Independence measured as Pr(r) ≈ Pr(r|p) is a cheap, computable signal for whether an embedded presupposition should be projected globally, though the paper shows it is not sufficient alone.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (frames): prag could store the conditional presupposition p ⊃ r and, as a separate flagged inference, the strengthened r, so every commitment shows where it came from.
• I2 (frames): it could serve as a template test, checking whether Mova's discourse model would license such an objection after a given sentence.
• I3 (learn): evaluation suites for presupposition handling could include such paired items as negative controls, so a rule that always globalizes or never globalizes is caught.
• I4 (answer): QA tests on tales could add adversarial contexts where the "obvious" inference contradicts earlier text, checking that readers track the actual commitments.
• I5 (world): the knowledge graph could supply this as one weighted feature for deciding whether to add an entity (e.g. "Theo's wife") to the text world unconditionally, never as a hard rule.