Bridge: Relevance Theory → Scalar Implicatures #
RT derives scalar implicatures through BOTH components of the theory:
Comprehension procedure (clause a): the enriched "some but not all" interpretation is selected over the literal "at least some" because it produces more cognitive effects. The literal reading fails the relevance threshold — it's too weak for an optimally relevant stimulus.
Clause (b) reasoning: the speaker chose "some" over "all". Since "all" would have been more relevant (more informative, same effort), the hearer infers the speaker wasn't in a position to say "all" — deriving ¬Bel_S(all) (weak) or Bel_S(¬all) (strong, with competence).
DE blocking: in downward-entailing contexts, pragmatic enrichment ("not all") doesn't produce additional cognitive effects — narrowing "some" to "some but not all" actually WEAKENS the overall DE claim. The literal reading suffices, so the procedure stops there.
RT vs NeoGricean #
Both derive "some → not all", but by different mechanisms:
- NeoGricean: Horn scales + Standard Recipe (Q-principle generates, R-principle constrains). The scale ⟨some, all⟩ is a grammatical object.
- RT: Comprehension procedure + clause (b). No scales needed — the implicature follows from the general presumption of optimal relevance.
Candidate interpretations for a scalar utterance like "Some students passed". The comprehension procedure considers these in order of accessibility.
- lowerBound : SIInterpretation
Lower-bound (literal): "at least some", compatible with all
- enriched : SIInterpretation
Pragmatically enriched: "some but not all"
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RT scenario for "Some students passed" in an upward-entailing context.
- Lower-bound is more accessible (decoded semantic content, tried first)
- But it fails the relevance threshold: an optimally relevant speaker who knew all students passed would have said "all" — so the mere lower-bound reading doesn't produce enough cognitive effects
- The enriched reading produces more effects: "some passed" + "not all passed" + information about the speaker's epistemic state
- The enriched reading is selected as the first acceptable interpretation
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The comprehension procedure selects the enriched interpretation in UE.
The literal reading fails its threshold (1 < 2), so the procedure moves on. The enriched reading passes (3 ≥ 2), so it's accepted.
The literal reading is subthreshold: it doesn't produce enough effects to justify processing an optimally relevant stimulus.
This is key to RT's account: the literal "at least some" is REJECTED not because it's false but because it's insufficiently informative.
RT scenario for "some" in a downward-entailing context (e.g., "No one ate some of the cookies").
In DE contexts, enriching "some" to "some but not all" does NOT produce additional cognitive effects — narrowing the restrictor of a DE operator weakens the overall claim, which is the opposite of being informative. The literal reading suffices: it's already informative enough.
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The comprehension procedure selects the literal reading in DE.
The literal reading passes its threshold (2 ≥ 2) and is the most accessible candidate, so the procedure stops immediately. The enriched reading is never even considered — satisficing, not optimizing.
Processing effort can block enrichment even when effects are present.
When the pragmatic enrichment is costly (e.g., in rapid conversational exchange, or when the context doesn't readily supply the enriched reading), the effort-adjusted threshold rises above the enriched reading's effects.
The literal reading is selected because the enriched one isn't "worth the effort" — a distinctive RT argument with no NeoGricean counterpart.
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When effort is high, the literal reading is selected despite the enriched reading having more raw effects.
The enriched reading is blocked by effort: it would pass at zero effort (threshold 2 ≤ effects 3) but the effort-adjusted threshold (2 + 1*3 = 5) exceeds its effects (3).
Clause (b) argument for the "some → not all" implicature.
The speaker said "some" rather than "all". Since "all" would have been more relevant (more informative, similar effort), clause (b) of optimal relevance lets the hearer infer that the speaker wasn't able or willing to say "all".
- Weak implicature: ¬Bel_S(all) — follows from clause (b) alone
- Strong implicature: Bel_S(¬all) — requires additional competence assumption (speaker is opinionated about "all")
This mechanism doesn't require Horn scales — any case where a more informative alternative was available triggers the same reasoning.
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The or/and clause (b) argument follows the same pattern.
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The possible/necessary clause (b) argument.
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RT predicts that scalar implicature arises in UE contexts. The comprehension procedure selects the enriched reading, matching the empirical observation that "some" implicates "not all" in UE.
RT predicts that scalar implicature is blocked in DE contexts. The comprehension procedure selects the literal reading, matching the empirical observation that "some" does NOT implicate "not all" in DE.
RT's effort mechanism is consistent with the weak/strong distinction: the weak implicature (¬Bel_S(all)) comes from clause (b) alone, while the strong (Bel_S(¬all)) requires a competence assumption.
Data confirms: weak does not require competence, strong does.