@cite{rett-2015} — Neo-Gricean Account of Evaluativity #
@cite{rett-2015} @cite{horn-1984} @cite{bierwisch-1989} @cite{kennedy-2007} @cite{lassiter-goodman-2017}
Self-contained study of @cite{rett-2015} "The Semantics of Evaluativity"
Chapters 3–5: theoretical analysis (Q-implicature, Marked Meaning Principle,
markedness machinery) plus prediction-matching against the empirical data
from Rett2015.lean.
Insight #
Evaluativity (the requirement that a degree exceed a contextual standard) is NOT semantically encoded but derived pragmatically via implicature.
Two Implicature Types #
Quantity implicature (Q-principle):
- For positive constructions ("John is tall")
- Without evaluativity, the utterance is uninformative
- Listener strengthens to evaluative reading
Manner implicature (R-principle):
- For polar-INVARIANT constructions (equatives, questions)
- "How tall?" and "How short?" have the SAME truth conditions
- Using marked "short" when unmarked "tall" exists signals something extra
- That extra is evaluativity (presupposes shortness)
The Asymmetry Explained #
Why do equatives show asymmetry (marked antonyms evaluative) but comparatives don't?
Polar variance is key:
- Comparatives: polar-VARIANT ("taller than" ≠ "shorter than") → No equivalent unmarked alternative → No manner implicature → No asymmetry
- Equatives: polar-INVARIANT ("as tall as" = "as short as" semantically) → Unmarked alternative exists → Manner implicature → Asymmetry
File Structure #
§1. Polarity, cost, and implicature types
§2. Per-construction evaluativity source + derivation
§3. Q-implicature for positive constructions (degree tautology)
§4. R-implicature / Marked Meaning Principle (MMP)
§5. Lexicon-grounded derivation (full pipeline)
§6. Rett's core predictions (theorems)
§7. Bridge to empirical data (Rett2015.lean)
Polarity of an adjective: positive (unmarked) vs negative (marked).
From @cite{bierwisch-1989}, @cite{kennedy-2007}:
- Positive-polar (tall, happy, expensive): unmarked, default
- Negative-polar (short, unhappy, cheap): marked, requires more justification
Markedness is reflected in:
- Morphological complexity (happy → un-happy)
- Distributional restrictions ("How tall?" is neutral, "How short?" presupposes)
- Processing cost (marked forms are costlier)
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- Phenomena.Gradability.Studies.Rett2015Implicature.instDecidableEqPolarity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Is this polarity marked?
Negative-polar adjectives are marked (require more contextual support).
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Production cost associated with polarity.
Marked forms cost more to produce, licensing manner implicatures. This follows @cite{horn-1984}'s Division of Pragmatic Labor.
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Does manner implicature apply to this construction?
Manner implicature requires polar INVARIANCE:
- If the two antonyms have the same meaning, using the costlier marked form signals something extra (evaluativity)
- If they have different meanings, no pragmatic competition occurs
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Types of implicature that can derive evaluativity.
Following @cite{rett-2015} Chapter 4-5:
- Quantity (Q): Avoid uninformative utterances → strengthen to evaluative
- Manner (R): Use of costly form signals marked meaning → evaluativity
These correspond to Horn's Q-principle (say enough) and R-principle (don't say more than needed, modulated by form cost).
- quantity : EvaluativityImplicature
- manner : EvaluativityImplicature
- none : EvaluativityImplicature
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- Phenomena.Gradability.Studies.Rett2015Implicature.instDecidableEqEvaluativityImplicature x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Which implicature type derives evaluativity for this construction + polarity?
From @cite{rett-2015} Chapter 5:
| Construction | Positive-polar | Negative-polar |
|---|---|---|
| Positive | Quantity | Quantity |
| Comparative | None | None |
| Equative | None | Manner |
| Degree Question | None | Manner |
| Measure Phrase | None | N/A (ungramm.) |
Key insight: The asymmetry in equatives/questions comes from MANNER implicature, which only applies to marked forms in polar-invariant constructions.
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Derivation of evaluativity for a construction + polarity combination.
Records:
- Which implicature type applies
- Whether evaluativity is predicted
- The mechanism (Q vs R)
- construction : Semantics.Degree.AdjectivalConstruction
- polarity : Polarity
- implicatureType : EvaluativityImplicature
- isEvaluative : Bool
- mechanism : String
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Derive evaluativity for a construction + polarity.
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All predictions for positive-polar adjectives.
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All predictions for negative-polar adjectives.
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Summary table matching Rett's Table 5.1.
| Positive-polar | Negative-polar | |
|---|---|---|
| Positive | evaluative (Q) | evaluative (Q) |
| Comparative | non-eval | non-eval |
| Equative | non-eval | evaluative (R) |
| Measure Phrase | non-eval | (ungrammatical) |
| Degree Question | non-eval | evaluative (R) |
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Theorem: Positive constructions are evaluative for both polarities
This is derived from Q-implicature (uninformativity avoidance).
Theorem: Comparatives are never evaluative
The comparative morpheme (-er) binds the degree argument, leaving no room for threshold inference.
Theorem: Equatives show polarity asymmetry
Positive antonym: not evaluative Negative antonym: evaluative (manner implicature)
Theorem: Degree questions show polarity asymmetry
Same pattern as equatives (polar-invariant → manner implicature for marked).
Theorem: Polar-invariant constructions show asymmetry
Equatives and degree questions show different evaluativity for positive vs negative polarity.
Theorem: Polar-variant constructions show symmetry
Positives and comparatives have the same evaluativity for both polarities.
Theorem: Manner implicature only applies to marked forms in invariant constructions
Q-implicature derivation for positive constructions.
Standard Recipe applied to "John is tall":
- Speaker said "John is tall"
- Alternative: "John is tall to degree d" (for any d)
- Without evaluativity, this is true for any d - UNINFORMATIVE
- Listener strengthens: John's height exceeds contextual standard
This is the same mechanism as scalar implicatures, applied to threshold inference.
- construction : Semantics.Degree.AdjectivalConstruction
- uninformativeWithout : Bool
The utterance is uninformative without evaluativity
- informativeWith : Bool
Evaluativity makes it informative
- evaluativityLicensed : Bool
Q-implicature licenses evaluativity
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Derive Q-implicature for positive constructions.
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- Phenomena.Gradability.Studies.Rett2015Implicature.deriveQImplicature c = { construction := c, uninformativeWithout := false, informativeWith := false, evaluativityLicensed := false }
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R-implicature derivation for equatives/questions.
Division of Pragmatic Labor applied to "How short is John?":
- Speaker used marked form "short" (cost = 2)
- Unmarked alternative "tall" available (cost = 1)
- Same truth conditions (polar-invariant)
- Using costly form must signal something extra
- That something = evaluativity (presupposes shortness)
- construction : Semantics.Degree.AdjectivalConstruction
- polarity : Polarity
- unmarkedAlternativeExists : Bool
Is there an unmarked alternative with same truth conditions?
- formIsMarked : Bool
Is the current form marked (costly)?
- evaluativityLicensed : Bool
R-implicature licenses evaluativity
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Derive R-implicature for equatives/questions.
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The Marked Meaning Principle (MMP) derivation record.
From @cite{rett-2015} Chapter 5, following @cite{horn-1984}:
The MMP states that using a marked form when an unmarked equivalent exists signals that the speaker intends the marked meaning.
For evaluativity: using "as short as" instead of "as tall as" in an equative signals that the speaker presupposes shortness.
- adjForm : String
The adjective form used
- unmarkedAlternative : Option String
The unmarked alternative (if any)
- construction : Semantics.Degree.AdjectivalConstruction
The construction
- mmpApplies : Bool
Does MMP apply? (marked form + polar-invariant + alternative exists)
- implicature : Option EvaluativityImplicature
The resulting evaluativity implicature (if any)
- explanation : String
Explanation of the derivation
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Apply the Marked Meaning Principle.
MMP applies when:
- The form is marked (has higher cost)
- The construction is polar-invariant (alternatives have same TCs)
- An unmarked alternative exists
When MMP applies, using the marked form implicates evaluativity.
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Extended evaluativity derivation with lexicon grounding.
This structure records:
- The adjective and its morphological properties
- Markedness determination via objective criteria
- M-alternative generation
- Q/R implicature derivation
- Final evaluativity prediction
- adjective : Implicature.Markedness.GradableAdjWithMorphology
The adjective entry with morphology
The antonym entry with morphology
- construction : Semantics.Degree.AdjectivalConstruction
The construction
- mAlternatives : Option Implicature.Markedness.MAlternativeSet
M-alternatives generated (if any)
- mmpDerivation : MMPDerivation
MMP derivation
- isEvaluative : Bool
Final evaluativity prediction
- source : EvaluativityImplicature
Source of evaluativity
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Derive evaluativity with full lexicon grounding.
This is the main entry point for the Neo-Gricean evaluativity derivation. It:
- Looks up morphological properties of the adjective
- Computes markedness from objective criteria
- Generates M-alternatives for polar-invariant constructions
- Applies Q-implicature (positive) or MMP (equative/question)
- Returns a fully grounded derivation
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Degree tautology analysis for positive constructions.
Following @cite{rett-2015} Chapter 3:
Without evaluativity, "John is tall" is a degree tautology:
- It asserts that John has SOME degree of height
- This is trivially true for any entity with height
Q-implicature resolves this by strengthening to evaluative reading:
- "John is tall" → John's height exceeds the contextual standard
This explains why positive constructions are evaluative for BOTH polarities.
- construction : Semantics.Degree.AdjectivalConstruction
The construction type
- isTautologyWithout : Bool
Is this a degree tautology without evaluativity?
- qImplicatureResolves : Bool
Does Q-implicature resolve the tautology?
- explanation : String
Explanation
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Analyze degree tautology for a construction.
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MMP only applies in polar-invariant constructions (equative case).
MMP only applies in polar-invariant constructions (question case).
MMP does not apply in comparative constructions.
MMP applies for "short" in equative constructions.
MMP does not apply for "tall" in equative constructions (not marked).
Equative asymmetry emerges from MMP + markedness.
Lexicon-grounded derivation matches simple derivation for tall.
Lexicon-grounded derivation matches simple derivation for short in equative.
These theorems formalize the key empirical predictions from Rett's account:
- Evaluativity distribution: Which constructions are evaluative?
- Asymmetry pattern: When do we see polarity asymmetry?
- Mechanism attribution: Q-implicature vs MMP?
- Morphological grounding: How does markedness determine asymmetry?
Rett Prediction 1: Positive constructions require evaluativity.
"John is tall" asserts that John's height exceeds a contextual standard. This is derived from Q-implicature: without evaluativity, the utterance would be uninformative (a "degree tautology").
Rett Prediction 2: Comparatives never require evaluativity.
"John is taller than Mary" is true even if both are short. The comparative morpheme (-er) binds the degree argument, leaving no threshold to be inferred.
Rett Prediction 3: Equatives show polarity asymmetry.
"John is as tall as Mary" — no evaluativity (unmarked form) "John is as short as Mary" — evaluative (marked form triggers MMP)
The asymmetry arises from the Marked Meaning Principle.
Rett Prediction 4: Degree questions show polarity asymmetry.
"How tall is John?" — neutral question (unmarked form) "How short is John?" — presupposes shortness (marked form triggers MMP)
Same pattern as equatives: polar-invariant → MMP for marked forms.
Core Insight: Asymmetry requires polar invariance.
Constructions where antonyms have the SAME truth conditions (polar-invariant) show asymmetry. Constructions where antonyms differ (polar-variant) don't.
This is because MMP only applies when an unmarked alternative EXISTS with the same meaning.
Polar invariance is the key to M-alternative availability.
Q-implicature mechanism: Positive constructions use Quantity.
Q-implicature resolves the "degree tautology" of positive constructions. Without evaluativity, "John is tall" is trivially true for anyone with height.
MMP mechanism: Equatives and questions use Manner for marked forms.
The Marked Meaning Principle (MMP) derives evaluativity from using a marked form when an unmarked equivalent exists.
No mechanism for comparatives: They're never evaluative.
Markedness determines asymmetry direction.
The marked form (higher cost) triggers MMP, not the unmarked form.
Cost differential: Marked forms cost more to produce.
Morphological complexity determines markedness for happy/unhappy.
Complete derivation for "as short as": From morphology to evaluativity.
This theorem traces the full derivation:
- "short" has negative pole → marked by scale direction
- Equative is polar-invariant → M-alternatives exist
- Using marked "short" when unmarked "tall" exists → MMP applies
- MMP → manner implicature → evaluativity
Complete derivation for "as tall as": No evaluativity for unmarked.
- "tall" has positive pole → unmarked
- Equative is polar-invariant → M-alternatives exist, but...
- "tall" is the unmarked form → MMP doesn't apply
- No implicature → no evaluativity
Convert this study's derivation prediction to the empirical data format.
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Check if prediction matches an empirical datum.
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Theorem: Predictions match positive_tall datum
Theorem: Predictions match comparative_tall datum
Theorem: Predictions match equative_tall datum
Theorem: Predictions match equative_short datum
Theorem: Predictions match question_tall datum
Theorem: Predictions match question_short datum