Morzycki (2009)

@cite{morzycki-2009}

Degree modification of gradable nouns: size adjectives and adnominal degree morphemes. Natural Language Semantics 17:175–203.

Key claims formalized

1. Gradable nouns as measure functions (§3.1, eq. 48b): ⟦idiot⟧ = λx . ιd[x is d-idiotic] = idiot

2. MEAS_N operator (§4.3, eq. 76): Size adjectives are introduced by a nominal counterpart of the adjectival MEAS morpheme. The combined denotation requires the individual's degree to exceed both the size adjective's minimum and the noun's contextual standard.

3. Bigness Generalization (§2.2, ex. 29): Adjectives that predicate bigness systematically license degree readings; adjectives of smallness do not.

4. Position Generalization (§2.1, ex. 18): Degree readings of size adjectives are possible only in attributive positions (prenominally in English).

5. Adnominal degree morphemes (§3.4, ex. 55): real, true, complete, total, absolute are DegN heads — the nominal counterpart of adjectival degree words like very.

6. Scale structure compatibility (p. 190, ex. 60): complete is restricted to nouns whose scales have maxima (complete idiot OK, #complete smoker not).

Theory–data connection

The Bigness Generalization is derived from scale structure (§4.4, eqs. 81–85):

• Positive (big): min{d : big(d)} = θ_big > 0 → substantive restriction
• Negative (small): min{d : small(d)} = d₀ → vacuous; "small N" ≡ bare "N"

small_idiot_vacuous and big_idiot_restrictive from GradableNouns.lean predict the acceptability pattern recorded in the data below.

inductive Phenomena.Gradability.Studies.Morzycki2009.SizePolarity : Type

• positive : SizePolarity
• negative : SizePolarity

instance Phenomena.Gradability.Studies.Morzycki2009.instReprSizePolarity : Repr SizePolarity

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instReprSizePolarity = { reprPrec := Phenomena.Gradability.Studies.Morzycki2009.instReprSizePolarity.repr }

def Phenomena.Gradability.Studies.Morzycki2009.instReprSizePolarity.repr : SizePolarity → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Phenomena.Gradability.Studies.Morzycki2009.instDecidableEqSizePolarity : DecidableEq SizePolarity

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instDecidableEqSizePolarity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Gradability.Studies.Morzycki2009.instBEqSizePolarity.beq : SizePolarity → SizePolarity → Bool

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instBEqSizePolarity.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Gradability.Studies.Morzycki2009.instBEqSizePolarity : BEq SizePolarity

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instBEqSizePolarity = { beq := Phenomena.Gradability.Studies.Morzycki2009.instBEqSizePolarity.beq }

structure Phenomena.Gradability.Studies.Morzycki2009.BignessGeneralizationDatum : Type

• sizeAdj : String
• polarity : SizePolarity
• degreeReadingAvailable : Bool
• sentence : String
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.bigIdiotDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.hugeEnthusiastDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.enormousIdiotDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.smallIdiotDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.tinyIdiotDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.minuteIdiotDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.slightExaggerationDatum : BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.bignessExamples : List BignessGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

structure Phenomena.Gradability.Studies.Morzycki2009.PositionGeneralizationDatum : Type

• noun : String
• sizeAdj : String
• position : String
• degreeReadingAvailable : Bool
• sentence : String
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.bigStampCollectorAttributive : PositionGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.bigStampCollectorPredicative : PositionGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.positionExamples : List PositionGeneralizationDatum

Equations

• One or more equations did not get rendered due to their size.

inductive Phenomena.Gradability.Studies.Morzycki2009.NominalScaleType : Type

• evaluative : NominalScaleType
• enthusiasm : NominalScaleType
• frequency : NominalScaleType
• intensity : NominalScaleType

instance Phenomena.Gradability.Studies.Morzycki2009.instReprNominalScaleType : Repr NominalScaleType

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instReprNominalScaleType = { reprPrec := Phenomena.Gradability.Studies.Morzycki2009.instReprNominalScaleType.repr }

def Phenomena.Gradability.Studies.Morzycki2009.instReprNominalScaleType.repr : NominalScaleType → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Phenomena.Gradability.Studies.Morzycki2009.instDecidableEqNominalScaleType : DecidableEq NominalScaleType

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instDecidableEqNominalScaleType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Gradability.Studies.Morzycki2009.instBEqNominalScaleType.beq : NominalScaleType → NominalScaleType → Bool

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instBEqNominalScaleType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Gradability.Studies.Morzycki2009.instBEqNominalScaleType : BEq NominalScaleType

Equations

• Phenomena.Gradability.Studies.Morzycki2009.instBEqNominalScaleType = { beq := Phenomena.Gradability.Studies.Morzycki2009.instBEqNominalScaleType.beq }

structure Phenomena.Gradability.Studies.Morzycki2009.GradableNounExample : Type

• noun : String
• scaleType : NominalScaleType
• degreeAdjectives : List String
• sentence : String
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.idiotExample : GradableNounExample

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.enthusiastExample : GradableNounExample

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.stampCollectorExample : GradableNounExample

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.bastardExample : GradableNounExample

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.gradableNounExamples : List GradableNounExample

Equations

• One or more equations did not get rendered due to their size.

structure Phenomena.Gradability.Studies.Morzycki2009.NominalComparisonDatum : Type

• noun : String
• comparativeForm : String
• sentence : String
• acceptable : Bool
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.moreOfAnIdiot : NominalComparisonDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.biggerIdiotComparison : NominalComparisonDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.nominalComparisonExamples : List NominalComparisonDatum

Equations

• One or more equations did not get rendered due to their size.

structure Phenomena.Gradability.Studies.Morzycki2009.CrossLinguisticDatum : Type

• language : String
• sizeAdj : String
• polarity : SizePolarity
• degreeReadingAvailable : Bool
• translation : String
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.germanGrossIdiot : CrossLinguisticDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.germanKleinIdiot : CrossLinguisticDatum

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.crossLinguisticExamples : List CrossLinguisticDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.crossLinguisticExamples = [Phenomena.Gradability.Studies.Morzycki2009.germanGrossIdiot, Phenomena.Gradability.Studies.Morzycki2009.germanKleinIdiot]

structure Phenomena.Gradability.Studies.Morzycki2009.AdnominalDegreeMorpheme : Type

• morpheme : String
• attributiveDegreeReading : Bool
• predicativeDegreeReading : Bool
• adjDegreeModCooccurrence : Bool
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.realDegN : AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.trueDegN : AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.totalDegN : AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.completeDegN : AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.absoluteDegN : AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Gradability.Studies.Morzycki2009.adnominalDegreeMorphemes : List AdnominalDegreeMorpheme

Equations

• One or more equations did not get rendered due to their size.

structure Phenomena.Gradability.Studies.Morzycki2009.ScaleMaximumDatum : Type

• noun : String
• hasScaleMaximum : Bool
• completeAcceptable : Bool
• source : String

def Phenomena.Gradability.Studies.Morzycki2009.idiotScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.idiotScaleMax = { noun := "idiot", hasScaleMaximum := true, completeAcceptable := true, source := "Morzycki 2009 (ex. 60a)" }

def Phenomena.Gradability.Studies.Morzycki2009.dorkScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.dorkScaleMax = { noun := "dork", hasScaleMaximum := true, completeAcceptable := true, source := "Morzycki 2009 (ex. 60a)" }

def Phenomena.Gradability.Studies.Morzycki2009.fascistScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.fascistScaleMax = { noun := "fascist", hasScaleMaximum := true, completeAcceptable := true, source := "Morzycki 2009 (ex. 60a)" }

def Phenomena.Gradability.Studies.Morzycki2009.smokerScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.smokerScaleMax = { noun := "smoker", hasScaleMaximum := false, completeAcceptable := false, source := "Morzycki 2009 (ex. 60b)" }

def Phenomena.Gradability.Studies.Morzycki2009.enthusiastScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.enthusiastScaleMax = { noun := "goat cheese enthusiast", hasScaleMaximum := false, completeAcceptable := false, source := "Morzycki 2009 (ex. 60b)" }

def Phenomena.Gradability.Studies.Morzycki2009.curlingFanScaleMax : ScaleMaximumDatum

Equations

• Phenomena.Gradability.Studies.Morzycki2009.curlingFanScaleMax = { noun := "fan of curling", hasScaleMaximum := false, completeAcceptable := false, source := "Morzycki 2009 (ex. 60b)" }

def Phenomena.Gradability.Studies.Morzycki2009.scaleMaximumExamples : List ScaleMaximumDatum

Equations

• One or more equations did not get rendered due to their size.

theorem Phenomena.Gradability.Studies.Morzycki2009.negative_polarity_vacuous {E : Type} (noun : Semantics.Lexical.Noun.GradableNouns.GradableNoun E) (x : E) : Semantics.Lexical.Noun.GradableNouns.smallIdiot noun x = noun.pos x

The theory predicts that negative-polarity size adjectives are vacuous: "small idiot" has the same truth conditions as bare "idiot". This is Morzycki's key result (§4.4, eqs. 81–85): min{d : d ∈ scale(idiot) ∧ standard(small) ≤ small(d)} = d₀, so the size adjective contributes nothing.

theorem Phenomena.Gradability.Studies.Morzycki2009.positive_polarity_restrictive {E : Type} (noun : Semantics.Lexical.Noun.GradableNouns.GradableNoun E) (h : noun.standard < Core.Scale.deg 5 ⋯) (x : E) : Semantics.Lexical.Noun.GradableNouns.bigIdiot noun x = true → noun.pos x = true

The theory predicts that positive-polarity size adjectives are genuinely restrictive: "big idiot" entails "idiot".

theorem Phenomena.Gradability.Studies.Morzycki2009.big_idiot_strictly_stronger : Semantics.Lexical.Noun.GradableNouns.exampleIdiot.pos Semantics.Lexical.Noun.GradableNouns.Person.sarah = true ∧ Semantics.Lexical.Noun.GradableNouns.bigIdiot Semantics.Lexical.Noun.GradableNouns.exampleIdiot Semantics.Lexical.Noun.GradableNouns.Person.sarah = false

There exist entities that are idiots but not big idiots — demonstrating bigIdiot is strictly stronger than bare pos. This matches Morzycki's entailment (§4.3, ex. 75): "#Clyde is a big idiot, but not an idiot."

theorem Phenomena.Gradability.Studies.Morzycki2009.positive_examples_have_degree_readings : ((List.filter (fun (x : BignessGeneralizationDatum) => x.polarity == SizePolarity.positive) bignessExamples).all fun (x : BignessGeneralizationDatum) => x.degreeReadingAvailable) = true

All positive-polarity examples in the data have degree readings.

theorem Phenomena.Gradability.Studies.Morzycki2009.negative_size_adj_lack_degree_readings : ((List.filter (fun (d : BignessGeneralizationDatum) => d.polarity == SizePolarity.negative && d.sizeAdj != "slight") bignessExamples).all fun (x : BignessGeneralizationDatum) => !x.degreeReadingAvailable) = true

All negative-polarity size adjectives in the data lack degree readings. "slight" is excluded because Morzycki (p. 179) argues it is not a size adjective.

theorem Phenomena.Gradability.Studies.Morzycki2009.position_generalization_holds : ((List.filter (fun (x : PositionGeneralizationDatum) => x.position == "attributive") positionExamples).all fun (x : PositionGeneralizationDatum) => x.degreeReadingAvailable) = true ∧ ((List.filter (fun (x : PositionGeneralizationDatum) => x.position == "predicative") positionExamples).all fun (x : PositionGeneralizationDatum) => !x.degreeReadingAvailable) = true

Position Generalization: attributive has degree reading, predicative does not.

theorem Phenomena.Gradability.Studies.Morzycki2009.degN_obey_position_generalization : (adnominalDegreeMorphemes.all fun (x : AdnominalDegreeMorpheme) => x.attributiveDegreeReading) = true ∧ (adnominalDegreeMorphemes.all fun (x : AdnominalDegreeMorpheme) => !x.predicativeDegreeReading) = true

All adnominal degree morphemes have degree readings attributively but not predicatively — they obey the Position Generalization.

theorem Phenomena.Gradability.Studies.Morzycki2009.degN_no_adj_degree_mod_cooccurrence : (adnominalDegreeMorphemes.all fun (x : AdnominalDegreeMorpheme) => !x.adjDegreeModCooccurrence) = true

Adnominal degree morphemes cannot co-occur with adjectival degree modifiers — they occupy the same structural position (DegN).

theorem Phenomena.Gradability.Studies.Morzycki2009.complete_iff_scale_maximum : (scaleMaximumExamples.all fun (d : ScaleMaximumDatum) => d.hasScaleMaximum == d.completeAcceptable) = true

"complete" is acceptable exactly when the noun's scale has a maximum.

theorem Phenomena.Gradability.Studies.Morzycki2009.min_big_substantive : Semantics.Lexical.Noun.GradableNouns.minDegree Semantics.Lexical.Noun.GradableNouns.posBig = some (Core.Scale.deg 5 ⋯)

The minimum degree satisfying POS(big) is d5 (substantive).

theorem Phenomena.Gradability.Studies.Morzycki2009.min_small_vacuous_d0 : Semantics.Lexical.Noun.GradableNouns.minDegree Semantics.Lexical.Noun.GradableNouns.posSmall = some (Core.Scale.deg 0 ⋯)

The minimum degree satisfying POS(small) is d0 (vacuous).

theorem Phenomena.Gradability.Studies.Morzycki2009.george_big_idiot : Semantics.Lexical.Noun.GradableNouns.bigIdiot Semantics.Lexical.Noun.GradableNouns.exampleIdiot Semantics.Lexical.Noun.GradableNouns.Person.george = true

George (idiocy d8): big idiot ✓, small idiot = bare idiot ✓

theorem Phenomena.Gradability.Studies.Morzycki2009.george_small_eq_bare : Semantics.Lexical.Noun.GradableNouns.smallIdiot Semantics.Lexical.Noun.GradableNouns.exampleIdiot Semantics.Lexical.Noun.GradableNouns.Person.george = Semantics.Lexical.Noun.GradableNouns.exampleIdiot.pos Semantics.Lexical.Noun.GradableNouns.Person.george

theorem Phenomena.Gradability.Studies.Morzycki2009.floyd_not_big_idiot : Semantics.Lexical.Noun.GradableNouns.bigIdiot Semantics.Lexical.Noun.GradableNouns.exampleIdiot Semantics.Lexical.Noun.GradableNouns.Person.floyd = false

Floyd (idiocy d1): big idiot ✗, small idiot = bare idiot ✗

theorem Phenomena.Gradability.Studies.Morzycki2009.floyd_small_eq_bare : Semantics.Lexical.Noun.GradableNouns.smallIdiot Semantics.Lexical.Noun.GradableNouns.exampleIdiot Semantics.Lexical.Noun.GradableNouns.Person.floyd = Semantics.Lexical.Noun.GradableNouns.exampleIdiot.pos Semantics.Lexical.Noun.GradableNouns.Person.floyd