@cite{israel-2001}: Minimizers, Maximizers, and the Rhetoric of Scalar Reasoning #

Formalizes the core contributions of Israel's Scalar Model of Polarity:

The 2×2 taxonomy (Figure 1): polarity items classified by scalar value (high/low) × rhetorical force (emphatic/attenuating)
Inverted polarity items (§3, Figure 3): maximizer NPIs (wild horses, all the tea in China) and minimizer PPIs (at the drop of a hat, for a pittance) — items whose scalar value is opposite to what the basic Scalar Model predicts
The thematic resolution (§4): inversion tracks propositional role — facilitating roles (stimulus, instrument, reward) produce inverted items, impeding roles (patient, theme, resource) produce canonical items
The pecuniary paradox: a red cent (NPI, resource = impeding) vs for peanuts (PPI, reward = facilitating) — same monetary domain, different propositional roles

Connection to linglib infrastructure #

ScalarValue, Canonicity, LikelihoodEffect defined in Core/Lexical/PolarityItem.lean
Inverted items added to Fragments/English/PolarityItems.lean
LikelihoodEffect is a propositional-role concept, not a theta-role function. It connects to proto-role entailments (Dowty 1991) via bridge theorems below, but is independently defined: the relevant distinction is how a participant affects event likelihood, which cross-cuts traditional theta labels.

The basic Scalar Model predicts four cells:

	Emphatic	Attenuating
NPI	low: a wink, inch	high: much, long
PPI	high: tons, utterly	low: sorta, rather

Emphatic items license maximally informative interpretations; attenuating items license minimally informative interpretations. NPI contexts are scale-reversing (DE); PPI contexts are scale-preserving (UE).

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structure Phenomena.Polarity.Studies.Israel2001.IsraelDatum :

Type

A polarity item datum with its Israel 2001 classification.

item : Core.Lexical.PolarityItem.PolarityItemEntry
sentence : String
Example sentence
grammatical : Bool
Is the item grammatical in this sentence?

Instances For

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def Phenomena.Polarity.Studies.Israel2001.instReprIsraelDatum.repr :

IsraelDatum → Nat → Std.Format

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instance Phenomena.Polarity.Studies.Israel2001.instReprIsraelDatum :

Repr IsraelDatum

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Phenomena.Polarity.Studies.Israel2001.instReprIsraelDatum = { reprPrec := Phenomena.Polarity.Studies.Israel2001.instReprIsraelDatum.repr }

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def Phenomena.Polarity.Studies.Israel2001.sleepAWink :

IsraelDatum

"I didn't sleep a wink." — canonical emphatic NPI (low, impeding)

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def Phenomena.Polarity.Studies.Israel2001.didntBudge :

IsraelDatum

"She didn't budge an inch." — canonical emphatic NPI (low, impeding)

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Phenomena.Polarity.Studies.Israel2001.didntBudge = { item := Fragments.English.PolarityItems.budgeAnInch, sentence := "She didn't budge an inch.", grammatical := true }

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def Phenomena.Polarity.Studies.Israel2001.insanely :

IsraelDatum

"She is insanely good-looking." — canonical emphatic PPI (high)

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def Phenomena.Polarity.Studies.Israel2001.sorta :

IsraelDatum

"She's sorta clever." — canonical attenuating PPI (low)

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def Phenomena.Polarity.Studies.Israel2001.allThat :

IsraelDatum

"He's not all that clever." — canonical attenuating NPI (high)

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Inverted items break the simple correlation between scalar value and polarity type. They are explained by propositional role (§4).

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def Phenomena.Polarity.Studies.Israel2001.wildHorsesDatum :

IsraelDatum

"Wild horses couldn't keep me away." — inverted emphatic NPI (high, facilitating)

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Phenomena.Polarity.Studies.Israel2001.wildHorsesDatum = { item := Fragments.English.PolarityItems.wildHorses, sentence := "Wild horses couldn't keep me away.", grammatical := true }

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def Phenomena.Polarity.Studies.Israel2001.teaInChinaDatum :

IsraelDatum

"I wouldn't do it for all the tea in China." — inverted emphatic NPI (high, facilitating)

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def Phenomena.Polarity.Studies.Israel2001.tenFootPoleDatum :

IsraelDatum

"I wouldn't touch it with a ten-foot pole." — inverted emphatic NPI (high, facilitating)

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Phenomena.Polarity.Studies.Israel2001.tenFootPoleDatum = { item := Fragments.English.PolarityItems.aTenFootPole, sentence := "I wouldn't touch it with a ten-foot pole.", grammatical := true }

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def Phenomena.Polarity.Studies.Israel2001.ownShadowDatum :

IsraelDatum

"Godfrey is scared of his own shadow." — inverted emphatic PPI (low, facilitating)

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def Phenomena.Polarity.Studies.Israel2001.withAFeatherDatum :

IsraelDatum

"You could have knocked me over with a feather." — inverted emphatic PPI (low, facilitating)

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def Phenomena.Polarity.Studies.Israel2001.jiffyDatum :

IsraelDatum

"We'll be back in a jiffy." — inverted emphatic PPI (low, facilitating)

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Phenomena.Polarity.Studies.Israel2001.jiffyDatum = { item := Fragments.English.PolarityItems.inAJiffy, sentence := "We'll be back in a jiffy.", grammatical := true }

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def Phenomena.Polarity.Studies.Israel2001.peanutsDatum :

IsraelDatum

"He got Madonna to play for peanuts." — inverted emphatic PPI (low, facilitating)

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Phenomena.Polarity.Studies.Israel2001.peanutsDatum = { item := Fragments.English.PolarityItems.forAPittance, sentence := "He got Madonna to play for peanuts.", grammatical := true }

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The pecuniary paradox (§3, examples 15–16): both a red cent and for peanuts denote small monetary values, but a red cent is an NPI and for peanuts is a PPI. The resolution: they occupy different propositional roles.

a red cent = Resource (what you spend) → impeding → canonical NPI
for peanuts = Reward (what you gain) → facilitating → inverted PPI

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def Phenomena.Polarity.Studies.Israel2001.redCentDatum :

IsraelDatum

"He won't spend a red cent on your wedding." — canonical NPI, resource/expense

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def Phenomena.Polarity.Studies.Israel2001.forPeanutsDatum :

IsraelDatum

"He got Madonna to play for peanuts." — inverted PPI, reward

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def Phenomena.Polarity.Studies.Israel2001.allData :

List IsraelDatum

All items from this paper with full classification.

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@cite{israel-2001} §4 discusses Dowty's proto-roles (fn. 6) as a possible basis for the canonical/inverted distinction. The connection to EntailmentProfile is:

Proto-Agent entailments (causation, volition, movement, independent existence) → participant facilitates event realization
Proto-Patient entailments (change of state, incremental theme, causally affected, stationary) → participant impedes event realization (bigger obstacle → less likely)

This is NOT a function on ThetaRole (which is a derived convenience label in linglib). Instead, LikelihoodEffect is an independent propositional-role concept that correlates with proto-role entailments but cross-cuts theta labels in cases like the pecuniary paradox (where both arguments may be "themes" in a traditional analysis).

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def Phenomena.Polarity.Studies.Israel2001.pAgentDominant_suggests_facilitating (pAg pPat : Nat) :

Core.Lexical.PolarityItem.LikelihoodEffect

Proto-Agent dominance predicts facilitating role.

If an argument position has more P-Agent entailments than P-Patient entailments, the participant tends to facilitate event realization. This is a heuristic, not a theorem — the pecuniary paradox shows that propositional role can diverge from proto-role counts.

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Fauconnier (1975b) noted that perception verbs allow dual scalar readings. "Eve didn't hear even the faintest noise" and "Eve didn't hear even the loudest noise" are both emphatic, but use different scales:

faintest: existential scale (ranking stimuli by likely existence) → canonical impeding role
loudest: perceptual-ability scale (ranking experiencers by acuity) → inverted facilitating role

The dual reading arises because perception is bicausal: it depends both on the stimulus's salience AND the perceiver's acuity.

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inductive Phenomena.Polarity.Studies.Israel2001.PerceptionScaleType :

Type

Scale type for the ambiguous-superlative phenomenon

existential : PerceptionScaleType
perceptualAbility : PerceptionScaleType

Instances For

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instance Phenomena.Polarity.Studies.Israel2001.instDecidableEqPerceptionScaleType :

DecidableEq PerceptionScaleType

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Phenomena.Polarity.Studies.Israel2001.instDecidableEqPerceptionScaleType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def Phenomena.Polarity.Studies.Israel2001.instBEqPerceptionScaleType.beq :

PerceptionScaleType → PerceptionScaleType → Bool

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Phenomena.Polarity.Studies.Israel2001.instBEqPerceptionScaleType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Polarity.Studies.Israel2001.instBEqPerceptionScaleType :

BEq PerceptionScaleType

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Phenomena.Polarity.Studies.Israel2001.instBEqPerceptionScaleType = { beq := Phenomena.Polarity.Studies.Israel2001.instBEqPerceptionScaleType.beq }

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instance Phenomena.Polarity.Studies.Israel2001.instReprPerceptionScaleType :

Repr PerceptionScaleType

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Phenomena.Polarity.Studies.Israel2001.instReprPerceptionScaleType = { reprPrec := Phenomena.Polarity.Studies.Israel2001.instReprPerceptionScaleType.repr }

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def Phenomena.Polarity.Studies.Israel2001.instReprPerceptionScaleType.repr :

PerceptionScaleType → Nat → Std.Format

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structure Phenomena.Polarity.Studies.Israel2001.AmbiguousSuperlativeDatum :

Type

sentence : String
superlative : String
scaleType : PerceptionScaleType
likelihoodEffect : Core.Lexical.PolarityItem.LikelihoodEffect
notes : String

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instance Phenomena.Polarity.Studies.Israel2001.instReprAmbiguousSuperlativeDatum :

Repr AmbiguousSuperlativeDatum

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Phenomena.Polarity.Studies.Israel2001.instReprAmbiguousSuperlativeDatum = { reprPrec := Phenomena.Polarity.Studies.Israel2001.instReprAmbiguousSuperlativeDatum.repr }

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def Phenomena.Polarity.Studies.Israel2001.instReprAmbiguousSuperlativeDatum.repr :

AmbiguousSuperlativeDatum → Nat → Std.Format

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def Phenomena.Polarity.Studies.Israel2001.faintestNoise :

AmbiguousSuperlativeDatum

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def Phenomena.Polarity.Studies.Israel2001.loudestNoise :

AmbiguousSuperlativeDatum

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@cite{israel-2001} §2 connects the Scalar Model to the Fauconnier-Ladusaw tradition of monotonicity-based licensing:

Scale-reversing contexts (NPI-licensing): inferences run from high to low values. In formal terms, these are downward entailing (DE) contexts — Mathlib's Antitone, linglib's IsDE.
Scale-preserving contexts (PPI-licensing): inferences run from low to high values. In formal terms, these are upward entailing (UE) contexts — Mathlib's Monotone, linglib's IsUE.

Israel's key departure from Ladusaw: the relevant inferences need not be strictly logical — they can be pragmatic entailments within a scalar model. This is why the Scalar Model can handle cases that pure monotonicity misses.

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inductive Phenomena.Polarity.Studies.Israel2001.ScaleDirection :

Type

Israel's "scale-reversing" corresponds to formal DE (= Antitone). This is the bridge between the Scalar Model (pragmatic) and the Fauconnier-Ladusaw tradition (logical).