Partee (2010): Privative Adjectives: Subsective plus Coercion #

[Par10]

[Par10] argues no adjectives are genuinely [Kam75]-privative: apparent privatives are subsective after NVP-driven noun-coercion (the NVP and HPP of [KP95] p. 161, restated as formulae (18) and (20) in [Par10] § 4). Polish NP-splitting data from [Now00] is the empirical wedge.

Main results #

isPrivative_no_LicensedCoercion: Kamp-privative adjectives admit no LicensedCoercion — the formal obstruction motivating reanalysis.
fakeReanalysis : SubsectiveReanalysis Kamp1975.fakeAdj — the constructive reanalysis of Kamp's paradigm privative — with fakeCoercion, the coercion it licenses (the positive half of the obstruction), and fakeReanalysis_RevisedClass_subsective, placing the reanalysed meaning in RevisedClass.subsective.
split_tracks_subsectivity: over the [Now00] sample, NP-split acceptability tracks the reading's class (splittable ⟺ not non-subsective) — the § 3 generalization.
Witness bridges from Kamp's grayAdj/skillfulAdj/allegedAdj to RevisedClass cases.

The obstruction: privatives admit no licensed coercion #

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theorem Partee2010.isPrivative_no_LicensedCoercion {W : Type u_1} {E : Type u_2} {adj : Modifier (Modification.Property W E)} (hp : adj.isPrivative) (N : Modification.Property W E) (w : W) :

IsEmpty (Modification.LicensedCoercion N adj w)

Kamp-privative adjectives admit no NVP-licensed coercion. For any shift, NVP requires a positive witness x with adj shift w x ∧ shift w x; privativity forces adj shift w x → ¬ shift w x.

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theorem Partee2010.fakeAdj_no_LicensedCoercion (N : Modification.Property Kamp1975.W2 Kamp1975.E3) (w : Kamp1975.W2) :

IsEmpty (Modification.LicensedCoercion N Kamp1975.fakeAdj w)

Specialisation to Kamp1975.fakeAdj.

The reanalysis, and the coercion it licenses #

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def Partee2010.fakeReanalysis :

Modification.SubsectiveReanalysis Kamp1975.fakeAdj

Reanalysis of Kamp1975.fakeAdj: widen N by ∨ with fakeAdj N, take the reanalysed meaning to be membership-in-N-and-of- fake-type. Inert hypothesis is vacuously satisfied because the direct application of fakeAdj N to entities in N is empty (privative).

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def Partee2010.furN :

Modification.Property Kamp1975.W2 Kamp1975.E3

A toy noun for the fur scenario: a is (real) fur.

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Partee2010.furN x✝ x = (x = Kamp1975.E3.a)

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theorem Partee2010.fakeReanalysis_isNonVacuous (w : Kamp1975.W2) :

Modification.isNonVacuous (fakeReanalysis.adjSubsective (fakeReanalysis.nounShift furN)) w (fakeReanalysis.nounShift furN w)

With the noun widened to "real or fake fur", the reanalysed meaning is non-vacuous in the shifted domain: b is fake fur (positive extension), a is real fur (negative extension).

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def Partee2010.fakeCoercion (w : Kamp1975.W2) :

Modification.LicensedCoercion furN fakeReanalysis.adjSubsective w

The coercion fakeReanalysis licenses at the fur noun — the positive counterpart to fakeAdj_no_LicensedCoercion: the reanalysed meaning admits exactly the coercion the classical privative typing forbids.

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Partee2010.fakeCoercion w = Partee2010.fakeReanalysis.licensedCoercion ⋯

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theorem Partee2010.fakeReanalysis_RevisedClass_subsective :

Modification.RevisedClass.subsective.satisfies fakeReanalysis.adjSubsective

The reanalysed meaning lands in RevisedClass.subsective: the "former privatives are subsective after coercion" collapse, as a theorem rather than prose.

§ 3: the splitting diagnostic #

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@[reducible, inline]

abbrev Partee2010.predictsSplit (c : Modification.RevisedClass) :

Prop

[Par10] § 3's diagnostic prediction: NP-splitting is available exactly outside the non-subsective class.

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Partee2010.predictsSplit c = (c ≠ Modification.RevisedClass.nonSubsective)

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def Partee2010.splitSample :

List (Features.Judgment × Modification.RevisedClass)

The [Now00] split sample: each split datum (or reading, for ambiguous biedny) paired with the class [Par10] § 3 assigns to the adjective's reading.

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theorem Partee2010.split_tracks_subsectivity (p : Features.Judgment × Modification.RevisedClass) :

p ∈ splitSample → (p.1 = Features.Judgment.acceptable ↔ predictsSplit p.2)

Splitting tracks (non)subsectivity, not privativity: over the [Now00] sample a split is acceptable iff the reading's class predicts it. The reading-level biedny rows carry the paper's sharpest claim: the diagnostic tracks the reading, not the lexeme.