Documentation

Linglib.Phenomena.Gradability.Studies.Partee2010

Partee (2010): Privative Adjectives: Subsective plus Coercion @cite{partee-2010} #

@cite{kamp-1975} @cite{kamp-partee-1995}

In R. Bäuerle, U. Reyle, & T. E. Zimmermann (eds.), Presuppositions and Discourse: Essays Offered to Hans Kamp, 273–292. Brill.

(Circulated as a manuscript since 2001.)

Overview #

@cite{partee-2010} argues that there are no genuinely privative adjectives. What @cite{kamp-1975} classified as "privative" (fake, counterfeit, fictitious) are actually subsective — they trigger coercion of the noun's denotation.

Core Argument #

Key evidence:

  1. "Is that gun real or fake?" — the noun "gun" must include both real and fake guns for this question to be well-formed (§ 1, ex. 10b)
  2. Polish NP-splitting data (Nowak 2000): intersective, subsective, AND "privative" adjectives can all participate in NP-splitting, but non-subsective/modal adjectives (alleged, potential) cannot (§ 2)

Result #

The traditional 4-class hierarchy collapses to three classes:

intersective > subsective > non-subsective (modal)

The "privative" class is eliminated. The mathematical basis is any_adj_subsective_under_selfcoercion: ANY adjective is subsective when the noun is coerced to include the adjective's own extension. The empirical question is whether this coercion is linguistically real — the Polish data argues it is.

Structure #

@cite{partee-2010}'s central mechanism: when a "privative" adjective combines with a noun N, the noun's denotation is coerced to N* = N ∪ adj(N). The adjective is then subsective within N*.

source
def Phenomena.Gradability.Studies.Partee2010.coerceNoun {W : Type u_1} {E : Type u_2} (N ext : Semantics.Lexical.Adjective.Classification.Property W E) :
Semantics.Lexical.Adjective.Classification.Property W E

Noun coercion: expand the noun's denotation to include entities in an additional extension. coerceNoun N ext = N ∪ ext.

In @cite{partee-2010}'s analysis, ext is the adjective's own extension for that noun: "gun" → "gun*" = guns ∪ fake-guns.

Equations
Instances For
    source
    theorem Phenomena.Gradability.Studies.Partee2010.any_adj_subsective_under_selfcoercion {W : Type u_1} {E : Type u_2} (adj : Semantics.Lexical.Adjective.Classification.AdjMeaning W E) (N : Semantics.Lexical.Adjective.Classification.Property W E) (w : W) (x : E) :
    adj N w x = true → coerceNoun N (adj N) w x = true

    Core theorem. Any adjective is affirmative (subsective) when the noun is coerced to include the adjective's own extension. This is the mathematical content of @cite{partee-2010}'s argument: the privative class is not a genuine semantic class but an artifact of ignoring noun coercion.

    The proof is trivially true — adj(N)(w)(x) → N(w)(x) ∨ adj(N)(w)(x) — which is exactly Partee's point: the "privative" classification can always be dissolved by acknowledging that the noun's denotation shifts. The substantive claim is that this coercion is linguistically real, not ad hoc (see § 3).

    source
    theorem Phenomena.Gradability.Studies.Partee2010.coerceNoun_extends {W : Type u_1} {E : Type u_2} (N ext : Semantics.Lexical.Adjective.Classification.Property W E) (w : W) (x : E) (h : N w x = true) :
    coerceNoun N ext w x = true

    Coercion is monotone: the coerced noun always extends the original.

    Under @cite{partee-2010}'s analysis, the adjective hierarchy collapses from four classes to three. The privative class is absorbed into the subsective class (via noun coercion).

    source
    inductive Phenomena.Gradability.Studies.Partee2010.RevisedClass :
    Type

    The revised three-class hierarchy.

    • intersective : RevisedClass

      ⟦AN⟧ = ⟦A⟧ ∩ ⟦N⟧ (Kamp's intersective)

    • subsective : RevisedClass

      ⟦AN⟧ ⊆ ⟦N*⟧ — includes former "privatives" via coercion (Kamp's subsective, generalized)

    • nonSubsective : RevisedClass

      No entailment: alleged, potential, putative (Kamp's non-subsective)

    Instances For
      source
      instance Phenomena.Gradability.Studies.Partee2010.instDecidableEqRevisedClass :
      DecidableEq RevisedClass
      Equations
      source
      def Phenomena.Gradability.Studies.Partee2010.instReprRevisedClass.repr :
      RevisedClass → ℕ → Std.Format
      Equations
      • One or more equations did not get rendered due to their size.
      Instances For
        source
        instance Phenomena.Gradability.Studies.Partee2010.instReprRevisedClass :
        Repr RevisedClass
        Equations

        @cite{partee-2010} § 2 uses Polish NP-splitting data (Nowak 2000) as evidence for the reclassification. In Polish, Adj+N phrases can be "split" across the sentence (Adj sentence-initial, N sentence-final).

        The critical observation: the split does NOT track the traditional
4-class boundary. Instead, intersective, subsective, AND traditionally
"privative" adjectives can all split, but non-subsective/modal
adjectives (alleged, potential, predicted) cannot.

This patterns exactly as the 3-class hierarchy predicts: the split
tracks subsectivity (with coercion), not the traditional privative/
non-privative distinction.
        source
        def Phenomena.Gradability.Studies.Partee2010.canSplitNP :
        RevisedClass → Bool

        Which adjective classes allow Polish NP-splitting (Nowak 2000, cited in @cite{partee-2010} § 2).

        CAN split: rozległy "large" (intersective), biedny "poor/not rich" (intersective), Chinese/generous/pretty (intersective), skillful/ recent/good/typical (subsective), counterfeit/past/spurious/imaginary/ fictitious (traditionally "privative").

        CANNOT split: biedny "pitiful" (non-subsective), Polish translations of alleged/potential/predicted/disputed (non-subsective/modal).

        Equations
        Instances For
          source
          theorem Phenomena.Gradability.Studies.Partee2010.splitting_tracks_revised_hierarchy :
          canSplitNP RevisedClass.intersective = true ∧ canSplitNP RevisedClass.subsective = true ∧ canSplitNP RevisedClass.nonSubsective = false

          The NP-splitting data supports the revised hierarchy: the split tracks the 3-class boundary (subsective vs non-subsective), not the traditional 4-class boundary (privative vs non-privative).

          source
          theorem Phenomena.Gradability.Studies.Partee2010.traditional_mispredicts_privative_splitting :
          canSplitNP RevisedClass.subsective = true

          The traditional 4-class analysis wrongly predicts that "privative" adjectives should NOT be able to split (since they share a class boundary with non-subsective adjectives). The revised 3-class analysis correctly predicts they CAN split (since they are subsective).