Partee (2010): Privative Adjectives: Subsective plus Coercion

Partee argues that no adjective is privative in Kamp's sense. A privative adjective is vacuous within its literal head, so Kamp and Partee's non-vacuity principle shifts the head to include the adjective's value, fur to real or fake fur, and on the shifted head fake is subsective; the tautologous real needs the same shift. Nowak's Polish NP-splitting data motivate the move. The adjectives that split are the intersective, subsective and privative ones, which form no natural class of the traditional scale, while the modal ones do not, and once the privatives are reanalysed the adjectives that split are exactly the subsective ones. Former, normally privative, does not split, a puzzle Partee leaves open.

Main statements

• modal_no_split, nonmodal_split_except_former: modal adjectives never split, and the others all split except former.
• splittable_not_ordConnected, reanalyse_splittable_iff: the classes that split are no interval of the traditional scale, and after the reanalysis they are exactly the subsective ones.
• postulates_not_linear: the meaning postulates do not order the subsective and privative classes.
• real_isNonVacuous_iff, real_xor_fake: real is vacuous on its literal head and non-vacuous on the head that a privative shifts, where everything is real or fake and not both.

Implementation notes

The classes are the paper's labels for the meaning postulates, ordered by the traditional scale that its footnote 1 says the postulates do not give, and a natural class is read as an interval of that scale. Each Polish adjective's class is the paper's, recorded in the rows' paperFeatures; for most adjectives of its lists the paper gives only the English. The shift is Semantics.Property.ShiftsHead, and real is the identity modifier.

References

• [Par10]
• [Kam75]
• [KP95]
• [Now00]

The traditional classification

inductive Partee2010.AdjectiveClass : Type

The four labels of the traditional classification, which the paper reads as labels for the meaning postulates (7)–(9); nonsubsective is the plain, modal class.

• intersective : AdjectiveClass
• subsective : AdjectiveClass
• nonsubsective : AdjectiveClass
• privative : AdjectiveClass

@[instance_reducible]

instance Partee2010.instDecidableEqAdjectiveClass : DecidableEq AdjectiveClass

Equations

• Partee2010.instDecidableEqAdjectiveClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance Partee2010.instFintypeAdjectiveClass : Fintype AdjectiveClass

Equations

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

def Partee2010.instReprAdjectiveClass.repr : AdjectiveClass → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance Partee2010.instReprAdjectiveClass : Repr AdjectiveClass

Equations

• Partee2010.instReprAdjectiveClass = { reprPrec := Partee2010.instReprAdjectiveClass.repr }

def Partee2010.AdjectiveClass.rank : AdjectiveClass → Fin 4

The position of a class on the traditional scale, intersective to privative.

Equations

• Partee2010.AdjectiveClass.intersective.rank = 0
• Partee2010.AdjectiveClass.subsective.rank = 1
• Partee2010.AdjectiveClass.nonsubsective.rank = 2
• Partee2010.AdjectiveClass.privative.rank = 3

@[instance_reducible]

instance Partee2010.AdjectiveClass.instLinearOrder : LinearOrder AdjectiveClass

The traditional scale, which footnote 1 (p. 277) says the postulates do not give.

Equations

• Partee2010.AdjectiveClass.instLinearOrder = LinearOrder.lift' Partee2010.AdjectiveClass.rank Partee2010.AdjectiveClass.instLinearOrder._proof_1

def Partee2010.AdjectiveClass.postulate {W : Type u_1} {E : Type u_2} : AdjectiveClass → Modifier (Semantics.Property W E) → Prop

The meaning postulate each class stands for; the plain non-subsective class has none.

Equations

• Partee2010.AdjectiveClass.intersective.postulate = Modifier.IsIntersective
• Partee2010.AdjectiveClass.subsective.postulate = Modifier.IsSubsective
• Partee2010.AdjectiveClass.nonsubsective.postulate = fun (x : Modifier (Semantics.Property W E)) => True
• Partee2010.AdjectiveClass.privative.postulate = Modifier.IsPrivative

def Partee2010.AdjectiveClass.reanalyse : AdjectiveClass → AdjectiveClass

The reanalysis moves the privatives into the subsective class.

Equations

• Partee2010.AdjectiveClass.privative.reanalyse = Partee2010.AdjectiveClass.subsective
• x✝.reanalyse = x✝

def Partee2010.classTable : List (String × AdjectiveClass)

The paper's class labels as the rows record them.

Equations

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

theorem Partee2010.postulates_not_linear : (¬∀ (adj : Modifier (Semantics.Property Kamp1975.W2 Kamp1975.E3)), AdjectiveClass.subsective.postulate adj → AdjectiveClass.privative.postulate adj) ∧ ¬∀ (adj : Modifier (Semantics.Property Kamp1975.W2 Kamp1975.E3)), AdjectiveClass.privative.postulate adj → AdjectiveClass.subsective.postulate adj

The meaning postulates do not order the subsective and the privative classes (footnote 1), since Kamp's skillful is subsective and not privative and his fake privative and not subsective.

The splitting data

def Partee2010.Splittable (c : AdjectiveClass) : Prop

A class splits when some adjective the paper assigns to it splits.

Equations

• Partee2010.Splittable c = ∃ e ∈ Partee2010.Examples.all, e.parse? "class" Partee2010.classTable = some c ∧ e.judgment = Judgment.acceptable

@[instance_reducible]

instance Partee2010.instDecidablePredAdjectiveClassSplittable : DecidablePred Splittable

Equations

• Partee2010.instDecidablePredAdjectiveClassSplittable x✝ = Partee2010.instDecidablePredAdjectiveClassSplittable._aux_1 x✝

theorem Partee2010.modal_no_split (e : Datum) : e ∈ Examples.all → e.parse? "class" classTable = some AdjectiveClass.nonsubsective → e.judgment = Judgment.ungrammatical

Modal adjectives never split (16b).

theorem Partee2010.nonmodal_split_except_former (e : Datum) : e ∈ Examples.all → ∀ c ∈ e.parse? "class" classTable, c ≠ AdjectiveClass.nonsubsective → (e.judgment = Judgment.acceptable ↔ e.feature? "adjective" ≠ some "former")

Every other adjective of the paper's classes splits (15c)–(15e), except former (14), the puzzle that remains (p. 282).

theorem Partee2010.splittable_not_ordConnected : ¬{c : AdjectiveClass | Splittable c}.OrdConnected

The classes that split are no natural class of the traditional scale (p. 279), since the subsective and the privative adjectives split while the non-subsective ones between them do not.

theorem Partee2010.reanalyse_splittable_iff (c : AdjectiveClass) : (∃ (c' : AdjectiveClass), Splittable c' ∧ c'.reanalyse = c) ↔ c ≤ AdjectiveClass.subsective

Once the privatives are reanalysed as subsective, the classes that split are exactly the subsective ones, an initial segment of the scale.

real and fake on the shifted head

theorem Partee2010.real_isNonVacuous_iff {W : Type u_1} {E : Type u_2} {adj : Modifier (Semantics.Property W E)} (hp : adj.IsPrivative) (N : Semantics.Property W E) (w : W) : ¬(id N).IsNonVacuous w (N w) ∧ ((id N).IsNonVacuous w (N w ⊔ adj N w) ↔ (∃ (x : E), N w x) ∧ ∃ (x : E), adj N w x)

real, the identity modifier, is vacuous on its literal head, and on the head that a privative shifts it is non-vacuous exactly when there are both Ns and things in the privative's value (p. 280).

theorem Partee2010.real_xor_fake {W : Type u_1} {E : Type u_2} {adj : Modifier (Semantics.Property W E)} (hp : adj.IsPrivative) {N : Semantics.Property W E} {w : W} {x : E} (hx : (N w ⊔ adj N w) x) : Xor (N w x) (adj N w x)

On the head that a privative shifts, everything is real or fake and not both, as the question Is that gun real or fake? (10b) presupposes.