Kaplan's Anti-Monster Thesis (Tower Formulation)

@cite{anand-nevins-2004} @cite{kaplan-1989} @cite{schlenker-2003}

@cite{kaplan-1989} "Demonstratives" VIII: the claim that natural language operators are content operators (shifting circumstances of evaluation) rather than context operators (shifting contexts of utterance).

Under the tower analysis, a monster is a non-identity context shift: an embedding operator that pushes a shift where.apply c != c for some c. Kaplan's thesis for English says attitude verbs push identity shifts — they embed without changing the context of utterance.

Cross-linguistic counterexamples are languages where attitude verbs push non-identity shifts (e.g., attitudeShift changes the agent to the attitude holder).

Key Definitions

• IsTowerMonster: a shift where apply c != c for some c
• kaplansThesisAsTower: English embedding verbs push identity shifts
• sayM: Schlenker's monster operator, rewritten via tower push + fold
• Bridge: old IsMonster concept <-> IsTowerMonster

def Semantics.Reference.Monsters.IsTowerMonster {C : Type u_1} (σ : Core.Context.ContextShift C) : Prop

A context shift is a tower monster iff it is non-identity: there exists some context c where applying the shift produces a different context.

Under the tower analysis, monsters are exactly the non-identity shifts. English attitude verbs push identity shifts (not monsters); Amharic attitude verbs push attitude shifts (monsters).

Equations

• Semantics.Reference.Monsters.IsTowerMonster σ = ∃ (c : C), σ.apply c ≠ c

theorem Semantics.Reference.Monsters.identityShift_not_monster {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} : ¬IsTowerMonster Core.Context.identityShift

The identity shift is not a monster.

theorem Semantics.Reference.Monsters.attitudeShift_is_monster {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (holder : E) (attWorld : W) (c : Core.Context.KContext W E P T) (hAgent : c.agent ≠ holder) : IsTowerMonster (Core.Context.attitudeShift holder attWorld)

An attitude shift is a monster when the holder differs from some context's agent.

def Semantics.Reference.Monsters.KaplansThesisHolds {C : Type u_1} (embeddingShifts : List (Core.Context.ContextShift C)) : Prop

Kaplan's thesis as a tower property: embedding verbs in a language push shifts that are not monsters (i.e., identity shifts).

For English, this means all attitude verbs push identityShift: "John said that I am happy" evaluates "I" at the original context, because the embedding verb didn't shift anything.

The embeddingShifts parameter lists the shifts that the language's embedding verbs produce. The thesis holds iff none of them is a monster.

Equations

• Semantics.Reference.Monsters.KaplansThesisHolds embeddingShifts = ∀ σ ∈ embeddingShifts, ¬Semantics.Reference.Monsters.IsTowerMonster σ

theorem Semantics.Reference.Monsters.kaplansThesisAsTower {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} : KaplansThesisHolds [Core.Context.identityShift]

English embedding verbs push identity shifts. Kaplan's thesis holds.

def Semantics.Reference.Monsters.sayMTower {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (assert : E → W → W → Prop) (attHolder : E) (φ : Core.Context.ContextTower (Core.Context.KContext W E P T) → W → Prop) (t : Core.Context.ContextTower (Core.Context.KContext W E P T)) (w : W) : Prop

Schlenker's monstrous Say_m, rewritten via tower push.

Standard analysis: "John says that phi" quantifies over worlds compatible with John's assertion. Schlenker's monster analysis: "John says that phi" pushes an attitude shift onto the tower, making the embedded clause see John as the agent.

sayMTower assert attHolder phi t w pushes attitudeShift attHolder w' for each compatible world w', evaluating phi against the shifted tower.

Equations

• Semantics.Reference.Monsters.sayMTower assert attHolder φ t w = ∀ (w' : W), assert attHolder w w' → φ (t.push (Core.Context.attitudeShift attHolder w')) w'

theorem Semantics.Reference.Monsters.sayMTower_shifts_agent {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (assert : E → W → W → Prop) (attHolder : E) (w w' : W) (hCompat : assert attHolder w w') (φ : Core.Context.ContextTower (Core.Context.KContext W E P T) → W → Prop) (t : Core.Context.ContextTower (Core.Context.KContext W E P T)) (h : sayMTower assert attHolder φ t w) : φ (t.push (Core.Context.attitudeShift attHolder w')) w'

sayMTower accesses shifted contexts: the embedded clause is evaluated with the attitude holder as agent at the compatible world.