Shifted Indexicals

@cite{anand-nevins-2004} @cite{deal-2020} @cite{schlenker-2003}

Cross-linguistic variation in indexical interpretation via tower depth: English "I" reads from the origin (.origin), Amharic "I" reads from the innermost context (.local), and Nez Perce exhibits mixed shifting where person shifts but time does not.

Key Definitions

• amharic_pronI: Amharic first person — ⟨.local, KContext.agent⟩
• UniformShiftParam: @cite{anand-nevins-2004} constraint — all shifted indexicals in a language read from the same depth
• MixedShiftLexicon: @cite{deal-2020} — person shifts but time doesn't (Nez Perce)
• schlenker_counterexample: English "I" and Amharic "I" diverge in the same tower configuration

def Semantics.Reference.ShiftedIndexicals.amharic_pronI {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} : Core.Context.AccessPattern (Core.Context.KContext W E P T) E

Amharic first person pronoun: reads the agent from the innermost (most deeply embedded) context.

"John yä-nä Ïnä dässïtäñ alä" ≈ "John said that I am happy" where "I" refers to John (the shifted agent), not the actual speaker.

@cite{schlenker-2003}: Amharic attitude verbs are context-shifting operators (monsters). Under the tower analysis, the monster pushes an attitude shift, and the shifted "I" reads from .local rather than .origin.

Equations

• Semantics.Reference.ShiftedIndexicals.amharic_pronI = { depth := Core.Context.DepthSpec.local, project := Core.Context.KContext.agent }

def Semantics.Reference.ShiftedIndexicals.amharic_opHere {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} : Core.Context.AccessPattern (Core.Context.KContext W E P T) P

Amharic "here": reads position from the local (shifted) context. Under attitude shift, this yields the location of the attitude holder's reported speech act, not the actual speaker's location.

Equations

• Semantics.Reference.ShiftedIndexicals.amharic_opHere = { depth := Core.Context.DepthSpec.local, project := Core.Context.KContext.position }

@[simp]

theorem Semantics.Reference.ShiftedIndexicals.amharic_pronI_depth {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} : amharic_pronI.depth = Core.Context.DepthSpec.local

theorem Semantics.Reference.ShiftedIndexicals.schlenker_counterexample {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (c : Core.Context.KContext W E P T) (holder : E) (attWorld : W) (hDistinct : c.agent ≠ holder) : have t := Core.Context.ContextTower.root c; have σ := Core.Context.attitudeShift holder attWorld; Kaplan.pronI_access.resolve (t.push σ) ≠ amharic_pronI.resolve (t.push σ)

English "I" and Amharic "I" diverge when an attitude shift is pushed onto the tower. English "I" reads from the origin (unaffected), while Amharic "I" reads from the innermost context (shifted to the attitude holder).

This is the formal content of @cite{schlenker-2003}'s counterexample to Kaplan's thesis: the SAME lexical item ("I") receives different interpretations cross-linguistically because of a depth parameter.

theorem Semantics.Reference.ShiftedIndexicals.no_shift_agreement {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (c : Core.Context.KContext W E P T) : Kaplan.pronI_access.resolve (Core.Context.ContextTower.root c) = amharic_pronI.resolve (Core.Context.ContextTower.root c)

In a root tower (no embedding), English and Amharic "I" agree: both return the context's agent.

structure Semantics.Reference.ShiftedIndexicals.UniformShiftParam : Type

@cite{anand-nevins-2004} Uniform Shift: in languages with indexical shift, ALL shifted indexicals must shift to the same depth.

In Zazaki, if "I" shifts under an attitude verb, then "you" must also shift. You cannot have "I" shifted but "you" unshifted in the same embedded clause.

The parameter records the shared depth that all person indexicals use.

• personDepth : Core.Context.DepthSpec

  The shared depth for all person indexicals in this language

• language : String

  The language exhibiting this pattern

def Semantics.Reference.ShiftedIndexicals.zazaki : UniformShiftParam

Zazaki: both first and second person shift uniformly to .local.

Equations

• Semantics.Reference.ShiftedIndexicals.zazaki = { personDepth := Core.Context.DepthSpec.local, language := "Zazaki" }

def Semantics.Reference.ShiftedIndexicals.english : UniformShiftParam

English: both first and second person uniformly read from .origin.

Equations

• Semantics.Reference.ShiftedIndexicals.english = { personDepth := Core.Context.DepthSpec.origin, language := "English" }

def Semantics.Reference.ShiftedIndexicals.UniformShiftParam.pronI {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (u : UniformShiftParam) : Core.Context.AccessPattern (Core.Context.KContext W E P T) E

Generate the first person access pattern from a uniform shift parameter.

Equations

• u.pronI = { depth := u.personDepth, project := Core.Context.KContext.agent }

def Semantics.Reference.ShiftedIndexicals.UniformShiftParam.pronYou {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (u : UniformShiftParam) : Core.Context.AccessPattern (Core.Context.KContext W E P T) E

Generate the second person access pattern from a uniform shift parameter.

Equations

• u.pronYou = { depth := u.personDepth, project := Core.Context.KContext.addressee }

theorem Semantics.Reference.ShiftedIndexicals.uniform_depth {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (u : UniformShiftParam) : u.pronI.depth = u.pronYou.depth

Uniformity: first and second person share the same depth.

structure Semantics.Reference.ShiftedIndexicals.MixedShiftLexicon : Type

@cite{deal-2020}: Nez Perce exhibits MIXED shifting — person indexicals shift under attitude verbs but temporal indexicals do not.

"Hii-pe-n'wi-ye kuhet hi-ppeew-n-e" ≈ "She_i said that she_i/*the speaker was going to arrive" Person shifts, but tense is evaluated relative to the actual speech time.

A MixedShiftLexicon records per-coordinate depth specifications, allowing person and time to diverge.

• personDepth : Core.Context.DepthSpec

  Depth for person indexicals (first/second)

• temporalDepth : Core.Context.DepthSpec

  Depth for temporal indexicals ("now", tense)

• spatialDepth : Core.Context.DepthSpec

  Depth for spatial indexicals ("here")

• language : String

  The language exhibiting this pattern

def Semantics.Reference.ShiftedIndexicals.nezPerce : MixedShiftLexicon

Nez Perce: person shifts to local, time stays at origin.

Equations

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

def Semantics.Reference.ShiftedIndexicals.MixedShiftLexicon.pronI {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (m : MixedShiftLexicon) : Core.Context.AccessPattern (Core.Context.KContext W E P T) E

Generate the first person access pattern from a mixed shift lexicon.

Equations

• m.pronI = { depth := m.personDepth, project := Core.Context.KContext.agent }

def Semantics.Reference.ShiftedIndexicals.MixedShiftLexicon.opNow {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (m : MixedShiftLexicon) : Core.Context.AccessPattern (Core.Context.KContext W E P T) T

Generate the temporal indexical from a mixed shift lexicon.

Equations

• m.opNow = { depth := m.temporalDepth, project := Core.Context.KContext.time }

theorem Semantics.Reference.ShiftedIndexicals.nezPerce_mixed : nezPerce.personDepth ≠ nezPerce.temporalDepth

In Nez Perce, person and time have different depths.

def Semantics.Reference.ShiftedIndexicals.englishMixed : MixedShiftLexicon

English is uniformly origin-reading: all coordinates share depth.

Equations

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

theorem Semantics.Reference.ShiftedIndexicals.english_not_mixed : englishMixed.personDepth = englishMixed.temporalDepth