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A Theory of Indexical Shift: Meaning, Grammar, and Crosslinguistic Variation

Deal, A. R. (2020). MIT Press

Indexical shift comes from shifty operators at the edge of attitude complements, each overwriting coordinates of the context with those of the index the attitude quantifies over. The operators sit in a functional sequence, OP_LOC > OP_ADDR > OP_AUTH > OP_TIME (152), and a complement projects a bottom segment of it (128), so an indexical class shifts only if the classes below it do (G2). The complementizer may sit anywhere in the sequence; operators below it overwrite from the index and force de se readings, those above it overwrite from the attitude event and do not (G3).

Main definitions

sequence, stack n: the functional sequence of shifty operators, lowest first, and a complement projecting the lowest n of them.
comp, eventOp: the finite complementizer (140) and an event-based shifter (143)–(144).
complement n p: a complement of size n with the complementizer after the lowest p.
Verb: the complements a verb selects and where their complementizer sits.
complement_apply and the apply_complementContext lemmas: an indexical in a complement reads the index, the attitude event or the utterance context by its class's position relative to C, (G3).

Implementation notes

The rows are Data.Examples.Deal2020. Nez Perce has no temporal indexicals, so its complements' OP_TIME is unobservable; the example of Anderson English is filed as English.

TODO

(G1), the hierarchy of verbs by complement size (§3.2.2), has no rows.
(171): Nez Perce 'think' with a second person, which needs the defective addressee of (140c); the obligatoriness of Uyghur shift from bundling C with the operators (173).
The quotation, role shift, fake indexical and indexiphor boundaries of chapter 5.

References

Deal 2020, A Theory of Indexical Shift: Meaning, Grammar, and Crosslinguistic Variation
Anand & Nevins 2004, Shifty Operators in Changing Contexts formalized

The functional sequence

A stack of operators overwrites the union of their coordinates, so a lexical bundle of the operators of (126) is their composition (172).

theorem stack_eq L98–102

{W E P T : Type u} {α : Type u_1} (n : ℕ) (χ : Kaplan.Character (Kaplan.Context W E P T) (Kaplan.Context W E P T) α) :

stack n χ = Kaplan.shiftyOp (shifted n) χ

Built from ,

Unembedded, a stack of operators is vacuous (65), since a sentence's truth at a context is its truth at that context as index (64).

theorem diag_stack L104–109

{W E P T : Type u} {α : Type u_1} (n : ℕ) (χ : Kaplan.Character (Kaplan.Context W E P T) (Kaplan.Context W E P T) α) :

Kaplan.Character.diag id (stack n χ) = Kaplan.Character.diag id χ

Built from

(G2): in a complement of any size, an indexical class shifts only if every class below it in the sequence shifts as well (§4.4).

theorem mem_shifted_of_lt L111–115

{n : ℕ} {k k' : Kaplan.Context.Coord} (hk : k ∈ shifted n) (hk' : k' ∈ sequence) (h : rank k' < rank k) :

k' ∈ shifted n

Built from , ,

The complementizer and the de se

Local Determination

In Katie says that I think that I am here the lowest first person refers as the medial one does, both shifted or neither ((77), (83)).

theorem medial_eq_lowest L207–212

{W E P T : Type u} (s₁ s₂ : Finset Kaplan.Context.Coord) (c j₁ j₂ : Kaplan.Context W E P T) (hj₂ : j₂.agent = (Kaplan.Context.overwrite s₁ c j₁).agent) :

(Kaplan.Context.overwrite s₂ (Kaplan.Context.overwrite s₁ c j₁) j₂).agent = (Kaplan.Context.overwrite s₁ c j₁).agent

Lexical bundling

Coordinates in the same bundles shift together, so (G2) fails only as co-shifting, as of Korean locatives and temporals (175) (§4.4).

theorem mem_ofBundles_iff L241–247

{bs : Finset (Finset Kaplan.Context.Coord)} {k k' : Kaplan.Context.Coord} (h : ∀ b ∈ bs, k ∈ b ↔ k' ∈ b) {s : Finset Kaplan.Context.Coord} (hs : s ∈ ofBundles bs) :

k ∈ s ↔ k' ∈ s

Built from

The languages

A reading of the rows' indexicals is available iff a complement the verb selects overwrites exactly the coordinates it shifts, per (G2) and Shift Together (72).

theorem rows_shift L326–332

(r : Datum) :

r ∈ Examples.all → ∀ p ∈ (verbCoords? r).toList, ∀ x ∈ r.readings, ∀ ps ∈ (shifted? x.1).toList, Judgment.marginal ≤ x.2 ↔ ∃ s ∈ p.1.options, ∀ q ∈ p.2.zipIdx, q.1 ∈ s ↔ q.2 ∈ ps

Built from ,

A judged de se reading of the rows' shifted indexicals is available exactly when a complement the verb selects shifts their coordinates.

theorem rows_deSe L334–339

(r : Datum) :

r ∈ Examples.all → ∀ p ∈ (verbCoords? r).toList, ∀ x ∈ r.readings, x.1 = "de se" → (Judgment.marginal ≤ x.2 ↔ ∃ s ∈ p.1.options, ∀ k ∈ p.2, k ∈ s)

Built from

(G3) in the rows: a judged non-de se reading of the rows' shifted indexicals is available exactly when a complement the verb selects shifts their coordinates with operators above the complementizer, eventShifted n c = shifted n \ shifted c.

theorem rows_nonDeSe L341–348

(r : Datum) :

r ∈ Examples.all → ∀ p ∈ (verbCoords? r).toList, ∀ c ∈ p.1.cPosition.toList, ∀ x ∈ r.readings, x.1 = "non-de se" → (Judgment.marginal ≤ x.2 ↔ ∃ s ∈ p.1.options, ∀ k ∈ p.2, k ∈ s \ shifted c)

Built from ,

In the lowest of two reports, a first-person reading is available iff the two verbs' complements make it read the context at that depth (87).

theorem rows_double_report L350–358

(r : Datum) :

r ∈ Examples.all → r.feature? "lowest_shift" = some "yes" → ∀ p ∈ (verbCoords? r).toList, ∀ v₂ ∈ ((r.feature? "lower_verb").bind verb?).toList, ∀ x ∈ r.readings, ∀ d ∈ (depth? x.1).toList, Judgment.marginal ≤ x.2 ↔ ∃ s₁ ∈ p.1.options, ∃ s₂ ∈ v₂.options, Kaplan.Context.Coord.addressee ∈ s₂ ∧ ∀ k ∈ p.2, Kaplan.Context.localDepth [s₁, s₂] k = d

Built from , ,