Harris & Potts 2009: Orientation variables for CI items

@cite{harris-potts-2009}

Harris, J. A. & Potts, C. (2009). Perspective-shifting with appositives and expressives. Linguistics and Philosophy 32(6), 523–552.

Defining commitment

Each occurrence of a conventional-implicature item (expressive, slur, NRRC) carries a covert free orientation variable whose value is flexibly resolved in discourse. Speaker-oriented readings arise when the orientation resolves to the speaker; non-speaker-oriented readings arise when it resolves to some other discourse participant.

This is the alternative analysis K-G argues against in §8.2 (paper p.40-41). H&P's view: non-speaker-oriented readings of (26)-(28) come from orientation-variable resolution, NOT from quotation. K-G's view: they come from covert mixed quotation, with the peripheral attribution introduced by 𝔐 substituting for the discarded original CI.

K-G's objections (paper p.40-41)

1. H&P offer no explanation for the strong default preference for speaker-oriented readings of CI items (their proposal would predict roughly equal frequencies if context permits both).

2. H&P's account collapses certain theories of speaker-oriented uses of slurs (e.g., K-G 2019's directive analysis): the orientation-variable machinery cannot accommodate non-propositional CI content.

The two analyses make different empirical predictions on when non-speaker-oriented readings are available — this stub encodes H&P's key commitment so K-G's KirkGiannini2024.lean can host the inequality theorems.

Note on scope

Stub formalisation. Sufficient to host inequality theorems against K-G's strip-then-mix architecture. Does not formalize the full appositive syntax/semantics or the experimental data H&P present.

inductive HarrisPotts2009.Orientation (Person : Type) : Type

Discourse participants who can be the orientation of a CI item. H&P's apparatus is open-ended; for the stub we use a small enum.

• speaker {Person : Type} : Orientation Person
• other {Person : Type} (p : Person) : Orientation Person

@[implicit_reducible]

instance HarrisPotts2009.instDecidableEqOrientation {Person✝ : Type} [DecidableEq Person✝] : DecidableEq (Orientation Person✝)

Equations

• HarrisPotts2009.instDecidableEqOrientation = HarrisPotts2009.instDecidableEqOrientation.decEq

def HarrisPotts2009.instDecidableEqOrientation.decEq {Person✝ : Type} [DecidableEq Person✝] (x✝ x✝¹ : Orientation Person✝) : Decidable (x✝ = x✝¹)

Equations

• HarrisPotts2009.instDecidableEqOrientation.decEq HarrisPotts2009.Orientation.speaker HarrisPotts2009.Orientation.speaker = isTrue ⋯
• HarrisPotts2009.instDecidableEqOrientation.decEq HarrisPotts2009.Orientation.speaker (HarrisPotts2009.Orientation.other p) = isFalse ⋯
• HarrisPotts2009.instDecidableEqOrientation.decEq (HarrisPotts2009.Orientation.other p) HarrisPotts2009.Orientation.speaker = isFalse ⋯
• HarrisPotts2009.instDecidableEqOrientation.decEq (HarrisPotts2009.Orientation.other a) (HarrisPotts2009.Orientation.other b) = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance HarrisPotts2009.instReprOrientation {Person✝ : Type} [Repr Person✝] : Repr (Orientation Person✝)

Equations

• HarrisPotts2009.instReprOrientation = { reprPrec := HarrisPotts2009.instReprOrientation.repr }

def HarrisPotts2009.instReprOrientation.repr {Person✝ : Type} [Repr Person✝] : Orientation Person✝ → ℕ → Std.Format

Equations

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

structure HarrisPotts2009.CIItem (Person W : Type) : Type

H&P's CI item. The orientation is a free variable resolved in discourse. The CI content is parameterized on the orientation — different resolutions produce different speaker-attributions of the expressive/slur attitude.

• ciFor : Orientation Person → W → Prop

  The CI content as a function of who's oriented.

• atIssue : W → Prop

  The at-issue content (independent of orientation).

def HarrisPotts2009.CIItem.resolve {Person W : Type} (item : CIItem Person W) (o : Orientation Person) : Pragmatics.Expressives.TwoDimProp W

Resolve the orientation variable to a particular value, producing a flat TwoDimProp.

Equations

• item.resolve o = { atIssue := item.atIssue, ci := item.ciFor o }

theorem HarrisPotts2009.non_speaker_oriented_via_orientation_var {Person W : Type} (item : CIItem Person W) (p : Person) : item.resolve (Orientation.other p) = { atIssue := item.atIssue, ci := item.ciFor (Orientation.other p) }

H&P's central claim: non-speaker-oriented readings via free orientation variable, no quotation invoked.

For any CI item with orientation-dependent content, there exist discourse situations where the orientation resolves to a non-speaker individual p, producing a non-speaker-oriented reading. The mechanism is purely contextual resolution; nothing about the syntactic structure or pure quotation is invoked.

theorem HarrisPotts2009.any_orientation_available {Person W : Type} (item : CIItem Person W) (o : Orientation Person) : ∃ (p : Pragmatics.Expressives.TwoDimProp W), p = item.resolve o

The orientation variable can in principle resolve to any discourse participant. This is the property K-G complains is too permissive: H&P predict that any contextually salient individual can serve as orientation, but the data show speaker-orientation is the strong default.