Plunkett & Sundell 2013: Disagreement without incompatible contents

@cite{plunkett-sundell-2013}

Plunkett, D. & Sundell, T. (2013). Disagreement and the semantics of normative and evaluative terms. Philosophers' Imprint 13(23), 1–37.

Defining commitment

In a metalinguistic negotiation — a dispute that "employs competing metalinguistic usages of an expression, and that reflects a disagreement about the proper deployment of linguistic representations" (P&S 2013 p.3) — the disputants A and B literally express mutually consistent contents. The disagreement is genuine but does NOT consist in expressing incompatible propositions.

Canonical case (paper p.18, attributed to Ludlow 2008):

A: Secretariat is an athlete. B: No, Secretariat is not an athlete.

P&S argue that A's 'athlete' has a different extension from B's 'athlete' (broad vs. narrow athleticism), so the propositions A and B literally express are jointly satisfiable: A's "Secretariat ∈ athlete₍A₎" can be true at the same world as B's "Secretariat ∉ athlete₍B₎". Plunkett & Sundell (paper p.18): "the connection between genuine disagreement and sameness of meaning is broken."

K-G's disagreement (paper §6, p.33-34)

K-G argues against P&S's diagnosis. On K-G's account, A and B express literally incompatible appropriateness contents on a SHARED standard (see KirkGiannini2024.lean §4). The disagreement is about which appropriateness standard for 'athlete' should be operative; A asserts "appropriate(athlete, S)" and B asserts "¬ appropriate(athlete, S)" on the same S, which are contradictories.

The two analyses make incompatible claims about the SHAPE of the metalinguistic-negotiation phenomenon. P&S → consistent contents; K-G → incompatible contents on a shared standard. This stub encodes P&S's commitment so the inequality theorem can be stated in K-G's file.

Note on scope

Stub formalisation. Encodes P&S's "consistent contents" diagnosis as a predicate on disputes; K-G's KirkGiannini2024.lean will host the refutation theorem. Does not formalize P&S's broader normative account of metalinguistic negotiation as a category.

structure PlunkettSundell2013.MetalinguisticDispute (Entity W : Type) : Type

A metalinguistic dispute between two speakers A and B over a target individual t and a predicate slot. The propositions are parameterised on each speaker's idiolectal extension of the contested term.

• target : Entity

  Target individual (e.g., Secretariat).

• predA : Entity → W → Prop

  A's idiolectal extension of the contested predicate.

• predB : Entity → W → Prop

  B's idiolectal extension of the contested predicate.

def PlunkettSundell2013.MetalinguisticDispute.assertionA {Entity W : Type} (d : MetalinguisticDispute Entity W) (w : W) : Prop

A's expressed proposition: target instantiates predicate-as-A-uses-it.

Equations

• d.assertionA w = d.predA d.target w

def PlunkettSundell2013.MetalinguisticDispute.assertionB {Entity W : Type} (d : MetalinguisticDispute Entity W) (w : W) : Prop

B's expressed proposition (the denial): target does NOT instantiate predicate-as-B-uses-it.

Equations

• d.assertionB w = ¬d.predB d.target w

def PlunkettSundell2013.MetalinguisticDispute.consistentContents {Entity W : Type} (d : MetalinguisticDispute Entity W) : Prop

P&S 2013's defining commitment: in a metalinguistic negotiation, A's and B's literal contents are jointly satisfiable.

Because A and B use different extensions for the contested predicate (predA ≠ predB), there exists a world where A's assertion holds AND B's denial holds. Their disagreement is NOT a clash of incompatible propositions in the standard truth-conditional sense.

Equations

• d.consistentContents = ∃ (w : W), d.assertionA w ∧ d.assertionB w

theorem PlunkettSundell2013.metalinguistic_negotiation_consistent_contents {Entity W : Type} (d : MetalinguisticDispute Entity W) (w : W) (hA : d.predA d.target w) (hB : ¬d.predB d.target w) : d.consistentContents

The classic Secretariat case. When A's broader extension includes the target and B's narrower extension excludes it at the same world, P&S's consistentContents is witnessed.

theorem PlunkettSundell2013.MetalinguisticDispute.consistentContents_excludes_shared_standard {Entity W : Type} (d : MetalinguisticDispute Entity W) (hShared : d.predA = d.predB) : ¬d.consistentContents

Structural property of consistentContents: extensional difference is a precondition. When predA = predB (e.g. when a competing analysis commits to a SHARED standard for both speakers), P&S's consistentContents necessarily fails. The proof unfolds assertionA/assertionB to expose the underlying predA d.target w ∧ ¬ predB d.target w shape, then derives a contradiction from the predicate identity.

This lemma is the structural skeleton of any cross-framework refutation of P&S: a competing analysis that commits to predA = predB automatically produces a counterexample to consistentContents. K-G's applyApprop-chain analysis (which uses a single shared AppropStandard) is exactly such a competitor; see Phenomena.Quotation.Studies.KirkGiannini2024.kg_refutes_plunkett_sundell.