Tenses and Pronouns: Partee's Structural Analogy

[Par73] [Pri67]

Formalizes [Par73]: tenses in English exhibit the same three-way interpretive ambiguity as pronouns — indexical, anaphoric, and bound-variable — and share the same formal mechanisms (assignment functions, variable lookup, lambda abstraction). The substrate carrier is TensePronoun (Semantics/Tense/Pronoun.lean).

Mode	Pronouns	Tenses
Indexical	"I" → agent of context	present → speech time
Anaphoric	"he" → salient individual	past → salient narrative time
Bound	"his" in ∀x...his...	tense in "whenever...is..."

Partee's main argument against [Pri67]'s tense-as-operator view: "I didn't turn off the stove" with past tense does not mean "at SOME past time I didn't turn off the stove" (trivially true) but "at THAT specific time I didn't turn off the stove" — tenses refer, they don't quantify (stove_refutes_prior).

The definitions here are the temporal counterparts of the entity variable infrastructure in Semantics.Montague.Variables; both instantiate the generic Assignment infrastructure, which is Partee's point: the same referential mechanism operates over different domains.

Later engagements with the analogy live in their own studies: Ogihara1989 (operator–referential reconciliation), Kratzer1998 (zero tense, SOT deletion), Elbourne2013 (situation-variable coarsening).

def Partee1973.parteeStoveExample {Time : Type u_1} (turnedOff : Time → Bool) (g : Tense.TemporalAssignment Time) (n : ℕ) : Bool

Partee's stove example: "I didn't turn off the stove."

Past tense introduces a temporal variable resolved to a specific contextually salient time. The negation scopes over the temporal reference, giving ¬P(t_i) rather than Prior's ∃t < now. ¬P(t).

Equations

• Partee1973.parteeStoveExample turnedOff g n = !turnedOff (Tense.interpTense n g)

theorem Partee1973.stove_refutes_prior : parteeStoveExample (fun (x : ℤ) => x == -1) (fun (x : ℕ) => -1) 0 = false ∧ ∃ (s : Intensional.Index Unit ℤ), Tense.PAST (fun (s : Intensional.Index Unit ℤ) => (s.time == -1) = false) s { world := (), time := 0 }

[Par73]'s argument against [Pri67], as a countermodel: in a context where the stove WAS turned off at the salient time (−1), the referential reading is false — the utterance is correctly predicted false — while the Priorean existential reading stays true (witnessed by any other past time), so the operator analysis trivializes the sentence.

def Partee1973.narrativeAnaphora {Time : Type u_1} (P Q : Time → Bool) (g : Tense.TemporalAssignment Time) (n : ℕ) : Bool

Partee's narrative example: "He turned the corner. He saw a house."

Both past tenses refer to the same narrative time — temporal anaphora. Under the referential analysis both clauses evaluate at g(n) for the same discourse-salient temporal variable n, just as anaphoric pronouns corefer with an established individual.

Equations

• Partee1973.narrativeAnaphora P Q g n = (P (Tense.interpTense n g) && Q (Tense.interpTense n g))