[Coh13]: No Quantification without Reinterpretation #

Ariel Cohen, "No Quantification without Reinterpretation." Chapter 13 in Genericity (ed. Mari, Beyssade, Del Prete), OUP, pp. 334–351.

Thesis #

The generic quantifier GEN is not a phonologically null version of an overt quantifier — it is introduced by the hearer through reinterpretation of quantifier-free input. The two reinterpretation mechanisms (Predicate Transfer for generics, type-shifting for habituals) explain the different scopal properties of generics vs habituals.

Empirical Generalizations (§13.2) #

Construction	Scope behavior
Overt quantifier (every, ∀)	Full scope ambiguity
Generic (bare plural subject)	Ambiguous, except in opaque contexts
Habitual (no restrictor)	Narrow scope only
Habitual (with restrictor)	Ambiguous (restrictor provides Q site)
Bare plural in habitual	Scope below habitual (DRT constraint)

Core Proposal (§§13.3–13.4) #

Generics arise from Predicate Transfer (T_g, [Nun95]): T_g can apply locally (narrow scope) or globally (wide scope), yielding scope ambiguity. But T_g requires the intension of the transferred property, so it cannot scope out of opaque contexts like believe.
Habituals arise from type-shifting (γ): Eventive verbs require interval arguments; present tense provides a moment → type mismatch → γ fires at the verb level (locally). Since the shift is local, the resulting GEN takes narrow scope only. With an overt restrictor or contextual restriction, there is no mismatch, so normal scope obtains.

Argumentation Chain (§13.3.1 → §13.4.2) #

The paper's key argument flows through the Partee-Rooth SHIFT operator:

SHIFT does not commute with negation (shift_neg_noncommutative)
Any type-shift shares this non-commutativity property
γ is a type-shift, so γ does not commute with ∃ (gamma_noncommutative)
Therefore γ must apply at the type-mismatch site (locally)
Therefore the existential from the indefinite scopes over γ
Therefore habituals take narrow scope (habitual_narrow_scope)

Formalization Strategy #

We verify Cohen's scope predictions using finite models, with definitions built directly on transferGen and gamma from (below):

Storks / nesting areas: T_g applied locally vs globally gives different truth conditions → generics are scopally ambiguous
Mary / cigarettes: γ applied locally gives the implausible narrow- scope reading; the plausible wide-scope reading would require global γ, which is unavailable because the type mismatch is at the verb level
Scope hierarchy: overt > predicateTransfer > typeShift

These connect to (below) (T_g, γ, SHIFT, QuantifierSource), the canonical relativized restricted universal Quantification.everyOn (Counting.lean) that both T_g and γ bottom out in, and Scope.lean (ScopeConfig). A local 3-cell Occasion enum (below) supplies the habitual-side domain.

Reinterpretation mechanisms ([Coh13], [Nun95]) #

Two mechanisms that introduce covert quantifiers into logical form with different scope consequences: Predicate Transfer (T_g, [Nun95]), pragmatically triggered and applicable at any composition level (→ scope ambiguity except in opaque contexts), and habitual type-shift (γ, [Coh13]), semantically triggered by type mismatch and applied locally (→ narrow scope only). Same quantifier (GEN), different scope behavior driven by the introducing mechanism.

The argument for γ's locality goes through the Partee-Rooth SHIFT operator: since SHIFT does not commute with negation (shift_neg_noncommutative), neither does γ — so γ must apply before negation, i.e., locally.