Partee (1987): Noun Phrase Interpretation and Type-shifting Principles

[Par87]

Partee's §5 sketches an analysis of English be as a type-shifting functor that lowers a generalized quantifier (⟨⟨e,t⟩,t⟩) to a predicate (⟨e,t⟩):

BE = λQ.λx. Q(λy. y = x) : ⟨⟨e,t⟩,t⟩ → ⟨e,t⟩

The copula's combined effect for "John is a teacher" is then BE(⟦a teacher⟧)(⟦John⟧) = teacher'(john'). On proper-name subjects the composition reduces to the ident shift λx. [j = x].

Partee's paper is about type-shifting principles in general; the be treatment is one section's sketch, not the paper's main content, and is explicitly framed as for English. Cross-linguistic predictions over typological samples are outside the paper's scope and do not belong in this study file.

@[reducible, inline]

abbrev Partee1987.be_sem (E W : Type) : Intensional.Denot E W Intensional.Ty.ett → Intensional.Denot E W Intensional.Ty.et

⟦be⟧ = BE: the copula IS the type-shifting functor, taking a generalized quantifier to a predicate.

Equations

• Partee1987.be_sem E W = Semantics.Composition.TypeShifting.BE

theorem Partee1987.be_transparent {E W : Type} (j : Intensional.Denot E W Intensional.Ty.e) : be_sem E W (Semantics.Composition.TypeShifting.lift j) = Semantics.Composition.TypeShifting.ident j

The copula is semantically transparent for proper names. "John is a teacher" with ⟦John⟧ = lift(j): BE(lift(j)) = ident(j) = λx. [j = x].

Toy-fragment examples