Comparative vs. superlative quantifiers Superlative and comparative ...

Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
The semantics of superlative modifiers
The argument of a superlative modifier is any predicate (it may be a
quantifier, for example).
◮ ‖at least α‖ = λX[□α(X) ∧ ∃α ′ [α ′ ⊲ α ∧ ⋄α ′ (X)]]
◮ ‖at most α‖ = λX[⋄α(X) ∧ ¬∃α ′ [α ′ ⊲ α ∧ ⋄α ′ (X)]]
[1] a. Betty read [at least ∅[[four] F books]].
b. □∃x[4(x) ∧ book(x) ∧ read(b, x)] ∧
⋄∃x[#x > 4 ∧ book(x) ∧ read(b, x)]
[2] a. Betty read [at most ∅[[four] F books]].
b. ⋄∃x[4(x) ∧ book(x) ∧ read(b, x)] ∧
¬⋄∃x[#x > 4 ∧ book(x) ∧ read(b, x)]
☞ In either case, the phrase ‘four books’ may be specific.
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers
Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
Modal concord
[1] Hij moet zeker in Parijs zijn.
he must certainly in Paris be
◮ Compositional reading: I suppose he has to be in Paris.
◮ Concord reading: He (definitely) has to be in Paris.
[2] Hij moet misschien in Parijs zijn.
he must perhaps in Paris be
◮ Compositional reading: Perhaps he has to be in Paris.
◮ Concord reading: none
[3] Ze zou misschien wel eens dronken kunnen zijn.
she could maybe wel eens drunk can be
◮ Compositional reading: ⋄. . .⋄(she is drunk) [not available]
◮ Concord reading: ⋄(she is drunk)
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers