Comparative vs. superlative quantifiers Superlative and comparative ...

Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
Modal concord with superlative quantifiers
◮ The two conjuncts introduced by a superlative quantifier do not
have the same status:
↓
primary operator
□∃x[n(x) ∧ φ(x)]
}{{}
∧ ⋄∃x[#x > n ∧ φ(x)]
principal message
◮ If a superlative quantifier combines with a modal expression
whose force is the same as that of its primary operator, the two
operators will fuse by default (modal concord).
◮ Otherwise, we have a double modal (compositional reading).
◮ The modal operators contributed by the quantifier are epistemic
by default, hence will prefer to take wide scope in most cases.
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers
Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
Examples
[1] You may take at most three cakes.
a. ∃x[3(x) ∧ cake(x) ∧ take(y, x)] ∧
¬∃x[#x > 3 ∧ cake(x) ∧ take(y, x)]
b. ⋄∃x[3(x) ∧ cake(x) ∧ take(y, x)] ∧
¬⋄∃x[#x > 3 ∧ cake(x) ∧ take(y, x)]
[2] You must take at least three cakes.
a. ⊡∃x[3(x) ∧ cake(x) ∧ take(y, x)] ∧
∃x[#x > 3 ∧ cake(x) ∧ take(y, x)]
b. □⊡∃x[3(x) ∧ cake(x) ∧ take(y, x)] ∧
⋄⊡∃x[#x > 3 ∧ cake(x) ∧ take(y, x)]
[concord]
[compositional]
[concord]
[compositional]
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers