Comparative vs. superlative quantifiers Superlative and comparative ...

Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
The grammar of scalar quantifiers
◮ Scalar quantifiers are standardly parsed like this:
[[more than three] books]
◮ This is problematic for several reasons. E.g.
[1] Betty read more than [three] F books: she read four.
[2] Betty read more than [three books] F : she read fifteen essays
as well.
◮ Alternative analysis:
[more than [three books]]
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers
Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence
The semantics of comparative modifiers
◮ The argument of a comparative modifier is a first-order
predicate: ‘more than happy’, ‘more than three books’, but
‘∗more than Fred’.
◮ This explains why ‘three books’ in ‘more than three books’ does
not allow for a specific construal.
◮ ‖more than α‖ = λx∃α ′ [α ′ ⊲ α ∧ α ′ (x)]
[1] With λx[scalding(x)] ⊲ λx[hot(x)] ⊲ λx[warm(x)],
‖more than warm‖ = λx[hot(x) ∨ scalding(x)]
[2] With . . . λx[3(x)] ⊲ λx[2(x)] ⊲ λx[1(x)],
‖more than [[three] F books]‖ =
λx[[4(x) ∨ 5(x) ∨ . . .] ∧ book(x)] = λx[#x > 3 ∧ book(x)]
So: ‖Betty read ∅[more than [[three] F books]]‖ =
∃x[#x > 3 ∧ book(x) ∧ read(b, x)]
Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers