The Algebraic Structure of Amounts: Evidence from Comparatives

Heim [9] notes certain restrictions on quantifier intervention in comparatives and proposes an LF-constraint to account for this. I show that these restrictions are identical to constraints on intervention in wh-questions widely discussed under the heading of weak islands. I also show that Heim’s proposal is too restrictive: existential quantifiers can intervene. Both of these facts follow from the algebraic semantic theory of weak islands in Szabolcsi & Zwarts [25], which assigns different algebraic structures to amounts and counting expressions. This theory also makes novel predictions about the interaction of degree operators with conjunction and disjunction, which I show to be correct. Issues involving modal interveners [9], interval semantics for degrees [23,1], and density [4] are also considered.