Approximation and the coercion of gradable predicates

The modifier approximately shows a surprising pattern of distribution when combined with non-numeral items, such as scalarly-coerced nouns like lasagna in (2). (1) John read approximately five books. (2) a. ??John served approximately lasagna. b. What John served was approximately lasagna. I propose a explanation in terms of semantic types such that approximately+NP is only licit in copular-type constructions. This pattern does not carry over to prepositional modifiers (e.g. about), and I propose that the difference lies in their ability to coerce scalar predicates out of their complements. (3) What John served was ??about/??around lasagna.