Introductions such as the one from SEP state that Montague semantics is a higher-order logic. I understand that Montague makes heavy use of higher-order functions, but does he ever use higher-order quantifiers?
In all the examples I have seen, the interpretation of a grammatical sentence is always a closed first-order logic formula. Am I mistaken thinking that Montague is in fact higher-order computation of first-order modal logic?
