* Generalized quantifiers are a special case of operating on continuations. [[!wikipedia Richard_Montague]] analyzed all NPs, including, e.g., proper names, as sets of properties.
This gives names and quantificational NPs the same semantic type, which explain why we can coordinate them (*John and everyone*, *Mary or some graduate student*). So instead of thinking of a name as refering to an individual, which then serves as the argument to a verb phrase, in the Generalized Quantifier conception, the name denotes a higher-order function that takes the verb phrase (its continuation) as an argument. Montague only continuized
one syntactic category (NPs), but a more systematic approach would continuize uniformly throughout the grammar.
* Generalized quantifiers are a special case of operating on continuations. [[!wikipedia Richard_Montague]] analyzed all NPs, including, e.g., proper names, as sets of properties.
This gives names and quantificational NPs the same semantic type, which explain why we can coordinate them (*John and everyone*, *Mary or some graduate student*). So instead of thinking of a name as refering to an individual, which then serves as the argument to a verb phrase, in the Generalized Quantifier conception, the name denotes a higher-order function that takes the verb phrase (its continuation) as an argument. Montague only continuized
one syntactic category (NPs), but a more systematic approach would continuize uniformly throughout the grammar.