Reflexives and non-Fregean quantifiers

Natural languages display a great variety of constructions which denote non-Freagean quantifiers that is complex quantifiers which are not iterations of simpler quantifiers. Such quantifiers have been extensively studied by Ed (Clark and Keenan (1986), Keenan (1987b), Keenan (1992)). Usually expressions denoting non-Fregean quantifiers are not lexically simple and often they are not syntactic constituents. They are sequences composed of an NP (DP) and of an expression which can be called a generalised NP (GNP). GNPs are linguistic objects that can play the role of syntactic arguments of transitive VPs. So "ordinary" NPs or DPs are GNPs. However there are genuine GNPs which differ from "ordinary" NPs in that they cannot play the role of all verbal arguments; in particular they cannot occur in subject position. For instance the reflexive pronoun himself/herself or the reciprocal each other are such genuine GNPs. A sequence NP...GNP can be considered as applying to a transitive VP to give a sentence S. In this case such sequence denotes a type 〈2〉 quantifier. If the GNP is a genuine GNP then often the sequence NP...GNP denotes a non-Fregean type 〈2〉 quantifier. In this note I present some general results concerning non-Fregean quantifiers denoted by the sequence NP...GNP in case when GNP is the reflexive pronoun or a Boolean compound of the reflexive pronoun and another expression. Thus, roughly speaking, I will show that the type 〈2〉 quantifiers involved in the interpretation of the following examples have different properties: