A Formal Semantics for Plural Quantification, Intersentential Binding and Anaphoric Pronouns as Rigid Designators

Abstract

It is well known that certain kinds of plural quantification as well as intersentential pronominal cross-reference in natural language cannot be formalizable by the devices of standard first-order logic, i.e., by a formal language containing variables x,y,z,..., ranging over individuals, the quantifiers V and 3, the truth functional connectives and the equal sign. The most famous example of the former is perhaps the Geach-Kaplan sentence, (1) Some critics admire only one another. An example of the latter is (2) Some woman will land on Mars in the year 2010. (3) She will be an American. (2) and (3) cannot be represented as, (2') ∃x(x is a woman & x lands on Mars in the year 2010) (3') x is an American (2') and (3'), respectively, since the variable in (3'), representing the anaphoric pronoun 'she', is free. But for it to refer to the woman who lands on Mars in the year 2010, it should be bound by the quantifier ∃x' in (2'). In this paper, we shall present a formal language and a model-theoretic semantics (hereafter, a formal semantical system) for such plural quantification and for anaphoric expressions requiring intersentential.binding.