Plural Quantifications and Generalized Quantifiers

This paper discusses two important results on the expressive limitations of elementary languages that David Kaplan established a few decades ago, and clarifies how they relate to the expressive power of plural constructions of natural languages. Kaplan proved that such plural quantifications as the following cannot be paraphrased into elementary languages: Most things are funny. (1) Some critics admire only one another. (2) The proof that (1) cannot be paraphrased into elementary languages is often taken to support the generalized quantifier approach to natural languages, and the proof that (2) cannot be so paraphrased is usually taken to mean that (2) is a second-order sentence. The paper presents an alternative interpretation: Kaplan’s results provide important steps toward clarifying the expressive power of plural constructions of natural languages vis-à-vis their singular cousins. In doing so, the paper compares (regimented) plural languages with generalized quantifier languages, and plural logic with second-order logic.