Plural Quantifications and Generalized Quantifiers
This paper discusses two important results about expressive limitations of elementary languages due to David Kaplan, 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 and contrasts (regimented) plural languages with generalized quantifier languages, and plural logic with second-order logic.
Keywordssemantics natural language plural construction plural logic Geach-Kaplan sentence generalized quantifier theory Rescher quantifier plural quantifier the semantics of ‘most’
Unable to display preview. Download preview PDF.
- Kaplan, D.: Rescher’s plurality-quantification (Abstract). Journal of Symbolic Logic 31, 153–154 (1966)Google Scholar
- Kaplan, D.: Generalized plurality quantification (Abstract). Journal of Symbolic Logic 31, 154–155 (1966)Google Scholar
- Quine, W.V.: Methods of Logic, 3rd edn. London, RKP (1974)Google Scholar
- Rescher, N.: Plurality quantification revisited. Philosophical Inquiry 26, 1–6 (2004)Google Scholar
- Väänänen, J.: A Short Course on Finite Model Theory. Manuscript Based on Lectures in 1993-1994 (1994), http://www.math.helsinki.fi/logic/people/jouko.vaananen/shortcourse.pdf
- Yi, B.-U.: Understanding the Many. Routledge, New York & London (2002)Google Scholar
- Yi, B.-U.: Is logic axiomatizable? unpublished manuscriptGoogle Scholar