On the grammar and processing of proportional quantifiers: most versus more than half
Proportional quantifiers have played a central role in the development of formal semantics because they set a benchmark for the expressive power needed to describe quantification in natural language (Barwise and Cooper Linguist Philos 4:159–219, 1981). The proportional quantifier most, in particular, supplied the initial motivation for adopting Generalized Quantifier Theory (GQT) because its meaning is definable as a relation between sets of individuals, which are taken to be semantic primitives in GQT. This paper proposes an alternative analysis of most that does not treat it as a lexical item whose meaning is accessible without the help of compositional processes. Instead, proportional most is analyzed as the superlative of many (cf. Bresnan Linguist Inq 4(3):274–344, 1973). Two types of empirical evidence are presented in support of this view, both exploiting the fact that only a decompositional analysis of proportional quantifiers provides the means to generate different logical forms for seemingly equivalent statements of the form most A B and more than half of the A B.
KeywordsQuantification Generalized Quantifier Theory Superlatives Degrees Verification Psycholinguistics
Unable to display preview. Download preview PDF.
- Bresnan, Joan. (1973) Syntax of the comparative clause construction in English. Linguistic Inquiry 4(3): 275–344Google Scholar
- Fox, Danny. 2006. Free choice and a theory of scalar implicature. MIT.Google Scholar
- Hackl Fox, Danny, Martin Hackl. (2006) On the universal density of measurement. Linguistics and Philosophy 29: 537–586Google Scholar
- Hackl, Martin. 2000. Comparative quantifiers. PhD dissertation, MIT.Google Scholar
- Heim, Irene. 1985. Notes on comparatives and related matters. University of Texas at Austin. Available at http://semanticsarchive.net/Archive/zc0ZjY0M.
- Heim, Irene. 1999. Superlatives. MIT lecture notes. Available at http://semanticsarchive.net/Archive/TI1MTlhZ/Superlative.pdf.
- Heim, Irene. 2001. Degree operators and scope. In Audiatur Vox Sapientiae, ed. C. Féry and W. Sternefeld, 214–239. Berlin: Akademie-Verlag.Google Scholar
- Horn, L. 2005. The border wars: a neo-Gricean perspective. In Where semantics meets pragmatics, ed. Klaus von Heusinger and Ken Turner, 21–48. Oxford: Oxford University Press.Google Scholar
- Keenan, Edward, and Dag Westerstahl. 1997. Generalized quantifiers in linguistics and logic. In Handbook of logic and language, ed. Johann van Benthem and Alice ter Meulen, 873–893. Amsterdam: Elsevier.Google Scholar
- Kennedy, Chris. (1999) Projecting the adjective: The syntax and semantics of gradability and comparison. Garland Press, New YorkGoogle Scholar
- Krifka, Manfred. 1989. Nominal reference, temporal constitution and quantification in event semantics. In Semantic and contextual expressions, ed. Renate Bartsch, Johann van Benthem, and Peter van Emde Boas, 75–115. Dordrecht: Foris.Google Scholar
- Krifka, Manfred. 1999. At least some determiners aren't determiners. In The semantics/pragmatics interface from different points of view. (=Current research in the semantics/pragmatics interface, Vol. 1), ed. Ken Turner, 257–291. Amsterdam: Elsevier.Google Scholar
- Link, Godehard. 1983. The logical analysis of plurals and mass terms: a lattice-theoretical approach. In Meaning, use, and interpretation of language, ed. Rainer Bäuerle, Christoph Schwarze, and Arnim von Stechow, 302–323. Berlin: de GruyterGoogle Scholar
- Mostowski, Andrzej. (1957) On a generalization of quantifiers. Fundamenta Mathematicae 44: 12–36Google Scholar
- Nerbonne, John. 1994. A semantics for nominal comparatives. In Proceedings of the 9th Amsterdam Colloquium. ed. Paul Dekker and Martin Stockhof, 487–506. Amsterdam: ILLG.Google Scholar
- Papafragou, Anna, and Naomi Schwarz. 2006. Most wanted. Language Acquisition 13 (Special issue: On the acquisition of quantification): 207–251.Google Scholar
- Stateva, Penka. 2005. Presuppositions in superlatives. GLOW abstract.Google Scholar
- Szabolcsi, Anna. 1986. Comparative superlatives. In Papers in theoretical linguistics, ed. Naoki Fukui, Tova Rapoport, and Elizabeth Sagey, 245–265. Cambridge, Mass: MITWPL 8.Google Scholar
- Szabolcsi, A. 1997. Strategies for scope taking. In Ways of scope taking, ed. Anna Szabolcsi, 109–155. Dordrecht: Kluwer.Google Scholar
- van Benthem, Johan. (1986) Essays in logical semantics. Reidel, DordrechtGoogle Scholar
- Yabushita, Katsuhiko. 1989. The semantics of plurality quantification: the proportion problem is a pseudo-problem. In Proceedings of ESCOL ’89, 301–312.Google Scholar
- Yabushita, Katsuhiko. 1998: The unified semantics of most. In Proceedings of WCCFL 18, 320–334.Google Scholar