Abstract
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.
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References
Ariel Mira. (2004) Most. Language 80: 658–706
Barwise, Jon, Robin Cooper. (1981) Generalized quantifiers and natural language. Linguistics and Philosophy 4: 159–219
Bresnan, Joan. (1973) Syntax of the comparative clause construction in English. Linguistic Inquiry 4(3): 275–344
Farkas, Donka, Katalin Kiss. E. (2000) On the comparative and absolute readings of superlatives. Natural Language and Linguistic Theory 18: 417–455
Fox, Danny. 2006. Free choice and a theory of scalar implicature. MIT.
Hackl Fox, Danny, Martin Hackl. (2006) On the universal density of measurement. Linguistics and Philosophy 29: 537–586
Geurts, Bart, Rick Nouwen. (2005) “At least” et al.: the semantics of scalar modifiers. Language 83: 533–559
Hackl, Martin. 2000. Comparative quantifiers. PhD dissertation, MIT.
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.
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.
Ionin, Tania, Matushansky. Ora (2006) The composition of complex cardinals. Journal of Semantics 23(4): 315–360
Keenan, Edward. (2003) The definiteness effect: Semantics or pragmatics?. Natural Language Semantics 11(2): 187–216
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.
Kennedy, Chris. (1999) Projecting the adjective: The syntax and semantics of gradability and comparison. Garland Press, New York
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.
Krifka, Manfr (1996) Parametrized sum individuals for plural reference and partitive quantification. Linguistics and Philosophy 19(6): 555–598
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.
Landman, Fred (2004) Indefinites and the type of sets. Blackwell, Oxford
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 Gruyter
Mostowski, Andrzej. (1957) On a generalization of quantifiers. Fundamenta Mathematicae 44: 12–36
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.
Papafragou, Anna, and Naomi Schwarz. 2006. Most wanted. Language Acquisition 13 (Special issue: On the acquisition of quantification): 207–251.
Sharvit, Yael, Penka Stateva. (2002) Superlative expressions, context, and focus. Linguistics and Philosophy 25: 453–505
Stateva, Penka. 2005. Presuppositions in superlatives. GLOW abstract.
Szabolcsi, Anna. 1986. Comparative superlatives. In Papers in theoretical linguistics, ed. Naoki Fukui, Tova Rapoport, and Elizabeth Sagey, 245–265. Cambridge, Mass: MITWPL 8.
Szabolcsi, A. 1997. Strategies for scope taking. In Ways of scope taking, ed. Anna Szabolcsi, 109–155. Dordrecht: Kluwer.
van Benthem, Johan. (1986) Essays in logical semantics. Reidel, Dordrecht
von Stechow, Arnim. (1984) Comparing semantic theories of comparison. Journal of Semantics 3: 1–77
Yabushita, Katsuhiko. 1989. The semantics of plurality quantification: the proportion problem is a pseudo-problem. In Proceedings of ESCOL ’89, 301–312.
Yabushita, Katsuhiko. 1998: The unified semantics of most. In Proceedings of WCCFL 18, 320–334.
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Hackl, M. On the grammar and processing of proportional quantifiers: most versus more than half . Nat Lang Semantics 17, 63–98 (2009). https://doi.org/10.1007/s11050-008-9039-x
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DOI: https://doi.org/10.1007/s11050-008-9039-x