Cardinal nominals as collective predicates
DOI:
https://doi.org/10.24201/clecm.v8i0.137Keywords:
semantics, plural, numerals, distributivity, collectivityAbstract
I propose a novel semantic mechanism for explaining the fact that when modified cardinal terms like less than ten months or between two and five times are combined with distributive predicates, they impose an upper bound, but not when they are combined with non-distributive predicates. My explanation is based on the simple fact that distributive and non-distributive predicates have different domains of denotation and that, therefore, when we mix predicates of both kinds (for example when a cardinal predicate –which is non-distributive– pronominally modifies a distributive predicate), some kind of domain adjustment is required. To model this adjustment, I introduce a silent, totalizing operator that assigns to any distributive plural property P the collective plural property of being all the Ps.
Downloads
References
Alxatib, Sam & Ivlieva, Natasha. 2018. Van Benthem’s problem, exhaustification, and distributivity. Proceedings of Sinn und Bedeutung 21(1). 1–18. https://doi.org/10.18148/sub/2018.v21i1.121.
Barwise, Jon & Cooper, Robin. 1981. Generalized quantifiers and natural language. Linguistics and Philosophy 4(2). 159–219. http://www.jstor.org/stable/25001052.
Ben-Avi, Gilad & Winter, Yoad. 2003. Monotonicity and collective quantification. Journal of Logic, Language, and Information 12(2). 127–151. https://www.jstor.org/stable/40180323.
Bosque, Ignacio. 1999. Adjetivo y participio. En Ignacio Bosque & Violeta Demonte (eds.), Gramática Descriptiva de la Lengua Española. 217–310. Madrid: Espasa Calpe.
Brisson, Catherine. 2003. Plurals, all, and the nonuniformity of collective predication. Linguistics and Philosophy 26. 129–184.
Buccola, Brian & Spector, Benjamin. 2016. Modified numerals and maximality. Linguistics and Philosophy 39. 151–199.
Buccola, Brian. 2015. Variable monotonicity and less than: when Van Benthem’s problem is not a problem. North East Linguistic Society (NELS) 45. 125–134.
Carlson, Greg N. 1977. A unified analysis of the English bare plural. Linguistics and Philosophy 1. 413–457.
Chatzikyriakidis, Stergios & Luo, Zhaohui. 2017. On the interpretation of common nouns: types versus predicates. Studies in Linguistics and Philosophy 98. 43–70. doi: https://doi.org/10.1007/978-3-319-50422-3_3
Church, Alonzo. 1940. A formulation of the simple theory of types. Journal of Symbolic Logic 5(2). 56–68. https://doi.org/10.2307/2266170
de Swart, Henriëtte. 2001. Weak readings of indefinites: type shifting and closure. The Linguistic Review 18. 69–96.
Dowty, David. 1987. A note on collective predicates, distributive predicates, and all. En Marshall, Fred, Miller, Ann & Zhang, Zhengsheng (eds.), Eastern States Conference on Linguistics (ESCOL) 3. 97–116. Columbus: The Ohio State University.
Etxeberria, Urtzi & Giannakidou, Anastasia. 2017. A unified analysis of Spanish algún/algunos: anti-specificity, plurality, and NP-anaphora. (Manuscrito inédito).
Farkas, Donka 1981. Quantifier scope and syntactic islands. En R. Hendrik, C. Masek, & Mary Frances (eds.), Papers from the Seventh Regional Meeting, Chicago Linguistic Society. Chicago; Chicago University Press. 59–66.
Fernández Díez, Gustavo. 2018. El análisis lógico de la predicación colectiva. Crítica: Revista Hispanoamericana de Filosofía 38(114). 21–44. doi: https://doi.org/10.22201/iifs.18704905e.2006.487.
Gamut, L.T.F. 1993. Logic, language and meaning, vol. 2: intensional Logic and Logical Grammar. Chicago: The University of Chicago Press.
Geurts, Bart. 2006. Take ‘five’: the meaning and use of a number word. En Vogeleer, Svetlana & Tasmowski, Liliane (eds.), Non-definiteness and plurality. 311–330. Ámsterdam: John Benjamins. https://doi.org/10.1075/la.95.16geu.
Gutiérrez-Rexach, Javier. 2001. The semantics of Spanish plural existential determiners and the dynamics of judgment types. Probus 13(1). 113–154. doi: https://doi.org/10.1515/prbs.13.1.113.
Hackl, Martin. 2002. The ingredients of essentially plural predicates. Proceedings of NELS 32(1). 171–182.
Hackl, Martin. 2009. On the grammar and processing of proportional quantifiers: most versus more than half. Natural Language Semantics 17. 63–98.
Heim, Irene. 2000. Degree operators and scope. En Jackson, Brendan & Matthews, Tanya (eds.), Proceedings of Semantics and Linguistic Theory X. 40–64. Ithaca: Cornell University. doi: https://doi.org/10.3765/salt.v10i0.2722.
Herburger, Elena. 1997. Focus and weak noun phrases. Natural Language Semantics 5. 53–78.
Hoeksema, Jack. 1983. Plurality and conjunction. En Ter Meulen, Alice (ed.), Studies in Modeltheoretic Semantics. 1–63. Dordrecht: Foris Publications.
Jiménez Juliá, Tomás. 2007. Aspectos gramaticales de la frase nominal en español. Lugo: Servizo de Publicacións e Intercambio Científico da Universidade de Santiago de Compostela.
Kennedy, Christopher. 2015. A ‘de-Fregean’ semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics 8. 1–44. http://dx.doi.org/10.3765/sp.8.10.
Knowles, Robert. 2015. What ‘the number of planets is eight’ means. Philosophical Studies 172. 2757–2775. https://doi.org/10.1007/s11098-015-0443-z.
Koenig, Jean-Pierre. 1991. Scalar predicates and negation: punctual semantics and interval interpretations. Proceedings of the Parasession on Negation of the 27th Meeting of the Chicago Linguistics Society. 130–144.
Krifka, Manfred. 1990. Boolean and non-boolean ‘and’. En Kálmán, László & Polos, László (eds.), Papers from the Second Symposium on Logic and Language, 161–188. Budapest: Akadémiai Kiadó.
Landman, Fred. 2004. Indefinites and the type of sets. Oxford: Blackwell. doi: https://doi.org/10.1002/9780470759318.
Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. En Bäuerle, Rainer; Schwarze, Christoph, & von Stechow; Arnim (eds.), Meaning, use, and interpretation of language, 302–323. Berlín: de Gruyter. doi: https://doi.org/10.1515/9783110852820.
Martí, Luisa. 2008. The semantics of plural indefinite noun phrases in Spanish and Portuguese. Natural Language Semantics 16. 1–37. doi: https://doi.org/10.1007/s11050-007-9023-x.
McNally, Louise. 1998. Existential sentences without existential quantification. Linguistics and Philosophy 21. 353–392.
Montague, Richard. 1973. The proper treatment of quantification in ordinary English. En Hintikka J.; Moravcsik J. & Suppes P. (eds.), Approaches to natural languages. 221–242. Holanda: Springer.
Montague, Richard. 1974. Formal philosophy: selected papers. Connecticut: Yale University Press.
Partee, Barbara H. 1987. Noun phrase interpretation and type-shifting principles. En Jeroen Groenendijk. Jeroen; de Jongh, Dick & Stokhof, Martin (eds.), Studies in discourse representation theory and the theory of generalized quantifiers, 115–41. Dordrecht: Foris.
Peters, Stanley & Dag Westerståhl. 2006. Quantifiers in language and logic. Oxford: Oxford University Press.
Van Benthem, Johan. 1986. Essays in logical semantics. Dordrecht: D. Reidel.
Verkuyl, Henk J. 1981. Numerals and quantifiers in X-Bar syntax and their semantic interpretation. En Groenendijk, Jeroen; Janssen, Theo & Stokhof; Martin (eds.), Formal methods in the study of language, 567–599. Ámsterdam: Mathematical Centre Tracts.
Winter, Yoad. 2001. Plural predication and the strongest meaning hypothesis. Journal of Semantics 18(4). 333–365. https://doi.org/10.1093/jos/18.4.333.
Winter, Yoad & Remko Scha. 2015. Plurals. Handbook of Contemporary Semantics, 2a. ed. En Lappin, Shalom & Fox, Chris (eds.), 77–113. Hoboken: John Wiley & Sons.
Zweig, Eytan. 2005. Nouns and adjectives in numeral NPs. En Bateman, Leah & Ussery, Cherlon (eds.), NELS 35: Proceedings of the thirty-fifth annual meeting of the North East Linguistic Society, 663–676. Amherst: University of Massachusetts.
Published
How to Cite
-
Abstract725
-
PDF (Español)281
-
XML (Español)11
-
EPUB (Español)88
-
Kindle (Español)88
-
MP3 (Español)27
Issue
Section
License
Copyright (c) 2021 Axel Arturo Barcelo Aspeitia

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright of their work and are free to disseminate it, make copies for any use, and/or deposit in any repository or archive of their choice, but they grant Cuadernos de Lingüística de El Colegio de México the right to publish the work for the first time. Authors agree to acknowledge Cuadernos de Lingüística de El Colegio de México as the site of original publication of their article / note / review through proper citation.
Articles appearing in Cuadernos de Lingüística de El Colegio de México are made available to readers under a Attribution-NonCommercial-NoDerivatives 4.0 International.