Collective quantification and the homogeneity constraint

Carmen Dobrovie-Sorin

Abstract


The main theoretical claim of the paper is that a slightly revised version of the analysis of mass quantifiers proposed in Roeper 1983, Lønning 1987 and Higginbotham 1994 extends to collective quantifiers: such quantifiers denote relations between sums of entities (type e), rather than relations between sets of sums (type <e,t>). Against this background I will explain a puzzle observed by Dowty (1986) for all and generalized to all quantifiers by Winter 2002: plural quantification is not allowed with all the predicates that are traditionally classified as ”collective”. The Homogeneity Constraint – as well as the weaker requirement of divisiveness - will be shown to be too strong (for both collective and mass quantifiers). What is required is that the nominalization of the nuclear-scope predicate denotes a maximal sum (rather than a group). Divisiveness is a sufficient, but not a necessary condition for this to happen. Non-divisive predicates such as form a circle, which denote sets of ‘extensional’ groups are allowed, because extensional groups are equivalent to the maximal sum of their members. It is only intensional group predicates that block collective Qs.

Keywords: collective quantification, mass quantification, homogeneous, cumulative, divisive, groups, sums, maximality operator, plural logic


Full Text:

PDF

References


References

Boolos, George. 1984. To be is to be a value of a variable (or to be some values of some variables). Journal of Philosophy, 81: 430–50.

Boolos, George. 1985. Nominalist Platonism. Philosophical Review, 94: 327–44.

Bunt, Harry C. 1985. Mass terms and model-theoretic semantics. Cambridge, UK: Cambridge University Press.

Champollion, Lucas. 2010. Parts of a whole: Distributivity as a bridge between aspect and measurement, PhD, Penn.

Chierchia, Gennaro, 1998. Reference to kinds across language. Natural Language Semantics 6(4), 339-405.

Crnič, Luka. 2009. On the (non-) cumulativity of cumulative quantifiers. In Martin Prinzhorn, Viola Schmitt and Sarah Zobel (eds.), Sinn und Bedeutung (SuB) 14, 117-133.

Dobrovie-Sorin, Carmen. 2012. Generic plural and mass indefinites. In Alda Mari, Claire Beyssade and Fabio del Prete (eds.), Genericity, 93-115. Oxford: Oxford University Press.

Dobrovie-Sorin, Carmen. 2013. Most: the view from mass. In Maria Aloni, Michael Franke, Floris Roelofsen (eds.), Amsterdam Colloquium (AC) 19, 99-107.

Dowty, David. 1986. A note on collective predicates, distributive predicates, and all. In Eastern States Conference on Linguistics 3 (ESCOL 86), 97-115. Columbus: the Ohio State University.

Gillon, Brendan. 1992. Towards a common semantics for english count and mass nouns. Linguistics and Philosophy, 15(6): 597–639.

Groenendijk, Jeroen, Theo Janssen and Martin Stokhof (eds). 1984. Truth, interpretation, information. Dordrecht, Netherlands: Foris.

Hackl, Martin. 2002. The ingredients of essentially plural predicates. In North East Linguistic Society (NELS) 32, 171-182.

Hackl, Martin. 2009. On the grammar and processing of proportional quantifiers: Most versus more than half. Natural Language Semantics 17(1): 63-98.

Higginbotham, James. 1994. Mass and count quantifiers. Linguistics and Philosophy 17: 447­480.

Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Bäuerle, Reiner, Schwarze, Christoph, and von Stechow, Arnim (eds), Meaning, use and interpretation of language, 303–323. Berlin, Germany: de Gruyter.

Landman, Fred. 1989. Groups, I. Linguistics and philosophy, 12(5), 559-605.

Landman, Fred. 2000. Events and Plurality, Kluwer, Dordrecht.

Lønning, Jon Tore. 1987. Mass terms and quantification. Linguistics and Philosophy 10.1: 1­52.

Lønning, Jon Tore 1997. Plurals and collectivity. In Johan van Benthem and Alice ter Meulen (eds.), Handbook of logic and language, volume 3, 1009–1053. Elsevier, Amsterdam, Netherlands.

Matthewson, Lisa. 2001. Quantification and the nature of crosslinguistic variation. Natural Language Semantics, 9(2): 145-189.

Moltmann, Friederike. 1997. Parts and Wholes in Semantics. Oxford: Oxford University Press.

Nicolas, David. 2008. Mass nouns and plural logic. Linguistics and Philosophy 31(2) : 211-244.

Quine, Willard Van Orman. 1960, Word and Object, Cambridge: MIT Press.

Rayo, Agustín. 2002. Word and Objects. Noûs, 36: 436–64.

Roeper, Peter. 1983. Semantics for mass terms with quantifiers, Noûs,17: 251­265.

Simons, Peter. 1987. Parts. A Study in Ontology. Clarendon, Oxford.

Solt, Stephanie. 2011. How many Most’s. In Reich, Ingo et al. (eds.), Sinn und Bedeutung, 15, 565-579. Universaar – Saarland University Press: Saarbrücken, Germany.

Scha, Remko. 1981. Distributive, collective and cumulative quantification. In: Groenendijk, Jeroen, Janssen, Theo, and Stokhof, Martin (eds), Formal methods in the study of language. Amsterdam, Netherlands: Mathematical Center Tracts. Reprinted in Groenendijk et al. (1984).

Schwarzschild, Roger. 1996. Pluralities. Dordrecht, Netherlands: Kluwer.

Szabolcsi, Anna & Frans Zwarts. 1993. Weak islands and an algebraic semantics for scope taking. Natural language semantics, 1(3), 235-284.

van der Does, Jaap. (1993). Sums and quantifiers. Linguistics and Philosophy, 16:509–550.

Winter, Yoad. 2002. Atoms and sets: a characterization of semantic number. Linguistic Inquiry 33: 493-505.




DOI: http://dx.doi.org/10.3765/salt.v24i0.2428