Abstract
This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of the boys owned three cars, though the same sentence withouttogether could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers likeeach and non-distributive or collective readings that arise withouttogether.
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References
Bennett, Michael: 1974,Some Extensions of a Montague Fragment of English, PhD dissertation, University of California at Los Angeles.
Cooper, Robin: 1983,Quantification and Syntactic Theory, Reidel, Dordrecht.
Dougherty, R. C.: 1970, ‘A Grammar of Coordinate Conjoined Structures I’,Language 46(4), 850–898.
Dowty, David and Belinda Brodie: 1984, ‘The Semantics of Floated Quantifiers in a Transformationless Grammar’, in M. Cobler, S. MacKaye and M. T. Wescoat (eds.),Proceedings of WCCFL III, Stanford Linguistics Association, Stanford University, pp. 75–90.
Gillon, Brendan: 1987, ‘The Readings of Plural Noun Phrases in English’,Linguistics and Philosophy 10, 199–219.
Higginbotham, James: 1981, ‘Reciprocal Interpretation’,Journal of Linguistic Research 1(3), 97–117.
Hoeksema, Jack: 1983, ‘Plurality and Conjunction’, in A. ter Meulen (ed.),Studies in Modeltheoretic Semantics (GRASS 1), Foris, Dordrecht, pp. 63–83.
Landman, Fred: 1989, ‘Groups I’,Linguistics and Philosophy 12(5), 559–605.
Lasersohn, Peter: 1988,A Semantics for Groups and Events, PhD dissertation, Ohio State University, Columbus.
Lasersohn, Peter: 1989, ‘On the Readings of Plural Noun Phrases’,Linguistic Inquiry 20(1), 130–134.
Lasersohn, Peter: 1990, ‘Group Action and Spatio-Temporal Proximity’,Linguistics and Philosophy 13(2), 179–206.
Link, Godehard: 1983, ‘The Logical Analysis of Plurals and Mass Terms: A Lattice Theoretical Approach’, in R. Bäuerle, Ch. Schwarze, and A. von Stechow (eds.),Meaning, Use, and the Interpretation of Language, de Gruyter, Berlin, pp. 302–323.
Link, Godehard: 1987, ‘Generalized Quantifiers and Plurals’, in P. Gärdenfors (ed.),Generalized Quantifiers: Linguistic and Logical Approaches (Studies in Linguistics and Philosophy 31), Reidel, Dordrecht, pp. 151–180.
Loebner, Sebastian: 1987, ‘The Conceptual Nature of Natural Language Quantification’, in I. Ruzsa and A. Szabolcsi (eds.),Proceedings of the '87 Debrecen Symposium on Logic and Language, Akademiai Kaido, Budapest.
Moltmann, Friederike: 1990, ‘Semantic Selection and the Determination of Part Structures in the Use of Natural Language’, in M. Stokhof and L. Torenvliet (eds.),Proceedings of the Seventh Amsterdam Colloquium, ITLI, University of Amsterdam, pp. 353–378.
Moltmann, Friederike: 1992, ‘Reciprocals andSame/Different: Towards a Semantic Analysis’,Linguistics and Philosophy 15(4), pp. 411–462.
Quirk, R., S. Greenbaum, G. Leech, and J. Svartik: 1985,A Comprehensive Grammar of the English Language, Longman, New York.
Roberts, Craige: 1987,Modal Subordination, Anaphora and Distributivity, PhD dissertation, University of Massachusetts, Amherst.
Scha, Remko J. H.: 1984, ‘Distributive, Collective and Cumulative Quantification’, in J. Groenendijk et al. (eds.),Truth, Interpretation, and Information (GRASS 2), Foris, Dordrecht, pp. 131–158.
Schein, Barry: 1986,Event Logic and the Interpretation of Plurals, PhD dissertation, MIT.
Schwarzschild, Roger: 1991, ‘Together as Non-Distributivity Marker’, in P. Dekker and M. Stokhof (eds.),Proceedings of the Eighth Amsterdam Colloquium, ITLI, University of Amsterdam.
Schwarzschild, Roger: 1992, ‘Types of Plural Individuals’,Linguistics and Philosophy 15(6), 641–675.
van Eijck, Jan: 1983, ‘Discourse Representation Theory and Plurality’, in A. ter Meulen (ed.),Studies in Modeltheoretic Semantics (GRASS 1), Foris, Dordrecht, pp. 85–106.
Verkuyl, Henk and Jaap van der Does: 1991, ‘The Semantics of Plural Noun Phrases’, ITLI Prepublication LP-91-07, University of Amsterdam.
Westerståhl, Dag: 1985, ‘Determiners and Context Sets’, in J. F. van Benthem and A. ter Meulen (eds.),Generalized Quantifiers in Natural Language (GRASS 4), Foris, Dordrecht, pp. 45–72.
Wilkinson, Karina: to appear, ‘Towards a Unified Semantics ofEven’, in S. Moore and A. Z. Wyner (eds.),Proceedings of SALT III, Cornell Working Papers, Cornell University, Ithaca.
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This paper is in large measure a response to the work of Peter Lasersohn. I am indebted to him both for his work on plurals and for discussion of this topic. I have also gotten help on this project from: Jaap van der Does, Regine Eckhardt, Irene Heim, Angelika Kratzer, Fred Landman, Yutaka Ohno, Barbara Partee, Barry Schein, Karina Wilkinson, Ede Zimmermann and Alessandro Zucchi. Finally, I am grateful for having had the opportunity to present this work at the Eighth Amsterdam Colloquium.
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Schwarzschild, R. Plurals, presuppositions and the sources of distributivity. Nat Lang Seman 2, 201–248 (1993). https://doi.org/10.1007/BF01256743
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DOI: https://doi.org/10.1007/BF01256743