Linguistics and Philosophy

, Volume 31, Issue 2, pp 211–244 | Cite as

Mass nouns and plural logic

  • David Nicolas
Research Article


A dilemma put forward by Schein (1993, Plurals and events. Cambridge MIT Press) and Rayo (2002, Noûs, 36, 436–464) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but plural logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets when characterizing their semantics, we arrive at a Russellian paradox. And if we use predicate logic and mereological sums, the semantics turns out to be too weak. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: The silverware that is on the table comes from Italy. We show that this account provides a satisfactory semantics for a wide range of sentences.


Mass nouns Singular terms Plurals Plural logic Mereology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boolos G. (1984) To be is to be a value of a variable (or to be some values of some variables). Journal of Philosophy 81: 430–449CrossRefGoogle Scholar
  2. Bunt H.C. (1985) Mass terms and model-theoretic semantics. Cambridge University Press, CambridgeGoogle Scholar
  3. Burge T. (1972) Truth and mass terms. Journal of Philosophy 69: 263–282CrossRefGoogle Scholar
  4. Cartwright H. (1965) Heraclitus and the bath water. Philosophical Review 74: 466–485CrossRefGoogle Scholar
  5. Casati R., Varzi A. (1999) Parts and places. The structures of spatial representation. MIT Press, CambridgeGoogle Scholar
  6. Chierchia G. (1998) Plurality of mass nouns and the notion of “semantic parameter”. In: Rothstein S. (eds) Events and grammar. Kluwer Academic Publishers, Dordrecht, pp 53–103Google Scholar
  7. Corbett G. (2000) Number. Cambridge University Press, CambridgeGoogle Scholar
  8. Corblin F. (1987) Indéfini, défini et démonstratif. Droz, GenevaGoogle Scholar
  9. Farkas, D. & de Swart, H. (2007). Inclusive and exclusive plurals reconciled. In M. Aloni, P. Dekker, & F. Roelofsen (Eds.), Proceedings of the 16th Amsterdam Colloquium. Palteam.Google Scholar
  10. Gillon B.S. et al (1990) Bare plurals as plural indefinite noun phrases. In: Kyburg H.E. Jr (Eds) Knowledge representation and defeasible reasoning. Kluwer Academic Publishers, Dordrecht, pp 119–166Google Scholar
  11. Gillon B.S. (1992) Towards a common semantics for English count and mass nouns. Linguistics and Philosophy 15: 597–639CrossRefGoogle Scholar
  12. Gillon B.S. (1996) Collectivity and distributivity internal to English noun phrases. Language Sciences 18: 443–468CrossRefGoogle Scholar
  13. Glanzberg M. (2004) Quantification and realism. Philosophy and Phenomenological Research 69: 541–572CrossRefGoogle Scholar
  14. Hawley K. (2001) How things persist. Clarendon Press, OxfordGoogle Scholar
  15. Kaplan D. (1989) Demonstratives. In: Almog J., Perry J., Wettstein H. (Eds) Themes from Kaplan. Oxford University Press, New York, pp 481–563Google Scholar
  16. Krifka M. (1991) Massennomina. In: von Stechow A., Wunderlich D. (eds). Semantik, ein internationales Handbuch. de Gruyter, Berlin, pp 399–417Google Scholar
  17. Krifka M., Pelletier F.J., Carlson G.N., Chierchia G., Link G., ter Meulen A. (1995) Introduction to genericity. In: Carlson G.N., Pelletier F.J.(eds) The generic book. Chicago University Press, Chicago, pp 1–124Google Scholar
  18. La Palme-Reyes M., Macnamara J., Reyes G.E. (1994) Reference, kinds and predicates. In: Macnamara J., Reyes G.E. (Eds) The logical foundations of cognition. Oxford University Press, Oxford, pp 91–145Google Scholar
  19. La Palme-Reyes M., Macnamara J., Reyes G.E., Zolfaghari H. (1999) Count nouns, mass nouns, and their transformations: A unified category-theoretic semantics. In: Jackendoff R., Bloom P., Wynn K. (Eds) Language, logic and concepts. MIT Press, Cambridge, pp 427–452Google Scholar
  20. Laycock H. (1972) Some questions of ontology. Philosophical Review 81: 3–42CrossRefGoogle Scholar
  21. Lewis D. (1991) Parts of classes. Oxford University Press, OxfordGoogle Scholar
  22. Link G. (1983) The logical analysis of plurals and mass terms: A lattice-theoretical approach. In: Bauerle R., Schwartze C., von Stechow A. (Eds) Meaning, use and interpretation of language. Mouton de Gruyter, Berlin, pp 302–323Google Scholar
  23. Linnebo, Ø (2008). Plural quantification. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Spring 2008 edition). Retrieved from
  24. Linnebo Ø, Nicolas D. (2008) Superplurals in English. Analysis 68(3): 186–197CrossRefGoogle Scholar
  25. McKay T. (2006) Plural predication. Oxford University Press, OxfordGoogle Scholar
  26. Nicolas, D. (1997, unpublished). Count nouns, mass nouns and their acquisition. Retrieved from
  27. Nicolas, D. (2002a). La distinction entre noms massifs et noms comptables. Aspects linguistiques et conceptuels. Louvain: ÉEditions Peeters.Google Scholar
  28. Nicolas, D. (2002b, unpublished). Conversions of count nouns into mass nouns in French: The roles of semantic and pragmatic factors in their interpretations. Retrieved from
  29. Oliver A., Smiley T. (2001) Strategies for a logic of plurals. Philosophical Quarterly 51: 289–306CrossRefGoogle Scholar
  30. Oliver A., Smiley T (2006) A modest logic of plurals. Journal of Philosophical Logic 35: 317–348CrossRefGoogle Scholar
  31. Parsons T. (1970) An analysis of mass and amount terms. Foundations of Language 6: 363–388Google Scholar
  32. Pelletier J.F., Asher N. (1997) Generics and defaults. In: van Benthem J., terMeulen A. (Eds) Handbook of logic and language. Elsevier Science, Amsterdam, pp 1125–1177CrossRefGoogle Scholar
  33. Pelletier, J. F., & Schubert, L. (2003). Mass expressions. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (2nd ed., Vol. 10, pp. 249–336). Dordrecht: Kluwer Academic Publishers.Google Scholar
  34. Quine W.V.O. (1960) Word and object. MIT Press, CambridgeGoogle Scholar
  35. Rayo A. (2002) Word and objects. Noûs 36: 436–464Google Scholar
  36. Rayo A. (2006) Beyond plurals. In: Rayo A., Uzquiano G.(eds) Absolute generality. Oxford University Press, Oxford, pp 220–254Google Scholar
  37. Rayo, A., Uzquiano , G. (Eds) (2006a) Absolute generality. Oxford University Press, OxfordGoogle Scholar
  38. Rayo A., Uzquiano G. (2006b) Introduction. In: Rayo A., Uzquiano G. (Eds) Absolute generality. Oxford University Press, Oxford, pp 1–19Google Scholar
  39. Roeper P. (1983) Semantics for mass terms with quantifiers. Noûs 17: 251–265CrossRefGoogle Scholar
  40. Sauerland U., Andersen J., Yatsushiro K. (2005) The plural is semantically unmarked. In: Kepser S., Reis M. (Eds) Linguistic evidence. Mouton de Gruyter, BerlinGoogle Scholar
  41. Schein B. (1993) Plurals and events. MIT Press, CambridgeGoogle Scholar
  42. Schein B. (2006) Plurals. In: Lepore E., Smith B. (Eds) Handbook of philosophy of language. Oxford University Press, Oxford, pp 716–767Google Scholar
  43. Schwarzschild R. (1996) Pluralities. Kluwer Academic Publishers, DordrechtGoogle Scholar
  44. Simons P. (1982) Plural reference and set theory. In: Smith B. (Eds) Parts and moments: Studies in logic and formal ontology. Philosophia Verlag, Munich, pp 113–159Google Scholar
  45. Simons P. (1987) Parts. A study in ontology. Oxford University Press, OxfordGoogle Scholar
  46. Simons P. (1997) Bolzano on collections. Grazer Philosophische Studien 53: 87–108Google Scholar
  47. Strawson P.F. (1950) On referring. Mind 59: 320–344CrossRefGoogle Scholar
  48. Strawson P.F. (1959) Individuals. An essay in descriptive metaphysics. Methuen, LondonGoogle Scholar
  49. Uzquiano G. (2006) The price of universality. Philosophical Studies 129: 137–169CrossRefGoogle Scholar
  50. van Inwagen P. (1990) Material beings. Cornell University Press, IthacaGoogle Scholar
  51. van Inwagen P. (1994) Composition as identity. Philosophical Perspectives 8: 207–220CrossRefGoogle Scholar
  52. Varzi A. (2000) Mereological commitments. Dialectica 54: 283–305Google Scholar
  53. Varzi, A. (2006). Mereology. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2006 edition). Retrieved from
  54. Williamson T. (2003) Everything. Philosophical Perspectives 17: 415–465CrossRefGoogle Scholar
  55. Yi B.-Y. (1999) Is mereology ontologically innocent?. Philosophical Studies 93: 141–160CrossRefGoogle Scholar
  56. Yi B.-Y. (2005) The logic and meaning of plurals. Part I. Journal of Philosophical Logic 34: 459–506CrossRefGoogle Scholar
  57. Yi B.-Y. (2006) The logic and meaning of plurals. Part II. Journal of Philosophical Logic 35: 239–288CrossRefGoogle Scholar
  58. Zimmerman D.W. (1995) Theories of masses and problems of constitution. Philosophical Review 104: 53–110CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institut Jean Nicod (EHESS-ENS-CNRS), ENSParisFrance

Personalised recommendations