Vague Determiner Phrases and Distributive Predication

  • Heather Burnett
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7415)


The goal of this paper is to provide the formal basis for a new approach to modelling the application of vague predicates like tall and bald to plural subjects like John and Mary and the men. In other words, we are interested in developing a new logical analysis for natural language sentences like Mary is tall and The men are bald. In the past 30 years, much research has been devoted to finding the proper logical framework to model the application of non-vague predicates to pluralities (cf. [16], [21] among others). Additionally, there has been a lot of work on how to model the application of vague predicates to singular terms (cf. [8], [5] among many others). However, the question of how to apply vague predicates to plural subjects and what complexities may arise in doing so has yet to be examined. This paper is a contribution to filling this gap. In particular, I argue that extending an analysis of predicate vagueness to incorporate pluralities is not immediately straightforward; that is, I show that sentences with vague predicates and certain kinds of plural subjects give rise to additional vague effects that are not present with singular subjects. Extending previous work on both plural predication and vague language, I propose a new logical system (Plural TCS) that models these effects.


Mass Noun Distributive Predication Vague Predicate Determiner Phrase Plural Subject 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Brisson, C.: Plurals, ALL and the Non-uniformity of Collective Predication. Linguistics and Philosophy 26, 129–184 (2003)CrossRefGoogle Scholar
  2. 2.
    Burnett, H.: The Grammar of Tolerance: On Vagueness, Context-Sensitivity, and the Origin of Scale Structure. PhD Thesis. University of California, Los Angeles (2012)Google Scholar
  3. 3.
    Champollion, L.: Parts of a Whole: Distributivity as a Bridge between Aspect and Measurement. PhD Thesis, University of Pennsylvania (2011)Google Scholar
  4. 4.
    Chierchia, G.: Mass Nouns, Vagueness and Semantic Variation. Synthese 174, 99–149 (2010)CrossRefGoogle Scholar
  5. 5.
    Cobreros, P., Égré, P., Ripley, D., van Rooij, R.: Tolerant, Classical, Strict. Journal of Philosophical Logic (2011) (forthcoming)Google Scholar
  6. 6.
    Dowty, D.: Collective predicates, Distributive predicates, and all. In: Marshall, F. (ed.) Proceedings of the 3rd ESCOL, pp. 97–115. Ohio State University, Ohio (1987)Google Scholar
  7. 7.
    Fara, D.: Shifting Sands: An interest-relative theory of vagueness. Philosophical Topics 20, 45–81 (2000)Google Scholar
  8. 8.
    Fine, K.: Vagueness, Truth and Logic. Synthese 30, 265–300 (1975)zbMATHCrossRefGoogle Scholar
  9. 9.
    Hovda, P.: What is Classical Mereology? Journal of Philosophical Logic 38, 55–82 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Keenan, E., Faltz, L.: Boolean Semantics for Natural Language. Riedel, Dordrecht (1985)zbMATHGoogle Scholar
  11. 11.
    Kennedy, C.: Vagueness and Grammar: The study of relative and absolute gradable predicates. Linguistics and Philosophy 30, 1–45 (2007)CrossRefGoogle Scholar
  12. 12.
    Krifka, M.: Approximate Interpretation of Number Words: A Case for Strategic Communication. In: Bouma, G., Krämer, I., Zwarts, J. (eds.) Cognitive Foundations of Interpretation, Koninklijke Nederlandse Akademie van Wetenschapen, Amsterdam, pp. 111–126 (2007)Google Scholar
  13. 13.
    Lasersohn, P.: Pragmatic Halos. Language 75, 522–571 (1999)CrossRefGoogle Scholar
  14. 14.
    Lappin, S.: An Intensional Parametric Semantics for Vague Quantifiers. Linguistics and Philosophy 23, 599–620 (2000)CrossRefGoogle Scholar
  15. 15.
    Lewis, D.: Score-keeping in the Language Game. Journal of Philosophical Logic 8, 339–359 (1979)CrossRefGoogle Scholar
  16. 16.
    Link, G.: The Logical Analysis of Plurals and Mass Nouns. In: Bauerle, R., Schwartze, C., von Stechow, A. (eds.) Meaning, Use and the Interpretation of Language, pp. 302–322. Mouton de Gruyter, The Hague (1983)CrossRefGoogle Scholar
  17. 17.
    Malamud, S.: Non-Maximality and Distributivity: A Decision-Theoretic Approach. In: The Proceedings of Semantics and Linguistic Theory 16, Tokyo, Japan (2006)Google Scholar
  18. 18.
    Montague, R.: The Proper Treatment of Quantification in Ordinary English. In: Thomason, R. (ed.) Formal Philosophy: Selected Papers of Richard Montague, pp. 247–270. Yale University Press, New Haven (1974)Google Scholar
  19. 19.
    Pinkal, M.: Logic and Lexicon. Kluwer Academic Publishers, Dordrecht (1995)Google Scholar
  20. 20.
    Pogonowski, J.: Tolerance Spaces with Applications in Linguistics. Poznan University Press, Poznan (1981)Google Scholar
  21. 21.
    Rayo, A.: Word and Objects. Noûs 36, 436–464 (2002)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Simons, P.: Parts. MIT Press, CambridgeGoogle Scholar
  23. 23.
    Smith, N.: Vagueness and Degrees of Truth. OUP, Oxford (2008)CrossRefGoogle Scholar
  24. 24.
    Unger, P.: Ignorance. Clarendon Press, Oxford (1975)Google Scholar
  25. 25.
    Wright, C.: On the Coherence of Vague Predicates. Synthese 30, 325–365 (1975)CrossRefGoogle Scholar
  26. 26.
    Yoon, Y.: Total and Partial Predicates and the Weak and Strong Interpretations. Natural Language Semantics 4, 217–236 (1996)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Heather Burnett
    • 1
  1. 1.University of CaliforniaLos AngelesUSA

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