Linguistics and Philosophy

, 33:513

Stanley Peters and Dag Westerståhl: Quantifiers in language and logic

OUP, New York, 2006, 528 pp
Review Article

Abstract

Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, “The Logical Conception of Quantifiers and Quantification” with an introductory section “Quantification”. II, “Quantifiers of Natural Language”, the most extensive section in the book and of the most direct interest to linguists. III, “Beginnings of a Theory of Expressiveness, Translation, and Formalization” introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory.

Keywords

Quantifiers Logic Natural language Finite definability Expressive power Philosophy of language Generalized quantifiers 

References

  1. Bach, E. (eds) et al (1995) Quantification in natural languages. Kluwer, DordrechtGoogle Scholar
  2. Barker C. (1995) Possessive descriptions. CSLI Publications, Stanford, CAGoogle Scholar
  3. Barwise J. (1978) On branching quantifiers in English. Journal of Philosophical Logic 8: 47–80Google Scholar
  4. Barwise J., Cooper R. (1981) Generalized quantifiers and natural language. Linguistics and Philosophy 4: 159–219CrossRefGoogle Scholar
  5. Beghelli F. (1994) Structured quantifiers. In: Kanazawa M., Piñón C. (eds) Dynamics, polarity, and quantification. CSLI Publications, Stanford, CA, pp 119–145Google Scholar
  6. Chierchia G. (1992) Anaphora and dynamic binding. Linguistics and Philosophy 15: 111–184CrossRefGoogle Scholar
  7. Chomsky N. (1965) Aspects of the theory of syntax. MIT Press, Cambridge, MAGoogle Scholar
  8. Chomsky N. (1985) Knowledge of language. Praeger, New YorkGoogle Scholar
  9. Dalrymple M., Kanazawa M., Kim Y., Mchombo S., Peters S. (1998) Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy 21: 159–210CrossRefGoogle Scholar
  10. Fauconnier G. (1975) Polarity and the scale principle. In: Grossman R.E., San I.J., Vance T.J. (eds) Proceedings of the 11th meeting of the Chicago Linguistic Society. Chicago Linguistic Society, Chicago, IL, pp 188–199Google Scholar
  11. Garcia-Alvarez I. (2003) Quantifiers in exceptive NPs. In: Garding G., Tsujimura M. (eds) WCCFL 22 proceedings. Cascadilla Press, Somerville, MA, pp 207–216Google Scholar
  12. Geach P. (1962) Reference and generality. Cornell University Press, Ithaca, NYGoogle Scholar
  13. Hoeksema J. (1996) The semantics of exception phrases. In: Does J., Eijck J. (eds) Quantifiers, logic and language. CSLI Publications, Stanford, CA, pp 145–177Google Scholar
  14. Hornstein N. (1995) Logical form: From GB to minimalism. Blackwell, OxfordGoogle Scholar
  15. Jacobson P. (1999) Towards a variable-free semantics. Linguistics and Philosophy 22: 117–184CrossRefGoogle Scholar
  16. Jenson, P. A., & Vikner, C. (2002). The English prenominal genitive and lexical semantics. Ms., Dept of Computational Linguistics, Copenhagen Business School.Google Scholar
  17. Kanazawa M. (1994) Weak vs. strong readings of donkey sentences and monotonicity inference in a dynamic setting. Linguistics and Philosophy 17: 109–158CrossRefGoogle Scholar
  18. Keenan E.L. (1983) Some advantages of direct interpretation. Linguistics and Philosophy 6: 335–371CrossRefGoogle Scholar
  19. Keenan E.L. (1989) Semantic case theory. In: Bartsch R., Van Benthem J., Van Emde Boas P. (eds) Semantics and contextual expression Groningen-Amsterdam Studies in Semantics (GRASS). Vol. 11. Foris, Dordrecht, pp 33–57Google Scholar
  20. Keenan E.L. (1992) Beyond the Frege boundary. Linguistics and Philosophy 15: 199–221CrossRefGoogle Scholar
  21. Keenan E.L. (2003) The definiteness effect: Semantics or pragmatics?. Natural Language Semantics 11(2): 187–216CrossRefGoogle Scholar
  22. Keenan E.L. (2005) Excursions in natural logic. In: Casadio C., Scott P., Seely R. (eds) Language and grammar: Studies in mathematical linguistics and natural language. CSLI Publications, Stanford, CA, pp 3–24Google Scholar
  23. Keenan E.L. (2008) Voice and relativization without movement in Malagasy. Natural Language and Linguistic Theory 26(3): 467–497CrossRefGoogle Scholar
  24. Keenan, E. L., & Faltz, L. (1985). Boolean semantics for natural language. Dordrecht: D. Reidel, Synthese Language Library.Google Scholar
  25. Keenan E.L., Moss L.S. (1985) Generalized quantifiers and the expressive power of natural language. In: Benthem J., Meulen A. (eds) Generalized quantifiers in natural language. Foris, Dordrecht, pp 73–127Google Scholar
  26. Keenan E.L., Stavi J. (1986) A semantic characterization of natural language determiners. Linguistics and Philosophy 9: 253–326CrossRefGoogle Scholar
  27. Ladusaw, W. (1979). Polarity sensitivity as inherent scope relations. PhD dissertation, University of Texas, Austin.Google Scholar
  28. Ladusaw W. (1983) Logical form and conditions on grammaticality. Linguistics and Philosophy 6: 389–422CrossRefGoogle Scholar
  29. Lewis D. (1970) General semantics. Synthese 22: 18–67CrossRefGoogle Scholar
  30. Lindström P. (1966) First-order predicate logic with generalized quantifiers. Theoria 32: 186–195Google Scholar
  31. May R. (1989) Interpreting logical form. Linguistics and Philosophy 12: 387–435CrossRefGoogle Scholar
  32. Moltmann F. (1995) Exception sentences and polyadic quantification. Linguistics and Philosophy 18: 223–280CrossRefGoogle Scholar
  33. Montague, R. (1970). English as a formal language. In B. Visentini et al. (Eds.), Linguaggi nella società e nella tecnica (pp. 189–224). Milan: Edizioni di Comunità. (Reprinted in R. H. Thomason (Ed.), Formal philosophy: Selected papers of Richard Montague, pp. 188–221, 1974. New Haven, CT: Yale University Press.)Google Scholar
  34. Mostowski A. (1957) On a generalization of quantifiers. Fundamenta Mathematicae 44: 12–36Google Scholar
  35. Nam S. (2005) n-ary quantifiers and the expressive power of DP-compositions. Research on Language and Computation 3: 411–428CrossRefGoogle Scholar
  36. Paperno, D. (2009). On the syntax and the semantics of the hybrid coordination construction in Russian. MA Thesis, Department of Linguistics, UCLA.Google Scholar
  37. Quine W.v.O. (1961) Logic as a source of syntactical insights. In: Jakobson R. (eds) Proceedings of the twelfth symposium in applied mathematics. American Mathematical Society, Providence, RI, pp 1–6Google Scholar
  38. Russell B. (1908) Mathematical logic as based on the theory of types. In: Marsh R.C. (eds) Logic and knowledge: Essays 1901–1950. George Allen and Unwin, London, pp 57–103Google Scholar
  39. Suppes, P. (1976). Elimination of quantifiers in the semantics of natural language by use of extended relation algebras. Revue Internationale de Philosophie, 117–118, 243–259.Google Scholar
  40. Thomason Richmond H. (1974) Formal Philosophy: Selected Papers of Richard Montague. Conn. Yale Univ. Press, New HavenGoogle Scholar
  41. Väänänen J., Westerståhl D. (2002) On the expressive power of monotone natural language quantifiers over finite models. Journal of Philosophical Logic 31: 327–358CrossRefGoogle Scholar
  42. van Benthem J. (1986) Essays in logical semantics. D. Reidel Publishing Company, DordrechtCrossRefGoogle Scholar
  43. van der Does J. (1996) Quantification and nominal anaphora. In: von Heusinger K., Egli U. (eds) Proceedings of the Konstanz workshop “Reference and anaphoric relations”. Universität Konstanz, Konstanz, pp 27–56Google Scholar
  44. van der Wouden T. (1997) Negative contexts: Collocation, polarity, and multiple negation. Routledge, LondonGoogle Scholar
  45. von Fintel K. (1993) Exceptive constructions. Natural Language Semantics 1: 123–148CrossRefGoogle Scholar
  46. Zuber R. (2007) Symmetric and contrapositional quantifiers. Journal of Logic, Language and Information 16: 1–13CrossRefGoogle Scholar
  47. Zwarts F. (1981) Negatif polaire uitdrukkingen 1. GLOT 4: 35–132Google Scholar
  48. Zwarts F. (1998) Three types of polarity. In: Hamm F., Hinrichs E. (eds) Plurality and quantification. Kluwer, Dordrecht, pp 177–238Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of LinguisticsUniversity of California at Los AngelesLos AngelesUSA

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