Linguistics and Philosophy

, Volume 35, Issue 2, pp 135–169 | Cite as

Granularity and scalar implicature in numerical expressions

Open Access
Research Article

Abstract

It has been generally assumed that certain categories of numerical expressions, such as ‘more than n’, ‘at least n’, and ‘fewer than n’, systematically fail to give rise to scalar implicatures in unembedded declarative contexts. Various proposals have been developed to explain this perceived absence. In this paper, we consider the relevance of scale granularity to scalar implicature, and make two novel predictions: first, that scalar implicatures are in fact available from these numerical expressions at the appropriate granularity level, and second, that these implicatures are attenuated if the numeral has been previously mentioned or is otherwise salient in the context. We present novel experimental data in support of both of these predictions, and discuss the implications of this for recent accounts of numerical quantifier usage.

Keywords

Granularity Implicature Quantifiers Constraints Pragmatics Numerals Salience Relevance 

References

  1. Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4, 159–219.CrossRefGoogle Scholar
  2. Breheny, R. (2008). A new look at the semantics and pragmatics of numerically quantified noun phrases. Journal of Semantics, 25, 93–139.CrossRefGoogle Scholar
  3. Chierchia, G. (2004). Scalar implicatures, polarity phenomena and the syntax/pragmatics interface. In A. Belletti (Ed.), Structures and beyond (pp. 39–103). Oxford: Oxford University Press.Google Scholar
  4. Chierchia, G., Fox, D., & Spector, B. (2008). The grammatical view of scalar implicatures and the relationship between semantics and pragmatics. Ms.Google Scholar
  5. Cummins, C. (2011). The interpretation and use of numerically-quantified expressions. PhD thesis, University of Cambridge.Google Scholar
  6. Cummins, C., & Katsos, N. (2010). Comparative and superlative quantifiers: Pragmatic effects of comparison type. Journal of Semantics, 27, 271–305.CrossRefGoogle Scholar
  7. Curtin, P. (1995). Prolegomena to a theory of granularity. MA thesis, University of Texas at Austin.Google Scholar
  8. Fox, D., & Hackl, M. (2006). The universal density of measurement. Linguistics and Philosophy, 29, 537–586.CrossRefGoogle Scholar
  9. Geurts, B. (2010). Quantity implicatures. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  10. Geurts, B., Katsos, N., Cummins, C., Moons, J., & Noordman, L. (2010). Scalar quantifiers: Logic, acquisition, and processing. Language and Cognitive Processes, 25(1), 130–148.CrossRefGoogle Scholar
  11. Geurts, B., & Nouwen, R. (2007). “At least” et al.: The semantics of scalar modifiers. Language, 83, 533–559.CrossRefGoogle Scholar
  12. Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69, 383–393.CrossRefGoogle Scholar
  13. Horn, L. (1972). On the semantic properties of logical operators in English. UCLA dissertation, distributed by Indiana University Linguistics Club, 1976.Google Scholar
  14. Horn, L. (1984). Toward a new taxonomy for pragmatic inference: Q-based and R-based implicatures. In D. Schiffrin (Ed.), Meaning, form, and use in context (pp. 11–42). Washington: Georgetown University Press.Google Scholar
  15. Jansen, C. J. M., & Pollmann, M. M. W. (2001). On round numbers: Pragmatic aspects of numerical expressions. Journal of Quantitative Linguistics, 8, 187–201.CrossRefGoogle Scholar
  16. Krifka, M. (1999). At least some determiners aren’t determiners. In K. Turner (Ed.), The semantics/pragmatics interface from different points of view. Current research in the semantics/pragmatics interface (Vol. 1, pp. 257–292). Oxford: Elsevier.Google Scholar
  17. Krifka, M. (2002). Be brief and vague! And how bidirectional optimality theory allows for verbosity and precision. In D. Restle & D. Zaefferer (Eds.), Sounds and systems. Studies in structure and change: A festschrift for Theo Vennemann (pp. 439–458). Berlin: Mouton de Gruyter.CrossRefGoogle Scholar
  18. Krifka, M. (2009). Approximate interpretations of number words: A case for strategic communication. In E. Hinrichs & J. Nerbonne (Eds.), Theory and evidence in semantics (pp. 109–132). Stanford: CSLI Publications.Google Scholar
  19. Mason, J. D., Healy, A. F., & Marmie, W. R. (1996). The effects of rounding on memory for numbers in addition problems. Canadian Journal of Experimental Psychology, 50(3), 320–323.CrossRefGoogle Scholar
  20. Nouwen, R. (2008). Upper-bounded no more: The exhaustive interpretation of non-strict comparison. Natural Language Semantics, 16(4), 271–295.CrossRefGoogle Scholar
  21. Sauerland, U. (2012). The computation of scalar implicatures: Pragmatic, lexical or grammatical? Language and Linguistics Compass, 6, 36–49. doi:10.1002/lnc3.321.CrossRefGoogle Scholar
  22. Sperber, D., & Wilson, D. (1986). Relevance: Communication and cognition. Oxford: Blackwell.Google Scholar
  23. Sprouse, J. (2011). A validation of Amazon Mechanical Turk for the collection of acceptability judgments in linguistic theory. Behavior Research Methods, 43, 155–167.CrossRefGoogle Scholar
  24. Wilson, D., & Sperber, D. (2002). Truthfulness and relevance. Mind, 111, 583–632.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.SFB 673, Alignment in CommunicationUniversität BielefeldBielefeldGermany
  2. 2.Zentrum für Allgemeine Sprachwissenschaft (ZAS)BerlinGermany
  3. 3.Institute for Logic, Language and Computation (ILLC)Universiteit van AmsterdamAmsterdamThe Netherlands

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