Linguistics and Philosophy

, Volume 39, Issue 3, pp 151–199 | Cite as

Modified numerals and maximality

Research Article
  • 223 Downloads

Abstract

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not (they sometimes even impose a lower bound). We propose and explore in detail four solutions to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved (‘standard’ maximality versus ‘informativity-based’ maximality) and in the source of maximality (lexically encoded in the meaning of the numeral modifier versus non-lexical). While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence (i) goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and (ii) suggests the need for a pragmatic blocking mechanism that filters out readings (logical forms) of sentences that are generated by the grammar but intuitively unavailable.

Keywords

Semantics Pragmatics Quantification Plurality Modified numerals Monotonicity Distributivity Collectivity Cumulativity Mereology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abrusán, M. (2007). Contradiction and grammar: The case of weak islands. PhD thesis. Massachusetts Institute of Technology. http://hdl.handle.net/1721.1/41704
  2. Abrusán M., Spector B.: A semantics for degree questions based on intervals: Negative islands and their obviation. Journal of Semantics, 28(1), 107–147 (2011). doi:10.1093/jos/ffq013.CrossRefGoogle Scholar
  3. Beck S., Rullmann H.: A flexible approach to exhaustivity in questions. Natural Language Semantics, 7(3), 249–298 (1999). doi:10.1023/A:1008373224343.CrossRefGoogle Scholar
  4. Ben-Avi G., Winter Y.: Monotonicity and collective quantification. Journal of Logic, Language and Information, 12(2), 127–151 (2003). doi:10.1023/A:1022305918225.CrossRefGoogle Scholar
  5. Bresnan, J. W. (1973). Syntax of the comparative clause construction in English. Linguistic Inquiry, 4(3), 275–343. http://www.jstor.org/stable/4177775.
  6. Buccola, B. (2015). Variable monotonicity and less than: when Van Benthem’s problem is not a problem. In T. Bui & D. Özyıldız (Eds.), Proceedings of the 45th annual meeting of the north east Linguistic Society (NELS 45) (Vol. 1, pp. 125–134). http://ling.auf.net/lingbuzz/002512.
  7. Buccola, B. (2016). Severing maximality from fewer than: Evidence from genericity. In Proceedings of Sinn und Bedeutung 20. http://ling.auf.net/lingbuzz/002847.
  8. Cable, S. (2010). Class notes on Manfred Krifka (1999): At least some Determiners aren’t Determiners. Class handout, proseminar on semantic theory, University of Massachusetts, Amherst. http://people.umass.edu/scable/LING720-FA10/Handouts/Krifka-1999.pdf.
  9. Champollion, L. (2014). Distributivity, collectivity, and cumulativity. In L. Matthewson et al. (Eds.), Companion to semantics. New York: Wiley-Blackwell. http://ling.auf.net/lingbuzz/002133.
  10. Champollion L.: Stratified reference: The common core of distributivity, aspect, and measurement. Theoretical Linguistics, 41(3–4), 109–149 (2015). doi:10.1515/tl-2015-0008.Google Scholar
  11. Champollion, L., & Krifka, M. (2015). Mereology. In M. Aloni & P. Dekker (Eds.), Cambridge handbook of semantics. Cambridge: Cambridge University Press. http://ling.auf.net/lingbuzz/002099.
  12. Chemla E., Bott L.: Processing inferences at the semantic/pragmatic frontier: Disjunctions and free choice. Cognition, 130(3), 380–396 (2014). doi:10.1016/j.cognition.2013.11.013.CrossRefGoogle Scholar
  13. Dayal, V. (1996). Locality in WH quantification: Questions and relative clauses in Hindi. Studies in linguistics and philosophy. Berlin: Kluwer Academic Publishers.Google Scholar
  14. Fox, D. (2007). Free Choice and the theory of scalar implicatures. In U. Sauerland & P. Stateva (Eds.), Presupposition and implicature in compositional semantics, chap. 4 (pp. 71–120). Palgrave studies in pragmatics, language and cognition series. London: Palgrave Macmillan. doi:10.1057/9780230210752.
  15. Fox D., Hackl M.: The universal density of measurement. Linguistics and Philosophy, 29(5), 537–586 (2006). doi:10.1007/s10988-006-9004-4.CrossRefGoogle Scholar
  16. Gajewski, J. (2003). On analyticity in natural language. Manuscript, Massachusetts Institute of Technology. http://www.gajewski.uconn.edu/papers/analytic.pdf.
  17. Geurts, B. (2006). Take five: The meaning and use of a number word. In S. Vogeleer & L. Tasmowski (Eds.), Non-definiteness and plurality (pp. 311–329). Amsterdam: Benjamins. doi:10.1075/la.95.16geu.
  18. Hackl, M. (2000). Comparative quantifiers. PhD thesis. Massachusetts Institute of Technology.Google Scholar
  19. Heim, I. (1982). The semantics of definite and indefinite noun phrases. PhD thesis. University of Massachusetts, Amherst.Google Scholar
  20. Heim, I. (2000). Degree operators and scope. In B. Jackson & T. Matthews (Eds.), Proceedings of Semantics and Linguistic Theory X (pp. 40–64). Ithaca, NY: Cornell University. doi:10.3765/salt.v10i0.3102.
  21. Heim, I. (2006). Little. In M. Gibson & J. Howell (Eds.), Proceedings of semantics and linguistic theory XVI (pp. 35–58). Ithaca, NY: Cornell University. doi:10.3765/salt.v16i0.2941.
  22. Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell Publishers Inc.Google Scholar
  23. Hilbert, D. (1899). Grundlagen der Geometrie. Berlin: Springer-Verlag.Google Scholar
  24. Hoeksema, J. (1983). Plurality and conjunction. In A. ter Meulen (Ed.), Studies in modeltheoretic semantics. Dordrecht: Foris Publications.Google Scholar
  25. Horn, L. R. (2006). The border wars: A neo-Gricean perspective. In K. von Heusinger & K. Turner (Eds.), Where semantics meets pragmatics (pp. 21–48). Oxford: Elsevier.Google Scholar
  26. Johnson K.: Sluicing and constraints on quantifier scope. Glot International, 5, 217–221 (2001)Google Scholar
  27. Katzir R.: Structurally-defined alternatives. Linguistics and Philosophy, 30(6), 669–690 (2007). doi:10.1007/s10988-008-9029-y.CrossRefGoogle Scholar
  28. Kennedy, C. (1997). Projecting the adjective: The syntax and semantics of gradability and comparison. PhD thesis. University of California Santa Cruz.Google Scholar
  29. Kennedy C.: A “de-Fregean” semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics, 8(10), 1–44 (2015). doi:10.3765/sp.8.10.Google Scholar
  30. Koenig, J.-P. (1991). Scalar predicates and negation: Punctual semantics and interval interpretations. In Papers from the 27th regional meeting of the Chicago Linguistics Society, Part 2: The Parasession on Negation (pp. 140–155).Google Scholar
  31. Krifka, M. (1989). Nominal reference, temporal constitution, and quantification in event semantics. In R. Bartsch, J. van Benthem & P. van Emde Boas (Eds.), Semantics and contextual expressions (pp. 75–115). Dordrecht: Foris. http://www.worldcat.org/title/semantics-and-contextual-expression/oclc/21675604.
  32. Krifka, M. (1999). At least some determiners aren’t determiners. In K. Turner (Ed.), The semantics/pragmatics interface from different points of view (Vol. 1, pp. 257–291). Oxford: Elsevier.Google Scholar
  33. Ladusaw, W. A. (1979). Polarity sensitivity as inherent scope relations. PhD thesis. University of Texas, Austin.Google Scholar
  34. Landman, F. (2004). Indefinites and the type of sets. Malden, MA: Blackwell Publishing. Link, G. (1983). The logical analysis of plurals and mass terms: A lattice-theoretical approach. In R. Bäuerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use, and interpretation of language (pp. 303–323). Berlin: de Gruyter.Google Scholar
  35. Link, G. (1987). Generalized quantifiers and plurals. In P. Gärdenfors (Ed.), Generalized quantifiers: Linguistic and logical approaches (pp. 151–180). Dordrecht: Reidel.Google Scholar
  36. Marty P., Chemla E., Spector B.: Interpreting numerals and scalar items undermemory load. Lingua, 133, 152–163 (2013). doi:10.1016/j.lingua.2013.03.006.CrossRefGoogle Scholar
  37. Marty P., Chemla E., Spector B.: Phantom readings: The case of modified numerals. Language, Cognition and Neuroscience, 30(4), 462–477 (2015). doi:10.1080/23273798.2014.931592.CrossRefGoogle Scholar
  38. Musolino J.: The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition, 93(1), 1–41 (2004). doi:10.1016/j.cognition.2003.10.002.CrossRefGoogle Scholar
  39. Nouwen, R. (2015). Plurality. In M. Aloni & P. Dekker (Eds.), Cambridge handbook of semantics. Cambridge: Cambridge University Press. http://semanticsarchive.net/Archive/DJkMTZlZ/nouwen-pluralitycambridge-handbook.pdf.
  40. Papafragou A., Musolino J.: Scalar implicatures: experiments at the semantics-pragmatics interface. Cognition, 86(3), 253–282 (2003). doi:110.1016/S0010-0277(02)00179-8.CrossRefGoogle Scholar
  41. Partee, B. H. (1987). Noun phrase interpretation and type-shifting principles. In J. Groenendijk, D. de Jongh, & M. Stokhof (Eds.), Studies in discourse representation theory and the theory of generalized quantifiers (pp. 115–143). Dordrecht: Foris Publications.Google Scholar
  42. Romero, M. (1998). Focus and reconstruction effects in Wh-Phrases. PhD thesis. University of Massachusetts, Amherst.Google Scholar
  43. Rullmann, H. (1995). Maximality in the semantics of Wh-Constructions. PhD thesis. University of Massachusetts, Amherst.Google Scholar
  44. Sauerland, U. (2003). A new semantics for number. In R. B. Young & Y. Zhou (Eds.), Proceedings of semantics and linguistic theory XIII. Ithaca, NY: CLC Publications. doi:10.3765/salt.v13i0.2898.
  45. Scha, R. (1981). Distributive, collective and cumulative quantification. In J. Groenendijk, T. Janssen, & M. Stokhof (Eds.), Formal methods in the study of language (pp. 483–517). Amsterdam: Mathematical Centre Tracts.Google Scholar
  46. Schlenker P.: Informativity-based maximality conditions. Snippets, 26, 18–19 (2012). doi:10.7358/snip-2012-026-schl.Google Scholar
  47. Schmitt, V. (2015). Scopelessness. Talk given at Institut Jean Nicod. Solt, S. (2007). Few and fewer. Snippets, 15, 8–9. http://www.ledonline.it/snippets/allegati/snippets15003.pdf.
  48. Spector, B. (2007). Aspects of the pragmatics of plural morphology: On higher-order implicatures. In U. Sauerland & P. Stateva (Eds.), Presupposition and implicature in compositional semantics, chap. 9 (pp. 243–281). Palgrave studies in pragmatics, language and cognition series. London: Palgrave Macmillan. doi:10.1057/9780230210752_9.
  49. Spector B.: Bare numerals and scalar implicatures. Language and Linguistics Compass, 7(5), 273–294 (2013) . doi:10.1111/lnc3.12018.CrossRefGoogle Scholar
  50. Spector, B. (2014). Plural indefinites and maximality. UCLA colloquium talk.Google Scholar
  51. Van Benthem, J. (1986). Essays in logical semantics. Dordrecht, Holland: D. Reidel Publishing Company.Google Scholar
  52. Van der Does, J. (1992). Applied quantifier logics: Collectives, naked infinitives. PhD thesis. University of Amsterdam.Google Scholar
  53. Van Eijk, J. (1983). Discourse representation theory and plurality. In A. ter Meulen (Ed.), Studies in model theoretic semantics (pp. 85–106). Dordrecht: Foris.Google Scholar
  54. Verkuyl, H. J. (1981). Numerals and quantifiers in X-bar syntax and their semantic interpretation. In J. Groenendijk, T. Janssen, & M. Stokhof (Eds.), Formal methods in the study of language (pp. 567–599). Amsterdam: Mathematical Centre Tracts.Google Scholar
  55. von Fintel, K., Fox, D., & Iatridou, S. (2014). Definiteness as maximal informativeness. In L. Crnič & U. Sauerland (Eds.), The Art and Craft of Semantics: A Festschrift for Irene Heim (Vol. 1, pp. 165–174). MITWPL 70. http://semanticsarchive.net/Archive/jZiNmM4N/FintelFoxIatridou.pdf.
  56. Winter, Y. (2001). Flexibility principles in boolean semantics: The interpretation of coordination, plurality, and scope in natural language. Cambridge, MA: The MIT Press.Google Scholar
  57. Zweig E.: Number-neutral bare plurals and the multiplicity implicature. Linguistics and Philosophy, 32(4), 353–407 (2009). doi:10.1007/s10988-009-9064-3.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Language, Logic and Cognition CenterHebrew University of JerusalemJerusalemIsrael
  2. 2.Institut Jean Nicod (CNRS – ENS – EHESS), Département d’études cognitivesÉcole normale supérieure – PSL Research UniversityParisFrance

Personalised recommendations