The Proposal

  • Sam Alxatib
Part of the Studies in Linguistics and Philosophy book series (SLAP, volume 104)


This chapter provides an answer to the second main question of the book: why only∼[(very) few]F and only∼[(very) rarely]F have the meanings that they do intuitively. A possible scope-based account is discussed but rejected, and replaced with an account where “few” and “rarely” are existentially-closed.


  1. Alxatib, S. (2013). Only and Association with Negative Antonyms. Ph.D. thesis, MIT.Google Scholar
  2. Alxatib, S. (2019). Actuality entailment and free choice. To appear in Journal of Semantics, 701–720.Google Scholar
  3. Alxatib, S., & Ivlieva, N. (2018). van Benthem’s problem, exhaustification, and distributivity. In R. Truswell, C. Cummins, C. Heycock, B. Rabern, & H. Rohde (Eds.), Sinn und Bedeutung 21 (pp. 1–18). Edinburgh: University of Edinburgh.Google Scholar
  4. Atlas, J. D. (1993). The importance of being only: Testing the neo-Gricean versus neo-entailment paradigms. Journal of Semantics, 10, 301–318.CrossRefGoogle Scholar
  5. Barner, D., Hochstein, L. K., Rubenson, M. P., & Bale, A. (2018). Four-year-old children compute scalar implicatures in absence of epistemic reasoning. In K. Syrett & S. Arunachalam (Eds.), Semantics in language acquisition (pp. 325–349). Amsterdem: John Benjamins.Google Scholar
  6. Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4, 159–219.CrossRefGoogle Scholar
  7. Beaver, D., & Clark, B. (2008). Sense and sensitivity. Chichester: Wiley Blackwell.CrossRefGoogle Scholar
  8. Beck, S. (2012). DegP scope revisited. Natural Language Semantics, 20, 227–272.CrossRefGoogle Scholar
  9. Bonomi, A., & Casalegno, P. (1993). Only: Association with focus in event semantics. Natural Language Semantics, 2, 1–45.CrossRefGoogle Scholar
  10. Buccola, B., & Haida, A. (2019). Obligatory irrelevance and the computation of ignorance inferences. To appear in Journal of Semantics, 36: 583–616.Google Scholar
  11. Buccola, B., & Spector, B. (2016). Modified numerals and maximality. Linguistics and Philosophy, 39, 151–199.CrossRefGoogle Scholar
  12. Büring, D. (2008). The least at least can do. In C. B. Chang & H. J. Haynie (Eds.), WCCFL 26. Somerville: Cascadilla Press.Google Scholar
  13. Chomsky, N. (1986). Barriers. Cambridge: MIT Press.Google Scholar
  14. Drubig, H. B. (1994). Island constraints and the syntactic nature of focus and association with focus. In Arbeitspapiere des Sonderforschungsbereichs 340. Universität Tübingen/Universität Stuttgart, Tübingen/Stuttgart.Google Scholar
  15. Fauconnier, G. (1979). Implication reversal in natural language. In F. Guenther & S. J. Schmidt (Eds.), Formal semantics and pragmatics for natural language. Dordrecht: Reidel.Google Scholar
  16. von Fintel, K. (1993). Exceptive constructions. Natural Language Semantics, 1, 123–148.CrossRefGoogle Scholar
  17. Fox, D. (2007b). Too many alternatives: Density, symmetry, and other predicaments. In T. Friedman & M. Gibson (Eds.), SALT XVII. Ithaca: CLC Publications.Google Scholar
  18. Fox, D. (2016). On why ignorance might be part of literal meaning. Handout of Talk presented at the MIT Exhaustivity Workshop—Commentary on Meyer, Marie-Christine.Google Scholar
  19. Fox, D., & Hackl, M. (2006). The universal density of measurement. Linguistics and Philosophy, 29, 537–586.CrossRefGoogle Scholar
  20. Gajewski, J. (2002). On analyticity in natural language. Unpublished manuscript.Google Scholar
  21. Gajewski, J. (2009). Innocent Exclusion is not contradiction free. Ms. Available at
  22. Gamut, L. T. F. (1991). Logic, language, and meaning (Vol. 1). Chicago: University of Chicago Press.Google Scholar
  23. Gazdar, G. (1979). Pragmatics: Implicature, presupposition, and logical form. New York: Academic Press.Google Scholar
  24. Heim, I. (2000). Degree operators and scope. In B. Jackson & T. Matthews (Eds.), SALT X. Ithaca: CLC Publications.Google Scholar
  25. Heim, I. (2006). Little. In C. Tancredi, M. Kanazawa, I. Imani, & K. Kusumoto (Eds.), SALT XVI. Ithaca: CLC Publications.Google Scholar
  26. Heim, I., & Kratzer, A. (1998). Semantics in generative grammer. Malden, MA: Blackwell.Google Scholar
  27. Hochstein, L., Bale, A., Fox, D., & Barner, D. (2016). Ignorance and inference: Do problems with Gricean epistemic reasoning explain children’s difficulty with scalar implicature? Journal of Semantics, 33, 107–135.Google Scholar
  28. Horn, L. R. (1969). A presuppositional analysis of only and even. In R. I. Binnick, A. Davidson, G. M. Green, & J. L. Morgan (Eds.), CLS 5 (pp. 98–107). University of Chicago Department of Linguistics.Google Scholar
  29. Horn, L. R. (1996). Exclusive company: only and the dynamics of vertical inference. Journal of Semantics, 13, 1–40.CrossRefGoogle Scholar
  30. Horn, L. R. (2002). Assertoric inertia and NPI licensing. In M. Andronis, E. Debenport, A. Pycha, & K. Yoshimura (Eds.), CLS 38 (Vol. 2, pp. 55–82). University of Chicago Department of Linguistics.Google Scholar
  31. Ippolito, M. (2008). On the meaning of only. Journal of Semantics, 25, 45–91.CrossRefGoogle Scholar
  32. Katzir, R. (2007). Structurally-defined alternatives. Linguistics and Philosophy, 30, 669–690.CrossRefGoogle Scholar
  33. Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In R. Bartsch, J. van Benthem, & P. van Erode Boas (Eds.), Semantics and contextual expression. Dordrecht: Foris.Google Scholar
  34. 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). Kidlington/Oxford: Elsevier Science Ltd.Google Scholar
  35. Ladusaw, W. (1979). Polarity sensitivity as inherent scope relations. Ph.D. thesis, University of Texas at Austin.Google Scholar
  36. Linebarger, M. (1980). The Grammar of negative polarity. Ph.D. thesis, Massachusetts Institute of Technology.Google Scholar
  37. Linebarger, M. (1987). Negative polarity and grammatical representation. Linguistics and Philosophy, 10, 325–387.CrossRefGoogle Scholar
  38. 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. Berlin: de Gruyter.Google Scholar
  39. Magri, G. (2009). A theory of individual-level predicates based on blind mandatory scalar implicatures. Natural Language Semantics, 17, 245–297.CrossRefGoogle Scholar
  40. Magri, G. (2011). Another argument for embedded scalar implicatures based on oddness in downward entailing environments. Semantics and Pragmatics, 4, 1–51.CrossRefGoogle Scholar
  41. Morzycki, M. (2016). Modification. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  42. Nissenbaum, J. (2000). Investigations of Covert Phrase Movement. Ph.D. thesis, MIT.Google Scholar
  43. Romoli, J. (2013). A problem for the structural characterization of alternatives. Snippets, 27, 14–15.Google Scholar
  44. Sauerland, U. (2004). Scalar implicatures in complex sentences. Linguistics and Philosophy, 27, 367–391.CrossRefGoogle Scholar
  45. Schwarz, B. (2011). Remarks on class-B numeral modifiers. Handout of talk delivered at Göttingen University.Google Scholar
  46. Schwarz, B. (2016). Consistency preservation in Quantity implicature: The case of at least. Semantics and Pragmatics, 9, 1–47.CrossRefGoogle Scholar
  47. Singh, R. (2009). Maximize Presupposition! and informationally encapsulated implicatures. In A. Riester & T. Solstad (Eds.), Proceedings of Sinn und Bedeutung 13 (pp. 513–526). Stuttgart: OPUS.Google Scholar
  48. Spector, B. (2005). Aspects de la pragmatique des opérateurs logiques,. Ph.D. thesis, Université Paris 7.Google Scholar
  49. Stump, G. T. (1981). The interpretation of frequency adjectives. Linguistics and Philosophy, 4, 221–257.CrossRefGoogle Scholar
  50. Trinh, T. & Haida, A. (2015). Constraining the derivation of alternatives. Natural Language Semantics, 23, 249–270.CrossRefGoogle Scholar
  51. Wagner, M. (2006). Association by movement: Evidence from NPI-licensing. Natural Language Semantics, 14, 297–324.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Sam Alxatib
    • 1
  1. 1.The Graduate CenterCUNYNew YorkUSA

Personalised recommendations