The many readings of many: POS in the reverse proportional reading

  • 21 Accesses


Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading (Westerståhl in Linguist and Philos 8:387–413, 1985). This reading has later been characterised in two opposite directions: Cohen’s (Nat Lang Semant 69:41–67, 2001) reading where the proportion \(|P\cap Q|:|P|\) matters and Herburger’s (Nat Lang Semant 5:53–78, 1997) where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerståhl-style sentences while (i) maintaining conservativity, (ii) assuming a standard syntax/semantics mapping and (iii) reducing their context-dependence to mechanisms independently needed for degree constructions in general. In a nutshell, mirroring the decomposition of other degree expressions like tall, many is decomposed into the parametrized determiner many and the operator POS, where POS combines with a contextually salient comparison class C matching the alternatives triggered by some element X\(_{\text {ALT}}\) in the sentence. Non-reverse readings obtain when X\(_{\text {ALT}}\) is external to the original host NP and reverse readings when X\(_{\text {ALT}}\) is internal to the host NP. Cohen’s (2001) (amended) truth conditions for Westerståhl-style sentences are derived as a (true) reverse proportional reading and Herburger’s (1997) interpretation as a sub-case of the non-reverse cardinal reading.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.


  1. Bale, A. (2011). Scales and comparison classes. Natural Language Semantics, 19, 169–190.

  2. Bale, A., & Schwarz, B. (2018). Reverse proportionality without context dependent standards. Talk at Sinn und Bedeutung 23. September 5–7, 2018.

  3. Bartsch, R., & Vennemann, T. (1972). The grammar of relative adjectives and comparison. Linguistische Berichte, 20, 19–32.

  4. Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 5, 159–219.

  5. Beaver, D., & Clark, B. (2008). Sense and sensitivity: How focus determines meaning. Oxford: Blackwell.

  6. Blizard, W. (1989). Multiset theory. Notre Dame Journal of Formal Logic, 30(1), 36–66.

  7. Büring, D. (1996). A weak theory of strong readings. In T. Galloway & J. Spence (Eds.), Proceedings of Semantics and Linguistic Theory 6 (pp. 17–34).

  8. Cohen, A. (2001). Relative readings of many, often and generics. Natural Language Semantics, 69, 41–67.

  9. Cresswell, M. J. (1990). Entities and indices. Dordrecht: Kluwer.

  10. Cresswell, M. J. (1976). The semantics of degree. In B. Partee (Ed.), Montague grammar (pp. 261–292). New York: Academic Press.

  11. van der Does, J., & van Eijck, J. (1996). Quantifiers, logic, and language. Stanford, CA: CSLI Publications.

  12. Fernando, T., & Kamp, H. (1996) Expecting many. In T. Galloway & J. Spence (Eds.), Proceedings of Semantics and Linguistic Theory 6 (pp. 53–68).

  13. von Fintel, K. (1999). NPI licensing, Strawson entailment and context dependency. Journal of Semantics, 16, 97–148.

  14. Fox, D. (2000). Economy and semantic interpretation. Cambridge, MA: MIT Press.

  15. Greer, K. A. (2014). Extensionality in natural language quantification: the case of many and few. Linguistics and Philosophy, 37(4), 315–351.

  16. Hackl, M. (2000). Comparative quantifiers. MIT dissertation.

  17. Hackl, M. (2009). On the grammar and processing of proportional quantifiers: most versus more than half. Natural Language Semantics, 17, 63–98.

  18. Heim, I. (1985). Notes on comparatives and related matters. Ms, University of Texas.

  19. Heim, I. (1999). Notes on superlatives. Ms, MIT.

  20. Heim, I. (2006). Little. In M. Gibson & J. Howell (Eds.), Proceedings of Semantics and Linguistic Theory 16 (pp. 35–58).

  21. Herburger, E. (1997). Focus and weak noun phrases. Natural Language Semantics, 5, 53–78.

  22. Herdan, S., & Sharvit, Y. (2006). Definite and nondefinite superlatives and NPI licensing. Syntax, 9(1), 1–31.

  23. de Hoop, H., & Solà, J. (1996). Determiners, context sets, and focus. In Proceedings of the 14th West Coast Conference on Formal Linguistics (pp. 155–167). Stanford, CA: CSLI Publications.

  24. Keenan, E. L., & Stavi, J. (1986). A semantic characterization of natural language determiners. Linguistics and Philosophy, 9, 253–326.

  25. Kennedy, C. (2007). Vagueness and grammar: The semantics of relative and absolute gradable predicates. Linguistics and Philosophy, 30, 1–45.

  26. Kennedy, C., & McNally, L. (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language, 81(2), 345–381.

  27. Krifka, M. (1998). Additive particles under stress. In D. Strolovitch & A. Lawson (Eds.), Proceedings of Semantics and Linguistic Theory 8 (pp. 111–128).

  28. Lappin, S. (1988). The semantics of “many” as a weak determiner. Linguistics, 26, 977–998.

  29. Milsark, G. (1974). Existential sentences in English. MIT dissertation.

  30. Musan, R. (1995). On the temporal interpretation of noun phrases. MIT dissertation.

  31. Pancheva, R., & Tomaszewicz, B. (2012). Cross-linguistic differences in superlative movement out of nominal phrases. In N. Arnett & R. Bennett (Eds.), Proceedings of the 30th West Coast Conference on Formal Linguistics (pp. 292–302). Sommerville, MA: Cascadilla.

  32. Partee, B. H. (1989). Many quantifiers. In J. Powers & K. de Jong (Eds.), Proceedings of the 5th Eastern States Conference on Linguistics (pp. 383–402). Columbus: The Ohio State University.

  33. Penka, D. (2011). Negative indefinites. Oxford: Oxford University Press.

  34. Penka, D. (2018). One many, many readings. In R. Truswell, C. Cummins, C. Heycock, B. Rabern & H. Rohde (Eds.), Proceedings of Sinn und Bedeutung 21 (pp. 933–950).

  35. Percus, O. (2000). Constraints on some other variables in syntax. Natural Language Semantics, 8, 173–229.

  36. Prior, A. N. (1867). Past, present, and future. Oxford: Clarendon Press.

  37. Qing, C., & Franke, M. (2014a). Gradable adjectives, vagueness, and optimal language use: A speaker-oriented model. In S. D’Antonio, T. Snider & M. Weigand (Eds.), Proceedings of the Semantics and Linguistic theory 24 (pp. 23–41).

  38. Qing, C., & Franke, M. (2014b). Meaning and use of gradable adjectives: Formal modeling meets empirical data. In M. McShane, P. Bello, M. Guarini & B. Scassellati (Eds.), Annual Meeting of the Cognitive Science Society 2014 (p. 1204–1209). Quebec City: Cognitive Science Society.

  39. Romero, M. (2015). The conservativity of many. In F. Roelofsen, T. Brochhagen & N. Theiler (Eds.), Proceedings of the 20th Amsterdam Colloquium (pp. 20–29). Amsterdam: ILLC.

  40. Romero, M. (2016). POS, -est and reverse readings of many and most. In C. Hammerly & B. Prickettto (Eds.), Proceedings of North East Linguistic Society 46 (pp. 141–154). Amherst, MA: GLSA.

  41. Romero, M. (2017). Attributive uses of many. In D. Burgdorf, J. Collard, S. Maspong, MA & B. Stefánsdóttir (Eds.), Proceedings of Semantics and Linguistic Theory 27 (pp. 480–503).

  42. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics, 1, 75–116.

  43. Schmidt, L., Goodman, N., Barner, D., & Tenenbaum, J. (2009). How tall is tall? Compositionality, statistics, and gradable adjectives. In N. Taatgen & H. van Rijn (Eds.), Annual Meeting of the Cognitive Science Society 2009 (p. 3151–3156). Amsterdam: Cognitive Science Society.

  44. Schöller, A., & Franke, M. (2016). How many manys? Exploring semantic theories with data-driven computational models. In P. Berezovskaya, N. Bade & A. Schöller (Eds.), Proceedings of Sinn und Bedeutung 20 (pp. 622–639).

  45. Schöller, A., & Franke, M. (2017). Semantic vales as latent parameters: Testing a fixed threshold hypothesis for cardinal readings of few and many. Linguistics Vanguard, 3, 1–15.

  46. Schwarz, B. (2010). A note on for-phrases and derived scales. Handout for talk at Sinn und Bedeutung 15.

  47. Seuren, P. A. M. (1973). The comparative. In F. Kiefer & N. Ruwet (Eds.), Generative grammar in Europe (pp. 528–564). Dordrecht: Reidel.

  48. Solt, S. (2009). The semantics of adjectives of quantity. CUNY dissertation.

  49. Solt, S. (2011). Notes on the comparison class. In R. Nouwen, R. van Rooij, U. Sauerland, & H.-C. Schmitz (Eds.), Vagueness in communication. Revised selected papers (pp. 189–206). Berlin: Springer.

  50. Solt, S. (2015). Q-adjectives and the semantics of quantity. Journal of Semantics, 32, 221–273.

  51. Solt, S. (2018). Proportional comparatives and relative scales. In R. Truswell, C. Cummins, C. Heycock, B. Rabern & H. Rohde (Eds.), Proceedings of Sinn und Bedeutung 21 (pp. 1123–1140).

  52. Solt, S., & Gotzner, N. (2012). Experimenting with degree. In A. Chereches (Ed.), Proceedings of Semantics and Linguistic Theory 22 (pp. 166–187).

  53. von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics, 3, 1–77.

  54. von Stechow, A. (2009). The temporal degree adjectives früher/später ‘early(er)’/‘late(r)’ and the semantics of the positive. In A. Giannakidou & M. Rathert (Eds.), Quantification, definiteness and nominalization (pp. 214–233). Oxford: Oxford University Press.

  55. Szabolcsi, A. (1986). Comparative superlatives. In N. Fukui, T. Rapoport & E. Sagey (Eds.), MWPL8: Papers in theoretical linguistics (pp. 245–265). Cambridge, MA: MITWPL.

  56. Westerståhl, D. (1985). Logical constants in quantifier languages. Linguistics and Philosophy, 8, 387–413.

  57. Wilson, C. (2016). Deriving the most internal relative reading. In P. Berezovskaya, N. Bade & A. Schöller (Eds.), Proceedings of Sinn und Bedeutung 20 (pp. 779–797).

  58. Wilson, C. (2018). Amount superlatives and measure phrases. CUNY dissertation.

  59. Yanovich, I. (2015). Expressive power of “now” and “then” operators. Journal of Logic, Language and Information, 24, 65–93.

Download references

Author information

Correspondence to Maribel Romero.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

I would like to thank Lucas Champollion, Irene Heim, Sven Lauer, Sophia Malamud, Doris Penka, Robert van Rooij, Bernhard Schwarz, Yasutada Sudo and the audiences of the Amsterdam Colloquium 20, NELS 46 and SALT 27 for their valuable input. Special thanks to three reviewers, from whose comments this paper has benefited significantly. Remaining errors are mine.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Romero, M. The many readings of many: POS in the reverse proportional reading. Linguist and Philos (2020) doi:10.1007/s10988-019-09288-1

Download citation